StivenLancheros/xwikis-augmented-processed

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summarize: The only chemical elements that are stable diatomic homonuclear molecules at STP are hydrogen (H), nitrogen (N), oxygen (O), and two halogens: fluorine (F) and chlorine (Cl). When grouped together with the monatomic noble gases – helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn) – these gases are called "elemental gases". The word "gas" was first used by the early 17th-century Flemish chemist Jan Baptist van Helmont. He identified carbon dioxide, the first known gas other than air. Van Helmont's word appears to have been simply a phonetic transcription of the Ancient Greek word χάος "Chaos" – the "g" in Dutch being pronounced like "ch" in "loch" (voiceless velar fricative, ) – in which case Van Helmont was simply following the established alchemical usage first attested in the works of Paracelsus. According to Paracelsus's terminology, "chaos" meant something like "ultra-rarefied water". An alternative story is that Van Helmont's word is corrupted from "gahst" (or "geist"), signifying a ghost or spirit. This was because certain gases suggested a supernatural origin, such as from their ability to cause death, extinguish flames, and to occur in "mines, bottom of wells, churchyards and other lonely places". In contrast, French-American historian Jacques Barzun speculated that Van Helmont had borrowed the word from the German "Gäscht", meaning the froth resulting from fermentation. Because most gases are difficult to observe directly, they are described through the use of four physical properties or macroscopic characteristics: pressure, volume, number of particles (chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below). Gas particles are widely separated from one another, and consequently, have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from electrostatic interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another; gases that contain permanently charged ions are known as plasmas. Gaseous compounds with polar covalent bonds contain permanent charge imbalances and so experience relatively strong intermolecular forces, although the molecule while the compound's net charge remains neutral. Transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of "boiling points" for compounds formed by ionic and covalent bonds leads us to this conclusion. The drifting smoke particles in the image provides some insight into low-pressure gas behavior. Compared to the other states of matter, gases have low density and viscosity. Pressure and temperature influence the particles within a certain volume. This variation in particle separation and speed is referred to as "compressibility". This particle separation and size influences optical properties of gases as can be found in the following list of refractive indices. Finally, gas particles spread apart or diffuse in order to homogeneously distribute themselves throughout any container. When observing a gas, it is typical to specify a frame of reference or length scale. A larger length scale corresponds to a macroscopic or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the "average" behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. In contrast, a smaller length scale corresponds to a microscopic or particle point of view. Macroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube manometer which looks like a test tube in the shape of the letter J. Boyle trapped an inert gas in the closed end of the test tube with a column of mercury, thereby making the number of particles and the temperature constant. He observed that when the pressure was increased in the gas, by adding more mercury to the column, the trapped gas' volume decreased (this is known as an inverse relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the product was constant. This relationship held for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field. There are many mathematical tools available for analyzing gas properties. As gases are subjected to extreme conditions, these tools become more complex, from the Euler equations for inviscid flow to the Navier–Stokes equations that fully account for viscous effects. These equations are adapted to the conditions of the gas system in question. Boyle's lab equipment allowed the use of algebra to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an "ideal" manner. These ideal relationships apply to safety calculations for a variety of flight conditions on the materials in use. The high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an "ideal" manner. This advanced math, including statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. An example is the analysis of the space shuttle reentry pictured to ensure the material properties under this loading condition are appropriate. In this flight regime, the gas is no longer behaving ideally. The symbol used to represent pressure in equations is "p" or "P" with SI units of pascals. When describing a container of gas, the term pressure (or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container. Within this volume, it is sometimes easier to visualize the gas particles moving in straight lines until they collide with the container (see diagram at top of the article). The force imparted by a gas particle into the container during this collision is the change in momentum of the particle. During a collision only the normal component of velocity changes. A particle traveling parallel to the wall does not change its momentum. Therefore, the average force on a surface must be the average change in linear momentum from all of these gas particle collisions. Pressure is the sum of all the normal components of force exerted by the particles impacting the walls of the container divided by the surface area of the wall. The symbol used to represent "temperature" in equations is "T" with SI units of kelvins. The speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any physical system is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a particle. The methods of storing this energy are dictated by the degrees of freedom of the particle itself (energy modes). Kinetic energy added (endothermic process) to gas particles by way of collisions produces linear, rotational, and vibrational motion. In contrast, a molecule in a solid can only increase its vibrational modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions. These heated gas molecules have a greater speed range which constantly varies due to constant collisions with other particles. The speed range can be described by the Maxwell–Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered. The symbol used to represent specific volume in equations is "v" with SI units of cubic meters per kilogram. The symbol used to represent volume in equations is "V" with SI units of cubic meters. When performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas (either by mass or volume) are called "extensive" properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of volume occupied by a "unit of mass" of a gas that is identical throughout a system at equilibrium. 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are incompressible compared to gases. However, volume itself --- not specific --- is an extensive property. The symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume. Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases. If one could observe a gas under a powerful microscope, one would see a collection of particles (molecules, atoms, ions, electrons, etc.) without any definite shape or volume that are in more or less random motion. These neutral gas particles only change direction when they collide with another particle or with the sides of the container. In an ideal gas, these collisions are perfectly elastic. This particle or microscopic view of a gas is described by the kinetic-molecular theory. The assumptions behind this theory can be found in the postulates section of kinetic theory. Kinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of momentum and kinetic energy, one can use the conservation of momentum and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule. The theory provides averaged values for these two properties. The theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is (in theory) perfectly still, its internal energy (temperature) is increased. As a gas is heated, the particles speed up and its temperature rises. This results in greater numbers of collisions with the container per unit time due to the higher particle speeds associated with elevated temperatures. The pressure increases in proportion to the number of collisions per unit time. Brownian motion is the mathematical model used to describe the random movement of particles suspended in a fluid. The gas particle animation, using pink and green particles, illustrates how this behavior results in the spreading out of gases (entropy). These events are also described by particle theory. Since it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions about how they move, but their motion is different from Brownian motion because Brownian motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as would be expected if an individual gas molecule were examined. As discussed earlier, momentary attractions (or repulsions) between particles have an effect on gas dynamics. In physical chemistry, the name given to these intermolecular forces is "van der Waals force". These forces play a key role in determining physical properties of a gas such as viscosity and flow rate (see physical characteristics section). Ignoring these forces in certain conditions allows a real gas to be treated like an ideal gas. This assumption allows the use of ideal gas laws which greatly simplifies calculations. Proper use of these gas relationships requires the kinetic-molecular theory (KMT). When gas particles experience intermolecular forces they gradually influence one another as the spacing between them is reduced (the hydrogen bond model illustrates one example). In the absence of any charge, at some point when the spacing between gas particles is greatly reduced they can no longer avoid collisions between themselves at normal gas temperatures. Another case for increased collisions among gas particles would include a fixed volume of gas, which upon heating would contain very fast particles. This means that these ideal equations provide reasonable results except for extremely high pressure (compressible) or high temperature (ionized) conditions. All of these excepted conditions allow energy transfer to take place within the gas system. The absence of these internal transfers is what is referred to as ideal conditions in which the energy exchange occurs only at the boundaries of the system. Real gases experience some of these collisions and intermolecular forces. When these collisions are statistically negligible (incompressible), results from these ideal equations are still meaningful. If the gas particles are compressed into close proximity they behave more like a liquid (see fluid dynamics). An "equation of state" (for gases) is a mathematical model used to roughly describe or predict the state properties of a gas. At present, there is no single equation of state that accurately predicts the properties of all gases under all conditions. Therefore, a number of much more accurate equations of state have been developed for gases in specific temperature and pressure ranges. The "gas models" that are most widely discussed are "perfect gas", "ideal gas" and "real gas". Each of these models has its own set of assumptions to facilitate the analysis of a given thermodynamic system. Each successive model expands the temperature range of coverage to which it applies. The equation of state for an ideal or perfect gas is the ideal gas law and reads where "P" is the pressure, "V" is the volume, "n" is amount of gas (in mol units), "R" is the universal gas constant, 8.314 J/(mol K), and "T" is the temperature. Written this way, it is sometimes called the "chemist's version", since it emphasizes the number of molecules "n". It can also be written as where formula_3 is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the "gas dynamicist's" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions. The ideal gas law does not make an assumption about the specific heat of a gas. In the most general case, the specific heat is a function of both temperature and pressure. If the pressure-dependence is neglected (and possibly the temperature-dependence as well) in a particular application, sometimes the gas is said to be a perfect gas, although the exact assumptions may vary depending on the author and/or field of science. For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the compressibility factor "Z" is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law. This approximation is more suitable for applications in engineering although simpler models can be used to produce a "ball-park" range as to where the real solution should lie. An example where the "ideal gas approximation" would be suitable would be inside a combustion chamber of a jet engine. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions. Each one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing "reasonable" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to plasma). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution. One of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different thermodynamic processes by adjusting the equation to read "pV = constant" and then varying the "n" through different values such as the specific heat ratio, "γ". Real gas effects include those adjustments made to account for a greater range of gas behavior: For most applications, such a detailed analysis is excessive. Examples where real gas effects would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures were present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt. Boyle's law was perhaps the first expression of an equation of state. In 1662 Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. The image of Boyle's equipment shows some of the exotic tools used by Boyle during his study of gases. Through these experiments, Boyle noted that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. For example, if the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Given the inverse relationship between pressure and volume, the product of pressure ("P") and volume ("V") is a constant ("k") for a given mass of confined gas as long as the temperature is constant. Stated as a formula, thus is: Because the before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same both equal the constant "k", they can be related by the equation: formula_5 In 1787, the French physicist and balloon pioneer, Jacques Charles, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature: In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charles' earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature. In 1811, Amedeo Avogadro verified that equal volumes of pure gases contain the same number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal exceptions. For his work with gases a century prior, the number that bears his name Avogadro's constant represents the number of atoms found in 12 grams of elemental carbon-12 (6.022×10 mol). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the molar volume. Avogadro's law states that the volume occupied by an ideal gas is proportional to the number of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm (or litres). The relation is given by where n is equal to the number of moles of gas (the number of molecules divided by Avogadro's number). In 1801, John Dalton published the law of partial pressures from his work with ideal gas law relationship: The pressure of a mixture of non reactive gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented for "n" species as: The image of Dalton's journal depicts symbology he used as shorthand to record the path he followed. Among his key journal observations upon mixing unreactive "elastic fluids" (gases) were the following: Thermodynamicists use this factor ("Z") to alter the ideal gas equation to account for compressibility effects of real gases. This factor represents the ratio of actual to ideal specific volumes. It is sometimes referred to as a "fudge-factor" or correction to expand the useful range of the ideal gas law for design purposes. "Usually" this "Z" value is very close to unity. The compressibility factor image illustrates how Z varies over a range of very cold temperatures. In fluid mechanics, the Reynolds number is the ratio of inertial forces ("vρ") to viscous forces ("μ/L"). It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. As such, the Reynolds number provides the link between modeling results (design) and the full-scale actual conditions. It can also be used to characterize the flow. Viscosity, a physical property, is a measure of how well adjacent molecules stick to one another. A solid can withstand a shearing force due to the strength of these sticky intermolecular forces. A fluid will continuously deform when subjected to a similar load. While a gas has a lower value of viscosity than a liquid, it is still an observable property. If gases had no viscosity, then they would not stick to the surface of a wing and form a boundary layer. A study of the delta wing in the Schlieren image reveals that the gas particles stick to one another (see Boundary layer section). In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. The satellite view of weather around Robinson Crusoe Islands illustrates one example. Particles will, in effect, "stick" to the surface of an object moving through it. This layer of particles is called the boundary layer. At the surface of the object, it is essentially static due to the friction of the surface. The object, with its boundary layer is effectively the new shape of the object that the rest of the molecules "see" as the object approaches. This boundary layer can separate from the surface, essentially creating a new surface and completely changing the flow path. The classical example of this is a stalling airfoil. The delta wing image clearly shows the boundary layer thickening as the gas flows from right to left along the leading edge. As the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity. In order to illustrate this principle, observe the skin temperature of a frozen metal bar. Using a thermal image of the skin temperature, note the temperature distribution on the surface. This initial observation of temperature represents a "microstate". At some future time, a second observation of the skin temperature produces a second microstate. By continuing this observation process, it is possible to produce a series of microstates that illustrate the thermal history of the bar's surface. Characterization of this historical series of microstates is possible by choosing the macrostate that successfully classifies them all into a single grouping. When energy transfer ceases from a system, this condition is referred to as thermodynamic equilibrium. Usually, this condition implies the system and surroundings are at the same temperature so that heat no longer transfers between them. It also implies that external forces are balanced (volume does not change), and all chemical reactions within the system are complete. The timeline varies for these events depending on the system in question. A container of ice allowed to melt at room temperature takes hours, while in semiconductors the heat transfer that occurs in the device transition from an on to off state could be on the order of a few nanoseconds.	Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture, such as air, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. 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summarize: Liquid is one of the four primary states of matter, with the others being solid, gas and plasma. A liquid is a fluid. Unlike a solid, the molecules in a liquid have a much greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, allowing a liquid to flow while a solid remains rigid. A liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, and, if placed in a sealed container, will distribute applied pressure evenly to every surface in the container. If liquid is placed in a bag, it can be squeezed into any shape. Unlike a gas, a liquid is nearly incompressible, meaning that it occupies nearly a constant volume over a wide range of pressures; it does not generally expand to fill available space in a container but forms its own surface, and it may not always mix readily with another liquid. These properties make a liquid suitable for applications such as hydraulics. Liquid particles are bound firmly but not rigidly. They are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the increased vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its boiling point, the cohesive forces that bind the molecules closely together break, and the liquid changes to its gaseous state (unless superheating occurs). If the temperature is decreased, the distances between the molecules become smaller. When the liquid reaches its freezing point the molecules will usually lock into a very specific order, called crystallizing, and the bonds between them become more rigid, changing the liquid into its solid state (unless supercooling occurs). Only two elements are liquid at standard conditions for temperature and pressure: mercury and bromine. Four more elements have melting points slightly above room temperature: francium, caesium, gallium and rubidium. Metal alloys that are liquid at room temperature include NaK, a sodium-potassium metal alloy, galinstan, a fusible alloy liquid, and some amalgams (alloys involving mercury). Pure substances that are liquid under normal conditions include water, ethanol and many other organic solvents. Liquid water is of vital importance in chemistry and biology; it is believed to be a necessity for the existence of life. Inorganic liquids include water, magma, inorganic nonaqueous solvents and many acids. Important everyday liquids include aqueous solutions like household bleach, other mixtures of different substances such as mineral oil and gasoline, emulsions like vinaigrette or mayonnaise, suspensions like blood, and colloids like paint and milk. Many gases can be liquefied by cooling, producing liquids such as liquid oxygen, liquid nitrogen, liquid hydrogen and liquid helium. Not all gases can be liquified at atmospheric pressure, however. Carbon dioxide, for example, can only be liquified at pressures above 5.1 atm. Some materials cannot be classified within the classical three states of matter; they possess solid-like and liquid-like properties. Examples include liquid crystals, used in LCD displays, and biological membranes. Liquids have a variety of uses, as lubricants, solvents, and coolants. In hydraulic systems, liquid is used to transmit power. In tribology, liquids are studied for their properties as lubricants. Lubricants such as oil are chosen for viscosity and flow characteristics that are suitable throughout the operating temperature range of the component. Oils are often used in engines, gear boxes, metalworking, and hydraulic systems for their good lubrication properties. Many liquids are used as solvents, to dissolve other liquids or solids. Solutions are found in a wide variety of applications, including paints, sealants, and adhesives. Naphtha and acetone are used frequently in industry to clean oil, grease, and tar from parts and machinery. Body fluids are water based solutions. Surfactants are commonly found in soaps and detergents. Solvents like alcohol are often used as antimicrobials. They are found in cosmetics, inks, and liquid dye lasers. They are used in the food industry, in processes such as the extraction of vegetable oil. Liquids tend to have better thermal conductivity than gases, and the ability to flow makes a liquid suitable for removing excess heat from mechanical components. The heat can be removed by channeling the liquid through a heat exchanger, such as a radiator, or the heat can be removed with the liquid during evaporation. Water or glycol coolants are used to keep engines from overheating. The coolants used in nuclear reactors include water or liquid metals, such as sodium or bismuth. Liquid propellant films are used to cool the thrust chambers of rockets. In machining, water and oils are used to remove the excess heat generated, which can quickly ruin both the work piece and the tooling. During perspiration, sweat removes heat from the human body by evaporating. In the heating, ventilation, and air-conditioning industry (HVAC), liquids such as water are used to transfer heat from one area to another. Similarly, liquids are often used in cooking for their better heat-transfer properties. In addition to better conductivity, because warmer fluids expand and rise while cooler areas contract and sink, liquids with low kinematic viscosity tend to transfer heat through convection at a fairly constant temperature, making a liquid suitable for blanching, boiling, or frying. This phenomenon was also exploited to produce lava lamps. Even higher rates of heat transfer can be achieved by condensing a gas into a liquid. At the liquid's boiling point, all of the heat energy is used to cause the phase change from a liquid to a gas, without an accompanying increase in temperature, and is stored as chemical potential energy. When the gas condenses back into a liquid this excess heat-energy is released at a constant temperature. This phenomenon is used in processes such as steaming. Since liquids often have different boiling points, mixtures or solutions of liquids or gases can typically be separated by distillation, using heat, cold, vacuum, pressure, or other means. Distillation can be found in everything from the production of alcoholic beverages, to oil refineries, to the cryogenic distillation of gases such as argon, oxygen, nitrogen, neon, or xenon by liquefaction (cooling them below their individual boiling points). Liquid is the primary component of hydraulic systems, which take advantage of Pascal's law to provide fluid power. Devices such as pumps and waterwheels have been used to change liquid motion into mechanical work since ancient times. Oils are forced through hydraulic pumps, which transmit this force to hydraulic cylinders. Hydraulics can be found in many applications, such as automotive brakes and transmissions, heavy equipment, and airplane control systems. Various hydraulic presses are used extensively in repair and manufacturing, for lifting, pressing, clamping and forming. Liquids are sometimes used in measuring devices. A thermometer often uses the thermal expansion of liquids, such as mercury, combined with their ability to flow to indicate temperature. A manometer uses the weight of the liquid to indicate air pressure. Quantities of liquids are measured in units of volume. These include the SI unit cubic metre (m) and its divisions, in particular the cubic decimeter, more commonly called the litre (1 dm = 1 L = 0.001 m), and the cubic centimetre, also called millilitre (1 cm = 1 mL = 0.001 L = 10 m). The volume of a quantity of liquid is fixed by its temperature and pressure. Liquids generally expand when heated, and contract when cooled. Water between 0 °C and 4 °C is a notable exception. On the other hand, liquids have little compressibility. Water, for example, will compress by only 46.4 parts per million for every unit increase in atmospheric pressure (bar). At around 4000 bar (400 megapascals or 58,000 psi) of pressure at room temperature water experiences only an 11% decrease in volume. Incompressibility makes liquids suitable for transmitting hydraulic power, because a change in pressure at one point in a liquid is transmitted undiminished to every other part of the liquid and very little energy is lost in the form of compression. However, the negligible compressibility does lead to other phenomena. The banging of pipes, called water hammer, occurs when a valve is suddenly closed, creating a huge pressure-spike at the valve that travels backward through the system at just under the speed of sound. Another phenomenon caused by liquid's incompressibility is cavitation. Because liquids have little elasticity they can literally be pulled apart in areas of high turbulence or dramatic change in direction, such as the trailing edge of a boat propeller or a sharp corner in a pipe. A liquid in an area of low pressure (vacuum) vaporizes and forms bubbles, which then collapse as they enter high pressure areas. This causes liquid to fill the cavities left by the bubbles with tremendous localized force, eroding any adjacent solid surface. In a gravitational field, liquids exert pressure on the sides of a container as well as on anything within the liquid itself. This pressure is transmitted in all directions and increases with depth. If a liquid is at rest in a uniform gravitational field, the pressure formula_1 at depth formula_2 is given by where: For a body of water open to the air, formula_7 would be the atmospheric pressure. Static liquids in uniform gravitational fields also exhibit the phenomenon of buoyancy, where objects immersed in the liquid experience a net force due to the pressure variation with depth. The magnitude of the force is equal to the weight of the liquid displaced by the object, and the direction of the force depends on the average density of the immersed object. If the density is "smaller" than that of the liquid, the buoyant force points "upward" and the object floats, whereas if the density is "larger", the buoyant force points "downward" and the object sinks. This is known as Archimedes' principle. Unless the volume of a liquid exactly matches the volume of its container, one or more surfaces are observed. The presence of a surface introduces new phenomena which are not present in a bulk liquid. This is because a molecule at a surface possesses bonds with other liquid molecules only on the inner side of the surface, which implies a net force pulling surface molecules inward. Equivalently, this force can be described in terms of energy: there is a fixed amount of energy associated with forming a surface of a given area. This quantity is a material property called the surface tension, in units of energy per unit area (SI units: J/m). Liquids with strong intermolecular forces tend to have large surface tensions. A practical implication of surface tension is that liquids tend to minimize their surface area, forming spherical drops and bubbles unless other constraints are present. Surface tension is responsible for a range of other phenomena as well, including surface waves, capillary action, wetting, and ripples. In liquids under nanoscale confinement, surface effects can play a dominating role since – compared with a macroscopic sample of liquid – a much greater fraction of molecules are located near a surface. The surface tension of a liquid directly affects its wettability. Most common liquids have tensions ranging in the tens of mJ/m, so droplets of oil, water, or glue can easily merge and adhere to other surfaces, whereas liquid metals such as mercury may have tensions ranging in the hundreds of mJ/m, thus droplets do not combine easily and surfaces may only wet under specific conditions. The surface tensions of common liquids occupy a relatively narrow range of values, which contrasts strongly with the enormous variation seen in other mechanical properties, such as viscosity. An important physical property characterizing the flow of liquids is viscosity. Intuitively, viscosity describes the resistance of a liquid to flow. More technically, viscosity measures the resistance of a liquid to deformation at a given rate, such as when it is being sheared at finite velocity. A specific example is a liquid flowing through a pipe: in this case the liquid undergoes shear deformation since it flows more slowly near the walls of the pipe than near the center. As a result, it exhibits viscous resistance to flow. In order to maintain flow, an external force must be applied, such as a pressure difference between the ends of the pipe. The viscosity of liquids decreases with increasing temperature. Precise control of viscosity is important in many applications, particularly the lubrication industry. One way to achieve such control is by blending two or more liquids of differing viscosities in precise ratios. In addition, various additives exist which can modulate the temperature-dependence of the viscosity of lubricating oils. This capability is important since machinery often operate over a range of temperatures (see also viscosity index). The viscous behavior of a liquid can be either Newtonian or non-Newtonian. A Newtonian liquid exhibits a linear strain/stress curve, meaning its viscosity is independent of time, shear rate, or shear-rate history. Examples of Newtonian liquids include water, glycerin, motor oil, honey, or mercury. A non-Newtonian liquid is one where the viscosity is not independent of these factors and either thickens (increases in viscosity) or thins (decreases in viscosity) under shear. Examples of non-Newtonian liquids include ketchup, mayonnaise, hair gels, play dough, or starch solutions. The speed of sound in a liquid is given by formula_8 where formula_9 is the bulk modulus of the liquid and formula_10 the density. As an example, water has a bulk modulus of about 2.2 GPa and a density of 1000 kg/m, which gives "c" = 1.5 km/s. At a temperature below the boiling point, any matter in liquid form will evaporate until the condensation of gas above reach an equilibrium. At this point the gas will condense at the same rate as the liquid evaporates. Thus, a liquid cannot exist permanently if the evaporated liquid is continually removed. A liquid at its boiling point will evaporate more quickly than the gas can condense at the current pressure. A liquid at or above its boiling point will normally boil, though superheating can prevent this in certain circumstances. At a temperature below the freezing point, a liquid will tend to crystallize, changing to its solid form. Unlike the transition to gas, there is no equilibrium at this transition under constant pressure, so unless supercooling occurs, the liquid will eventually completely crystallize. Note that this is only true under constant pressure, so e.g. water and ice in a closed, strong container might reach an equilibrium where both phases coexist. For the opposite transition from solid to liquid, see melting. The phase diagram explains why liquids do not exist in space or any other vacuum. Since the pressure is zero (except on surfaces or interiors of planets and moons) water and other liquids exposed to space will either immediately boil or freeze depending on the temperature. In regions of space near the earth, water will freeze if the sun is not shining directly on it and vapourize (sublime) as soon as it is in sunlight. If water exists as ice on the moon, it can only exist in shadowed holes where the sun never shines and where the surrounding rock doesn't heat it up too much. At some point near the orbit of Saturn, the light from the sun is too faint to sublime ice to water vapour. This is evident from the longevity of the ice that composes Saturn's rings. Liquids can form solutions with gases, solids, and other liquids. Two liquids are said to be miscible if they can form a solution in any proportion; otherwise they are immiscible. As an example, water and ethanol (drinking alcohol) are miscible whereas water and gasoline are immiscible. In some cases a mixture of otherwise immiscible liquids can be stabilized to form an emulsion, where one liquid is dispersed throughout the other as microscopic droplets. Usually this requires the presence of a surfactant in order to stabilize the droplets. A familiar example of an emulsion is mayonnaise, which consists of a mixture of water and oil that is stabilized by lecithin, a substance found in egg yolks. The molecules which compose liquids are "disordered" and "strongly interacting", which makes liquids difficult to describe rigorously at the molecular level. This stands in contrast with the other two common phases of matter, gases and solids. Although gases are disordered, they are sufficiently dilute that many-body interactions can be ignored, and molecular interactions can instead be modeled in terms of well-defined binary collision events. Conversely, although solids are dense and strongly interacting, their regular structure at the molecular level (e.g. a crystalline lattice) allows for significant theoretical simplifications. For these reasons, the microscopic theory of liquids is less developed than that of gases and solids. In a liquid, atoms do not form a crystalline lattice, nor do they show any other form of long-range order. This is evidenced by the absence of Bragg peaks in X-ray and neutron diffraction. Under normal conditions, the diffraction pattern has circular symmetry, expressing the isotropy of the liquid. In radial direction, the diffraction intensity smoothly oscillates. This is usually described by the static structure factor "S(q)", with wavenumber "q"=(4π/λ)sinθ given by the wavelength λ of the probe (photon or neutron) and the Bragg angle θ. The oscillations of "S(q)" express the "near order" of the liquid, i.e. the correlations between an atom and a few shells of nearest, second nearest,... neighbors. A more intuitive description of these correlations is given by the radial distribution function "g(r)", which is basically the Fourier transform of "S(q)". It represents a spatial average of a temporal snapshot of pair correlations in the liquid. The above expression for the sound velocity formula_8 contains the bulk modulus "K". If "K" is frequency independent then the liquid behaves as a linear medium, so that sound propagates without dissipation and without mode coupling. In reality, any liquid shows some dispersion: with increasing frequency, "K" crosses over from the low-frequency, liquid-like limit formula_12 to the high-frequency, solid-like limit formula_13. In normal liquids, most of this cross over takes place at frequencies between GHz and THz, sometimes called hypersound. At sub-GHz frequencies, a normal liquid cannot sustain shear waves: the zero-frequency limit of the shear modulus is formula_14. This is sometimes seen as the defining property of a liquid. However, just as the bulk modulus "K", the shear modulus "G" is frequency dependent, and at hypersound frequencies it shows a similar cross over from the liquid-like limit formula_15 to a solid-like, non-zero limit formula_16. According to the Kramers-Kronig relation, the dispersion in the sound velocity (given by the real part of "K" or "G") goes along with a maximum in the sound attenuation (dissipation, given by the imaginary part of "K" or "G"). According to linear response theory, the Fourier transform of "K" or "G" describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz..THz region is also called structural relaxation. According to the fluctuation-dissipation theorem, relaxation "towards" equilibrium is intimately connected to fluctuations "in" equilibrium. The density fluctuations associated with sound waves can be experimentally observed by Brillouin scattering. On supercooling a liquid towards the glass transition, the crossover from liquid-like to solid-like response moves from GHz to MHz, kHz, Hz,...; equivalently, the characteristic time of structural relaxation increases from ns to μs, ms, s,... This is the microscopic explanation for the above-mentioned viscoelastic behaviour of glass-forming liquids. The mechanisms of atomic/molecular diffusion (or particle displacement) in solids are closely related to the mechanisms of viscous flow and solidification in liquid materials. Descriptions of viscosity in terms of molecular "free space" within the liquid were modified as needed in order to account for liquids whose molecules are known to be "associated" in the liquid state at ordinary temperatures. When various molecules combine together to form an associated molecule, they enclose within a semi-rigid system a certain amount of space which before was available as free space for mobile molecules. Thus, increase in viscosity upon cooling due to the tendency of most substances to become "associated" on cooling. Similar arguments could be used to describe the effects of pressure on viscosity, where it may be assumed that the viscosity is chiefly a function of the volume for liquids with a finite compressibility. An increasing viscosity with rise of pressure is therefore expected. In addition, if the volume is expanded by heat but reduced again by pressure, the viscosity remains the same. The local tendency to orientation of molecules in small groups lends the liquid (as referred to previously) a certain degree of association. This association results in a considerable "internal pressure" within a liquid, which is due almost entirely to those molecules which, on account of their temporary low velocities (following the Maxwell distribution) have coalesced with other molecules. The internal pressure between several such molecules might correspond to that between a group of molecules in the solid form.	A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. 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summarize: Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground and that they will stay that way if left alone. He distinguished between the innate tendency of objects to find their Sir Isaac Newton described the motion of all objects using the concepts of inertia and force, and in doing so he found they obey certain conservation laws. In 1687, Newton published his thesis "Philosophiæ Naturalis Principia Mathematica". In this work Newton set out three laws of motion that to this day are the way forces are described in physics. Newton's First Law of Motion states that objects continue to move in a state of constant velocity unless acted upon by an external net force (resultant force). This law is an extension of Galileo's insight that constant velocity was associated with a lack of net force (see a more detailed description of this below). Newton proposed that every object with mass has an innate inertia that functions as the fundamental equilibrium "natural state" in place of the Aristotelian idea of the "natural state of rest". That is, Newton's empirical First Law contradicts the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity. By making "rest" physically indistinguishable from "non-zero constant velocity", Newton's First Law directly connects inertia with the concept of relative velocities. Specifically, in systems where objects are moving with different velocities, it is impossible to determine which object is "in motion" and which object is "at rest". A modern statement of Newton's Second Law is a vector equation: where formula_2 is the momentum of the system, and formula_3 is the net (vector sum) force. If a body is in equilibrium, there is zero "net" force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an "unbalanced" force acting on an object it will result in the object's momentum changing over time. By the definition of momentum, where "m" is the mass and formula_5 is the velocity. If Newton's second law is applied to a system of constant mass, "m" may be moved outside the derivative operator. The equation then becomes By substituting the definition of acceleration, the algebraic version of Newton's Second Law is derived: Newton never explicitly stated the formula in the reduced form Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if formula_8 is the force of body 1 on body 2 and formula_9 that of body 2 on body 1, then This law is sometimes referred to as the "action-reaction law", with formula_11 called the "action" and formula_12 the "reaction". Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are "interactions" between different bodies, and thus that there is no such thing as a unidirectional force or a force that acts on only one body. In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity. Newton's Second Law remains valid because it is a mathematical definition. But for relativistic momentum to be conserved, it must be redefined as: where formula_19 is the rest mass and formula_20 the speed of light. The relativistic expression relating force and acceleration for a Since forces are perceived as pushes or pulls, this can provide an intuitive understanding for describing forces. As with other physical concepts (e.g. temperature), the intuitive understanding of forces is quantified using precise operational definitions that are consistent with direct observations and compared to a standard measurement scale. Through experimentation, it is determined that laboratory measurements of forces are fully consistent with the conceptual definition of force offered by Newtonian mechanics. Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "vector quantities". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result. If both of these pieces of information are not known for each force, the situation is ambiguous. For example, if you know that two people are pulling on the same rope with known magnitudes of force but you do not know which direction either person is pulling, it is impossible to determine what the acceleration of the rope will be. The two people could be pulling against each other as in tug of war or the two people could be pulling in the same direction. In this simple one-dimensional example, without knowing the direction of the forces it is impossible to decide whether the net force is the result of adding the two force magnitudes or subtracting one from the other. Associating forces with vectors avoids such problems. Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction. When two forces act on a point particle, the resulting force, the "resultant" (also called the "net force"), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. However, if the forces are acting on an extended body, their respective lines of application must also be specified in order to account for their effects on the motion of the body. Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can be done to determine the net force. As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right-angles to the other two. All of the known forces of the universe are classified into four fundamental interactions. The strong and the weak forces are nuclear forces that act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charges, and the gravitational force acts between masses. All other forces in nature derive from these four fundamental interactions. For example, friction is a manifestation of the electromagnetic force acting between atoms of two surfaces, and the Pauli exclusion principle, which does not permit atoms to pass through each other. Similarly, the forces in springs, modeled by Hooke's law, are the result of electromagnetic forces and the Pauli exclusion principle acting together to return an object to its equilibrium position. Centrifugal forces are acceleration forces that arise simply from the acceleration of rotating frames of reference. The fundamental theories for forces developed from the unification of different ideas. For example, Sir. Isaac Newton unified, with his universal theory of gravitation, the force responsible for objects falling near the surface of the Earth with the force responsible for the falling of celestial bodies about the Earth (the Moon) and around the Sun (the planets). Michael Faraday and James Clerk Maxwell demonstrated that electric and magnetic forces were unified through a theory of electromagnetism. In the 20th century, the development of quantum mechanics led to a modern understanding that the first three fundamental forces (all except gravity) are manifestations of matter (fermions) interacting by exchanging virtual particles called gauge bosons. This Standard Model of particle physics assumes a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory, which was subsequently confirmed by observation. The complete formulation of the Standard Model predicts an as yet unobserved Higgs mechanism, but observations such as neutrino oscillations suggest that the Standard Model is incomplete. A Grand Unified Theory that allows for the combination of the electroweak interaction with the strong force is held out as a possibility with candidate theories such as supersymmetry proposed to accommodate some of the outstanding unsolved problems in physics. Physicists are still attempting to develop self-consistent unification models that would combine all four fundamental interactions into a theory of everything. Einstein tried and failed at this endeavor, but currently the most popular approach to answering this question is string theory. Some forces are consequences of the fundamental ones. In such situations, idealized models can be utilized to gain physical insight. The normal force is due to repulsive forces of interaction between atoms at close contact. When their electron clouds overlap, Pauli repulsion (due to fermionic nature of electrons) follows resulting in the force that acts in a direction normal Friction is a surface force that opposes relative motion. The frictional force is directly related to the normal force that acts to keep two solid objects separated at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction. The static friction force (formula_56) will exactly oppose forces applied to an object Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and unstretchable. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by An elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. However, in real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows: where formula_67 is the volume of the object in the fluid and formula_68 is the scalar function that describes There are forces that are frame dependent, meaning that they appear due to the adoption of non-Newtonian (that is, non-inertial) reference frames. Such forces include the centrifugal force and the Coriolis force. These forces are considered fictitious because they do not exist in frames of reference Forces that cause extended objects to rotate are associated with torques. Mathematically, the torque of a force formula_51 is defined relative to an arbitrary reference point as the cross-product: where Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's First Law of Motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an unbalanced torque. Likewise, Newton's Second Law of Motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body: where This provides a definition for the moment of inertia, which is the rotational equivalent for mass. In more advanced treatments of mechanics, where the rotation over a time interval is described, the moment of inertia must be substituted by the tensor that, when properly analyzed, fully determines the characteristics of rotations including precession and nutation. Equivalently, the differential form of Newton's Second Law provides an alternative definition of torque: Newton's Third Law of Motion requires that all objects exerting torques themselves experience equal and opposite torques, and therefore also directly implies the conservation of angular momentum for closed systems that experience rotations and revolutions through the action of internal torques. For an object accelerating in circular motion, the unbalanced force acting on the object equals: where formula_21 is the mass of the object, formula_28 is the velocity of the object and formula_43 is the distance to the center of the circular path and formula_44 is the unit vector pointing in the radial direction outwards from the center. This means that the unbalanced centripetal force felt by any Forces can be used to define a number of physical concepts by integrating with respect to kinematic variables. For example, integrating with respect to time gives the definition of impulse: which by Newton's Second Law must be equivalent to the change in momentum (yielding Instead of a force, often the mathematically related concept of a potential energy field can be used for convenience. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field formula_92 is defined as that field whose gradient is equal and opposite to the force produced at every point: Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not. A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space, and can be considered to be an artifact of the potential field in the same For certain physical scenarios, it is impossible to model forces as being due to gradient of potentials. This is often due to macrophysical considerations that yield forces as arising from a macroscopic statistical average of microstates. For example, friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or. The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or. A newton is thus equal to 100,000 dynes. The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of. The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. See force gauge, spring scale, load cell	In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. 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summarize: For most substances, melting and freezing points are approximately equal. For example, the melting point "and" freezing point of mercury is 234.32 Kelvin (−38.83 °C or −37.89 °F). However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from ; such direction dependence is known as hysteresis. The melting point of ice at 1 atmosphere of pressure is very close to ; this is also known as the ice point. In the presence of nucleating substances, the freezing point of water is not always the same as the melting point. In the absence of nucleators water can exist as a supercooled liquid down to −48.3 °C (−55 °F, 224.8 K) before freezing. The chemical element with the highest melting point is tungsten, at ; this property makes tungsten excellent for use as filaments in light bulbs. The often-cited carbon does not melt at ambient pressure but sublimes at about ; a liquid phase only exists above pressures of and estimated (see ). Tantalum hafnium carbide (TaHfC) is a refractory compound with a very high melting point of 4215 K (3942 °C, 7128 °F). Quantum mechanical computer simulations have predicted that the alloy HfNC will have an even higher melting point (about 4400 K), which would make it the substance with the highest melting point at ambient pressure. This prediction was later confirmed by experiment. At the other end of the scale, helium does not freeze at all at normal pressure even at temperatures arbitrarily close to absolute zero; a pressure of more than twenty times normal atmospheric pressure is necessary. Many laboratory techniques exist for the determination of melting points. A Kofler bench is a metal strip with a temperature gradient (range from room temperature to 300 °C). Any substance can be placed on a section of the strip, revealing its thermal behaviour at the temperature at that point. Differential scanning calorimetry gives information on melting point together with its enthalpy of fusion. A basic melting point apparatus for the analysis of crystalline solids consists of an oil bath with a transparent window (most basic design: a Thiele tube) and a simple magnifier. Several grains of a solid are placed in a thin glass tube and partially immersed in the oil bath. The oil bath is heated (and stirred) and with the aid of the magnifier (and external light source) melting of the individual crystals at a certain temperature can be observed. A metal block might be used instead of an oil bath. Some modern instruments have automatic optical detection. The measurement can also be made continuously with an operating process. For instance, oil refineries measure the freeze point of diesel fuel "online", meaning that the sample is taken from the process and measured automatically. This allows for more frequent measurements as the sample does not have to be manually collected and taken to a remote laboratory. For refractory materials (e.g. platinum, tungsten, tantalum, some carbides and nitrides, etc.) the extremely high melting point (typically considered to be above, say, 1800 °C) may be determined by heating the material in a black body furnace and measuring the black-body temperature with an optical pyrometer. For the highest melting materials, this may require extrapolation by several hundred degrees. The spectral radiance from an incandescent body is known to be a function of its temperature. An optical pyrometer matches the radiance of a body under study to the radiance of a source that has been previously calibrated as a function of temperature. In this way, the measurement of the absolute magnitude of the intensity of radiation is unnecessary. However, known temperatures must be used to determine the calibration of the pyrometer. For temperatures above the calibration range of the source, an extrapolation technique must be employed. This extrapolation is accomplished by using Planck's law of radiation. The constants in this equation are not known with sufficient accuracy, causing errors in the extrapolation to become larger at higher temperatures. However, standard techniques have been developed to perform this extrapolation. Consider the case of using gold as the source (mp = 1063 °C). In this technique, the current through the filament of the pyrometer is adjusted until the light intensity of the filament matches that of a black-body at the melting point of gold. This establishes the primary calibration temperature and can be expressed in terms of current through the pyrometer lamp. With the same current setting, the pyrometer is sighted on another black-body at a higher temperature. An absorbing medium of known transmission is inserted between the pyrometer and this black-body. The temperature of the black-body is then adjusted until a match exists between its intensity and that of the pyrometer filament. The true higher temperature of the black-body is then determined from Planck's Law. The absorbing medium is then removed and the current through the filament is adjusted to match the filament intensity to that of the black-body. This establishes a second calibration point for the pyrometer. This step is repeated to carry the calibration to higher temperatures. Now, temperatures and their corresponding pyrometer filament currents are known and a curve of temperature versus current can be drawn. This curve can then be extrapolated to very high temperatures. In determining melting points of a refractory substance by this method, it is necessary to either have black body conditions or to know the emissivity of the material being measured. The containment of the high melting material in the liquid state may introduce experimental difficulties. Melting temperatures of some refractory metals have thus been measured by observing the radiation from a black body cavity in solid metal specimens that were much longer than they were wide. To form such a cavity, a hole is drilled perpendicular to the long axis at the center of a rod of the material. These rods are then heated by passing a very large current through them, and the radiation emitted from the hole is observed with an optical pyrometer. The point of melting is indicated by the darkening of the hole when the liquid phase appears, destroying the black body conditions. Today, containerless laser heating techniques, combined with fast pyrometers and spectro-pyrometers, are employed to allow for precise control of the time for which the sample is kept at extreme temperatures. Such experiments of sub-second duration address several of the challenges associated with more traditional melting point measurements made at very high temperatures, such as sample vaporization and reaction with the container. For a solid to melt, heat is required to raise its temperature to the melting point. However, further heat needs to be supplied for the melting to take place: this is called the heat of fusion, and is an example of latent heat. From a thermodynamics point of view, at the melting point the change in Gibbs free energy (ΔG) of the material is zero, but the enthalpy ("H") and the entropy ("S") of the material are increasing (ΔH, ΔS > 0). Melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that: Here "T", "ΔS" and "ΔH" are respectively the temperature at the melting point, change of entropy of melting and the change of enthalpy of melting. The melting point is sensitive to extremely large changes in pressure, but generally this sensitivity is orders of magnitude less than that for the boiling point, because the solid-liquid transition represents only a small change in volume. If, as observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in pressure, substantial changes to the melting point are observed. For example, the melting point of silicon at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C. Melting points are often used to characterize organic and inorganic compounds and to ascertain their purity. The melting point of a pure substance is always higher and has a smaller range than the melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other components, the lower the melting point and the broader will be the melting point range, often referred to as the "pasty range". The temperature at which melting begins for a mixture is known as the "solidus" while the temperature where melting is complete is called the "liquidus". Eutectics are special types of mixtures that behave like single phases. They melt sharply at a constant temperature to form a liquid of the same composition. Alternatively, on cooling a liquid with the eutectic composition will solidify as uniformly dispersed, small (fine-grained) mixed crystals with the same composition. In contrast to crystalline solids, glasses do not possess a melting point; on heating they undergo a smooth glass transition into a viscous liquid. Upon further heating, they gradually soften, which can be characterized by certain softening points. The freezing point of a solvent is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This phenomenon is used in technical applications to avoid freezing, for instance by adding salt or ethylene glycol to water. In organic chemistry, Carnelley's rule, established in 1882 by Thomas Carnelley, states that "high molecular symmetry is associated with high melting point". Carnelley based his rule on examination of 15,000 chemical compounds. For example, for three structural isomers with molecular formula CH the melting point increases in the series isopentane −160 °C (113 K) n-pentane −129.8 °C (143 K) and neopentane −16.4 °C (256.8 K). Likewise in xylenes and also dichlorobenzenes the melting point increases in the order meta, ortho and then para. Pyridine has a lower symmetry than benzene hence its lower melting point but the melting point again increases with diazine and triazines. Many cage-like compounds like adamantane and cubane with high symmetry have relatively high melting points. A high melting point results from a high heat of fusion, a low entropy of fusion, or a combination of both. In highly symmetrical molecules the crystal phase is densely packed with many efficient intermolecular interactions resulting in a higher enthalpy change on melting. An attempt to predict the bulk melting point of crystalline materials was first made in 1910 by Frederick Lindemann. The idea behind the theory was the observation that the average amplitude of thermal vibrations increases with increasing temperature. Melting initiates when the amplitude of vibration becomes large enough for adjacent atoms to partly occupy the same space. The Lindemann criterion states that melting is expected when the vibration root mean square amplitude exceeds a threshold value. Assuming that all atoms in a crystal vibrate with the same frequency "ν", the average thermal energy can be estimated using the equipartition theorem as where "m" is the atomic mass, "ν" is the frequency, "u" is the average vibration amplitude, "k" is the Boltzmann constant, and "T" is the absolute temperature. If the threshold value of "u" is "ca" where "c" is the Lindemann constant and "a" is the atomic spacing, then the melting point is estimated as Several other expressions for the estimated melting temperature can be obtained depending on the estimate of the average thermal energy. Another commonly used expression for the Lindemann criterion is From the expression for the Debye frequency for "ν", we have where "θ" is the Debye temperature and "h" is the Planck constant. Values of "c" range from 0.15–0.3 for most materials. In February 2011, Alfa Aesar released over 10,000 melting points of compounds from their catalog as open data. This dataset has been used to create a random forest model for melting point prediction which is now freely available. Open melting point data are also available from "Nature Precedings". High quality data mined from patents and also models developed with these data were published by Tetko "et al".	The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. 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summarize: Research into the various aspects of the history of interpreting is quite new. For as long as most scholarly interest was given to professional conference interpreting, very little academic work was done on the practice of interpreting in history, and until the 1990s, only a few dozen publications were done on it. Considering the amount of interpreting activities that is assumed to have occurred for thousands of years, historical records are limited. Moreover, interpreters and their work have usually not found their way into the history books. One of the reasons for that is the dominance of the written text over the spoken word (in the sense that those who have left written texts are more likely to be recorded by historians). Another problem is the tendency to view it as an ordinary support activity which does not require any special attention, and the social status of interpreters, who were sometimes treated unfairly by scribes, chroniclers and historians. Our knowledge of the past of interpreting tends to come from letters, chronicles, biographies, diaries and memoirs, along with a variety of other documents and literary works, many of which (and with few exceptions) were only incidentally or marginally related to interpreting. Many Indo-European languages have words for 'interpreting' and 'interpreter'. Expressions in Germanic, Scandinavian and Slavic languages denoting an interpreter can be traced back to Akkadian, around 1900 BCE. The Akkadian root "targumânu"/"turgumânu" also gave rise to the term dragoman via an etymological sideline from Arabic. The English word ‘interpreter’, however, is derived from Latin "interpres" (meaning ‘expounder’, ‘person explaining what is obscure’), whose semantic roots are not clear. Some scholars take the second part of the word to be derived from "partes" or "pretium" (meaning ‘price’, which fits the meaning of a ‘middleman’, ‘intermediary’ or ‘commercial go-between’), but others have suggested a Sanskrit root. In consecutive interpreting (CI), the interpreter starts to interpret after the speaker pauses. Therefore, the time needed is much longer (possibly double the time needed). Traditionally, the interpreter will sit or stand near the speaker. Consecutive interpretation can be conducted in a pattern of short or long segments according to the interpreter's preference. In short CI, the interpreter relies mostly on memory whereas, in long CI, most interpreters will rely on note-taking. The notes must be clear and legible in order to not waste time on reading them. Consecutive interpreting of whole thoughts, rather than in small pieces, is desirable so that the interpreter has the whole meaning before rendering it in the target language. This affords a truer, more accurate, and more accessible interpretation than where short CI or simultaneous interpretation is used. An attempt at consensus about lengths of segments may be reached prior to commencement, depending upon complexity of the subject matter and purpose of the interpretation, though speakers generally face difficulty adjusting to unnatural speech patterns. On occasion, document sight translation is required of the interpreter during consecutive interpretation work. Sight translation combines interpretation and translation; the interpreter must render the source-language document to the target-language as if it were written in the target language. Sight translation occurs usually, but not exclusively, in judicial and medical work. Consecutive interpretation may be the chosen mode when bilingual listeners are present who wish to hear both the original and interpreted speech or where, as in a court setting, a record must be kept of both. When no interpreter is available to interpret directly from source to target, an intermediate interpreter will be inserted in a relay mode, e.g. a Greek source language could be interpreted into English and then from English to another language. This is also commonly known as double-interpretation. Triple-interpretation may even be needed, particularly where rare languages or dialects are involved. Such interpretation can only be effectively conducted using consecutive interpretation. Simultaneous interpretation (SI) suffers the disadvantage that if a person is performing the service the interpreter must do the best he or she can within the time permitted by the pace of source speech. However they also have the advantages of saving time and not disturbing the natural flow of the speaker. SI can also be accomplished by software where the program can simultaneously listen to incoming speech and speak the associated interpretation. The most common form is extempore SI, where the interpreter does not know the message until he or she hears it. Simultaneous interpretation using electronic equipment where the interpreter can hear the speaker's voice as well as the interpreter's own voice was introduced at the Nuremberg trials in 1945. The equipment facilitated large numbers of listeners, and interpretation was offered in French, Russian, German and English. The technology arose in the 1920s and 1930s when American businessman Edward Filene and British engineer Alan Gordon Finlay developed simultaneous interpretation equipment with IBM. Yvonne Kapp attended a conference with simultaneous translation in 1935 in the Soviet Union. As it proved successful, IBM was able to sell the equipment to the United Nations, where it is now widely used in the United Nations Interpretation Service. In the ideal setting for oral language, the interpreter sits in a sound-proof booth and speaks into a microphone, while clearly seeing and hearing the source-language speaker via earphones. The simultaneous interpretation is rendered to the target-language listeners via their earphones. Pavel Palazchenko's "My Years with Gorbachev and Shevardnadze: The Memoir of a Soviet Interpreter" gives a short history of modern interpretation and of the transition from its consecutive to simultaneous forms. He explains that during the nineteenth century interpreters were rarely needed during European diplomatic discussions; these were routinely conducted in French, and all government diplomats were required to be fluent in this language. Most European government leaders and heads of state could also speak French. Historian Harold Nicolson attributes the growing need for interpretation after World War I to the fact that U.S. President Woodrow Wilson and British Prime Minister David Lloyd George "were no linguists". At the time, the concept and special equipment needed for simultaneous interpretation, later patented by Alan Gordon Finlay, had not been developed, so consecutive interpretation was used. Consecutive interpreters, in order be accurate, used a specialized system of note-taking which included symbols abbreviations and acronyms. Because they waited until the speaker was finished to provide translation, the interpreters then had the difficult task of creating from these notes as much as half an hour of free-flowing sentences closely matching the speaker's meaning. Palazchenko cites, Jean Herbert and the Kaminker brothers as skilled interpreters, and notes one unusual case in which André Kaminker interpreted a speech by a French diplomat who spoke for two and a half hours without stopping. After World War II, simultaneous interpretation came into use at the Nuremberg trial, and began to be more accepted. Experienced consecutive interpreters asserted that the difficulties of listening and speaking at the same time, adjusting for differences in sentence structure between languages, and interpreting the beginning of a sentence before hearing its end, would produce an inferior result. As well, these interpreters, who to that point had been prominent speakers, would now be speaking invisibly from booths. In 1951, when the United Nations expanded its number of working languages to five (English, French, Russian, Chinese and Spanish), consecutive translation became impractical in most cases, and simultaneous translation became the most common process for the organization's large meetings. Consecutive interpretation, which provides a more fluent result without the need for specialized equipment, continued to be used for smaller discussions. Since time immemorial, whispering interpretation has been used, known in the trade by the French term "chuchotage". To avoid disturbing the original speaker and those present listening to the original speaker, the interpreter's voice is kept at a low volume. To do this, the interpreter and the person requiring interpretation must sit or stand in close proximity to one another. No actual whispering is involved as this is difficult to decipher as well as being too much of a strain on the voice: the interpreter uses normal 'voiced' speech at a low volume. Only one or at the most two people in need of interpretation can be accommodated, unless portable electronic equipment is used. This form of interpretation puts a strain on the interpreter who has to sit for long periods leaning towards the person in need of interpretation. Conference interpreting refers to interpretation at a conference or large meeting, either simultaneously or consecutively. The advent of multi-lingual meetings has reduced the amount of consecutive interpretation in the last 20 years. Conference interpretation is divided between two markets: institutional and private. International institutions (EU, UN, EPO, et cetera), which hold multilingual meetings, often favor interpreting several foreign languages into the interpreters' mother tongues. Local private markets tend to have bilingual meetings (the local language plus another), and the interpreters work both into and out of their mother tongues. These markets are not mutually exclusive. The International Association of Conference Interpreters (AIIC) is the only worldwide association of conference interpreters. Founded in 1953, its membership includes more than 2,800 professional conference interpreters, in more than 90 countries. Judicial, legal, or court interpreting occurs in courts of justice, administrative tribunals, and wherever a legal proceeding is held (i.e., a police station for an interrogation, a conference room for a deposition, or the locale for taking a sworn statement). Legal interpreting can be the consecutive interpretation of witnesses' testimony, for example, or the simultaneous interpretation of entire proceedings, by electronic means, for one person, or all of the people attending. In a legal context, where ramifications of misinterpretation may be dire, accuracy is paramount. Teams of two or more interpreters, with one actively interpreting and the second monitoring for greater accuracy, may be deployed. The right to a competent interpreter for anyone who does not understand the language of the court (especially for the accused in a criminal trial) is usually considered a fundamental rule of justice. Therefore, this right is often guaranteed in national constitutions, declarations of rights, fundamental laws establishing the justice system or by precedents set by the highest courts. However, it is not a constitutionally required procedure (in the United States) that a certified interpreter be present at police interrogation. This has been especially controversial in cases where illegal immigrants with no English skills are accused of crimes. In the US, depending upon the regulations and standards adhered to per state and venue, court interpreters usually work alone when interpreting consecutively, or as a team, when interpreting simultaneously. In addition to practical mastery of the source and target languages, thorough knowledge of law and legal and court procedures is required of court interpreters. They are often required to have formal authorization from the state to work in the courts – and then are called certified court interpreters. In many jurisdictions, the interpretation is considered an essential part of the evidence. Incompetent interpretation, or simply failure to swear in the interpreter, can lead to a mistrial. In escort interpreting, an interpreter accompanies a person or a delegation on a tour, on a visit, or to a business meeting or interview. An interpreter in this role is called an "escort interpreter" or an "escorting interpreter". An escort interpreter’s work session may run for days, weeks, or even months, depending on the period of the client’s visit. This type of interpreting is often needed in business contexts, during presentations, investor meetings, and business negotiations. As such, and escort interpreter needs to be equipped with some business and financial knowledge in order to best understand and convey messages back and forth. Also known as community interpreting, is the type of interpreting occurring in fields such as legal, health, and federal and local government, social, housing, environmental health, education, and welfare services. In community interpreting, factors exist which determine and affect language and communication production, such as speech's emotional content, hostile or polarized social surroundings, its created stress, the power relationships among participants, and the interpreter's degree of responsibility – in many cases more than extreme; in some cases, even the life of the other person depends upon the interpreter's work. Medical interpreting is a subset of public service interpreting, consisting of communication among Healthcare personnel and the patient and their family or among Healthcare personnel speaking different languages, facilitated by an interpreter, usually formally educated and qualified to provide such interpretation services. In some situations medical employees who are multilingual may participate part-time as members of internal language banks. Depending on country/state specific requirements, the interpreter is often required to have some knowledge of medical terminology, common procedures, the patient interview and exam process. Medical interpreters are often cultural liaisons for people (regardless of language) who are unfamiliar with or uncomfortable in hospital, clinical, or medical settings. For example, in China, there is no mandatory certificate for medical interpreters as of 2012. Most interpretation in hospitals in China is done by doctors, who are proficient in both Chinese and English (mostly) in his/her specialty. They interpret more in academic settings than for communications between doctors and patients. When a patient needs English language service in a Chinese hospital, more often than not the patient will be directed to a staff member in the hospital, who is recognized by his/her colleagues as proficient in English. The actual quality of such service for patients or medical translation for communications between doctors speaking different languages is unknown by the interpreting community as interpreters who lack Healthcare background rarely receive accreditation for medical translation in the medical community. Interpreters working in the Healthcare setting may be considered Allied Health Professionals. In the United States, however, providing a Medical Interpreter is required by law. Title VI of the Civil Rights Act of 1964 prohibits discrimination on the basis of race, color, or national origin in any program or activity that receives Federal funds or other Federal financial assistance. Because hospitals are federally funded, they are required by this law to provide a professional interpreter to any patient that may need one. A sign language interpreter must accurately convey messages between two different languages. An interpreter is there for both deaf and hearing individuals. The act of interpreting occurs when a hearing person speaks, and an interpreter renders the speaker's meaning into sign language, or other forms used by the deaf party(ies). The interpreting also happens in reverse: when a deaf person signs, an interpreter renders the meaning expressed in the signs into the oral language for the hearing party, which is sometimes referred to as voice interpreting or "voicing". This may be performed either as simultaneous or consecutive interpreting. Skilled sign language interpreters will position themselves in a room or space that allows them to be seen by the deaf participants and heard clearly by hearing participants, as well as be in a position to hear and/or see the speaker or speakers clearly. In some circumstances, an interpreter may interpret from one language to another whether that is English to British Sign Language, English to American Sign Language, Spanish to English to American Sign Language and so on. Deaf individuals also have the opportunity to work as interpreters. If they are certified they are referred to as a CDI (Certified Deaf Interpreter), if not they would be called a DI (Deaf Interpreter). The Deaf individual will team with a hearing counterpart to provide interpretation for deaf individuals who may not know the same sign language used in that country, who have minimal language skills, are developmentally delayed, have other mental and/or physical disabilities which make communication a unique challenge, or request one. In other cases the hearing interpreter may interpret in the sign language, whichever kind of sign language the team knows and the deaf team will then interpret into the language in which the individual can understand. They also interpret information from one medium of language into another – for example, when a person is signing visually, the deaf interpreter could be hired to copy those signs into a deaf-blind person's hand and add visual information. Some interpreters have been formally trained in an Interpreter Training Program (ITP), though this is not always required. ITP lengths vary, and are usually two or four years to obtain a degree or certificate. Graduate programs are also available. In the United States, Sign Language interpreters have National and some states have a State level certifications. The Registry of Interpreters for the Deaf (RID), a non-profit organization, is known for its national recognition and certification process. In addition to training requirements and stringent certification testing, RID members must abide by a Code of Professional Conduct, Grievance Process and Continuing Education Requirement. There are many interpreter-training programs in the U.S. The Collegiate Commission on Interpreter Education is the body that accredits Interpreter Preparation Programs. A list of accredited programs can be found on the CCIE web site. European countries and countries elsewhere have their own national associations of Sign Language Interpreters. Some countries have more than one national association due to regional or language differences. The European Forum of Sign Language Interpreters (efsli) is the umbrella organization of sign language interpreters in Europe. In Canada, the professional association that recognizes and nationally certifies sign language interpreters is the Association of Visual Language Interpreters of Canada (AVLIC). Under AVLIC holds several affiliate chapters representing a specified region of Canada. Sign language interpreters encounter a number of linguistic, environmental, interpersonal and intrapersonal factors that can have an effect on their ability to provide accurate interpretation. Studies have found that most interpreter training programs do not sufficiently prepare students for the highly variable day-to-day stresses that an interpreter must manage, and there is an ongoing conversation in the interpreting field as to how to appropriately prepare students for the challenges of the job. Proposed changes include having a more robust definition of what a qualified interpreter should know, as well as a post-graduate internship structure that would allow new interpreters to work with the benefit of supervision from more experienced interpreters, much like the programs in place in medicine, law enforcement, etc. In Israel, Naama Weiss, a board member of Malach, the Organization of the Israeli Sign Language Interpreters, advertised a video which she produced. It was her paraphrase of the video "So-Low", and showed her viewpoint upon the Israeli Sign Language interpreters' jobs. A study which was made in Finland found that, in comparison to the foreign language teachers and non-linguistic experts, a high cooperativeness was found to be more characteristic to simultaneous and consecutive interpreters, and Weiss showed it in her video, although she claimed to be comic. By its very nature, media interpreting has to be conducted in the simultaneous mode. It is provided particularly for live television coverages such as press conferences, live or taped interviews with political figures, musicians, artists, sportsmen or people from the business circle. In this type of interpreting, the interpreter has to sit in a sound-proof booth where ideally he/she can see the speakers on a monitor and the set. All equipment should be checked before recording begins. In particular, satellite connections have to be double-checked to ensure that the interpreter's voice is not sent back and the interpreter gets to hear only one channel at a time. In the case of interviews recorded outside the studio and some current affairs program, the interpreter interprets what he or she hears on a TV monitor. Background noise can be a serious problem. The interpreter working for the media has to sound as slick and confident as a television presenter. Media interpreting has gained more visibility and presence especially after the Gulf War. Television channels have begun to hire staff simultaneous interpreters. The interpreter renders the press conferences, telephone beepers, interviews and similar live coverage for the viewers. It is more stressful than other types of interpreting as the interpreter has to deal with a wide range of technical problems coupled with the control room's hassle and wrangling during live coverage. Interpreting services can be delivered in multiple modalities. The most common modality through which interpreting services are provided is on-site interpreting. Also called "in-person interpreting" or sometimes colloquialized as "face-to-face", this delivery method requires the interpreter to be physically present in order for the interpretation to take place. In on-site interpreting settings, all of the parties who wish to speak to one another are usually located in the same place. This is by far the most common modality used for most public and social service settings. Also referred to as "over-the-phone interpreting," "telephonic interpreting," and "tele-interpreting," telephone interpreting enables interpretation via telephone. Telephone interpreting can be used in community settings as well as conference settings. Telephone interpreting may be used in place of on-site interpreting when no on-site interpreter is readily available at the location where services are needed. However, it is more commonly used for situations in which all parties who wish to communicate are already speaking to one another via telephone (e.g. telephone applications for insurance or credit cards, or telephone inquiries from consumers to businesses). Interpretation services via Video Remote Interpreting (VRI) or a Video Relay Service (VRS) are useful for spoken language barriers where visual-cultural recognition is relevant, and even more applicable where one of the parties is deaf, hard-of-hearing or speech-impaired (mute). In such cases the direction of interpretation is normally within the same principal language, such as French Sign Language (FSL) to spoken French and Spanish Sign Language (SSL) to spoken Spanish. Multilingual sign language interpreters, who can also translate as well across principal languages (such as to and from SSL, to and from spoken English), are also available, albeit less frequently. Such activities involve considerable effort on the part of the translator, since sign languages are distinct natural languages with their own construction and syntax, different from the aural version of the same principal language. With video interpreting, sign language interpreters work remotely with live video and audio feeds, so that the interpreter can see the deaf or mute party, converse with the hearing party and vice versa. Much like telephone interpreting, video interpreting can be used for situations in which no on-site interpreters are available. However, video interpreting cannot be used for situations in which all parties are speaking via telephone alone. VRI and VRS interpretation requires all parties to have the necessary equipment. Some advanced equipment enables interpreters to control the video camera, in order to zoom in and out, and to point the camera toward the party that is signing. The majority of professional full-time conference interpreters work for phone interpreting agencies, health care institutions, courts, school systems and international organizations like the United Nations, (for the United Nations Interpretation Service), the European Union, or the African Union. The world's largest employer of interpreters is currently the European Commission, which employs hundreds of staff and freelance interpreters working into the official languages of the European Union and some others. The European Union's other institutions (the European Parliament and the European Court of Justice) have smaller interpreting services. The United Nations employs interpreters at almost all its sites throughout the world. Because it has only six official languages, however, it is a smaller employer than the European Union. Interpreters may also work as freelance operators in their local, regional and national communities, or may take on contract work under an interpreting business or service. They would typically take on work as described above. Militaries often use interpreters to better communicate with the local population. One notable example is the US military during the war in Iraq and Afghanistan. There are a number of interpreting and translation associations around the world, including NAATI (National Accreditation Authority for Translators and Interpreters), AIIC (The International Association of Conference Interpreters), CATTI (China Accreditation Test for Translators and Interpreters), CTTIC (Canadian Translators, Terminologists and Interpreters Council), and the Institute of Translation & Interpreting, in the UK. No worldwide testing or certification agency exists for all types of interpreters. For conference interpretation, there is the International Association of Conference Interpreters, or AIIC. Specific regions, countries, or even cities will have their own certification standards. In many cases, graduates of a certain caliber university program acts as a de facto certification for conference interpretation. The most recognized interpretation & translation certificate in P.R.C. is China Accreditation Test for Translation and Interpretation, short for CATTI. It is entrusted by the Ministry of Human Resources and Social Security of P.R.C. It is a translation and interpretation professional qualification accreditation test which is implemented throughout the country according to uniform standards, in order to assess examinees' bilingual translation or interpretation capability. CATTI was introduced in 2003. In later 2013, translation and interpreting tests of different levels in English, French, Japanese, Russian, German, Spanish and Arabic were held across the nation. Those examinees who pass CATTI and obtain translation and interpretation certificates acquire corresponding translation and interpretation professional titles. Relevant institutions from Australia, France, Japan, the Republic of Korea, Singapore and other countries as well as Hong Kong Special Administrative Region and the region of Taiwan have established work ties with CATTI.	Interpreting is a translational activity in which one produces a first and final translation on the basis of a one-time exposure to an expression in a source language.	en	en	29	[ 250004, 250054, 42477, 3934, 70, 67842, 128746, 111, 70, 32692, 111, 29481, 214, 83, 32233, 3525, 5, 1326, 237, 4989, 237, 2684, 191225, 538, 33946, 509, 34475, 47, 23182, 108870, 29481, 214, 4, 4552, 10176, 108858, 4488, 509, 16940, 98, 70, 41361, 111, 29481, 214, 23, 32692, 4, 136, 24189, 70, 11704, 7, 4, 4734, 10, 10846, 54, 3121, 104345, 7, 3542, 16940, 98, 442, 5, 137399, 214, 70, 41170, 111, 29481, 214, 69924, 450, 83, 41591, 71, 47, 765, 74918, 2822, 100, 137107, 111, 5369, 4, 186768, 115923, 621, 84046, 5, 5455, 5465, 4, 29481, 1314, 136, 2363, 4488, 765, 56104, 959, 14037, 2363, 3917, 3934, 70, 32692, 42840, 5, 6561, 111, 70, 89397, 100, 450, 83, 70, 139887, 329, 111, 70, 59121, 7986, 645, 70, 113091, 19, 2565, 15, 73, 70, 10422, 450, 8382, 2750, 765, 25737, 59121, 7986, 7, 621, 1286, 47041, 47, 186, 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summarize: In a solid, constituent particles (ions, atoms, or molecules) are closely packed together. The forces between particles are so strong that the particles cannot move freely but can only vibrate. As a result, a solid has a stable, definite shape, and a definite volume. Solids can only change their shape by an outside force, as when broken or cut. In crystalline solids, the particles (atoms, molecules, or ions) are packed in a regularly ordered, repeating pattern. There are various different crystal structures, and the same substance can have more than one structure (or solid phase). For example, iron has a body-centred cubic structure at temperatures below, and a face-centred cubic structure between 912 and. Ice has fifteen known crystal structures, or fifteen solid phases, which exist at various temperatures and pressures. Glasses and other non-crystalline, amorphous solids without long-range order are not thermal equilibrium ground states; therefore they are described below as nonclassical states of matter. Solids can be transformed into liquids by melting, and liquids can be transformed into solids by freezing. Solids can also change directly into gases through the process of sublimation, and gases can likewise change directly into solids through deposition. A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. The volume is definite if the temperature and pressure are constant. When a solid is heated above its melting point, it becomes liquid, given that the pressure is higher than the triple point of the substance. Intermolecular (or interatomic or interionic) forces are still important, but the molecules have enough energy to move relative to each other and the structure is mobile. This means that the shape of a liquid is not definite but is determined by its container. The volume is usually greater than that of the corresponding solid, the best known exception being water, HO. The highest temperature at which a given liquid can exist is its critical temperature. A gas is a compressible fluid. Not only will a gas conform to the shape of its container but it will also expand to fill the container. In a gas, the molecules have enough kinetic energy so that the effect of intermolecular forces is small (or zero for an ideal gas), and the typical distance between neighboring molecules is much greater than the molecular size. A gas has no definite shape or volume, but occupies the entire container in which it is confined. A liquid may be converted to a gas by heating at constant pressure to the boiling point, or else by reducing the pressure at constant temperature. At temperatures below its critical temperature, a gas is also called a vapor, and can be liquefied by compression alone without cooling. A vapor can exist in equilibrium with a liquid (or solid), in which case the gas pressure equals the vapor pressure of the liquid (or solid). A supercritical fluid (SCF) is a gas whose temperature and pressure are above the critical temperature and critical pressure respectively. In this state, the distinction between liquid and gas disappears. A supercritical fluid has the physical properties of a gas, but its high density confers solvent properties in some cases, which leads to useful applications. For example, supercritical carbon dioxide is used to extract caffeine in the manufacture of decaffeinated coffee. Like a gas, plasma does not have definite shape or volume. Unlike gases, plasmas are electrically conductive, produce magnetic fields and electric currents, and respond strongly to electromagnetic forces. Positively charged nuclei swim in a "sea" of freely-moving disassociated electrons, similar to the way such charges exist in conductive metal, where this electron "sea" allows matter in the plasma state to conduct electricity. A gas is usually converted to a plasma in one of two ways, e.g., either from a huge voltage difference between two points, or by exposing it to extremely high temperatures. Heating matter to high temperatures causes electrons to leave the atoms, resulting in the presence of free electrons. This creates a so-called partially ionised plasma. At very high temperatures, such as those present in stars, it is assumed that essentially all electrons are "free", and that a very high-energy plasma is essentially bare nuclei swimming in a sea of electrons. This forms the so-called fully ionised plasma. The plasma state is often misunderstood, and although not freely existing under normal conditions on Earth, it is quite commonly generated by either lightning, electric sparks, fluorescent lights, neon lights or in plasma televisions. The Sun's corona, some types of flame, and stars are all examples of illuminated matter in the plasma state. A state of matter is also characterized by phase transitions. A phase transition indicates a change in structure and can be recognized by an abrupt change in properties. A distinct state of matter can be defined as any set of states distinguished from any other set of states by a phase transition. Water can be said to have several distinct solid states. The appearance of superconductivity is associated with a phase transition, so there are superconductive states. Likewise, ferromagnetic states are demarcated by phase transitions and have distinctive properties. When the change of state occurs in stages the intermediate steps are called mesophases. Such phases have been exploited by the introduction of liquid crystal technology. The state or "phase" of a given set of matter can change depending on pressure and temperature conditions, transitioning to other phases as these conditions change to favor their existence; for example, solid transitions to liquid with an increase in temperature. Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point, boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons are so energized that they leave their parent atoms. Forms of matter that are not composed of molecules and are organized by different forces can also be considered different states of matter. Superfluids (like Fermionic condensate) and the quark–gluon plasma are examples. In a chemical equation, the state of matter of the chemicals may be shown as (s) for solid, (l) for liquid, and (g) for gas. An aqueous solution is denoted (aq). Matter in the plasma state is seldom used (if at all) in chemical equations, so there is no standard symbol to denote it. In the rare equations that plasma is used it is symbolized as (p). Glass is a non-crystalline or amorphous solid material that exhibits a glass transition when heated towards the liquid state. Glasses can be made of quite different classes of materials: inorganic networks (such as window glass, made of silicate plus additives), metallic alloys, ionic melts, aqueous solutions, molecular liquids, and polymers. Thermodynamically, a glass is in a metastable state with respect to its crystalline counterpart. The conversion rate, however, is practically zero. A plastic crystal is a molecular solid with long-range positional order but with constituent molecules retaining rotational freedom; in an orientational glass this degree of freedom is frozen in a quenched disordered state. Similarly, in a spin glass magnetic disorder is frozen. Liquid crystal states have properties intermediate between mobile liquids and ordered solids. Generally, they are able to flow like a liquid, but exhibiting long-range order. For example, the nematic phase consists of long rod-like molecules such as para-azoxyanisole, which is nematic in the temperature range. In this state the molecules flow as in a liquid, but they all point in the same direction (within each domain) and cannot rotate freely. Like a crystalline solid, but unlike a liquid, liquid crystals react to polarized light. Other types of liquid crystals are described in the main article on these states. Several types have technological importance, for example, in liquid crystal displays. Transition metal atoms often have magnetic moments due to the net spin of electrons that remain unpaired and do not form chemical bonds. In some solids the magnetic moments on different atoms are ordered and can form a ferromagnet, an antiferromagnet or a ferrimagnet. In a ferromagnet—for instance, solid iron—the magnetic moment on each atom is aligned in the same direction (within a magnetic domain). If the domains are also aligned, the solid is a permanent magnet, which is magnetic even in the absence of an external magnetic field. The magnetization disappears when the magnet is heated to the Curie point, which for iron is. An antiferromagnet has two networks of equal and opposite magnetic moments, which cancel each other out so that the net magnetization is zero. For example, in nickel(II) oxide (NiO), half the nickel atoms have moments aligned in one direction and half in the opposite direction. In a ferrimagnet, the two networks of magnetic moments are opposite but unequal, so that cancellation is incomplete and there is a non-zero net magnetization. An example is magnetite (FeO), which contains Fe and Fe ions with different magnetic moments. A quantum spin liquid (QSL) is a disordered state in a system of interacting quantum spins which preserves its disorder to very low temperatures, unlike other disordered states. It is not a liquid in physical sense, but a solid whose magnetic order is inherently disordered. The name "liquid" is due to an analogy with the molecular disorder in a conventional liquid. A QSL is neither a ferromagnet, where magnetic domains are parallel, nor an antiferromagnet, where the magnetic domains are antiparallel; instead, the magnetic domains are randomly oriented. This can be realized e.g. by geometrically frustrated magnetic moments that cannot point uniformly parallel or antiparallel. When cooling down and settling to a state, the domain must "choose" an orientation, but if the possible states are similar in energy, one will be chosen randomly. Consequently, despite strong short-range order, there is no long-range magnetic order. Copolymers can undergo microphase separation to form a diverse array of periodic nanostructures, as shown in the example of the styrene-butadiene-styrene block copolymer shown at right. Microphase separation can be understood by analogy to the phase separation between oil and water. Due to chemical incompatibility between the blocks, block copolymers undergo a similar phase separation. However, because the blocks are covalently bonded to each other, they cannot demix macroscopically as water and oil can, and so instead the blocks form nanometre-sized structures. Depending on the relative lengths of each block and the overall block topology of the polymer, many morphologies can be obtained, each its own phase of matter. Ionic liquids also display microphase separation. The anion and cation are not necessarily compatible and would demix otherwise, but electric charge attraction prevents them from separating. Their anions and cations appear to diffuse within compartmentalized layers or micelles instead of freely as in a uniform liquid. Close to absolute zero, some liquids form a second liquid state described as superfluid because it has zero viscosity (or infinite fluidity; i.e., flowing without friction). This was discovered in 1937 for helium, which forms a superfluid below the lambda temperature of. In this state it will attempt to "climb" out of its container. It also has infinite thermal conductivity so that no temperature gradient can form in a superfluid. Placing a superfluid in a spinning container will result in quantized vortices. These properties are explained by the theory that the common isotope helium-4 forms a Bose–Einstein condensate (see next section) in the superfluid state. More recently, Fermionic condensate superfluids have been formed at even lower temperatures by the rare isotope helium-3 and by lithium-6. In 1924, Albert Einstein and Satyendra Nath Bose predicted the "Bose–Einstein condensate" (BEC), sometimes referred to as the fifth state of matter. In a BEC, matter stops behaving as independent particles, and collapses into a single quantum state that can be described with a single, uniform wavefunction. In the gas phase, the Bose–Einstein condensate remained an unverified theoretical prediction for many years. In 1995, the research groups of Eric Cornell and Carl Wieman, of JILA at the University of Colorado at Boulder, produced the first such condensate experimentally. A Bose–Einstein condensate is "colder" than a solid. It may occur when atoms have very similar (or the same) quantum levels, at temperatures very close to absolute zero,. A "fermionic condensate" is similar to the Bose–Einstein condensate but composed of fermions. The Pauli exclusion principle prevents fermions from entering the same quantum state, but a pair of fermions can behave as a boson, and multiple such pairs can then enter the same quantum state without restriction. One of the metastable states of strongly non-ideal plasma is Rydberg matter, which forms upon condensation of excited atoms. These atoms can also turn into ions and electrons if they reach a certain temperature. In April 2009, "Nature" reported the creation of Rydberg molecules from a Rydberg atom and a ground state atom, confirming that such a state of matter could exist. The experiment was performed using ultracold rubidium atoms. A "quantum Hall state" gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow. A "quantum spin Hall state" is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat. This is a derivation of the Quantum Hall state of matter. Photonic matter is a phenomenon where photons interacting with a gas develop apparent mass, and can interact with each other, even forming photonic "molecules". The source of mass is the gas, which is massive. This is in contrast to photons moving in empty space, which have no rest mass, and cannot interact. A "quantum fog" of electrons and holes that flow around each other and even ripple like a liquid, rather than existing as discrete pairs. Under extremely high pressure, as in the cores of dead stars, ordinary matter undergoes a transition to a series of exotic states of matter collectively known as degenerate matter, which are supported mainly by quantum mechanical effects. In physics, "degenerate" refers to two states that have the same energy and are thus interchangeable. Degenerate matter is supported by the Pauli exclusion principle, which prevents two fermionic particles from occupying the same quantum state. Unlike regular plasma, degenerate plasma expands little when heated, because there are simply no momentum states left. Consequently, degenerate stars collapse into very high densities. More massive degenerate stars are smaller, because the gravitational force increases, but pressure does not increase proportionally. Electron-degenerate matter is found inside white dwarf stars. Electrons remain bound to atoms but are able to transfer to adjacent atoms. Neutron-degenerate matter is found in neutron stars. Vast gravitational pressure compresses atoms so strongly that the electrons are forced to combine with protons via inverse beta-decay, resulting in a superdense conglomeration of neutrons. Normally free neutrons outside an atomic nucleus will decay with a half life of just under 15 minutes, but in a neutron star, the decay is overtaken by inverse decay. Cold degenerate matter is also present in planets such as Jupiter and in the even more massive brown dwarfs, which are expected to have a core with metallic hydrogen. Because of the degeneracy, more massive brown dwarfs are not significantly larger. In metals, the electrons can be modeled as a degenerate gas moving in a lattice of non-degenerate positive ions. In regular cold matter, quarks, fundamental particles of nuclear matter, are confined by the strong force into hadrons that consist of 2–4 quarks, such as protons and neutrons. Quark matter or quantum chromodynanamical (QCD) matter is a group of phases where the strong force is overcome and quarks are deconfined and free to move. Quark matter phases occur at extremely high densities or temperatures, and there are no known ways to produce them in equilibrium in the laboratory; in ordinary conditions, any quark matter formed immediately undergoes radioactive decay. Strange matter is a type of quark matter that is suspected to exist inside some neutron stars close to the Tolman–Oppenheimer–Volkoff limit (approximately 2–3 solar masses), although there is no direct evidence of its existence. In strange matter, part of the energy available manifests as strange quarks, a heavier analogue of the common down quark. It may be stable at lower energy states once formed, although this is not known. Quark–gluon plasma is a very high-temperature phase in which quarks become free and able to move independently, rather than being perpetually bound into particles, in a sea of gluons, subatomic particles that transmit the strong force that binds quarks together. This is analogous to the liberation of electrons from atoms in a plasma. This state is briefly attainable in extremely high-energy heavy ion collisions in particle accelerators, and allows scientists to observe the properties of individual quarks, and not just theorize. Quark–gluon plasma was discovered at CERN in 2000. Unlike plasma, which flows like a gas, interactions within QGP are strong and it flows like a liquid. At high densities but relatively low temperatures, quarks are theorized to form a quark liquid whose nature is presently unknown. It forms a distinct color-flavor locked (CFL) phase at even higher densities. This phase is superconductive for color charge. These phases may occur in neutron stars but they are presently theoretical. Color-glass condensate is a type of matter theorized to exist in atomic nuclei traveling near the speed of light. According to Einstein's theory of relativity, a high-energy nucleus appears length contracted, or compressed, along its direction of motion. As a result, the gluons inside the nucleus appear to a stationary observer as a "gluonic wall" traveling near the speed of light. At very high energies, the density of the gluons in this wall is seen to increase greatly. Unlike the quark–gluon plasma produced in the collision of such walls, the color-glass condensate describes the walls themselves, and is an intrinsic property of the particles that can only be observed under high-energy conditions such as those at RHIC and possibly at the Large Hadron Collider as well. Various theories predict new states of matter at very high energies. An unknown state has created the baryon asymmetry in the universe, but little is known about it. In string theory, a Hagedorn temperature is predicted for superstrings at about 10 K, where superstrings are copiously produced. At Planck temperature (10 K), gravity becomes a significant force between individual particles. No current theory can describe these states and they cannot be produced with any foreseeable experiment. However, these states are important in cosmology because the universe may have passed through these states in the Big Bang. The gravitational singularity predicted by general relativity to exist at the center of a black hole is "not" a phase of matter; it is not a material object at all (although the mass-energy of matter contributed to its creation) but rather a property of spacetime at a location. It could be argued, of course, that all particles are properties of spacetime at a location, leaving a half-note of controversy on the subject. A supersolid is a spatially ordered material (that is, a solid or crystal) with superfluid properties. Similar to a superfluid, a supersolid is able to move without friction but retains a rigid shape. Although a supersolid is a solid, it exhibits so many characteristic properties different from other solids that many argue it is another state of matter. In a string-net liquid, atoms have apparently unstable arrangement, like a liquid, but are still consistent in overall pattern, like a solid. When in a normal solid state, the atoms of matter align themselves in a grid pattern, so that the spin of any electron is the opposite of the spin of all electrons touching it. But in a string-net liquid, atoms are arranged in some pattern that requires some electrons to have neighbors with the same spin. This gives rise to curious properties, as well as supporting some unusual proposals about the fundamental conditions of the universe itself. A superglass is a phase of matter characterized, at the same time, by superfluidity and a frozen amorphous structure.	In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates, neutron-degenerate matter, and quark–gluon plasma, which only occur, respectively, in situations of extreme cold, extreme density, and extremely high energy. 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summarize: To Isaac Newton, his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. When looking at the motion of many bodies all interacting with each other, such as the planets in the Solar System, dealing with the force between each pair of bodies separately rapidly becomes computationally inconvenient. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces. This quantity, the gravitational field, gave at each point in space the total gravitational acceleration which would be felt by a small object at that point. This did not change the physics in any way: it did not matter if all the gravitational forces on an object were calculated individually and then added together, or if all the contributions were first added together as a gravitational field and then applied to an object. The development of the independent concept of a field truly began in the nineteenth century with the development of the theory of electromagnetism. In the early stages, André-Marie Ampère and Charles-Augustin de Coulomb could manage with Newton-style laws that expressed the forces between pairs of electric charges or electric currents. However, it became much more natural to take the field approach and express these laws in terms of electric and magnetic fields; in 1849 Michael Faraday became the first to coin the term "field". The independent nature of the field became more apparent with James Clerk Maxwell's discovery that waves in these fields propagated at a finite speed. Consequently, the forces on charges and currents no longer just depended on the positions and velocities of other charges and currents at the same time, but also on their positions and velocities in the past. Maxwell, at first, did not adopt the modern concept of a field as a fundamental quantity that could independently exist. Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. If that were the case, the observed velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Despite much effort, no experimental evidence of such an effect was ever found; the situation was resolved by the introduction of the special theory of relativity by Albert Einstein in 1905. This theory changed the way the viewpoints of moving observers were related to each other. They became related to each other in such a way that velocity of electromagnetic waves in Maxwell's theory would be the same for all observers. By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities. In the late 1920s, the new rules of quantum mechanics were first applied to the electromagnetic field. In 1927, Paul Dirac used quantum fields to successfully explain how the decay of an atom to a lower quantum state led to the spontaneous emission of a photon, the quantum of the electromagnetic field. This was soon followed by the realization (following the work of Pascual Jordan, Eugene Wigner, Werner Heisenberg, and Wolfgang Pauli) that all particles, including electrons and protons, could be understood as the quanta of some quantum field, elevating fields to the status of the most fundamental objects in nature. That said, John Wheeler and Richard Feynman seriously considered Newton's pre-field concept of action at a distance (although they set it aside because of the ongoing utility of the field concept for research in general relativity and quantum electrodynamics). There are several examples of classical fields. Classical field theories remain useful wherever quantum properties do not arise, and can be active areas of research. Elasticity of materials, fluid dynamics and Maxwell's equations are cases in point. Some of the simplest physical fields are vector force fields. Historically, the first time that fields were taken seriously was with Faraday's lines of force when describing the electric field. The gravitational field was then similarly described. A classical field theory describing gravity is Newtonian gravitation, which describes the gravitational force as a mutual interaction between two masses. Any body with mass "M" is associated with a gravitational field g which describes its influence on other bodies with mass. The gravitational field of "M" at a point r in space corresponds to the ratio between force F that "M" exerts on a small or negligible test mass "m" located at r and the test mass itself: Stipulating that "m" is much smaller than "M" ensures that the presence of "m" has a negligible influence on the behavior of "M". According to Newton's law of universal gravitation, F(r) is given by where formula_3 is a unit vector lying along the line joining "M" and "m" and pointing from "M" to "m". Therefore, the gravitational field of M is The experimental observation that inertial mass and gravitational mass are equal to an unprecedented level of accuracy leads to the identity that gravitational field strength is identical to the acceleration experienced by a particle. This is the starting point of the equivalence principle, which leads to general relativity. Because the gravitational force F is conservative, the gravitational field g can be rewritten in terms of the gradient of a scalar function, the gravitational potential Φ(r): Michael Faraday first realized the importance of a field as a physical quantity, during his investigations into magnetism. He realized that electric and magnetic fields are not only fields of force which dictate the motion of particles, but also have an independent physical reality because they carry energy. These ideas eventually led to the creation, by James Clerk Maxwell, of the first unified field theory in physics with the introduction of equations for the electromagnetic field. The modern version of these equations is called Maxwell's equations. A charged test particle with charge "q" experiences a force F based solely on its charge. We can similarly describe the electric field E so that. Using this and Coulomb's law tells us that the electric field due to a single charged particle is The electric field is conservative, and hence can be described by a scalar potential, "V"(r): A steady current "I" flowing along a path "l" will create a field B, that exerts a force on nearby moving charged particles that is quantitatively different from the electric field force described above. The force exerted by "I" on a nearby charge "q" with velocity v is where B(r) is the magnetic field, which is determined from "I" by the Biot–Savart law: The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential. However, it can be written in terms of a vector potential, A(r): In general, in the presence of both a charge density ρ(r, "t") and current density J(r, "t"), there will be both an electric and a magnetic field, and both will vary in time. They are determined by Maxwell's equations, a set of differential equations which directly relate E and B to ρ and J. Alternatively, one can describe the system in terms of its scalar and vector potentials "V" and A. A set of integral equations known as "retarded potentials" allow one to calculate "V" and A from ρ and J, and from there the electric and magnetic fields are determined via the relations At the end of the 19th century, the electromagnetic field was understood as a collection of two vector fields in space. Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in space-time. Einstein's theory of gravity, called general relativity, is another example of a field theory. Here the principal field is the metric tensor, a symmetric 2nd-rank tensor field in space-time. This replaces Newton's law of universal gravitation. Waves can be constructed as physical fields, due to their finite propagation speed and causal nature when a simplified physical model of an isolated closed system is set. They are also subject to the inverse-square law. For electromagnetic waves, there are optical fields, and terms such as near- and far-field limits for diffraction. In practice though, the field theories of optics are superseded by the electromagnetic field theory of Maxwell. It is now believed that quantum mechanics should underlie all physical phenomena, so that a classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory. For example, quantizing classical electrodynamics gives quantum electrodynamics. Quantum electrodynamics is arguably the most successful scientific theory; experimental data confirm its predictions to a higher precision (to more significant digits) than any other theory. The two other fundamental quantum field theories are quantum chromodynamics and the electroweak theory. In quantum chromodynamics, the color field lines are coupled at short distances by gluons, which are polarized by the field and line up with it. This effect increases within a short distance (around 1 fm from the vicinity of the quarks) making the color force increase within a short distance, confining the quarks within hadrons. As the field lines are pulled together tightly by gluons, they do not "bow" outwards as much as an electric field between electric charges. These three quantum field theories can all be derived as special cases of the so-called standard model of particle physics. General relativity, the Einsteinian field theory of gravity, has yet to be successfully quantized. However an extension, thermal field theory, deals with quantum field theory at "finite temperatures", something seldom considered in quantum field theory. In BRST theory one deals with odd fields, e.g. Faddeev–Popov ghosts. There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. As above with classical fields, it is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. The equations governing the quantum fields are in fact PDEs (specifically, relativistic wave equations (RWEs)). Thus one can speak of Yang–Mills, Dirac, Klein–Gordon and Schrödinger fields as being solutions to their respective equations. A possible problem is that these RWEs can deal with complicated mathematical objects with exotic algebraic properties (e.g. spinors are not tensors, so may need calculus for spinor fields), but these in theory can still be subjected to analytical methods given appropriate mathematical generalization. Field theory usually refers to a construction of the dynamics of a field, i.e. a specification of how a field changes with time or with respect to other independent physical variables on which the field depends. Usually this is done by writing a Lagrangian or a Hamiltonian of the field, and treating it as a classical or quantum mechanical system with an infinite number of degrees of freedom. The resulting field theories are referred to as classical or quantum field theories. The dynamics of a classical field are usually specified by the Lagrangian density in terms of the field components; the dynamics can be obtained by using the action principle. It is possible to construct simple fields without any prior knowledge of physics using only mathematics from several variable calculus, potential theory and partial differential equations (PDEs). For example, scalar PDEs might consider quantities such as amplitude, density and pressure fields for the wave equation and fluid dynamics; temperature/concentration fields for the heat/diffusion equations. Outside of physics proper (e.g., radiometry and computer graphics), there are even light fields. All these previous examples are scalar fields. Similarly for vectors, there are vector PDEs for displacement, velocity and vorticity fields in (applied mathematical) fluid dynamics, but vector calculus may now be needed in addition, being calculus for vector fields (as are these three quantities, and those for vector PDEs in general). More generally problems in continuum mechanics may involve for example, directional elasticity (from which comes the term "tensor", derived from the Latin word for stretch), complex fluid flows or anisotropic diffusion, which are framed as matrix-tensor PDEs, and then require matrices or tensor fields, hence matrix or tensor calculus. The scalars (and hence the vectors, matrices and tensors) can be real or complex as both are fields in the abstract-algebraic/ring-theoretic sense. In a general setting, classical fields are described by sections of fiber bundles and their dynamics is formulated in the terms of jet manifolds (covariant classical field theory). In modern physics, the most often studied fields are those that model the four fundamental forces which one day may lead to the Unified Field Theory. A convenient way of classifying a field (classical or quantum) is by the symmetries it possesses. Physical symmetries are usually of two types: Fields are often classified by their behaviour under transformations of space-time. The terms used in this classification are: Fields may have internal symmetries in addition to space-time symmetries. In many situations, one needs fields which are a list of space-time scalars: (φ, φ,... φ). For example, in weather prediction these may be temperature, pressure, humidity, etc. In particle physics, the color symmetry of the interaction of quarks is an example of an internal symmetry, that of the strong interaction. Other examples are isospin, weak isospin, strangeness and any other flavour symmetry. If there is a symmetry of the problem, not involving space-time, under which these components transform into each other, then this set of symmetries is called an "internal symmetry". One may also make a classification of the charges of the fields under internal symmetries. Statistical field theory attempts to extend the field-theoretic paradigm toward many-body systems and statistical mechanics. As above, it can be approached by the usual infinite number of degrees of freedom argument. Much like statistical mechanics has some overlap between quantum and classical mechanics, statistical field theory has links to both quantum and classical field theories, especially the former with which it shares many methods. One important example is mean field theory. Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable functions, but they are in any case almost always twice differentiable. In contrast, generalized functions are not continuous. When dealing carefully with classical fields at finite temperature, the mathematical methods of continuous random fields are used, because thermally fluctuating classical fields are nowhere differentiable. Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions as its index set. In particular, it is often mathematically convenient to take a continuous random field to have a Schwartz space of functions as its index set, in which case the continuous random field is a tempered distribution. We can think about a continuous random field, in a (very) rough way, as an ordinary function that is formula_13 almost everywhere, but such that when we take a weighted average of all the infinities over any finite region, we get a finite result. The infinities are not well-defined; but the finite values can be associated with the functions used as the weight functions to get the finite values, and that can be well-defined. We can define a continuous random field well enough as a linear map from a space of functions into the real numbers.	In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space-time. For example, on a weather map, the surface temperature is described by assigning a real number to each point on a map; the temperature can be considered at a fixed point in time or over some time interval, to study the dynamics of temperature change. A surface wind map, assigning a vector to each point on a map that describes the wind velocity at that point, would be an example of a 1-dimensional tensor field, i.e. a vector field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, and the full description of electrodynamics can be formulated in terms of two interacting vector fields at each point in space-time, or as a single-rank 2-tensor field theory.	en	en	178	[ 250004, 250054, 717, 114636, 145076, 4, 1919, 27165, 111, 32813, 137352, 1363, 42856, 36510, 297, 70, 137352, 43315, 37772, 450, 10, 89829, 17721, 2499, 80836, 111, 106750, 36746, 7, 5, 14847, 16487, 99, 70, 78112, 111, 5941, 337, 34204, 756, 78974, 214, 678, 12638, 3789, 4, 6044, 237, 70, 23208, 7, 23, 70, 56944, 12353, 4, 184017, 678, 70, 37772, 17721, 12638, 80836, 111, 337, 34204, 84797, 538, 25545, 538, 24209, 7, 181135, 43315, 538, 192206, 5, 360, 70, 136659, 5997, 927, 142642, 4, 10, 3525, 102134, 939, 509, 97025, 297, 47, 112892, 18929, 70, 12877, 50453, 10366, 111, 756, 6097, 137352, 43315, 84616, 5, 3293, 102134, 939, 4, 70, 137352, 43315, 44457, 4, 26038, 99, 12638, 6275, 23, 32628, 70, 3622, 137352, 43315, 197108, 1830, 3129, 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summarize: In the hydraulic analogy, current flowing through a wire (or resistor) is like water flowing through a pipe, and the voltage drop across the wire is like the pressure drop that pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow. (Conductance and resistance are reciprocals.) The voltage drop (i.e., difference between voltages on one side of the resistor and the other), not the voltage itself, provides the driving force pushing current through a resistor. In hydraulics, it is similar: The pressure difference between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe. But there may be an equally large water pressure below the pipe, which tries to push water back up through the pipe. If these pressures are equal, no water flows. (In the image at right, the water pressure below the pipe is zero.) The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties: Geometry is important because it is more difficult to push water through a long, narrow pipe than a wide, short pipe. In the same way, a long, thin copper wire has higher resistance (lower conductance) than a short, thick copper wire. Materials are important as well. A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. Similarly, electrons can flow freely and easily through a copper wire, but cannot flow as easily through a steel wire of the same shape and size, and they essentially cannot flow at all through an insulator like rubber, regardless of its shape. The difference between copper, steel, and rubber is related to their microscopic structure and electron configuration, and is quantified by a property called resistivity. In addition to geometry and material, there are various other factors that influence resistance and conductance, such as temperature; see below. Substances in which electricity can flow are called conductors. A piece of conducting material of a particular resistance meant for use in a circuit is called a resistor. Conductors are made of high-conductivity materials such as metals, in particular copper and aluminium. Resistors, on the other hand, are made of a wide variety of materials depending on factors such as the desired resistance, amount of energy that it needs to dissipate, precision, and costs. For many materials, the current "I" through the material is proportional to the voltage "V" applied across it: over a wide range of voltages and currents. Therefore, the resistance and conductance of objects or electronic components made of these materials is constant. This relationship is called Ohm's law, and materials which obey it are called "ohmic" materials. Examples of ohmic components are wires and resistors. The current–voltage graph of an ohmic device consists of a straight line through the origin with positive slope. Other components and materials used in electronics do not obey Ohm's law; the current is not proportional to the voltage, so the resistance varies with the voltage and current through them. These are called "nonlinear" or "nonohmic". Examples include diodes and fluorescent lamps. The current-voltage curve of a nonohmic device is a curved line. The resistance of a given object depends primarily on two factors: What material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The resistance and conductance of a conductor of uniform cross section, therefore, can be computed as where formula_5 is the length of the conductor, measured in metres (m), "A" is the cross-sectional area of the conductor measured in square metres (m2), σ (sigma) is the electrical conductivity measured in siemens per meter (S·m), and ρ (rho) is the electrical resistivity (also called "specific electrical resistance") of the material, measured in ohm-metres (Ω·m). The resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are reciprocals: formula_6. Resistivity is a measure of the material's ability to oppose electric current. This formula is not exact, as it assumes the current density is totally uniform in the conductor, which is not always true in practical situations. However, this formula still provides a good approximation for long thin conductors such as wires. Another situation for which this formula is not exact is with alternating current (AC), because the skin effect inhibits current flow near the center of the conductor. For this reason, the "geometrical" cross-section is different from the "effective" cross-section in which current actually flows, so resistance is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the proximity effect. At commercial power frequency, these effects are significant for large conductors carrying large currents, such as busbars in an electrical substation, or large power cables carrying more than a few hundred amperes. The resistivity of different materials varies by an enormous amount: For example, the conductivity of teflon is about 10 times lower than the conductivity of copper. Loosely speaking, this is because metals have large numbers of "delocalized" electrons that are not stuck in any one place, so they are free to move across large distances. In an insulator, such as Teflon, each electron is tightly bound to a single molecule so a great force is required to pull it away. Semiconductors lie between these two extremes. More details can be found in the article: Electrical resistivity and conductivity. For the case of electrolyte solutions, see the article: Conductivity (electrolytic). Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See below. An instrument for measuring resistance is called an ohmmeter. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing. Many electrical elements, such as diodes and batteries do "not" satisfy Ohm's law. These are called "non-ohmic" or "non-linear", and their current–voltage curves are "not" straight lines through the origin. Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, non-linear resistance is not constant but varies with the voltage or current through the device; i.e., its operating point. There are two types of resistance: When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their phases. For example, in an ideal resistor, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a capacitor or inductor, the maximum current flow occurs as the voltage passes through zero and vice versa (current and voltage are oscillating 90° out of phase, see image below). Complex numbers are used to keep track of both the phase and magnitude of current and voltage: where: The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts: where "R" and "G" are resistance and conductance respectively, "X" is reactance, and "B" is susceptance. For ideal resistors, "Z" and "Y" reduce to "R" and "G" respectively, but for AC networks containing capacitors and inductors, "X" and "B" are nonzero. formula_12 for AC circuits, just as formula_13 for DC circuits. A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the universal dielectric response. One reason, mentioned above is the skin effect (and the related proximity effect). Another reason is that the resistivity itself may depend on frequency (see Drude model, deep-level traps, resonant frequency, Kramers–Kronig relations, etc.) Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. This electrical energy is dissipated, heating the resistor in the process. This is called "Joule heating" (after James Prescott Joule), also called "ohmic heating" or "resistive heating". The dissipation of electrical energy is often undesired, particularly in the case of transmission losses in power lines. High voltage transmission helps reduce the losses by reducing the current for a given power. On the other hand, Joule heating is sometimes useful, for example in electric stoves and other electric heaters (also called "resistive heaters"). As another example, incandescent lamps rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with thermal radiation (also called incandescence). The formula for Joule heating is: where "P" is the power (energy per unit time) converted from electrical energy to thermal energy, "R" is the resistance, and "I" is the current through the resistor. Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system. For the detailed behavior and explanation, see Electrical resistivity and conductivity. As a consequence, the resistance of wires, resistors, and other components often change with temperature. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. In some cases, however, the effect is put to good use. When temperature-dependent resistance of a component is used purposefully, the component is called a resistance thermometer or thermistor. (A resistance thermometer is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.) Resistance thermometers and thermistors are generally used in two ways. First, they can be used as thermometers: By measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with Joule heating (also called self-heating): If a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuit-protection role similar to fuses, or for feedback in circuits, or for many other purposes. In general, self-heating can turn a resistor into a nonlinear and hysteretic circuit element. For more details see Thermistor#Self-heating effects. If the temperature "T" does not vary too much, a linear approximation is typically used: where formula_16 is called the "temperature coefficient of resistance", formula_17 is a fixed reference temperature (usually room temperature), and formula_18 is the resistance at temperature formula_17. The parameter formula_16 is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, formula_16 is different for different reference temperatures. For this reason it is usual to specify the temperature that formula_16 was measured at with a suffix, such as formula_23, and the relationship only holds in a range of temperatures around the reference. The temperature coefficient formula_16 is typically +3×10 K to +6×10 K for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude. Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain. By placing a conductor under tension (a form of stress that leads to strain in the form of stretching of the conductor), the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under compression (strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on strain gauges for details about devices constructed to take advantage of this effect. Some resistors, particularly those made from semiconductors, exhibit "photoconductivity", meaning that their resistance changes when light is shining on them. Therefore, they are called "photoresistors" (or "light dependent resistors"). These are a common type of light detector. Superconductors are materials that have exactly zero resistance and infinite conductance, because they can have V = 0 and I ≠ 0. This also means there is no joule heating, or in other words no dissipation of electrical energy. Therefore, if superconductive wire is made into a closed loop, current flows around the loop forever. Superconductors require cooling to temperatures near 4K with liquid helium for most metallic superconductors like niobium–tin alloys, or cooling to temperatures near 77K with liquid nitrogen for the expensive, brittle and delicate ceramic high temperature superconductors. Nevertheless, there are many technological applications of superconductivity, including superconducting magnets.	In electronics and electromagnetism, the electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. 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summarize: Even amorphous materials have some shortrange order at the atomic length scale due to the nature of chemical bonding (see structure of liquids and glasses for more information on non-crystalline material structure). Furthermore, in very small crystals a large fraction of the atoms are the crystal; relaxation of the surface and interfacial effects distort the atomic positions, decreasing the structural order. Even the most advanced structural characterization techniques, such as x-ray diffraction and transmission electron microscopy, have difficulty in distinguishing between amorphous and crystalline structures on these length scales. Amorphous phases are important constituents of thin films, which are solid layers of a few nanometres to some tens of micrometres thickness deposited upon a substrate. So-called structure zone models were developed to describe the micro structure and ceramics of thin films as a function of the homologous temperature "T" that is the ratio of deposition temperature over melting temperature. According to these models, a necessary (but not sufficient) condition for the occurrence of amorphous phases is that "T" has to be smaller than 0.3, that is the deposition temperature must be below 30% of the melting temperature. For higher values, the surface diffusion of deposited atomic species would allow for the formation of crystallites with long range atomic order. Regarding their applications, amorphous metallic layers played an important role in the discovery of superconductivity in amorphous metals by Buckel and Hilsch. The superconductivity of amorphous metals, including amorphous metallic thin films, is now understood to be due to phonon-mediated Cooper pairing, and the role of structural disorder can be rationalized based on the strong-coupling Eliashberg theory of superconductivity. Today, optical coatings made from TiO, SiO, TaO etc. and combinations of them in most cases consist of amorphous phases of these compounds. Much research is carried out into thin amorphous films as a gas separating membrane layer. The technologically most important thin amorphous film is probably represented by few nm thin SiO layers serving as isolator above the conducting channel of a metal-oxide semiconductor field-effect transistor (MOSFET). Also, hydrogenated amorphous silicon, a-Si:H in short, is of technical significance for thin-film solar cells. In case of a-Si:H the missing long-range order between silicon atoms is partly induced by the presence by hydrogen in the percent range. The occurrence of amorphous phases turned out as a phenomenon of particular interest for studying thin-film growth. Remarkably, the growth of polycrystalline films is often used and preceded by an initial amorphous layer, the thickness of which may amount to only a few nm. The most investigated example is represented by thin multicrystalline silicon films, where such as the unoriented molecule. An initial amorphous layer was observed in many studies. Wedge-shaped polycrystals were identified by transmission electron microscopy to grow out of the amorphous phase only after the latter has exceeded a certain thickness, the precise value of which depends on deposition temperature, background pressure and various other process parameters. The phenomenon has been interpreted in the framework of Ostwald's rule of stages that predicts the formation of phases to proceed with increasing condensation time towards increasing stability. Experimental studies of the phenomenon require a clearly defined state of the substrate surface and its contaminant density etc., upon which the thin film is deposited.	In condensed matter physics and materials science, an amorphous (from the Greek "a", without, "morphé", shape, form) or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal. In some older books, the term has been used synonymously with glass. Nowadays, "glassy solid" or "amorphous solid" is considered to be the overarching concept, and glass the more special case: Glass is an amorphous solid that exhibits a glass transition. Polymers are often amorphous. Other types of amorphous solids include gels, thin films, and nanostructured materials such as glass. Amorphous materials have an internal structure made of interconnected structural blocks. These blocks can be similar to the basic structural units found in the corresponding crystalline phase of the same compound. Whether a material is liquid or solid depends primarily on the connectivity between its elementary building blocks so that solids are characterized by a high degree of connectivity whereas structural blocks in fluids have lower connectivity.	en	en	190	[ 250004, 250054, 31267, 10, 178851, 10821, 76319, 765, 3060, 16610, 94250, 12989, 99, 70, 34627, 1771, 140909, 105994, 4743, 47, 70, 31425, 111, 165045, 337, 33770, 15, 21231, 45646, 111, 41931, 7, 136, 47589, 90, 100, 1286, 4677, 98, 351, 9, 238, 1294, 24259, 2256, 4912, 45646, 194, 27766, 9319, 17678, 4, 23, 4552, 19336, 224128, 7, 10, 21334, 6, 175921, 111, 70, 34627, 7, 621, 70, 224128, 74, 20648, 2320, 111, 70, 71579, 136, 1940, 1021, 26136, 93425, 45, 20820, 18, 70, 34627, 1771, 19069, 7, 4, 8, 7612, 162, 214, 70, 118990, 141, 12989, 5, 31267, 70, 2684, 175961, 118990, 141, 62816, 47691, 53088, 4, 6044, 237, 1022, 9, 7092, 45755, 175921, 136, 179965, 77556, 19, 11948, 7, 137366, 4, 765, 34844, 53, 23, 157167, 54700, 17721, 10, 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summarize: EU citizenship was first introduced by the Maastricht Treaty, and was extended by the Treaty of Amsterdam. Prior to the 1992 Maastricht Treaty, the European Communities treaties provided guarantees for the free movement of economically active persons, but not, generally, for others. The 1951 Treaty of Paris establishing the European Coal and Steel Community established a right to free movement for workers in these industries and the 1957 Treaty of Rome provided for the free movement of workers and services. However, the treaty provisions were interpreted by the European Court of Justice not as having a narrow economic purpose, but rather a wider social and economic purpose. In "Levin", the Court found that the "freedom to take up employment was important, not just as a means towards the creation of a single market for the benefit of the member state economies, but as a right for the worker to raise her or his standard of living". Under the ECJ caselaw, the rights of free movement of workers applies regardless of the worker's purpose in taking up employment abroad, to both part-time and full-time work, and whether or not the worker required additional financial assistance from the member state into which he moves. Since the ECJ has held that a recipient of service has free movement rights under the treaty and this criterion is easily fulfilled, effectively every national of an EU country within another member state, whether economically active or not, had a right under Article 12 of the European Community Treaty to non-discrimination even prior to the Maastricht Treaty. In the case of "Martinez Sala", the European Court of Justice held that the citizenship provisions provided substantive equal treatment rights alongside those already granted by union law. The case of Baumbast later established that the right to equal treatment applies equally to both economically active and inactive citizens. Despite these broad interpretations, the landmark case of Dano combined the criteria of freedom to move and equal treatment, citing them as inter-dependant, subsequently limiting the scope of Martinez Sala. Historically, the main benefit of being a citizen of an EU state has been that of free movement. The free movement also applies to the citizens of European Economic Area countries and Switzerland. However, with the creation of EU citizenship, certain political rights came into being. The Treaty on the Functioning of the European Union provides for citizens to be "directly represented at Union level in the European Parliament" and "to participate in the democratic life of the Union" (Treaty on the European Union, Title II, Article 10). Specifically, the following rights are afforded: Article 21 (1) of the Treaty on the Functioning of the European Union states that Every citizen of the Union shall have the right to move and reside freely within the territory of the Member States, subject to the limitations and conditions laid down in this Treaty and by the measures adopted to give it effect. The European Court of Justice has remarked that, EU Citizenship is destined to be the fundamental status of nationals of the Member States The ECJ has held that this Article confers a directly effective right upon citizens to reside in another Member State. Before the case of "Baumbast", it was widely assumed that non-economically active citizens had no rights to residence deriving directly from the EU Treaty, only from directives created under the Treaty. In "Baumbast", however, the ECJ held that (the then) Article 18 of the EC Treaty granted a generally applicable right to residency, which is limited by secondary legislation, but "only" where that secondary legislation is proportionate. Member States can distinguish between nationals and Union citizens but only if the provisions satisfy the test of proportionality. Migrant EU citizens have a "legitimate expectation of a limited degree of financial solidarity... having regard to their degree of integration into the host society" Length of time is a particularly important factor when considering the degree of integration. The ECJ's case law on citizenship has been criticised for subjecting an increasing number of national rules to the proportionality assessment. Article 45 of the Treaty on the Functioning of the European Union states that 1. Freedom of movement for workers shall be secured within the Union.2. Such freedom of movement shall entail the abolition of any discrimination based on nationality between workers of the Member States as regards employment, remuneration and other conditions of work and employment. State employment reserved exclusively for nationals varies between member states. For example, training as a barrister in Britain and Ireland is not reserved for nationals, while the corresponding French course qualifies one as a 'juge' and hence can only be taken by French citizens. However, it is broadly limited to those roles that exercise a significant degree of public authority, such as judges, police, the military, diplomats, senior civil servants or politicians. Note that not all Member States choose to restrict all of these posts to nationals. Much of the existing secondary legislation and case law was consolidated in the Citizens' Rights Directive 2004/38/EC on the right to move and reside freely within the EU. New member states may undergo transitional regimes for Freedom of movement for workers, during which their nationals only enjoy restricted access to labour markets in other member states. EU member states are permitted to keep restrictions on citizens of the newly acceded countries for a maximum of seven years after accession. For the EFTA states (Iceland, Lichtenstein, Norway and Switzerland), the maximum is nine years. Following the 2004 enlargement, three "old" member states—Ireland, Sweden and the United Kingdom—decided to allow unrestricted access to their labour markets. By December 2009, all but two member states—Austria and Germany—had completely dropped controls. These restrictions too expired on 1 May 2011. Following the 2007 enlargement, all pre-2004 member states except Finland and Sweden imposed restrictions on Bulgarian and Romanian citizens, as did two member states that joined in 2004: Malta and Hungary. As of November 2012, all but 8 EU countries have dropped restrictions entirely. These restrictions too expired on 1 January 2014. Norway opened its labour market in June 2012, while Switzerland kept restrictions in place until 2016. Following the 2013 enlargement, some countries implemented restrictions on Croatian nationals following the country's EU accession on 1 July 2013. As of May 2019, all EU countries except Austria have dropped restrictions entirely., the Austrian restrictions are set to expire on 1 July 2020. There is no common EU policy on the acquisition of European citizenship as it is supplementary to national citizenship. (EC citizenship was initially granted to all citizens of European Community member states in 1994 by the Maastricht treaty concluded between the member states of the European community under international law, this changed into citizenship of the European Union in 2007 when the European Community changed its legal identity to be the European Union. Many more people became EU citizens when each new EU member state was added and, at each point, all the existing member states ratified the adjustments to the treaties to allow the creation of those extra citizenship rights for the individual. European citizenship is also generally granted at the same time as national citizenship is granted; likewise it is removed at the point of removal of national citizenship). (1) of the Treaty on the Functioning of the European Union states that: "Citizenship of the Union is hereby established. Every person holding the nationality of a Member State shall be a citizen of the Union. Citizenship of the Union shall be additional to and not replace national citizenship." While nationals of Member States are citizens of the union, "It is for each Member State, having due regard to Union law, to lay down the conditions for the acquisition and loss of nationality." As a result, there is a great variety in rules and practices with regard to the acquisition and loss of citizenship in EU member states. In practice this means that a member state may withhold EU citizenship from certain groups of citizens, most commonly in overseas territories of member states outside the EU. A previous example, was for the United Kingdom. Owing to the complexity of British nationality law, a 1982 declaration by Her Majesty's Government defined who would be deemed to be a British "national" for European Union purposes: This declaration therefore excluded from EU citizenship various historic categories of British citizenship generally associated with former British colonies, such as British Overseas Citizens, British Nationals (Overseas), British protected persons and any British subject who did not have the 'right of abode' under British immigration law. In 2002, with the passing of the British Overseas Territories Act 2002, EU citizenship was extended to almost all British overseas territories citizens when they were automatically granted full British citizenship (with the exception of those with an association to the British sovereign base areas of Akrotiri and Dhekelia on the Island of Cyprus). This had effectively granted them full EU citizenship rights, including free movement rights, although only residents of Gibraltar had the right to vote in European Parliament elections. In contrast, British citizens in the Crown Dependencies of Jersey, Guernsey and the Isle of Man had always been considered to be EU citizens but, unlike residents of the British overseas territories, were prohibited from exercising EU free movement rights under the terms of the UK Accession Treaty if they had no other connection with the UK (e.g. they had lived in the UK for five years, were born in the UK, or had parents or grandparents born in the UK) and had no EU voting rights. (see Guernsey passport, Isle of Man passport, Jersey passport). Another example are the residents of Faroe Islands of Denmark who, though in possession of full Danish citizenship, are outside the EU and are explicitly excluded from EU citizenship under the terms of the Danish Accession Treaty. This is in contrast to residents of the Danish territory of Greenland who, whilst also outside the EU as a result of the 1984 Greenland Treaty, do receive EU citizenship as this was not specifically excluded by the terms of that treaty (see Faroe Islands and the European Union; Greenland and the European Union). This is a summary of nationality laws for each of the twenty-seven EU member states. The general rule for losing EU citizenship is that European citizenship is lost if member state nationality is lost, but the automatic loss of EU citizenship as a result of a member state withdrawing from the EU is the subject of debate. One school of legal thought indicates that the Maastricht treaty created the European Union as a legal entity, it then also created the status of EU citizen which gave an individual relationship between the EU and its citizens, and a status of EU citizen. Clemens Rieder suggests a case can be made that "[n]one of the Member States were forced to confer the status of EU citizenship on their citizens but once they have, according to this argument, they cannot simply withdraw this status.". In this situation, no EU citizen would involuntarily lose their citizenship due to their nation's withdrawal from the EU. It is likely that only a court case before the European Court of Justice would be able to properly determine the correct legal position in this regard, as there is no definitive legal certainty in this area. As of 7 February 2018, the District Court of Amsterdam decided to refer the matter to the European Court of Justice, but the state of the Netherlands has appealed against this referral decision. Although Greenland withdrew from the European Communities in 1985, all citizens of Denmark residing in Greenland are eligible for EU citizenship by virtue of their Danish citizenship. This contrasts with Danish citizens living the Faroe Islands who are excluded from EU citizenship. As a result of the Withdrawal of the United Kingdom from the European Union, the opinion of both the European Union and the British government has been that British citizens would lose their EU citizenship and EU citizens would lose their automatic right to stay in the UK. To account for the problems arising from this, a provisional agreement outlines the right of UK citizens to remain in the EU (and vice versa) where they are resident in the Union on the day of the UK's withdrawal. EU citizens may remain in the UK post-Brexit if and only if they apply to EU Settlement Scheme. The only exception to this is citizens who possess dual citizenship with an EU state. This eligibility includes the majority of British citizens from Northern Ireland, who are automatically entitled to Irish citizenship as part of the Good Friday Agreement. As a result of the Brexit referendum, there were three European Citizens' Initiatives that were registered which sought to protect the rights and/or status of British EU citizens. Out of these three initiatives, the one with the strongest legal argument was registered on 27 March 2017 and officially named "EU Citizenship for Europeans: United in Diversity in Spite of jus soli and jus sanguinis". It is clear that the initiative abides by the first school of thought mentioned above because the annexe that was submitted with the initiative clearly makes reference to Rieder's work. In an article titled "[http://vip.politicsmeanspolitics.com/2017/09/06/extending-full-eu-citizenship-to-uk-nationals-especially-after-brexit/ <nowiki>Extending [full] EU citizenship to UK nationals ESPECIALLY after Brexit</nowiki>]" and published with the online magazine "Politics Means Politics", the creator of the Initiative argues that UK nationals "must" keep their EU citizenship by detaching citizenship of the European Union from Member State nationality. Perhaps the most convincing and authoritative source that is cited in the article is the acting President of the European Court of Justice, Koen Lenaerts who published an article where he explains how the Court analyses and decides cases dealing with citizenship of the European Union. Both Lenaerts and the creator of the Initiative refer to rulings by the European Court of Justice which state that: Based on the argument presented by "EU Citizenship for Europeans" and its creator, Brexit is a textbook definition of a Member State depriving a European citizen of his or her rights as EU citizens, and therefore a legal act is necessary to protect not just rights but the status of EU citizen itself. Despite variances in interpretation of some points of law raised by the Initiative, the European Commission's decision to register the initiative confirms the strength and merit of the initiative's legal argument. A proposal made first by Guy Verhofstadt, the European Parliament's Brexit negotiator, to help cover the rights of UK citizens post-Brexit would see UK citizens able to opt-out of the loss of EU citizenship as a result of the general clauses of the withdrawal agreement. This would allow visa-free working on the basis of their continuing rights as EU citizens. This, he termed, "associate citizenship". This has been discussed with the UK's negotiator David Davis. However, it was made clear by the UK government that there would be no role for EU institutions concerning its citizens, effectively removing the proposal as a possibility. Denmark obtained four opt-outs from the Maastricht Treaty following the treaty's initial rejection in a 1992 referendum. The opt-outs are outlined in the Edinburgh Agreement and concern the EMU (as above), the Common Security and Defence Policy (CSDP), Justice and Home Affairs (JHA) and the citizenship of the European Union. The citizenship opt-out stated that European citizenship did not replace national citizenship; this opt-out was rendered meaningless when the Amsterdam Treaty adopted the same wording for all members. The policy of recent Danish governments has been to hold referendums to abolish these opt-outs, including formally abolishing the citizenship opt-out which is still technically active even if redundant.	Citizenship of the European Union is afforded to qualifying citizens of European Union member states. It was created by the 1992 Maastricht Treaty, at the same time as the creation of the European Union (EU). 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summarize: Braising relies on heat, time, and moisture to break down the tough connective tissue (collagen) that binds together the muscle fibers collectively called "meat", making it an ideal way to cook tougher, more affordable cuts. Many classic braised dishes (e.g., coq au vin) are highly evolved methods of cooking tough and otherwise unpalatable foods. Both pressure cooking and slow cooking (e.g. in a crockpot) are forms of braising. Most braises follow the same basic steps. The food to be braised (meats, vegetables, mushrooms, etc.) is first pan-seared to brown its surface and enhance its flavor (through the Maillard reaction). If the food will not produce enough liquid of its own, a certain amount of cooking liquid that often includes an acidic element (e.g., tomatoes, beer, balsamic vinegar, wine) is added to the pot, often with stock. A classic braise is done with a relatively whole cut of meat, and the braising liquid will cover two-thirds of the food in the pan. The dish is then covered and cooked at a very low simmer until the meat becomes so tender that it can be "cut" with just the gentlest of pressure from a fork (versus a knife). Often the cooking liquid is finished to create a sauce or gravy as well. Sometimes foods with high water content (particularly vegetables) can be cooked in their own juices, making the addition of liquid unnecessary. A successful braise intermingles the flavors of the foods being cooked with those of the cooking liquid. This cooking method dissolves the meat's collagen into gelatin, which can greatly enrich and thicken the liquid. Braising is economical (as it allows the use of tough and inexpensive cuts), and efficient (as it often enables an entire meal to be prepared in a single pot or pan). Familiar braised dishes include pot roast, Swiss steak, chicken cacciatore, goulash, Carbonade Flamande, coq au vin, sauerbraten, beef bourguignon, beef brisket, oxtail, and tajines, among others. Braising is also used extensively in the cuisines of Asia, particularly Chinese cuisine and Vietnamese cuisine, where soy sauce (or in Vietnam, soy sauce and fish sauce) is often the braising liquid. <br	Braising (from the French word "braiser") is a combination-cooking method that uses both wet and dry heats: typically, the food is first sautéed or seared at a high temperature, then finished in a covered pot at a lower temperature while sitting in some (variable) amount of liquid (which may also add flavor). Braising of meat is often referred to as pot roasting, though some authors make a distinction between the two methods, based on whether additional liquid is added.	en	en	94	[ 250004, 250054, 6163, 72219, 28702, 90, 98, 80097, 4, 1733, 4, 136, 13411, 6644, 47, 36356, 7565, 70, 143033, 37067, 5844, 108055, 13, 15, 8447, 35738, 16, 450, 68557, 7, 25842, 70, 123635, 109197, 7, 143849, 538, 35839, 44, 282, 257, 830, 20662, 442, 142, 6397, 3917, 47, 110309, 143033, 56, 4, 1286, 202703, 314, 933, 5, 52455, 54704, 1620, 52021, 45, 114942, 15, 13, 5, 177, 5, 4, 552, 864, 531, 3862, 16, 621, 103210, 216479, 71, 150624, 111, 179065, 143033, 136, 120262, 51, 16917, 22819, 15381, 7, 5, 149766, 81147, 179065, 136, 72803, 179065, 15, 13, 5, 177, 5, 23, 10, 99546, 92, 7804, 16, 621, 3173, 7, 111, 1620, 72219, 5, 17006, 1620, 62093, 28960, 70, 5701, 62822, 98441, 5, 581, 15381, 47, 186, 1620, 52021, 15, 282, 9821, 4, 231718, 4, 79755, 28905, 7, 4, 3021, 5, 16, 83, 5117, 2652, 9, 184, 11, 2822, 47, 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summarize: In Japanese cities, yakitori carts, restaurants, or shops can be found. These contain charcoal-fired grills and marinated grilled meat on a stick. Yakiniku is a type of food where meat and vegetables are grilled directly over small charcoal or gas grills at high temperatures. (This style of cooking has become popular throughout Asia.) In Malaysia, Singapore, Indonesia, and Thailand, a popular food item from food vendors is satay, which is marinated meat on a bamboo skewer grilled over a charcoal fire and served with peanut (sate) sauce. In Germany, the most prominent outdoor form of grilling is using the gridiron over a bed of burning charcoal. Care is taken that the charcoal does not produce flames. Often beer is sprinkled over the sausages or meat and used to suppress flames. The meat is usually marinated before grilling. Besides charcoal, sometimes gas and electric heat sources are used. Other methods are used less frequently. In Northern Mexico, "carne asada" (Spanish for "grilled meat") is a staple food. Popular cuts include arrachera, beefsteak and rib eye, as well as chorizo and chicken, among others. Charcoal, mesquite or firewood are used for the grilling. In Argentina and Uruguay, both "asado" (beef roasted on a fire) and steak "a la parrilla" (beefsteak cooked on traditional grill) are staple dishes and even hailed as national specialties. In Sweden, grilling directly over hot coals is the most prominent form of grilling. Usually the meat is Boston butt, pork chops or pork fillet. It is also common to cook meat and vegetables together on a skewer, this is called "grillspett". In the United Kingdom, Commonwealth countries, and Ireland, grilling generally refers to cooking food directly under a source of direct, dry heat. The "grill" is usually a separate part of an oven where the food is inserted just under the element. This practice is referred to as "broiling" in North America. Sometimes the term grilling may refer to cooking with heat from below, as in the United States. In the 1970s and 1980s the electric, two sided vertical grill marketed by the Sunbeam company achieved cult status because of its quick, clean, and no added fat operation. In electric ovens, grilling may be accomplished by placing the food near the upper heating element, with the lower heating element off and the oven door partially open. Grilling in an electric oven may create a large amount of smoke and cause splattering in the oven. Both gas and electric ovens often have a separate compartment for grilling, such as a drawer below the flame or one of the stove top heating elements. In the United States, the use of the word grill refers to cooking food directly over a source of dry heat, typically with the food sitting on a metal grate that leaves "grill marks." Grilling is usually done outdoors on charcoal grills or gas grills; a recent trend is the concept of infrared grilling. Grilling may also be performed using stove-top "grill pans" which have raised metal ridges for the food to sit on, or using an indoor electric grill. A skewer, brochette, or rotisserie may be used to cook small pieces of food. The resulting food product is often called a "kabob" ("US term") or "kebab" which means "to grill" in Persian. Kebab is short for "shish kebab" (shish = skewer). Mesquite or hickory wood chips (damp) may be added on top of the coals to create a smoldering effect that provides additional flavor to the food. Other hardwoods such as pecan, apple, maple and oak may also be used. As is true of any high-temperature frying or baking, when meat is grilled at high temperatures, the cooking process can generate carcinogenic chemicals. Two processes are thought to be responsible. Heterocyclic amines (HCAs) are formed when amino acids, sugars, and creatine react at high temperatures. Polycyclic aromatic hydrocarbons (PAHs) are formed when fat and juices from meat grilled directly over an open fire drip onto the fire, causing flames. These flames contain PAHs that then adhere to the surface of the meat. However it is possible to significantly reduce carcinogens when grilling meat, or mitigate their effect. Garlic, rosemary, olive oil, cherries, and vitamin E have been shown to reduce formation of both HCAs and PAHs. V-profiled grill elements placed at an angle may help drain much of the meat juices and dripping fat, and transport them away from the heat source. Heat sources on the top (as in many electrical or gas ovens), or on the side (vertical grilling) avoid completely the burning of fat dripping from the meat, and the meat's contact with the flames. Another method is precooking the meat in the microwave, which can reduce HCA formation by reducing the time that meat must be in contact with high heat to finish cooking. Gridironing is the cooking of meats or other foods using a grill suspended above a heat source. Grilling is often performed outdoors using charcoal (real wood or preformed briquettes), wood, or propane gas. Food is cooked using direct radiant heat. Some outdoor grills include a cover so they can be used as smokers or for grill-roasting/barbecue. The suspended metal grate is often referred to as a gridiron.Outdoor grilling on a gridiron may be referred to as "barbecue", though in US usage, the term "barbecue" refers to the cooking of meat through indirect heat and smoke. "Barbecue" may refer to the grilled food itself, to a distinct type of cooked meat called Southern barbecue, to the grilling device used to cook the food (a "barbecue grill"), or to the social event of cooking and eating such food (which may also be called a "cook-out" or "braai"). Charcoal kettle-grilling refers to the process of grilling over a charcoal fire in a kettle, to the point that the edges are charred, or charred grill marks are visible. Some restaurants seek to re-create the charcoal-grilled experience via the use of ceramic lava rocks or infrared heat sources, offering meats that are cooked in this manner as "charcoal-cooked" or "charcoal-grilled". By using a baking sheet pan placed above the grill surface, as well as a drip pan below the surface, it is possible to combine grilling and roasting to cook meats that are stuffed or coated with breadcrumbs or batter, and to bake breads and even casseroles and desserts. When cooking stuffed or coated meats, the foods can be baked first on the sheet pan, and then placed directly on the grilling surface for char marks, effectively cooking twice; the drip pan will be used to capture any crumbs that fall off from the coating or stuffing. It is possible to braise meats and vegetables in a pot on top of a grill. A gas or electric grill would be the best choices for what is known as "barbecue-braising" or "grill-braising", or combining grilling directly on the surface and braising in a pot. To braise on a grill, put a pot on top of the grill, cover it, and let it simmer for a few hours. There are two advantages to barbecue-braising. The first is that this method allows for browning the meat directly on the grill before the braising, and the second is that it also allows for glazing the meat with sauce and finishing it directly over the fire after the braising, effectively cooking the meat three times, which results in a soft textured product that falls right off the bone. This method of cooking is slower than regular grilling but faster than pit-smoking, starting out fast, slowing down, and then speeding up again to finish. If a pressure cooker is used, the cooking time will be much faster. Many restaurants incorporate an indoor grill as part of their cooking apparatus. These grills resemble outdoor grills, in that they are made up of a grid suspended over a heat source. However, indoor grills are more likely to use electric or gas-based heating elements. Some manufacturers of residential cooking appliances now offer indoor grills for home use, either incorporated into a stove top or as a standalone electric device. Sear-grill and gear grilling is a process of searing meat or food items with an infrared grill. In sear grilling, propane or natural gas is used to heat a ceramic plate, which then radiates heat at temperatures over 480 °C (900 °F). Sear-grilling instantly sears the outside of meat to make the food more flavorful. Commonly, grilling heats the surrounding air to cook food. In this method, the infrared grill directly heats the food, not the air. Stove-top pan grilling is an indoor cooking process that uses a grill pan — similar to a frying pan but with raised ridges to emulate the function or look of a gridiron. In pan grilling, heat is applied directly to the food by the raised ridges and indirectly through the heat radiating off the lower pan surface by the stove-top flame. Stove-top grill pans can be used to put sear marks on meat before it is finished by overhead radiant heat. When cooking leaner meats, oil is often applied to the pan ridges to aid in food release. Some griddles designed for stove-top use incorporate raised ridges in addition to a flat cooking area. These are either on half of the cooking surface or, in the case of reversible two-sided griddles, on one side with the flat surface on the other. Foods termed "grilled" may actually be prepared on a hot griddle or flat pan. The griddle or pan may be prepared with oil (or butter), and the food is cooked quickly over a high heat. Griddle-grilling is best for relatively greasy foods such as sausages. Some griddle-grilled foods may have grill marks applied to them during the cooking process with a "branding plate", to mimic the appearance of charbroil-cooked food. A flattop grill is a cooking appliance that resembles a griddle but performs differently because the heating element is circular rather than straight (side to side). This heating technology creates an extremely hot and even cooking surface, as heat spreads in a radial fashion over the surface. The first flattop grills originated in Spain and are known as planchas or la plancha. Food that is cooked a la plancha means grilled on a metal plate. Plancha griddles or flat tops are chrome plated which prevents reaction with the food. Some base metal griddles will impart a subtle flavor to the food being cooked. The flattop grill is a versatile platform for many cooking techniques such as sautéing, toasting, steaming, stir frying, grilling, baking, braising, and roasting, and can also be used in flambéing. In addition, pots and pans can be placed directly on the cooking surface for even more cooking flexibility. In most cases, the steel cooking surface is seasoned like cast iron cookware, providing a natural non-stick surface. Charbroiling, or chargrilling outside North America, refers to grilling on a surface with wide raised ridges, to the point of having the food slightly charred in texture. In the United States, oven pan broiling refers to a method of cooking inside an oven on a broil pan with raised ridges, where the heat can be applied from either above or below. In gas and electric ovens, this is accomplished with a heating element and a broil pan. Sometimes, the food is placed near the upper heating element to intensify the heat. The lower heating element may or may not be left off and the oven door is sometimes opened partially. Gas ovens often have a separate compartment for broiling, sometimes a drawer below the bottom flame. A salamander (also salamander oven or salamander broiler) is a culinary grill characterized by very high temperature overhead electric or gas heating elements. It is used primarily in professional kitchens for overhead grilling. It is also used for toasting, browning of gratin dishes, melting cheeses onto sandwiches, and caramelizing desserts such as crème brûlée. Salamanders are generally similar to an oven without a front door; the heating element is at the top. They are also more compact: typically only half the height and depth of a conventional oven. For convenience, they are often wall mounted at eye level, enabling easy access and close control of the cooking process. Many salamanders can be fitted with a cast iron "branding" plate which is used to make grill marks on the surface of meat. Some grills can also be fitted with a rotisserie accessory for roasting meats. Overhead heat has the advantage of allowing foods containing fats, such as steaks, chops and other cuts of meat, to be grilled without the risk of flare-ups caused by the rendered fat dripping onto the heat source. The salamander's facility for extremely high temperature also takes less cooking time than other grilling techniques, reducing preparation time, which is a benefit in professional kitchens during a busy meal service. Modern salamanders take their name from the 18th century "salamander", the tool of choice for toasting the top of a dish. It consisted of a thick plate of iron attached to the end of a long handle, with two feet, or rests, arranged near the iron plate for propping the plate over the food to be browned. Its name in turn was taken from the legendary salamander, a mythical amphibian that was believed to be immune to fire. Some commercial devices permit the simultaneous grilling of both sides of the meat at the same time. The flame-grilling machine at Burger King, Carl's Jr./Hardee's, and other fast food restaurants is called a 'broiler'. It works by moving meat patties along a chain conveyor belt between top and bottom burners, grilling both sides of the meat patty at the same time. This concept was invented in 1898, when the Bridge and Beach Co. of St. Louis, Missouri, started manufacturing a vertical cast iron stove. These stoves were designed to allow the meat to be flame-broiled (flame-grilled) on both sides at the same time. Custom hinged steel wire gridirons were built for use in the vertical broilers. The hinged gridirons were slid in and out of the stoves holding the meat while it cooked evenly on both sides, like modern day oven racks. These stoves took up a small amount of counter space. They were used in lunch spots to feed factory workers. During the 1990s, double-sided grilling was popular in the USA using consumer electrical grills (e.g., the popular George Foreman Grill). US marketers of electric double-sided grilling appliances opted for the global term 'grill' rather than the geographically isolated term "broiler." Hinged double-sided grills are generically known as contact grills. Whole grilling involves grilling a whole carcass as opposed to grilling individual portion sized cuts. This method is often used in order to avoid the need for complicated grill equipment during, for example, a hunt or expedition in the wild. It is also the traditional method of cooking in several cultures where they do a pig roast, luau, or barbacoa. There are several primitive methods and modern equipment that copies and automates the primitive version:	Grilling is a form of cooking that involves dry heat applied to the surface of food, commonly from above, below or from the side. Grilling usually involves a significant amount of direct, radiant heat, and tends to be used for cooking meat and vegetables quickly. Food to be grilled is cooked on a grill (an open wire grid such as a gridiron with a heat source above or below), using a cast iron/frying pan, or a grill pan (similar to a frying pan, but with raised ridges to mimic the wires of an open grill).	en	en	109	[ 250004, 250054, 360, 148926, 162708, 4, 151, 301, 3826, 41718, 7, 4, 74812, 4, 707, 19927, 7, 831, 186, 14037, 5, 32255, 70541, 21441, 587, 289, 9, 1029, 2822, 28223, 7, 136, 64244, 3674, 28223, 297, 163, 257, 98, 10, 47593, 5, 2369, 301, 16694, 83, 10, 10644, 111, 15381, 7440, 163, 257, 136, 231718, 621, 28223, 297, 105237, 645, 19336, 21441, 587, 289, 707, 9060, 28223, 7, 99, 11192, 52768, 7, 5, 15, 73243, 20623, 111, 179065, 1556, 24209, 5700, 87420, 14237, 5, 16, 360, 3605, 4, 58888, 4, 3799, 4, 136, 33020, 4, 10, 5700, 15381, 35735, 1295, 15381, 116366, 7, 83, 57, 7164, 4, 3129, 83, 64244, 3674, 163, 257, 98, 10, 81020, 54487, 21177, 6488, 28223, 297, 645, 10, 21441, 587, 289, 11476, 136, 149976, 678, 16320, 3609, 15, 7, 2182, 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summarize: Heat is defined in physics as the transfer of thermal energy across a well-defined boundary around a thermodynamic system. The thermodynamic free energy is the amount of work that a thermodynamic system can perform. Enthalpy is a thermodynamic potential, designated by the letter "H", that is the sum of the internal energy of the system (U) plus the product of pressure (P) and volume (V). Joule is a unit to quantify energy, work, or the amount of heat. Heat transfer is a process function (or path function), as opposed to functions of state; therefore, the amount of heat transferred in a thermodynamic process that changes the state of a system depends on how that process occurs, not only the net difference between the initial and final states of the process. Thermodynamic and mechanical heat transfer is calculated with the heat transfer coefficient, the proportionality between the heat flux and the thermodynamic driving force for the flow of heat. Heat flux is a quantitative, vectorial representation of heat-flow through a surface. In engineering contexts, the term "heat" is taken as synonymous to thermal energy. This usage has its origin in the historical interpretation of heat as a fluid ("caloric") that can be transferred by various causes, and that is also common in the language of laymen and everyday life. The transport equations for thermal energy (Fourier's law), mechanical momentum (Newton's law for fluids), and mass transfer (Fick's laws of diffusion) are similar, and analogies among these three transport processes have been developed to facilitate prediction of conversion from any one to the others. Thermal engineering concerns the generation, use, conversion, and exchange of heat transfer. As such, heat transfer is involved in almost every sector of the economy. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. The fundamental modes of heat transfer are: By transferring matter, energy—including thermal energy—is moved by the physical transfer of a hot or cold object from one place to another. This can be as simple as placing hot water in a bottle and heating a bed, or the movement of an iceberg in changing ocean currents. A practical example is thermal hydraulics. This can be described by the formula: where On a microscopic scale, heat conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring particles. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from one atom to another. Conduction is the most significant means of heat transfer within a solid or between solid objects in thermal contact. Fluids—especially gases—are less conductive. Thermal contact conductance is the study of heat conduction between solid bodies in contact. The process of heat transfer from one place to another place without the movement of particles is called conduction, such as when placing a hand on a cold glass of water—heat is conducted from the warm skin to the cold glass, but if the hand is held a few inches from the glass, little conduction would occur since air is a poor conductor of heat. Steady state conduction is an idealized model of conduction that happens when the temperature difference driving the conduction is constant, so that after a time, the spatial distribution of temperatures in the conducting object does not change any further (see Fourier's law). In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out, since the change in temperature (a measure of heat energy) is zero. An example of steady state conduction is the heat flow through walls of a warm house on a cold—inside the house is maintained at a high temperature, and outside the temperature stays low, so the transfer of heat per unit time stays near a constant rate determined by the insulation in the wall, and the spatial distribution of temperature in the walls will be approximately constant over time. "Transient conduction" (see Heat equation) occurs when the temperature within an object changes as a function of time. Analysis of transient systems is more complex, and analytic solutions of the heat equation are only valid for idealized model systems. Practical applications are generally investigated using numerical methods, approximation techniques, or empirical study. The flow of fluid may be forced by external processes, or sometimes (in gravitational fields) by buoyancy forces caused when thermal energy expands the fluid (for example in a fire plume), thus influencing its own transfer. The latter process is often called "natural convection". All convective processes also move heat partly by diffusion, as well. Another form of convection is forced convection. In this case the fluid is forced to flow by using a pump, fan or other mechanical means. Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids, a process that is essentially the transfer of heat via mass transfer. Bulk motion of fluid enhances heat transfer in many physical situations, such as (for example) between a solid surface and the fluid. Convection is usually the dominant form of heat transfer in liquids and gases. Although sometimes discussed as a third method of heat transfer, convection is usually used to describe the combined effects of heat conduction within the fluid (diffusion) and heat transference by bulk fluid flow streaming. The process of transport by fluid streaming is known as advection, but pure advection is a term that is generally associated only with mass transport in fluids, such as advection of pebbles in a river. In the case of heat transfer in fluids, where transport by advection in a fluid is always also accompanied by transport via heat diffusion (also known as heat conduction) the process of heat convection is understood to refer to the sum of heat transport by advection and diffusion/conduction. Free, or natural, convection occurs when bulk fluid motions (streams and currents) are caused by buoyancy forces that result from density variations due to variations of temperature in the fluid. "Forced" convection is a term used when the streams and currents in the fluid are induced by external means—such as fans, stirrers, and pumps—creating an artificially induced convection current. Convective cooling is sometimes described as Newton's law of cooling: In a body of fluid that is heated from underneath its container, conduction and convection can be considered to compete for dominance. If heat conduction is too great, fluid moving down by convection is heated by conduction so fast that its downward movement will be stopped due to its buoyancy, while fluid moving up by convection is cooled by conduction so fast that its driving buoyancy will diminish. On the other hand, if heat conduction is very low, a large temperature gradient may be formed and convection might be very strong. The Rayleigh number (formula_7) is the product of the Grashof (formula_8) and Prandtl (formula_9) numbers. It is a measure which determines the relative strength of conduction and convection. where The Rayleigh number can be understood as the ratio between the rate of heat transfer by convection to the rate of heat transfer by conduction; or, equivalently, the ratio between the corresponding timescales (i.e. conduction timescale divided by convection timescale), up to a numerical factor. This can be seen as follows, where all calculations are up to numerical factors depending on the geometry of the system. The buoyancy force driving the convection is roughly formula_12, so the corresponding pressure is roughly formula_13. In steady state, this is canceled by the shear stress due to viscosity, and therefore roughly equals formula_14, where "V" is the typical fluid velocity due to convection and formula_15 the order of its timescale. The conduction timescale, on the other hand, is of the order of formula_16. Convection occurs when the Rayleigh number is above 1,000–2,000. Thermal radiation occurs through a vacuum or any transparent medium (solid or fluid or gas). It is the transfer of energy by means of photons in electromagnetic waves governed by the same laws. Thermal radiation is energy emitted by matter as electromagnetic waves, due to the pool of thermal energy in all matter with a temperature above absolute zero. Thermal radiation propagates without the presence of matter through the vacuum of space. Thermal radiation is a direct result of the random movements of atoms and molecules in matter. Since these atoms and molecules are composed of charged particles (protons and electrons), their movement results in the emission of electromagnetic radiation, which carries energy away from the surface. The Stefan-Boltzmann equation, which describes the rate of transfer of radiant energy, is as follows for an object in a vacuum : For radiative transfer between two objects, the equation is as follows: where Radiation is typically only important for very hot objects, or for objects with a large temperature difference. Radiation from the sun, or solar radiation, can be harvested for heat and power. Unlike conductive and convective forms of heat transfer, thermal radiation – arriving within a narrow angle i.e. coming from a source much smaller than its distance – can be concentrated in a small spot by using reflecting mirrors, which is exploited in concentrating solar power generation or a burning glass. For example, the sunlight reflected from mirrors heats the PS10 solar power tower and during the day it can heat water to. The reachable temperature at the target is limited by the temperature of the hot source of radiation. (T-law lets the reverse-flow of radiation back to the source rise.) The (on its surface) somewhat 4000 K hot sun allows to reach coarsly 3000 K (or 3000 °C, which is about 3273 K) at a small probe in the focus spot of a big concave, concentrating mirror of the Mont-Louis Solar Furnace in France. Phase transition or phase change, takes place in a thermodynamic system from one phase or state of matter to another one by heat transfer. Phase change examples are the melting of ice or the boiling of water. The Mason equation explains the growth of a water droplet based on the effects of heat transport on evaporation and condensation. Phase transitions involve the four fundamental states of matter: The boiling point of a substance is the temperature at which the vapor pressure of the liquid equals the pressure surrounding the liquid and the liquid evaporates resulting in an abrupt change in vapor volume. Saturation temperature means boiling point. The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition. At standard atmospheric pressure and low temperatures, no boiling occurs and the heat transfer rate is controlled by the usual single-phase mechanisms. As the surface temperature is increased, local boiling occurs and vapor bubbles nucleate, grow into the surrounding cooler fluid, and collapse. This is "sub-cooled nucleate boiling", and is a very efficient heat transfer mechanism. At high bubble generation rates, the bubbles begin to interfere and the heat flux no longer increases rapidly with surface temperature (this is the departure from nucleate boiling, or DNB). At similar standard atmospheric pressure and high temperatures, the hydrodynamically-quieter regime of film boiling is reached. Heat fluxes across the stable vapor layers are low, but rise slowly with temperature. Any contact between fluid and the surface that may be seen probably leads to the extremely rapid nucleation of a fresh vapor layer ("spontaneous nucleation"). At higher temperatures still, a maximum in the heat flux is reached (the critical heat flux, or CHF). The Leidenfrost Effect demonstrates how nucleate boiling slows heat transfer due to gas bubbles on the heater's surface. As mentioned, gas-phase thermal conductivity is much lower than liquid-phase thermal conductivity, so the outcome is a kind of "gas thermal barrier". Condensation occurs when a vapor is cooled and changes its phase to a liquid. During condensation, the latent heat of vaporization must be released. The amount of the heat is the same as that absorbed during vaporization at the same fluid pressure. There are several types of condensation: Melting is a thermal process that results in the phase transition of a substance from a solid to a liquid. The internal energy of a substance is increased, typically with heat or pressure, resulting in a rise of its temperature to the melting point, at which the ordering of ionic or molecular entities in the solid breaks down to a less ordered state and the solid liquefies. Molten substances generally have reduced viscosity with elevated temperature; an exception to this maxim is the element sulfur, whose viscosity increases to a point due to polymerization and then decreases with higher temperatures in its molten state. Heat transfer can be modeled in various ways. The heat equation is an important partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. In some cases, exact solutions of the equation are available; in other cases the equation must be solved numerically using computational methods such as DEM-based models for thermal/reacting particulate systems (as critically reviewed by Peng et al. ). Lumped system analysis often reduces the complexity of the equations to one first-order linear differential equation, in which case heating and cooling are described by a simple exponential solution, often referred to as Newton's law of cooling. System analysis by the lumped capacitance model is a common approximation in transient conduction that may be used whenever heat conduction within an object is much faster than heat conduction across the boundary of the object. This is a method of approximation that reduces one aspect of the transient conduction system—that within the object—to an equivalent steady state system. That is, the method assumes that the temperature within the object is completely uniform, although its value may be changing in time. In this method, the ratio of the conductive heat resistance within the object to the convective heat transfer resistance across the object's boundary, known as the "Biot number", is calculated. For small Biot numbers, the approximation of "spatially uniform temperature within the object" can be used: it can be presumed that heat transferred into the object has time to uniformly distribute itself, due to the lower resistance to doing so, as compared with the resistance to heat entering the object. Climate models study the radiant heat transfer by using quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice. Heat transfer has broad application to the functioning of numerous devices and systems. Heat-transfer principles may be used to preserve, increase, or decrease temperature in a wide variety of circumstances. Heat transfer methods are used in numerous disciplines, such as automotive engineering, thermal management of electronic devices and systems, climate control, insulation, materials processing, and power station engineering. Thermal insulators are materials specifically designed to reduce the flow of heat by limiting conduction, convection, or both. Thermal resistance is a heat property and the measurement by which an object or material resists to heat flow (heat per time unit or thermal resistance) to temperature difference. Radiance or spectral radiance are measures of the quantity of radiation that passes through or is emitted. Radiant barriers are materials that reflect radiation, and therefore reduce the flow of heat from radiation sources. Good insulators are not necessarily good radiant barriers, and vice versa. Metal, for instance, is an excellent reflector and a poor insulator. The effectiveness of a radiant barrier is indicated by its reflectivity, which is the fraction of radiation reflected. A material with a high reflectivity (at a given wavelength) has a low emissivity (at that same wavelength), and vice versa. At any specific wavelength, reflectivity=1 - emissivity. An ideal radiant barrier would have a reflectivity of 1, and would therefore reflect 100 percent of incoming radiation. Vacuum flasks, or Dewars, are silvered to approach this ideal. In the vacuum of space, satellites use multi-layer insulation, which consists of many layers of aluminized (shiny) Mylar to greatly reduce radiation heat transfer and control satellite temperature. A heat engine is a system that performs the conversion of a flow of thermal energy (heat) to mechanical energy to perform mechanical work. A thermocouple is a temperature-measuring device and widely used type of temperature sensor for measurement and control, and can also be used to convert heat into electric power. A thermoelectric cooler is a solid state electronic device that pumps (transfers) heat from one side of the device to the other when electric current is passed through it. It is based on the Peltier effect. A thermal diode or thermal rectifier is a device that causes heat to flow preferentially in one direction. A heat exchanger is used for more efficient heat transfer or to dissipate heat. Heat exchangers are widely used in refrigeration, air conditioning, space heating, power generation, and chemical processing. One common example of a heat exchanger is a car's radiator, in which the hot coolant fluid is cooled by the flow of air over the radiator's surface. Common types of heat exchanger flows include parallel flow, counter flow, and cross flow. In parallel flow, both fluids move in the same direction while transferring heat; in counter flow, the fluids move in opposite directions; and in cross flow, the fluids move at right angles to each other. Common types of heat exchangers include shell and tube, double pipe, extruded finned pipe, spiral fin pipe, u-tube, and stacked plate. Each type has certain advantages and disadvantages over other types. A heat sink is a component that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems or the radiator in a car. A heat pipe is another heat-transfer device that combines thermal conductivity and phase transition to efficiently transfer heat between two solid interfaces. Efficient energy use is the goal to reduce the amount of energy required in heating or cooling. In architecture, condensation and air currents can cause cosmetic or structural damage. An energy audit can help to assess the implementation of recommended corrective procedures. For instance, insulation improvements, air sealing of structural leaks or the addition of energy-efficient windows and doors. Climate engineering consists of carbon dioxide removal and solar radiation management. Since the amount of carbon dioxide determines the radiative balance of Earth atmosphere, carbon dioxide removal techniques can be applied to reduce the radiative forcing. Solar radiation management is the attempt to absorb less solar radiation to offset the effects of greenhouse gases. The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases. The principles of heat transfer in engineering systems can be applied to the human body in order to determine how the body transfers heat. Heat is produced in the body by the continuous metabolism of nutrients which provides energy for the systems of the body. The human body must maintain a consistent internal temperature in order to maintain healthy bodily functions. Therefore, excess heat must be dissipated from the body to keep it from overheating. When a person engages in elevated levels of physical activity, the body requires additional fuel which increases the metabolic rate and the rate of heat production. The body must then use additional methods to remove the additional heat produced in order to keep the internal temperature at a healthy level. Heat transfer by convection is driven by the movement of fluids over the surface of the body. This convective fluid can be either a liquid or a gas. For heat transfer from the outer surface of the body, the convection mechanism is dependent on the surface area of the body, the velocity of the air, and the temperature gradient between the surface of the skin and the ambient air. The normal temperature of the body is approximately 37 °C. Heat transfer occurs more readily when the temperature of the surroundings is significantly less than the normal body temperature. This concept explains why a person feels cold when not enough covering is worn when exposed to a cold environment. Clothing can be considered an insulator which provides thermal resistance to heat flow over the covered portion of the body. This thermal resistance causes the temperature on the surface of the clothing to be less than the temperature on the surface of the skin. This smaller temperature gradient between the surface temperature and the ambient temperature will cause a lower rate of heat transfer than if the skin were not covered. In order to ensure that one portion of the body is not significantly hotter than another portion, heat must be distributed evenly through the bodily tissues. Blood flowing through blood vessels acts as a convective fluid and helps to prevent any buildup of excess heat inside the tissues of the body. This flow of blood through the vessels can be modeled as pipe flow in an engineering system. The heat carried by the blood is determined by the temperature of the surrounding tissue, the diameter of the blood vessel, the thickness of the fluid, velocity of the flow, and the heat transfer coefficient of the blood. The velocity, blood vessel diameter, and the fluid thickness can all be related with the Reynolds Number, a dimensionless number used in fluid mechanics to characterize the flow of fluids. Latent heat loss, also known as evaporative heat loss, accounts for a large fraction of heat loss from the body. When the core temperature of the body increases, the body triggers sweat glands in the skin to bring additional moisture to the surface of the skin. The liquid is then transformed into vapor which removes heat from the surface of the body. The rate of evaporation heat loss is directly related to the vapor pressure at the skin surface and the amount of moisture present on the skin. Therefore, the maximum of heat transfer will occur when the skin is completely wet. The body continuously loses water by evaporation but the most significant amount of heat loss occurs during periods of increased physical activity. Evaporative cooling happens when water vapor is added to the surrounding air. The energy needed to evaporate the water is taken from the air in the form of sensible heat and converted into latent heat, while the air remains at a constant enthalpy. Latent heat describes the amount of heat that is needed to evaporate the liquid; this heat comes from the liquid itself and the surrounding gas and surfaces. The greater the difference between the two temperatures, the greater the evaporative cooling effect. When the temperatures are the same, no net evaporation of water in air occurs; thus, there is no cooling effect. In quantum physics, laser cooling is used to achieve temperatures of near absolute zero (−273.15 °C, −459.67 °F) of atomic and molecular samples to observe unique quantum effects that can only occur at this heat level. Magnetic evaporative cooling is a process for lowering the temperature of a group of atoms, after pre-cooled by methods such as laser cooling. Magnetic refrigeration cools below 0.3K, by making use of the magnetocaloric effect. Radiative cooling is the process by which a body loses heat by radiation. Outgoing energy is an important effect in the Earth's energy budget. In the case of the Earth-atmosphere system, it refers to the process by which long-wave (infrared) radiation is emitted to balance the absorption of short-wave (visible) energy from the Sun. Convective transport of heat and evaporative transport of latent heat both remove heat from the surface and redistribute it in the atmosphere. Thermal energy storage includes technologies for collecting and storing energy for later use. It may be employed to balance energy demand between day and nighttime. The thermal reservoir may be maintained at a temperature above or below that of the ambient environment. Applications include space heating, domestic or process hot water systems, or generating electricity.	Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. 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summarize: Frying is believed to have first appeared in the Ancient Egyptian kitchen, during the Old Kingdom, around 2500 BCE. Fats can reach much higher temperatures than water at normal atmospheric pressure. Through frying, one can sear or even carbonize the surface of foods while caramelizing sugars. The food is cooked much more quickly and has a characteristic crispness and texture. Depending on the food, the fat will penetrate it to varying degrees, contributing richness, lubricity, its own flavor, and calories. Frying techniques vary in the amount of fat required, the cooking time, the type of cooking vessel required, and the manipulation of the food. Sautéing, stir frying, pan frying, shallow frying, and deep frying are all standard frying techniques. Pan frying, sautéing and stir-frying involve cooking foods in a thin layer of fat on a hot surface, such as a frying pan, griddle, wok, or sauteuse. Stir frying involves frying quickly at very high temperatures, requiring that the food be stirred continuously to prevent it from adhering to the cooking surface and burning. Shallow frying is a type of pan frying using only enough fat to immerse approximately one-third to one-half of each piece of food; fat used in this technique is typically only used once. Deep-frying, on the other hand, involves totally immersing the food in hot oil, which is normally topped up and used several times before being disposed. Deep-frying is typically a much more involved process, and may require specialized oils for optimal results. Deep frying is now the basis of a very large and expanding worldwide industry. Fried products have consumer appeal in all age groups and in virtually all cultures, and the process is quick, can easily be made continuous for mass production, and the food emerges sterile and dry, with a relatively long shelf life. The end products can then be easily packaged for storage and distribution. Some include potato chips, french fries, nuts, doughnuts, and instant noodles.	Frying is the cooking of food in oil or another fat. Similar to sautéing, pan-fried foods are generally turned over once or twice during cooking, using tongs or a spatula, while sautéed foods are cooked by "tossing in the pan". 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summarize: "Aung San Suu Kyi", like other Burmese names, includes no surname, but is only a personal name, in her case derived from three relatives: "Aung San" from her father, "Suu" from her paternal grandmother, and Aung San Suu Kyi was born on 19 June 1945 in Rangoon (now Yangon), British Burma. According to Peter Popham, she was born in a small village outside Rangoon called Hmway Saung. Her father, Aung San, allied with the Japanese during World War II. Aung San founded the modern Burmese army and negotiated Burma's independence from the United Kingdom in 1947; he was assassinated by his rivals in the same year. She grew up with her mother, Khin Kyi, and two brothers, Aung San Lin and Aung San Oo, in Rangoon. Aung San Lin died at the age of eight, when he drowned in an ornamental lake on the grounds of the house. Her elder brother emigrated to San Diego, California, becoming a United States citizen. After Aung San Lin's death, the family moved to a house by Inya Lake where Aung San Suu Kyi met people of various backgrounds, political views and religions. She was educated in Methodist English High School (now Basic Education High School No. 1 Dagon) for much of her childhood in Burma, where she was noted as having a talent for learning languages. She speaks four languages: Burmese, English, French and Japanese. She is a Theravada Buddhist. Suu Kyi's mother, Khin Kyi, gained prominence as a political figure in the newly formed Burmese government. She was appointed Burmese ambassador to India and Nepal in 1960, and Aung San Suu Kyi followed her there. She studied in the Convent of Jesus and Mary School in New Delhi, and graduated from Lady Shri Ram College, a constituent college of the University of Delhi in New Delhi, with a degree in politics in 1964. Suu Kyi continued her education at St Hugh's College, Oxford, obtaining a B.A. degree in Philosophy, Politics and Economics in 1967, graduating with a third-class degree and M.A. degree Coincidentally, when Aung San Suu Kyi returned to Burma in 1988, the long-time military leader of Burma and head of the ruling party, General Ne Win, stepped down. Mass demonstrations for democracy followed that event on 8 August 1988 (8–8–88, a day seen as auspicious), which were violently suppressed in what came to be known as the 8888 Uprising. On 26 August 1988, she addressed half a million people at a mass rally in front of the Shwedagon Pagoda in the capital, calling for a democratic government. However, in September, a new military junta took power. Influenced by both Mahatma Gandhi's philosophy of non-violence and more specifically by Buddhist concepts, Aung San Suu Kyi entered politics to work for democratization, helped found the National League for Democracy on 27 September 1988, but was put under house arrest on 20 July 1989. She was offered freedom if she left the country, but she In 1990, the military junta called a general election, in which the National League for Democracy (NLD) received 59% of the votes, guaranteeing NLD 80% of the parliament seats. Some claim that Aung San Suu Kyi would have assumed the office of Prime Minister. Instead, the results were nullified and the military refused to hand over power, resulting in an international outcry. Aung San Suu Kyi was placed under house arrest at her home on University Avenue () in Rangoon, during which time she was On 9 November 1996, the motorcade that Aung San Suu Kyi was traveling in with other National League for Democracy leaders Tin Oo and Kyi Maung, was attacked in Yangon. About 200 men swooped down on the motorcade, wielding metal chains, metal batons, stones and other weapons. The car that Aung San Suu Aung San Suu Kyi was placed under house arrest for a total of 15 years over a 21-year period, on numerous occasions, since she began her political career, during which time she was prevented from meeting her party supporters and international visitors. In an interview, she said that while under house arrest she spent her time reading philosophy, politics and biographies that her husband had sent her. She also passed the time playing the piano, and was occasionally allowed visits from foreign diplomats as well as from her personal physician. Although under house arrest, Aung San Suu Kyi was granted permission to leave Burma under the condition that she never return, which she refused: "As a mother, the greater sacrifice was giving up my sons, but I was always aware of the fact that others had given up more than me. I never forget that my colleagues who are in prison suffer not only physically, but mentally for their families who have no security outside- in the larger prison of Burma under authoritarian rule." The United Nations (UN) has attempted to facilitate dialogue between the junta and Aung San Suu Kyi. On 6 May 2002, following secret confidence-building negotiations led by the UN, the government released her; a government spokesman said that she was free to move "because we are confident that we can trust each other". Aung San Suu Kyi proclaimed "a new dawn for the country". However, on 30 May 2003 in an incident similar to the 1996 attack on her, a government-sponsored mob attacked her caravan in the northern village of Depayin, murdering and wounding many of her supporters. Aung San Suu Kyi fled the Protests led by Buddhist monks began on 19 August 2007 following steep fuel price increases, and continued each day, despite the threat of a crackdown by the military. On 22 September 2007, although still under house arrest, Aung San Suu Kyi made a brief public On 3 May 2009, an American man, identified as John Yettaw, swam across Inya Lake to her house uninvited and was arrested when he made his return trip three days later. He had attempted to make a similar trip two years earlier, but for unknown reasons was turned away. He later claimed at trial that he was motivated by a divine vision requiring him to notify her of an impending terrorist assassination attempt. On 13 May, Aung San Suu Kyi was arrested for violating the terms of her house arrest because the swimmer, who pleaded exhaustion, was allowed to stay in her house for two days before he attempted the swim back. Aung San Aung San Suu Kyi has received vocal support from Western nations in Europe, Australia and North and South America, as well as India, Israel, Japan the Philippines and South Korea. In December 2007, the US House of Representatives voted unanimously 400–0 to award Aung San Suu Kyi the Congressional Gold Medal; the Senate concurred on 25 April 2008. On 6 May 2008, President George W. Bush signed legislation awarding Aung San Suu Kyi the Congressional Gold Medal. She is the first recipient in American history to receive the prize while imprisoned. More recently, there has been growing criticism of her detention by Burma's neighbours in the Association of Southeast Asian Nations, particularly from Indonesia, Thailand, the Philippines and Singapore. At On the evening of 13 November 2010, Aung San Suu Kyi was released from house arrest. This was the date her detention had been set to expire according to a court ruling in August 2009 and came six days after a widely criticised general election. She appeared in front of a crowd of her supporters, who rushed to her house in Rangoon when nearby barricades were removed by the security forces. Aung San Suu Kyi had been detained for 15 of the past 21 years. The government newspaper "New Light of Myanmar" reported the release positively, saying she had been granted a pardon after serving her sentence "in good conduct". The New York Times suggested that the military government may have released Suu Kyi because it felt it was in a confident position to control her supporters after the election. Her son Kim Aris was granted a visa in November 2010 to see his mother shortly after her release, for the first time in 10 years. He visited again on 5 July 2011, to accompany her on a trip to Bagan, her first In December 2011, there was speculation that Aung San Suu Kyi would run in the 2012 national by-elections to fill vacant seats. On 18 January 2012, Aung San Suu Kyi formally registered to contest a Pyithu Hluttaw (lower house) seat in the Kawhmu Township constituency in special parliamentary elections to be held on 1 April 2012. The seat was previously held by Soe Tint, who vacated it after being appointed Construction Deputy Minister, in the 2010 election. She ran against Union Solidarity and Development Party candidate Soe Min, On 16 June 2012, Aung San Suu Kyi was finally able to deliver her Nobel acceptance speech (Nobel lecture) at Oslo's City Hall, two decades after being awarded the peace prize. In September 2012, Aung San Suu Kyi received in person the United States Congressional Gold Medal, which is the highest Congressional award. Although she was awarded this medal in 2008, at the time she was under house arrest, and was unable to receive the medal. Aung San Suu Kyi was greeted with bipartisan support at Congress, as part of a coast-to-coast tour in the United States. In addition, Aung San Suu Kyi met President Barack Obama at the White House. The experience was described by Aung San Suu Kyi as "one of the most moving days of my life." In 2014, she was listed as the 61st most powerful woman in the world by "Forbes". On 6 July 2012, Aung San Suu Kyi announced on As soon as she became foreign minister, she invited Chinese Foreign Minister Wang Yi, Canadian Foreign Minister Stephane Dion and Italian Foreign Minister Paolo Gentiloni in April and Japanese Foreign Minister Fumio Kishida in May and discussed to have good diplomatic relationships with these countries. Initially, upon accepting the State Counsellor position, she granted amnesty to the students who were arrested for opposing the National Education Bill, and announced a creation of the commission on Rakhine state, which had a long record of persecution of the Muslim Rohingya minority. However, soon Aung San Suu Kyi's government did not manage with the ethnic In 2017, critics have called for Aung San Suu Kyi's Nobel prize to be revoked, citing her silence over the persecution of Rohingya people in Myanmar. Some activists criticised Aung San Suu Kyi for her silence on the 2012 Rakhine State riots (later repeated during the 2015 Rohingya refugee crisis), and her perceived indifference to the plight of the Rohingya, Myanmar's persecuted Muslim minority. In 2012, she told reporters she did not know if the Rohingya could be regarded as Burmese citizens. In a 2013 interview with the BBC's Mishal Husain, Aung San Suu Kyi did not condemn violence against the Rohingya and denied that Muslims in Myanmar have been subject to ethnic cleansing, insisting that the tensions were due to a "climate of fear" caused by "a worldwide perception that global Muslim power is'very great. She did condemn "hate of any kind" in the interview. According to Peter Popham, in the aftermath of the interview, she expressed anger at being interviewed by a Muslim. Husain had challenged Suu Kyi that almost all of the impact of violence was against the Rohingya, in response to Aung San Suu Kyi's claim that violence was happening on both sides, and Peter Popham described her position on the issue as one of purposeful ambiguity for political gain. However, she said that she wanted to work towards reconciliation and she cannot take sides as violence has been committed by both sides. According to "The Economist", her "halo In December 2017, two Reuters journalists, Wa Lone and Kyaw Soe Oo, were arrested while investigating the Inn Din massacre of Rohingyas alleged to have been carried out by Myanmar's security forces. Suu Kyi publicly commented in June 2018 that the journalists "weren't arrested for covering the Rakhine issue", but because they had broken Myanmar's Official Secrets Act. As the journalists were then on trial for violating the Official Secrets Act, Aung San Suu Kyi's presumption of their guilt were criticized by rights groups for potentially influencing the verdict. American diplomat Bill Richardson said that he had privately discussed the arrest with Suu Kyi, and he alleged that Aung San Suu Kyi reacted angrily and labelled the journalists "traitors". A police officer testified Asked what democratic models Myanmar could look to, she said: "We have many, many lessons to learn from various places, not just the Asian countries like South Korea, Taiwan, Mongolia, and Indonesia." She also cited "the eastern European countries, which made the transition from communist autocracy to democracy in the 1980s and 1990s, and the Latin American countries, which made the transition from military governments. "And we cannot of The life of Aung San Suu Kyi and her husband Michael Aris is portrayed in Luc Besson's 2011 film "The Lady", in which they are played by Michelle Yeoh and David Thewlis. Yeoh visited Suu Kyi in 2011 before the film's release in November. In the John Boorman's 1995 film "Beyond Rangoon", Aung San Suu Kyi was played by Adelle Lutz. Since 2009, Indian actress and Bharathanatyam dancer Rukmini Vijayakumar has been portraying She had surgery for a gynecological condition in September 2003 at Asia Royal Hospital during her house arrest. She underwent minor foot surgery in December 2013 and eye surgery in April 2016. Her doctor said that she had no serious health problems but weighed only 48 kg, had low blood pressure and could become weak easily.	Aung San Suu Kyi (; ; born 19 June 1945) is a Burmese politician, diplomat, author, and a 1991 Nobel Peace Prize laureate. The first and incumbent State Counsellor (a position akin to a prime minister leader) of Myanmar, she is also the leader of the National League for Democracy and played a vital role in the state's transition from military junta to partial democracy.	en	en	76	[ 250004, 250054, 44, 284, 1619, 1735, 116948, 8667, 14, 830, 1884, 3789, 6, 177539, 123055, 4, 96853, 110, 613, 11627, 4, 1284, 83, 4734, 10, 3357, 9351, 4, 23, 604, 7225, 16406, 4126, 1295, 17262, 35845, 7, 12, 44, 284, 1619, 1735, 58, 1295, 604, 67373, 4, 44, 14168, 34, 58, 1295, 604, 78840, 6236, 9963, 432, 9319, 4, 136, 62, 1619, 1735, 116948, 8667, 14, 509, 103122, 98, 953, 18237, 18608, 23, 32515, 16762, 15, 35613, 4954, 191, 247, 56101, 7362, 192, 5, 129551, 47, 7948, 11584, 3915, 4, 2412, 509, 103122, 23, 10, 19336, 54427, 50782, 32515, 16762, 35839, 572, 39, 7514, 947, 1619, 5, 1840, 67373, 4, 62, 1619, 1735, 4, 144, 71516, 678, 70, 148926, 20271, 6661, 5550, 1995, 5, 62, 1619, 1735, 14037, 297, 70, 5744, 6, 177539, 187, 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summarize: The area was long a part of the Austro-Hungarian Empire until the empire collapsed at the end of World War I. The new state was founded by Tomáš Garrigue Masaryk (1850–1937), who served as its first president from 14 November 1918 to 14 December 1935. He was succeeded by his close ally, Edvard Beneš (1884–1948). The roots of Czech nationalism go back to the 19th century, when philologists and educators, influenced by Romanticism, promoted the Czech language and pride in the Czech people. Nationalism became a mass movement in the second half of the 19th century. Taking advantage of the limited opportunities for participation in political life under Austrian rule, Czech leaders such as historian František Palacký (1798–1876) founded many patriotic, self-help organizations which provided a chance for many of their compatriots to participate in communal life prior to independence. Palacký supported Austro-Slavism and worked for a reorganized and federal Austrian Empire, which would protect the Slavic speaking peoples of Central Europe against Russian and German threats. An advocate of democratic reform and Czech autonomy within Austria-Hungary, Masaryk was elected twice to the "Reichsrat" (Austrian Parliament), first from 1891 to 1893 for the Young Czech Party, and again from 1907 to 1914 for the Czech Realist Party, which he had founded in 1889 with Karel Kramář and Josef Kaizl. During World War I small numbers of Czechs and Slovaks, the Czechoslovak Legions, fought with the Allies in France and Italy, while large numbers deserted to Russia in exchange for its support for the independence of Czechoslovakia from the Austrian Empire. With the outbreak of World War I, Masaryk began working for Czech independence in a union with Slovakia. With Edvard Beneš and Milan Rastislav Štefánik, Masaryk visited several Western countries and won support from influential publicists. The Bohemian Kingdom ceased to exist in 1918 when it was incorporated into Czechoslovakia. Czechoslovakia was founded in October 1918, as one of the successor states of the Austro-Hungarian Empire at the end of World War I and as part of the Treaty of Saint-Germain-en-Laye. It consisted of the present day territories of Bohemia, Moravia, Slovakia and Carpathian Ruthenia. Its territory included some of the most industrialized regions of the former Austria-Hungary. The new country was a multi-ethnic state, with Czechs and Slovaks as "constituent peoples". The population consisted of Czechs (51%), Slovaks (16%), Germans (22%), Hungarians (5%) and Rusyns (4%). Many of the Germans, Hungarians, Ruthenians and Poles and some Slovaks, felt oppressed because the political elite did not generally allow political autonomy for minority ethnic groups. This policy led to unrest among the non-Czech population, particularly in German-speaking Sudetenland, which initially had proclaimed itself part of the Republic of German-Austria in accordance with the self-determination principle. The state proclaimed the official ideology that there were no separate Czech and Slovak nations, but only one nation of Czechoslovaks (see Czechoslovakism), to the disagreement of Slovaks and other ethnic groups. Once a unified Czechoslovakia was restored after World War II (after the country had been divided during the war), the conflict between the Czechs and the Slovaks surfaced again. The governments of Czechoslovakia and other eastern European nations deported ethnic Germans to the West, reducing the presence of minorities in the nation. Most of the Jews had been killed during the war by the Nazis and their allies. During the period between the two world wars, democracy thrived in Czechoslovakia. Of all the new states established in central Europe after 1918, only Czechoslovakia preserved a democratic government until the war broke out. Thus, despite regional disparities, its level of development was much higher than that of neighboring states. The population was generally literate, and contained fewer alienated groups. The influence of these conditions was augmented by the political values of Czechoslovakia's leaders and the policies they adopted. Under Tomas Masaryk, Czech and Slovak politicians promoted progressive social and economic conditions that served to defuse discontent. Foreign minister Beneš became the prime architect of the Czechoslovak-Romanian-Yugoslav alliance (the "Little Entente", 1921–38) directed against Hungarian attempts to reclaim lost areas. Beneš worked closely with France. Far more dangerous was the German element, which after 1933 became allied with the Nazis in Germany. The increasing feeling of inferiority among the Slovaks, who were hostile to the more numerous Czechs, weakened the country in the late 1930s. Many Slovaks supported an extreme nationalist movement and welcomed the puppet Slovak state set up under Hitler's control in 1939. After 1933, Czechoslovakia remained the only democracy in central and eastern Europe. In September 1938, Adolf Hitler demanded control of the Sudetenland. On 29 September 1938, Britain and France ceded control in the Appeasement at the Munich Conference; France ignored the military alliance it had with Czechoslovakia. During October 1938, Nazi Germany occupied and annexed the Sudetenland border region, effectively crippling Czechoslovak defences. On 15 March 1939, the remainder ("rump") of Czechoslovakia was invaded and divided into the Protectorate of Bohemia and Moravia and the puppet Slovak State. Much of Slovakia and all of Carpathian Ruthenia were annexed by Hungary. Poland occupied Zaolzie, an area whose population was majority Polish, in October 1938. The eventual goal of the German state under Nazi leadership was to eradicate Czech nationality through assimilation, deportation, and extermination of the Czech intelligentsia; the intellectual elites and middle class made up a considerable number of the 200,000 people who passed through concentration camps and the 250,000 who died during German occupation. Under Generalplan Ost, it was assumed that around 50% Czechs would be fit for Germanization. The Czech intellectual elites were to be removed not only from Czech territories but from Europe completely. The authors of Generalplan Ost believed it would be best if they emigrated overseas, as even in Siberia they were considered a threat to German rule. Just like Jews, Poles, Serbs, and several other nations, Czechs were considered to be untermenschen by the Nazi state. In 1940, in a secret Nazi plan for the Germanization of the Protectorate of Bohemia and Moravia it was declared that those considered to be of racially Mongoloid origin and the Czech intelligentsia were not to be Germanized. The deportation of Jews to concentration camps was organized under the direction of Reinhard Heydrich, and the fortress town of Terezín was made into a ghetto way station for Jewish families. On 4 June 1942 Heydrich died after being wounded by an assassin in Operation Anthropoid. Heydrich's successor, Colonel General Kurt Daluege, ordered mass arrests and executions and the destruction of the villages of Lidice and Ležáky. In 1943 the German war effort was accelerated. Under the authority of Karl Hermann Frank, German minister of state for Bohemia and Moravia, some 350,000 Czech laborers were dispatched to the Reich. Within the protectorate, all non-war-related industry was prohibited. Most of the Czech population obeyed quiescently up until the final months preceding the end of the war, while thousands were involved in the resistance movement. For the Czechs of the Protectorate Bohemia and Moravia, German occupation was a period of brutal oppression. Czech losses resulting from political persecution and deaths in concentration camps totaled between 36,000 and 55,000. The Jewish population of Bohemia and Moravia (118,000 according to the 1930 census) was virtually annihilated. Many Jews emigrated after 1939; more than 70,000 were killed; 8,000 survived at Terezín. Several thousand Jews managed to live in freedom or in hiding throughout the occupation. Despite the estimated 136,000 deaths at the hands of the Nazi regime, the population in the Reichsprotektorate saw a net increase during the war years of approximately 250,000 in line with an increased birth rate. On 6 May 1945, the third US Army of General Patton entered Pilsen from the south west. On 9 May 1945, Soviet Red Army troops entered Prague. After World War II, pre-war Czechoslovakia was re-established, with the exception of Subcarpathian Ruthenia, which was annexed by the Soviet Union and incorporated into the Ukrainian Soviet Socialist Republic. The Beneš decrees were promulgated concerning ethnic Germans (see Potsdam Agreement) and ethnic Hungarians. Under the decrees, citizenship was abrogated for people of German and Hungarian ethnic origin who had accepted German or Hungarian citizenship during the occupations. In 1948, this provision was cancelled for the Hungarians, but only partially for the Germans. The government then confiscated the property of the Germans and expelled about 90% of the ethnic German population, over 2 million people. Those who remained were collectively accused of supporting the Nazis after the Munich Agreement, as 97.32% of Sudeten Germans had voted for the NSDAP in the December 1938 elections. Almost every decree explicitly stated that the sanctions did not apply to antifascists. Some 250,000 Germans, many married to Czechs, some antifascists, and also those required for the post-war reconstruction of the country, remained in Czechoslovakia. The Beneš Decrees still cause controversy among nationalist groups in the Czech Republic, Germany, Austria and Hungary. Carpathian Ruthenia (Podkarpatská Rus) was occupied by (and in June 1945 formally ceded to) the Soviet Union. In the 1946 parliamentary election, the Communist Party of Czechoslovakia was the winner in the Czech lands, and the Democratic Party won in Slovakia. In February 1948 the Communists seized power. Although they would maintain the fiction of political pluralism through the existence of the National Front, except for a short period in the late 1960s (the Prague Spring) the country had no liberal democracy. Since citizens lacked significant electoral methods of registering protest against government policies, periodically there were street protests that became violent. For example, there were riots in the town of Plzeň in 1953, reflecting economic discontent. Police and army units put down the rebellion, and hundreds were injured but no one was killed. While its economy remained more advanced than those of its neighbors in Eastern Europe, Czechoslovakia grew increasingly economically weak relative to Western Europe. The currency reform of 1953 caused dissatisfaction among Czechoslovak laborers. Prior to World War II, the Czech purchasing power surpassed that of the Soviet Union by 115–144%. This disparity was noted after Czechoslovakia came under the Soviet Bloc. To equalize the wage rate, Czechoslovaks had to turn in their old money for new at a decreased value. This lowered the real value of wages by about 11%. The banks also confiscated savings and bank deposits to control the amount of money in circulation. The economy continued to suffer as production achievements of bituminous coal was less than anticipated. Bituminous coal powered 85% of Czechoslovakia's economy. Because of low production, coal was utilized in industry only. Pre-war years, consumers used both coal and lignite for fuel, however due to low production, coal was for industrial use only which meant the consumer was only able to utilize lignite. In 1929, a typical family of four consumed approximately 2.34 tons of lignite, but by 1953 it was allowed to use only 1.6–1.8 tons per year. In 1968, when the reformer Alexander Dubček was appointed to the key post of First Secretary of the Czechoslovak Communist Party, there was a brief period of liberalization known as the Prague Spring. In response, after failing to persuade the Czechoslovak leaders to change course, five other members of the Warsaw Pact invaded. Soviet tanks rolled into Czechoslovakia on the night of 20–21 August 1968. Soviet Communist Party General Secretary Leonid Brezhnev viewed this intervention as vital for the preservation of the Soviet, socialist system and vowed to intervene in any state that sought to replace Marxism-Leninism with capitalism. In the week after the invasion there was a spontaneous campaign of civil resistance against the occupation. This resistance involved a wide range of acts of non-cooperation and defiance: this was followed by a period in which the Czechoslovak Communist Party leadership, having been forced in Moscow to make concessions to the Soviet Union, gradually put the brakes on their earlier liberal policies. In April 1969 Dubček was finally dismissed from the First Secretaryship of the Czechoslovak Communist Party. Meanwhile, one plank of the reform program had been carried out: in 1968–69, Czechoslovakia was turned into a federation of the Czech Socialist Republic and Slovak Socialist Republic. The theory was that under the federation, social and economic inequities between the Czech and Slovak halves of the state would be largely eliminated. A number of ministries, such as education, now became two formally equal bodies in the two formally equal republics. However, the centralized political control by the Czechoslovak Communist Party severely limited the effects of federalization. The 1970s saw the rise of the dissident movement in Czechoslovakia, represented among others by Václav Havel. The movement sought greater political participation and expression in the face of official disapproval, manifested in limitations on work activities, which went as far as a ban on professional employment, the refusal of higher education for the dissidents' children, police harassment and prison. In 1989, the Velvet Revolution restored democracy. This occurred at around the same time as the fall of communism in Romania, Bulgaria, Hungary and Poland. The word "socialist" was removed from the country's full name on 29 March 1990 and replaced by "federal". In 1992, because of growing nationalist tensions in the government, Czechoslovakia was peacefully dissolved by parliament. On 1 January 1993 it formally separated into two independent countries, the Czech Republic and the Slovak Republic. After World War II, a political monopoly was held by the Communist Party of Czechoslovakia (KSČ). Gustáv Husák was elected first secretary of the KSČ in 1969 (changed to general secretary in 1971) and president of Czechoslovakia in 1975. Other parties and organizations existed but functioned in subordinate roles to the KSČ. All political parties, as well as numerous mass organizations, were grouped under umbrella of the National Front. Human rights activists and religious activists were severely repressed. Czechoslovakia had the following constitutions during its history (1918–1992): In the 1930s, the nation formed a military alliance with France, which collapsed in the Munich Agreement of 1938. After World War II, active participant in Council for Mutual Economic Assistance (Comecon), Warsaw Pact, United Nations and its specialized agencies; signatory of conference on Security and Cooperation in Europe. Before World War II, the economy was about the fourth in all industrial states in Europe. The state was based on strong economy, manufacturing cars (Škoda, Tatra), trams, aircraft (Aero, Avia), ships, ship engines (Škoda), canons, shoes (Baťa), turbines, guns (Zbrojovka Brno). It was the industrial workshop for Austro-Hungarian empire. The Slovak lands were more in agriculture. After World War II, the economy was centrally planned, with command links controlled by the communist party, similarly to the Soviet Union. The large metallurgical industry was dependent on imports of iron and non-ferrous ores. After World War II, the country was short of energy, relying on imported crude oil and natural gas from Soviet Union, domestic brown coal, and nuclear and hydroelectric energy. Energy constraints were a major factor in the 1980s. Slightly after the foundation of Czechoslovakia in 1918, there was a lack of needful infrastructure in many areas – paved roads, railways, bridges etc. Massive improvement in the following years enabled Czechoslovakia to develop its industry. Prague's civil airport in Ruzyně became one of the most modern terminals in the world, when it was finished in 1937. Tomáš Baťa, Czech entrepreneur and visionary outlined his ideas in the publication "Budujme stát pro 40 milionů lidí", where he described the future motorway system. Construction of the first motorways in Czechoslovakia begun in 1939, nevertheless, they were stopped after Nazi occupation during the World War II. Education was free at all levels and compulsory from age 6 to 15. The vast majority of the population was literate. There was a highly developed system of apprenticeship training and vocational schools supplemented general secondary schools and institutions of higher education. In 1991: Roman Catholics 46%, Evangelical Lutheran 5.3%, Atheist 30%, n/a 17%, but there were huge differences in religious practices between the two constituent republics; see Czech Republic and Slovakia. After World War II, free health care was available to all citizens. National health planning emphasized preventive medicine; factory and local health care centres supplemented hospitals and other inpatient institutions. There was substantial improvement in rural health care during the 1960s and 1970s. During the era between the World Wars, Czechoslovak democracy and liberalism facilitated conditions for free publication. The most significant daily newspapers in these times were Lidové noviny, Národní listy, Český deník and Československá republika. During Communist rule, the mass media in Czechoslovakia were controlled by the Communist Party. Private ownership of any publication or agency of the mass media was generally forbidden, although churches and other organizations published small periodicals and newspapers. Even with this information monopoly in the hands of organizations under KSČ control, all publications were reviewed by the government's Office for Press and Information. The Czechoslovakia national football team was a consistent performer on the international scene, with eight appearances in the FIFA World Cup Finals, finishing in second place in 1934 and 1962. The team also won the European Football Championship in 1976, came in third in 1980 and won the Olympic gold in 1980. Well-known football players such as Pavel Nedvěd, Antonín Panenka, Milan Baroš, Tomáš Rosický, Vladimír Šmicer or Petr Čech were all born in Czechoslovakia. The International Olympic Committee code for Czechoslovakia is TCH, which is still used in historical listings of results. The Czechoslovak national ice hockey team won many medals from the world championships and Olympic Games. Peter Šťastný, Jaromír Jágr, Dominik Hašek, Peter Bondra, Petr Klíma, Marián Gáborík, Marián Hossa, Miroslav Šatan and Pavol Demitra all come from Czechoslovakia. Emil Zátopek, winner of four Olympic gold medals in athletics, is considered one of the top athletes in Czechoslovak history. Věra Čáslavská was an Olympic gold medallist in gymnastics, winning seven gold medals and four silver medals. She represented Czechoslovakia in three consecutive Olympics. Several accomplished professional tennis players including Ivan Lendl, Jan Kodeš, Miloslav Mečíř, Hana Mandlíková, Martina Hingis, Martina Navratilova, Jana Novotna, Petra Kvitová and Daniela Hantuchová were born in Czechoslovakia. Maps with Hungarian-language rubrics:	Czechoslovakia, or Czecho-Slovakia (; Czech and, "Česko-Slovensko"), was a sovereign state in Central Europe that existed from October 1918, when it declared its independence from the Austro-Hungarian Empire, until its peaceful dissolution into the Czech Republic and Slovakia on 1 January 1993.	en	en	52	[ 250004, 250054, 581, 16128, 509, 4989, 10, 2831, 111, 70, 5489, 2955, 9, 841, 28391, 9893, 145359, 24189, 70, 352, 95972, 3365, 127966, 71, 99, 70, 3564, 111, 6661, 5550, 87, 5, 581, 3525, 11341, 509, 14037, 297, 390, 103832, 195608, 6261, 19629, 50281, 7435, 2525, 74668, 118628, 4, 2750, 149976, 237, 6863, 5117, 13918, 1295, 616, 7582, 24531, 47, 616, 14487, 61540, 5, 1529, 509, 214493, 297, 390, 1919, 20903, 6, 25958, 4, 205340, 30543, 794, 7435, 13903, 74668, 72208, 5, 581, 74855, 7, 111, 103655, 15889, 8780, 738, 4420, 47, 70, 953, 927, 142642, 4, 3229, 44171, 365, 106622, 7, 136, 29574, 22230, 4, 79507, 71, 390, 174108, 8780, 4, 125568, 71, 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summarize: The Parliament, like the other institutions, was not designed in its current form when it first met on 10 September 1952. One of the oldest common institutions, it began as the "Common Assembly" of the European Coal and Steel Community (ECSC). It was a consultative assembly of 78 appointed parliamentarians drawn from the national parliaments of member states, having no legislative powers. The change since its foundation was highlighted by Professor David Farrell of the University of Manchester: "For much of its life, the European Parliament could have been justly labelled a'multi-lingual talking shop'." Its development since its foundation shows how the European Union's structures have evolved without a clear ‘master plan’. Some, such as Tom Reid of the "Washington Post", said of the union: "nobody would have deliberately designed a government as complex and as redundant as the EU". Even the Parliament's two seats, which have switched several times, are a result of various agreements or lack of agreements. Although most MEPs would prefer to be based just in Brussels, at John Major's 1992 Edinburgh summit, France engineered a treaty amendment to maintain Parliament's plenary seat permanently at Strasbourg. The body was not mentioned in the original Schuman Declaration. It was assumed or hoped that difficulties with the British would be resolved to allow the Parliamentary Assembly of the Council of Europe to perform the task. A separate Assembly was introduced during negotiations on the Treaty as an institution which would counterbalance and monitor the executive while providing democratic legitimacy. The wording of the ECSC Treaty demonstrated the leaders' desire for more than a normal consultative assembly by using the term "representatives of the people" and allowed for direct election. Its early importance was highlighted when the Assembly was given the task of drawing up the draft treaty to establish a European Political Community. By this document, the Ad Hoc Assembly was established on 13 September 1952 with extra members, but after the failure of the proposed European Defence Community the project was In 1979, its members were directly elected for the first time. This sets it apart from similar institutions such as those of the Parliamentary Assembly of the Council of Europe or Pan-African Parliament which are appointed. After that first election, the parliament held its first session on 11 July 1979, electing Simone Veil MEP as its president. Veil was also the first female president of the Parliament since it was formed as the Common Assembly. As an elected body, the Parliament began to draft proposals addressing the functioning of the EU. For example, in 1984, inspired by its previous work on the Political Community, it drafted the "draft Treaty establishing the European Union" (also known as the 'Spinelli Plan' after its rapporteur Altiero Spinelli MEP). Although it was not adopted, many ideas were later implemented by other treaties. Furthermore, the Parliament began holding votes on proposed Commission Presidents from the 1980s, before it was given any formal right to veto. Since it became an elected body, the membership of the In 2004, following the largest trans-national election in history, despite the European Council choosing a President from the largest political group (the EPP), the Parliament again exerted pressure on the Commission. During the Parliament's hearings of the proposed Commissioners MEPs raised doubts about some nominees with the Civil Liberties committee rejecting Rocco Buttiglione from the post of Commissioner for Justice, Freedom and Security over his views on homosexuality. That was the first time the Parliament had ever voted against an incoming Commissioner and despite Barroso's insistence upon Buttiglione the Parliament forced Buttiglione to be withdrawn. A number of other Commissioners also had to be withdrawn or reassigned before Parliament allowed the The Lisbon Treaty finally came into force on 1 December 2009, granting Parliament powers over the entire EU budget, making Parliament's legislative powers equal to the Council's in nearly all areas and linking the appointment of the Commission President to Parliament's own elections. Despite some calls for the parties to put forward candidates beforehand, only the EPP (which had re-secured their position as largest party) had one in re-endorsing Barroso. Barroso gained the support of the European Council for a second term and secured majority support from the Parliament in September 2009. Parliament voted 382 votes in favour and 219 votes against (117 abstentions ) with support of the European People's Party, European Conservatives and Reformists and the Alliance of Liberals and Democrats for Europe. The liberals gave support after Barroso gave them a number of concessions; the liberals previously joined the socialists' call for a delayed vote (the EPP had wanted to approve Barroso in July of that year). Once Barroso put forward the candidates for his next Commission, another opportunity to gain concessions arose. Bulgarian nominee Rumiana Jeleva The Parliament and Council have been compared to the two chambers of a bicameral legislature. However, there are some differences from national legislatures; for example, neither the Parliament nor the Council have the power of legislative initiative (except for the fact that the Council has the power in some intergovernmental matters). In Community matters, this is a power uniquely reserved for the European Commission (the executive). Therefore, while Parliament can amend and reject legislation, to make a proposal for legislation, it needs the Commission to draft a bill before anything can become law. The value of such a power has been questioned by noting that in the national legislatures of the member states 85% of initiatives introduced without executive support fail to become law. Yet it has been argued by former Parliament president Hans-Gert Pöttering that as the Parliament does have the right to ask the Commission to draft such legislation, and as the Commission is following Parliament's proposals more and more Parliament does have a "de facto" right of legislative initiative. The Parliament also has a great deal of indirect influence, through non-binding resolutions and committee hearings, as a "pan-European soapbox" with the ear of thousands of Brussels-based journalists. There is also an indirect effect on foreign policy; the Parliament must approve all development grants, including those overseas. For example, the support for post-war Iraq reconstruction, or incentives for the cessation of Iranian nuclear development, must be supported by the Parliament. Parliamentary support was also required for the transatlantic passenger data-sharing deal with the United States. Finally, Parliament holds a non-binding vote on new EU treaties but cannot veto it. However, when Parliament threatened to vote down the Nice Treaty, the Belgian and Italian Parliaments said they would veto the treaty on the European Parliament's behalf. With each new treaty, the powers of the Parliament, in terms of its role in the Union's legislative procedures, have expanded. The procedure which has slowly become dominant is the "ordinary legislative procedure" (previously named "codecision procedure"), which provides an equal footing between Parliament and Council. In particular, under the procedure, the Commission presents a proposal to Parliament and the Council which can only become law if both agree on a text, which they do (or not) through successive readings up to a maximum of three. In its first reading, Parliament may send amendments to the Council which can either adopt the text with those amendments or send back a "common position". That position may either be approved by Parliament, or it may reject the text by an absolute majority, causing it to fail, or it may adopt further amendments, also by an absolute majority. If the Council does not approve these, then a "Conciliation Committee" is formed. The Committee is composed of the Council members plus an equal number of MEPs who seek to agree a compromise. Once a position is agreed, it has to The legislative branch officially holds the Union's budgetary authority with powers gained through the Budgetary Treaties of the 1970s and the Lisbon Treaty. The EU budget is subject to a form of the ordinary legislative procedure with a single reading giving Parliament power over the entire budget (before 2009, its influence was limited to certain areas) on an equal footing to the Council. If there is a disagreement between them, it is taken to a conciliation committee as it is for legislative proposals. The President of the European Commission is proposed by the European Council on the basis of the European elections to Parliament. That proposal has to be approved by the Parliament (by a simple majority) who "elect" the President according to the treaties. Following the approval of the Commission President, the members of the Commission are proposed by the President in accord with the member states. Each Commissioner comes before a relevant parliamentary committee hearing covering the proposed portfolio. They are then, as a body, approved or rejected by the Parliament. In practice, the Parliament has never voted against a President or his Commission, but it did seem likely when the Barroso Commission was put forward. The resulting pressure forced the proposal to be withdrawn and changed to be more acceptable to parliament. That pressure was seen as an important sign by some of the evolving nature of the Parliament and its ability to make the Commission accountable, The Parliament also has other powers of general supervision, mainly granted by the Maastricht Treaty. The Parliament has the power to set up a Committee of Inquiry, for example over mad cow disease or CIA detention flights the former led to the creation of the European veterinary agency. The Parliament can call other institutions to answer questions and if necessary to take them to court if they break EU law or treaties. Furthermore, it has powers over The parliamentarians are known in English as Members of the European Parliament (MEPs). They are elected every five years by universal adult suffrage and sit according to political allegiance; about a third are women. Before 1979 they were appointed by their national parliaments. In 2017, an estimated 17 MEPs were not white. Of these, three were black; if the numbers were proportionate to the EU population, then 22 would be black. Under the Lisbon Treaty, seats are allocated to each state according to population and the maximum number of members is set at 751 (however, as the President cannot vote while in the chair there will only be 750 voting members at any one time). Since 1 February 2020, 705 MEPs (including the president of the Parliament) sit in the European Parliament, as there is no EU citizens' représentative of the United Kingdom anymore due to Brexit. Representation is currently limited to a maximum of 96 seats and a minimum of 6 seats per state and the seats are distributed according to "degressive proportionality", i.e., the larger the state, the more citizens are represented per MEP. As a result, Maltese and Luxembourgish voters have roughly 10x more influence per voter than citizens of the six large countries. , Germany (80.9 million inhabitants) has 96 seats (previously 99 seats), i.e. one seat for 843,000 inhabitants. Malta (0.4 million inhabitants) has 6 seats, i.e. one seat for 70,000 inhabitants. The new system implemented under the Lisbon Treaty, including revising the seating well before elections, was intended to avoid political horse trading when the allocations have to be revised to reflect demographic changes. Pursuant to this apportionment, the constituencies are formed. In four EU member states (Belgium, Ireland, Italy and Poland), the national territory is divided into a number of constituencies. In the remaining member states, the whole country forms a single constituency. All member states hold elections to the European Parliament using various forms of proportional representation. Due to the delay in ratifying the Lisbon Treaty, the seventh parliament was elected under the lower Nice Treaty cap. A small scale treaty amendment was ratified on 29 November 2011. This amendment brought Before 2009, members received the same salary as members of their national parliament. However, from 2009 a new members statute came into force, after years of attempts, which gave all members an equal monthly pay, of €8,484.05 each in 2016, subject to a European Union tax and which can also be taxed nationally. MEPs are entitled to a pension, paid by Parliament, from the age of 63. Members are also entitled to allowances for office MEPs in Parliament are organised into eight different parliamentary groups, including thirty non-attached members known as "non-inscrits". The two largest groups are the European People's Party (EPP) and the Socialists & Democrats (S&D). These two groups have dominated the Parliament for much of its life, continuously holding between 50 and 70 percent of the seats between them. No single group has ever held a majority in Parliament. As a result of being broad alliances of national parties, European group parties are very decentralised and hence have more in common with parties in federal states like Germany or the United States than unitary states like the majority of the EU states. Nevertheless, the European groups were actually more cohesive than their Given that the Parliament does not form the government in the traditional sense of a Parliamentary system, its politics have developed along more consensual lines rather than majority rule of competing parties and coalitions. Indeed, for much of its life it has been dominated by a grand coalition of the European People's Party and the Party of European Socialists. The two major parties tend to co-operate to find a compromise between their two groups leading to proposals endorsed by huge majorities. However, this does not always produce agreement, and each may instead try to build other alliances, the EPP normally with other centre-right or right wing Groups and the PES with centre-left or left wing groups. Sometimes, the Liberal Group is then in the pivotal position. There are also occasions where very sharp party political divisions have emerged, for example over the resignation of the Santer Elections have taken place, directly in every member state, every five years since 1979. there have been nine elections. When a nation joins mid-term, a by-election will be held to elect their representatives. This has happened six times, most recently when Croatia joined in 2013. Elections take place across four days according to local custom and, apart from having to be proportional, the electoral system is chosen by the member state. This includes allocation of sub-national constituencies; while most members have a national list, some, like the UK and Poland, divide their allocation between regions. Seats are allocated to member states according to their population, since 2014 with no state having more than 96, but no fewer than 6, to maintain proportionality. The most recent Union-wide elections to the European Parliament were the European elections of 2019, held from 23 to 26 May 2019. They were the largest simultaneous transnational elections ever held anywhere in the world. The first session of the ninth parliament started 2 July 2019. European political parties have the exclusive right to campaign during the European elections (as opposed to their corresponding EP groups). There have been a number of proposals Each year the activities of the Parliament cycle between committee weeks where reports are discussed in committees and interparliamentary delegations meet, political group weeks for members to discuss work within their political groups and session weeks where members spend 31⁄2 days in Strasbourg for part-sessions. In addition six 2-day part-sessions are organised in Brussels throughout the year. Four weeks are allocated as constituency week to allow members to do exclusively constituency work. Finally there are no meetings planned during the summer weeks. The Parliament has the power to meet without being convened by another authority. Its meetings are partly controlled by the treaties but are otherwise up to Parliament according to its own "Rules of Procedure" (the regulations governing the parliament). During sessions, members may speak after being called on by the President. Members of the Council or Commission may also attend and speak in debates. Partly due to the need for translation, and the politics of consensus in the chamber, debates tend to be calmer and more polite than, say, the Westminster system. Voting is conducted primarily by a show of hands, that may be checked on request by electronic voting. Votes of MEPs are not recorded in either case, however; that only occurs when there is a roll-call ballot. This is required for the final votes on legislation and also whenever a political group or 30 MEPs request it. The number of roll-call votes has increased with time. Votes can also be a completely secret ballot (for example, when the president is elected). All recorded votes, along with minutes and legislation, are recorded in the "Official Journal of the European Union" and can be accessed online. Votes usually do not follow a debate, but rather they are grouped with other due votes on specific occasions, usually at noon on Tuesdays, Wednesdays or Thursdays. This is because the length of the vote is unpredictable and if it continues for longer than allocated it can disrupt other debates and meetings later in the day. Members are arranged in a hemicycle according to their political groups (in the Common Assembly, prior to 1958, members sat alphabetically) who are ordered mainly by left to right, but some smaller groups are placed towards the outer ring of the Parliament. All desks are equipped with microphones, headphones for translation and electronic voting equipment. The leaders of the groups sit on the front benches at the centre, and in the very centre is a podium for guest speakers. The remaining half of the circular chamber is primarily composed of the raised area where the President and staff sit. Further benches are provided between the sides of this area and the MEPs, these are taken up by the Council on the far left and the Commission on the far right. Both the Brussels and Strasbourg hemicycle roughly follow this layout with only minor differences. The hemicycle design is a compromise between the different Parliamentary systems. The British-based system has the different groups directly facing each other while the French-based system is a semicircle (and the traditional German system had all members in rows facing a rostrum for speeches). Although the design is mainly based on a semicircle, the opposite ends of the spectrum do still face each other. With access to the chamber limited, entrance is controlled by ushers who aid MEPs in the chamber (for example in delivering documents). The ushers can also occasionally act as a form of police in enforcing the President, for example in ejecting an MEP who is disrupting the session (although this is rare). The first head of protocol in the Parliament was French, so many of the duties in the Parliament are based on the French model first developed following the French Revolution. The 180 ushers are highly visible in the Parliament, dressed in black tails and wearing a silver chain, and are recruited in the same manner as the European civil service. The President is allocated a personal usher. According to the European Parliament website, the annual parliament budget for 2016 was €1.838 billion. The main cost categories were: According to a European Parliament study prepared in 2013, the Strasbourg seat costs an extra €103 million over maintaining a single location and according to the Court of Auditors an additional €5 million is related to travel expenses caused by having two seats. As a comparison, the German lower house of parliament (Bundestag) is estimated to cost €517 million in total for 2018, for a parliament with The Parliament is based in three different cities with numerous buildings. A protocol attached to the Treaty of Amsterdam requires that 12 plenary sessions be held in Strasbourg (none in August but two in September), which is the Parliament's official seat, while extra part sessions as well as committee meetings are held in Brussels. Luxembourg City hosts the Secretariat of the European Parliament. The European Parliament is one of at least two assemblies in the world with more than one meeting place (another being the parliament of the Isle of Man, Tynwald) and one of the few that does not have the power to decide its own location. The Strasbourg seat is seen as a symbol of reconciliation between France and Germany, the Strasbourg region having been fought over by the two countries in the past. However, the cost and inconvenience of having two seats is questioned. While Strasbourg is the official seat, and sits alongside the Council of Europe, Brussels is home to nearly all other major EU institutions, with the majority of Parliament's work being carried out there. Critics have described the two-seat arrangement as a "travelling circus", and there is a strong movement to establish Brussels as the sole seat. This is because the other political institutions (the Commission, Council and European Council) are located there, and hence Brussels is treated as the 'capital' of the EU. This movement has received Over the last few years, European institutions have committed to promoting transparency, openness, and the availability of information about their work. In particular, transparency is regarded as pivotal to the action of European institutions and a general principle of EU law, to be applied to the activities of EU institutions in order to strengthen the Union's democratic foundation. The general principles of openness and transparency are reaffirmed in the articles 8 A, point 3 and 10.3 of the Treaty of Lisbon and the Maastricht Treaty respectively, stating that "every citizen shall have the right to participate in the democratic life of the Union. Decisions shall be taken as openly and as closely as possible to the citizen". Furthermore, both treaties acknowledge the value of dialogue between citizens, representative associations, civil society, and European institutions. Article 17 of the Treaty on the Functioning of the European Union (TFEU) lays the juridical foundation for an open, transparent dialogue between European institutions and churches, religious associations, and non-confessional and philosophical organisations. In July 2014, in The chair of European Parliament Mediator for International Parental Child Abduction was established in 1987 by initiative of British MEP Charles Henry Plumb, with the goal of helping minor children of international couples victim of parental abduction. The Mediator finds negotiated solutions in the higher interest of the minor when said minor is abducted by a parent following separation of the couple, regardless whether married or unmarried. Since its institution, the chair has been held by Mairead McGuinness (since 2014), Roberta Angelilli (2009-2014), Evelyne Gebhardt (2004-2009), The European Parliamentary Research Service (EPRS) is the European Parliament's in-house research department and think tank. It provides Members of the European Parliament and, where appropriate, parliamentary committees with independent, objective and authoritative analysis of, and research on, policy issues relating to the European Union, in order to assist them in their parliamentary work. It is also designed to increase Members' and EP committees' The European Parliament periodically commissions opinion polls and studies on public opinion trends in Member States to survey perceptions and expectations of citizens about its work and the overall activities of the European Union. Topics include citizens' perception of the Annually, the European Parliament awards four prizes to individuals and organisations that distinguished themselves in the areas of human rights, film, youth projects, and European participation and citizenship. With the Sakharov Prize for Freedom of Thought, created in 1998, the European Parliament supports human rights by awarding individuals that contribute to promoting human rights worldwide, The European Charlemagne Youth Prize seeks to encourage youth participation in the European integration process. It is awarded The European Citizens' Prize is awarded by the European Parliament to activities and actions carried Since 2007, the LUX Prize is awarded by the European Parliament to films dealing with current topics of public European	The European Parliament (EP) is the legislative branch of the European Union and one of its seven institutions. Together with the Council of the European Union, it adopts European legislation, normally on a proposal from the European Commission. The Parliament is composed of 705 members (MEPs). 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summarize: The first written mention of name "Slovakia" is in 1586 (). It derives from the Czech word "Slováky"; previous German forms were "Windischen landen" and "Windenland" (the 15th century). The native name Radiocarbon dating puts the oldest surviving human artefacts from Slovakia—found near Nové Mesto nad Váhom—at 270,000 BCE, in the Early Paleolithic era. These ancient tools, made by the Clactonian technique, bear witness to the ancient habitation of Slovakia. Other stone tools from the Middle Paleolithic era (200,000–80,000 BCE) come from the Prévôt (Prepoštská) cave in Bojnice and from other nearby sites. The most important discovery from that era is a Neanderthal cranium (c. 200,000 BCE), discovered near Gánovce, a village in northern Slovakia. Archaeologists have found prehistoric human skeletons in the region, as well as numerous objects and vestiges of the Gravettian culture, principally in the river valleys of Nitra, Hron, Ipeľ, Váh and as far as the city of Žilina, and near the foot of the Vihorlat, Inovec, and Tribeč mountains, as well as in the Myjava Mountains. The most well-known finds include the oldest female statue made of mammoth bone (22,800 BCE), the famous Venus of Moravany. The statue was found in the 1940s in Moravany nad Váhom near Piešťany. Numerous necklaces made of shells from Cypraca thermophile gastropods of the Tertiary period have come from the sites of Zákovská, Podkovice, Hubina, and Radošina. These findings provide the most ancient evidence of commercial exchanges carried out between the Mediterranean and Central Europe. During the Bronze Age, the geographical territory of modern-day Slovakia went through three stages of development, stretching from 2000 to 800 BCE. Major cultural, economic, and political development can be attributed to the significant growth in production of copper, especially in central Slovakia (for example in Špania Dolina) and northwest The arrival of tribes from Thrace disrupted the people of the Kalenderberg culture, who lived in the hamlets located on the plain (Sereď) and in the hill forts like Molpír, near Smolenice, in the Little Carpathians. During Hallstatt times, monumental burial mounds were erected in western Slovakia, with princely equipment consisting of richly decorated vessels, ornaments and decorations. The burial rites consisted From around 500 BCE, the territory of modern-day Slovakia was settled by Celts, who built powerful "oppida" on the sites of modern-day Bratislava and Devín. Biatecs, silver coins with inscriptions in the Latin alphabet, represent the first known use of writing in Slovakia. At the northern regions, From 2 AD, the expanding Roman Empire established and maintained a series of outposts around and just south of the Danube, the largest of which were known as Carnuntum (whose remains are on the main road halfway between Vienna and Bratislava) and Brigetio (present-day Szőny at the Slovak-Hungarian border). Such Roman border settlements were built on the present area of Rusovce, currently a suburb of Bratislava. The military fort was surrounded by a civilian vicus and several farms of the villa rustica type. The name of this In the 2nd and 3rd centuries AD, the Huns began to leave the Central Asian steppes. They crossed the Danube in 377 AD and occupied Pannonia, which they used for 75 years as their base for launching looting-raids into Western Europe. However, Attila's death in 453 brought about the disappearance of The Slavic tribes settled in the territory of present-day Slovakia in the 5th century. Western Slovakia was the centre of Samo's empire in the 7th century. A Slavic state known as the Principality of Nitra arose in the 8th century and its ruler Great Moravia arose around 830 when Mojmír I unified the Slavic tribes settled north of the Danube and extended the Moravian supremacy over them. When Mojmír I endeavoured to secede from the supremacy of the king of East Francia in 846, King Louis the German deposed him and assisted Mojmír's nephew Rastislav (846–870) in acquiring the throne. The new monarch pursued an independent policy: after stopping a Frankish attack in 855, he also sought to weaken the influence of Frankish priests preaching in his realm. Duke Rastislav asked the Byzantine Emperor Michael III to Following the disintegration of the Great Moravian Empire at the turn of the 10th century, the Hungarians annexed the territory comprising modern Slovakia. After their defeat on the Lech River they abandoned their nomadic ways; they settled in the centre of the Carpathian valley, adopted Christianity and began to build a new state—the Hungarian kingdom. From the 11th century, when the territory inhabited by the Slavic-speaking population of Danubian Basin was incorporated into the Kingdom of Hungary, until 1918, when the Austro-Hungarian empire collapsed, the territory of modern Slovakia was an integral part of the Hungarian state. The In late October 1918, the Czech nationalist Tomáš Masaryk declared the "independence" for the territories of Bohemia, Moravia, Silesia, Upper Hungary and Carpathian Ruthenia and proclaimed a common state, Czechoslovakia. The Slovaks were not consulted. In 1919, during the chaos following the break-up of Austria-Hungary, Czechoslovakia was formed with numerous Germans, Slovaks, Hungarians and Ruthenians within the newly set borders. The borders were set by the Treaty of Saint Germain and Treaty of Trianon. In the peace following the World War, Czechoslovakia emerged as a sovereign European state. It provided what were at the time rather extensive rights to its minorities, at least on paper. During the Interwar period, democratic Czechoslovakia was allied with France, and also with Romania and Yugoslavia (Little Entente); however, After the Munich Agreement and its Vienna Award, Nazi Germany threatened to annex part of Slovakia and allow the remaining regions to be partitioned by Hungary or Poland unless independence was declared. Thus, Slovakia seceded from Czecho-Slovakia in March 1939 and allied itself, as demanded by Germany, with Hitler's coalition. Secession had created the first Slovak state in history. The government of the First Slovak Republic, led by Jozef Tiso and Vojtech Tuka, was strongly influenced by Germany and gradually became a puppet regime in many respects. Meanwhile, the Czechoslovak government-in-exile sought to reverse the Munich Agreement and the subsequent German occupation of Czechoslovakia and to return the Republic to its 1937 boundaries. The government operated from London and it was ultimately considered, by those countries that recognised it, the legitimate government for Czechoslovakia throughout the Second World War. As part After World War II, Czechoslovakia was reconstituted and Jozef Tiso was executed in 1947 for collaboration with the Nazis. More than 80,000 Hungarians and 32,000 Germans were forced to leave Slovakia, in a series of population transfers initiated by the Allies at the Potsdam Conference. Out of about 130,000 Carpathian Germans in Slovakia in 1938, by 1947 only some 20,000 remained. As a result of the Yalta Conference, Czechoslovakia came under the influence and later under direct occupation of the Soviet Union and its Warsaw Pact, after a coup in 1948. Eight thousand two hundred and forty The end of Communist rule in Czechoslovakia in 1989, during the peaceful Velvet Revolution, was followed once again by the country's dissolution, this time into two successor states. The word "socialist" was dropped in the names of the two republics, with the Slovak Socialist Republic renamed as Slovak Republic. On 17 July 1992, Slovakia, led by Prime Minister Vladimír Mečiar, declared itself a sovereign state, meaning that its laws took precedence over those of the Slovakia lies between latitudes 47° and 50° N, and longitudes 16° and 23° E. The Slovak landscape is noted primarily for its mountainous nature, with the Carpathian Mountains extending across most of the northern half of the country. Among these mountain ranges are the high peaks of the Fatra-Tatra Area (including Tatra Mountains, Greater Fatra and Lesser Fatra), Slovak Ore Mountains, Slovak Central Mountains or Beskids. The largest lowland is the fertile Danubian Lowland in the southwest, followed by the Eastern Slovak Lowland in the southeast. Forests cover 41% of Slovak land surface. The Tatra Mountains, with 29 peaks higher than AMSL, are the highest mountain range in the Carpathian Mountains. The Tatras occupy an area of, of which the greater part lies in Slovakia. They are divided into several parts. To the north, close to the Polish border, are the High Tatras which are a popular hiking and skiing destination and home to There are 9 national parks Slovakia has hundreds of caves and caverns under its mountains, of which 30 are open to the public. Most of the caves have stalagmites rising from the ground and stalactites hanging Most of the rivers arise in the Slovak mountains. Some only pass through Slovakia, while others make a natural border with surrounding countries (more than ). For example, the Dunajec () to the north, the Danube () to the south or the Morava () to the West. The total length of the rivers on Slovak territory is. The longest river in Slovakia is The Slovak climate lies between the temperate and continental climate zones with relatively warm summers and cold, cloudy and humid winters. Temperature extremes are between although temperatures below are rare. The weather differs from the mountainous north to the plains in the south. The warmest region is Bratislava and Southern Slovakia where the temperatures may reach in summer, occasionally to in Hurbanovo. During night, the temperatures drop to. The daily temperatures in winter average in the range of to. During night it may be freezing, but usually not below. In Slovakia, there are four seasons, each season (spring, summer, autumn and winter) lasts three months. The dry continental air brings in the summer heat and winter frosts. In contrast, oceanic air brings rainfalls and reduces summer temperatures. In the lowlands and valleys, there is often fog, especially in winter. Spring starts with 21 March and is Slovakia signed the Rio Convention on Biological Diversity on 19 May 1993, and became a party to the convention on 25 August 1994. It has subsequently produced a National Biodiversity Strategy and Action Plan, which was received by the convention on 2 November 1998. The biodiversity of Slovakia comprises animals (such as annelids, arthropods, molluscs, nematodes and vertebrates), fungi (Ascomycota, Basidiomycota, Chytridiomycota, Glomeromycota and Zygomycota), micro-organisms (including Mycetozoa), and plants. The geographical position of Slovakia determines the richness of the diversity of fauna and flora. More than 11,000 plant species have been described throughout its territory, nearly 29,000 animal species and over 1,000 species of protozoa. Endemic biodiversity is also common. Slovakia is located in the biome of temperate broadleaf and mixed forests. As the altitude changes, the vegetation associations and animal communities are forming height levels (oak, beech, spruce, scrub pine, alpine meadows and subsoil). Forests cover 44% of the territory of Slovakia. In terms of forest stands, 60% are broadleaf trees and 40% are coniferous trees. The occurrence of animal species is strongly connected to the appropriate types of plant associations and biotopes. Over 4,000 species of fungi have been recorded from Slovakia. Of these, nearly 1,500 are lichen-forming species. Some of these fungi are undoubtedly endemic, but not enough is known to say how Slovakia is a parliamentary democratic republic with a multi-party system. The last parliamentary elections were held on 29 February 2020 and two rounds of presidential elections took place on 16 and 30 March 2019. The Slovak head of state and the formal head of the executive is the president (currently Zuzana Čaputová, the first female president), though with very limited powers. The president is elected by direct, popular vote under the two-round system for a five-year term. Most executive power lies with the head of government, the prime minister (currently Igor Matovič), who is usually the leader of the winning party, but he or she needs to form a majority coalition in the parliament. The prime minister is appointed by the president. The remainder of the cabinet is appointed by the president on the recommendation of the prime minister. Slovakia's highest legislative body is the 150-seat unicameral National Council of the Slovak Republic ("Národná rada Slovenskej republiky"). Delegates are elected for a four-year term on the basis of proportional representation. Slovakia's highest judicial body is the Constitutional Court of Slovakia ("Ústavný súd"), which rules on constitutional issues. The 13 members of this court are appointed by the president from a slate of candidates nominated by parliament. The Constitution of the Slovak Republic was ratified 1 September 1992, and became effective 1 January 1993. It was amended in September 1998 to allow direct election of the president and again in February 2001 due to EU admission requirements. The civil law system is based on Austro-Hungarian codes. The legal code was modified to comply with the obligations of Organization on Security and Cooperation in Europe (OSCE) and to expunge the Marxist–Leninist legal theory. Slovakia accepts the compulsory International Court of Justice jurisdiction with reservations. The Ministry of Foreign and European Affairs () is responsible for maintaining the Slovak Republic's external relations and the management of its international diplomatic missions. The ministry's director is Miroslav Lajčák. The ministry oversees Slovakia's affairs with foreign entities, including bilateral relations with individual nations and its representation in international organizations. Slovakia joined the European Union and NATO in 2004 and the Eurozone in 2009. Slovakia is a member of the United Nations (since 1993) and participates in its specialized agencies. The country was, on 10 October 2005, elected to a two-year term on the UN Security Council from 2006 to 2007. It is also a member of the Schengen Area, the Council of Europe (CoE), the Organization for Security and Cooperation in Europe (OSCE), The Armed Forces of the Slovak Republic number 14,000 uniformed personnel. Slovakia joined NATO in March 2004. The country has been an active participant in US- and NATO-led military actions. There is a joint Czech-Slovak peacekeeping force in Kosovo. From 2006 the army transformed into a fully professional organisation and compulsory military service was abolished. The US State Department in 2017 reported: The government generally respected the human rights of its citizens; however, there were problems in some areas. The most significant human rights issues included incidents of interference with privacy; corruption; widespread discrimination against Roma minority; and security force violence against ethnic and racial minorities government actions and rhetoric did little to discourage. The government investigated reports of abuses by members of the Slovakia is divided into 8 "krajov" (singular—"kraj", usually translated as "region"), each of which is named after its principal city. Regions have enjoyed a certain degree of autonomy since 2002. Their self-governing bodies are referred to as Self-governing (or autonomous) Regions (sg. "samosprávny kraj", pl. "samosprávne kraje") or Upper-Tier Territorial Units (sg. "vyšší územný celok", pl. "vyššie územné celky", abbr. The Slovak economy is a developed, high-income economy, with the GDP per capita equalling 78% of the average of the European Union in 2018. The country has difficulties addressing regional imbalances in wealth and employment. GDP per capita ranges from 188% of EU average in Bratislava to 54% in Eastern Slovakia. Although regional income inequality is high, 90% of citizens own their homes. The OECD in 2017 reported: The Slovak Republic continues exhibiting robust economic performance, with strong growth backed by a sound financial sector, low public debt and high international competitiveness drawing on large inward investment. In 2020, Slovakia was ranked by the International Monetary Fund as the 38th richest country in the world (out of 187 countries), with purchasing power parity per capita GDP of $38,321. The country used to be dubbed the "Tatra Tiger". Slovakia successfully transformed from a centrally planned economy to a market-driven economy. Major privatisations are completed, the banking sector is almost completely in private hands, and foreign investment has risen. The Slovak economy is one of the fastest-growing economies in Europe and 3rd-fastest in eurozone (2017). In 2007, 2008 and 2010 (with GDP growth of 10.5%, 6% and 4%, retrospectively). In 2016, more than 86% of Slovak exports went to European Union, and more than 50% of Slovak imports came from other European Union member states. The ratio of government debt to GDP in Slovakia reached 49.4% by the end of 2018, far below the OECD average. Unemployment, peaking at 19% at the end of 1999, decreased to 4,9% in 2019, lowest recorded rate in Slovak history. Slovakia adopted the Euro currency on 1 January 2009 as the 16th member of the Eurozone. The euro in Slovakia was approved by the European commission on 7 May 2008. The Slovak koruna was revalued on 28 May 2008 to 30.126 for 1 euro, which was also the exchange rate for the euro. The Slovak government encourages foreign investment since it is one of the driving forces of the economy. Slovakia is an attractive country for foreign investors mainly because of its low wages, low tax rates, well educated labour force, favourable geographic location in the heart of Central Europe, strong political stability and good international relations reinforced by the country's accession to the European Union. Some regions, mostly at the east of Slovakia have failed to attract major investment, which has aggravated regional disparities in many economic and social areas. Foreign direct investment inflow grew more than 600% from 2000 and cumulatively reached an all-time high of $17.3 billion in 2006, or around $22,000 per capita by the end of 2008. Slovakia ranks 45th out of 190 economies in terms of ease of doing business, according to the 2020 World Bank Doing Business Report and 57th out of the 63 countries in terms of competitive economy, according to the 2020 World Competitiveness Yearbook Report. The population is over 5.4 million and consists mostly of Slovaks. The average population density is 110 inhabitants per km2. According to the 2011 census, the majority of the inhabitants of Slovakia are Slovaks (80.7%). Hungarians are the largest ethnic minority (8.5%). Other ethnic groups include Roma (2%), Czechs (0.6%), Rusyns (0.6%) and others or unspecified (7.6%). Unofficial estimates on the Roma population are much higher, around 5.6%. In 2018 the median age of the Slovak population was 41 years. The largest waves of Slovak emigration occurred in the 19th and early 20th centuries. In the 1990 US census, 1.8 million people self-identified as having Slovak ancestry. The official language is Slovak, a member of the Slavic language family. Hungarian is widely spoken in the southern regions, and Rusyn is used in some parts of the Northeast. Minority languages hold co-official status in the municipalities in which the size of the minority population meets the legal threshold of 15% in two consecutive censuses. Slovakia is ranked among the top EU countries regarding The Slovak constitution guarantees freedom of religion. In 2011, 62.0% of Slovaks identified themselves as Roman Catholics, 8.9% as Protestants, 3.8% as Greek Catholics, 0.9% as Orthodox, 13.4% identified themselves as atheists or non-religious, and 10.6% did not answer the question about their belief. In 2004, about one third of the church members regularly attended church services. The Slovak Greek Catholic Church is an Eastern rite sui iuris Catholic Church. Before World War II, an estimated 90,000 Jews lived in Slovakia (1.6% The Programme for International Student Assessment, coordinated by the OECD, currently ranks Slovak secondary education the 30th in the world (placing it just below the United States and just above Spain). Education in Slovakia is compulsory from age 6 to 16. The education system consists of elementary school which is divided into two parts, the first grade (age 6–10) and the second grade (age 10–15) which is finished by taking nationwide testing called Monitor, from Slovak language and math. Parents may apply for social assistance for a child that is studying on an elementary school or a high-school. If approved, the state provides basic study necessities for the Folk tradition has rooted strongly in Slovakia and is reflected in literature, music, dance and architecture. The prime example is a Slovak national anthem, ""Nad Tatrou sa blýska"", which is based on a melody from ""Kopala studienku"" folk song. The manifestation of Slovak folklore culture is the ""Východná"" Folklore Festival. It is the oldest and largest nationwide festival with international participation, which takes place in Východná annually. Slovakia is usually represented by many groups but mainly by SĽUK ("Slovenský ľudový umelecký kolektív—Slovak folk art collective"). SĽUK is the largest Slovak folk art group, Visual art in Slovakia is represented through painting, drawing, printmaking, illustration, arts and crafts, sculpture, photography or conceptual art. The Slovak National Gallery founded in 1948, is the biggest network of galleries in Slovakia. Two displays in Bratislava are situated in Esterházy Palace ("Esterházyho palác") and the Water Barracks ("Vodné kasárne"), adjacent one to another. They are located on the For a list of notable Slovak writers and poets, see List of Slovak authors. Christian topics include poem Proglas as a foreword to the four Gospels, partial translations of the Bible into Old Church Slavonic, "Zakon sudnyj ljudem". Medieval literature, in the period from the 11th to the 15th centuries, was written in Latin, Czech and Slovakised Czech. Lyric (prayers, songs and formulas) was still controlled by the Church, while epic was concentrated on legends. Authors Traditional Slovak cuisine is based mainly on pork, poultry (chicken is the most widely eaten, followed by duck, goose, and turkey), flour, potatoes, cabbage, and milk products. It is relatively closely related to Hungarian, Czech, Polish and Austrian cuisine. On the east it is also influenced by Ukrainian, including Lemko and Rusyn. In comparison with other European countries, "game meat" is more accessible in Slovakia due to vast resources of forest and because hunting is relatively popular. Boar, rabbit, and venison are generally available throughout the year. Lamb and goat are eaten but are not widely popular. The traditional Slovak meals are Sporting activities are practised widely in Slovakia, many of them on a professional level. Ice hockey and football have traditionally been regarded as the most popular sports in Slovakia, though tennis, handball, basketball, volleyball, whitewater slalom, cycling and athletics are also popular. One of the most popular team sports in Slovakia is ice hockey. Slovakia became a member of the IIHF on 2 February 1993 and since then has won 4 medals in Ice Hockey World Championships, consisting of 1 gold, 2 silver and 1 bronze. The most recent success was a silver medal at the 2012 IIHF World Championship in Helsinki. The Slovak national hockey team made five appearances in the Olympic games, finishing 4th in the 2010 Winter Olympics in Vancouver. The country has 8,280 registered players and is ranked 7th in the IIHF World Ranking at present. Before 2012, the Slovak	Slovakia (; ), officially the Slovak Republic (, ), is a landlocked country in Central Europe. It is bordered by Poland to the north, Ukraine to the east, Hungary to the south, Austria to the southwest, and the Czech Republic to the northwest. Slovakia's territory spans about and is mostly mountainous. The population is over 5.4 million and consists mostly of ethnic Slovaks. The capital and largest city is Bratislava, and the second-largest city is Košice. 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summarize: In the mid-19th century, a 16th-century Aztec statue of Xochipilli was unearthed on the side of the volcano Popocatépetl near Tlalmanalco. The statue is of a single figure seated upon a temple-like base. Both the statue and the base upon which it sits are covered in carvings of sacred and psychoactive organisms including mushrooms ("Psilocybe aztecorum"), tobacco ("Nicotiana tabacum"), "Ololiúqui" ("Turbina corymbosa"), "sinicuichi" ("Heimia salicifolia"), possibly "cacahuaxochitl" ("Quararibea funebris"), and one unidentified flower. "The texts always use the flower in an entirely spiritual sense, and the aim of the religious colleges was to cause the flower of the body to bloom: This flower can be no other than the soul. The association of the flower with the sun is also evident. One of the hieroglyphs for the sun is a four-petalled flower, and the feasts of the ninth month, dedicated to Huitzilopochtliupo, were entirely given over to flower offerings." - Paul Pettennude, Ph.D. The figure himself sits on the base, head tilted up, eyes open, jaw tensed, with his mouth half open and his arms opened to the heavens. The statue is currently housed in the Aztec hall of the Museo Nacional de Antropología in Mexico City. In the popular reality television show, "Survivor", a statue of Xochipilli was used as the Immunity Idol for the. It has been suggested by Wasson, Schultes, and Hofmann that the statue of Xochipilli represents a figure in the throes of entheogenic ecstasy. The position and expression of the body, in combination with the very clear representations of hallucinogenic plants which are known to have been used in sacred contexts by the Aztec support this interpretation. Wasson says that in the statue's depiction Xochipilli "is absorbed by "temicxoch", 'dream flowers', as the Nahua say describing the awesome experience that follows the ingestion of an entheogen. I can think of nothing like it in the long and rich history of European art: Xochipilli absorbed in "temicxoch"".	' is the god of art, games, dance, flowers, and song in Aztec mythology. His name contains the Nahuatl words ("flower") and (either "prince" or "child") and hence means "flower prince". 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summarize: In a speech in 1929, French Foreign Minister Aristide Briand floated the idea of an organisation which would gather European nations together in a "federal union" to resolve common problems. But it was Britain's wartime leader Sir Winston Churchill who first publicly suggested the creation of "a Council of Europe" in a BBC radio broadcast on 21 March 1943, while the second world war was still raging. In his own words, he tried to "peer through the mists of the future to the end of the war," once victory had been achieved, and think about how to re-build and maintain peace on a shattered continent. Given that Europe had been at the origin of two world wars, the creation of such a body would be, he suggested, "a stupendous business". He returned to the idea during a well-known speech at the University of Zurich on 19 September 1946, throwing the full weight of his considerable post-war prestige behind it. The future structure of the Council of Europe was discussed at a specific congress of several hundred leading politicians, government representatives and civil society in The Hague, Netherlands, in 1948. There were two schools of thought competing: some favoured a classical international organisation with representatives of governments, while others preferred a political forum with parliamentarians. Both approaches were finally combined through the creation of a Committee of Ministers (in which governments were represented) and a Consultative Assembly (in which parliaments were represented), the two main bodies mentioned in the Statute of the Council of Europe. This dual intergovernmental and inter-parliamentary structure was later copied for the European Communities, North Atlantic Treaty Organization and the Organization for Security and Co-operation in Europe. The Council of Europe was founded on 5 May 1949 by the Treaty of London. The Statute was signed in London on that day by ten states: Belgium, Denmark, France, Ireland, Italy, Luxembourg, the Netherlands, Norway, Sweden and the United Kingdom, though Turkey and Greece joined three months later. On 10 August 1949, 100 members of the Council's Consultative Assembly, parliamentarians drawn from the twelve member nations, met in Strasbourg for its first plenary session, held over 18 sittings and lasting nearly a month. They debated how to reconcile and reconstruct a continent still reeling from war, yet already facing a new East-West divide, launched the concept of a trans-national court to protect the basic human rights of every European citizen, and took the first steps towards what would in time become the European Union. In August 1949, Paul-Henri Spaak of Belgium was elected as the first president of the Assembly, steering its early work. However, in December 1951, after nearly three years in the role, Spaak resigned in disappointment after the Assembly rejected proposals for a "European political authority". Convinced the Council of Europe was never going to be strong enough to achieve his long-term goal of European unification, he soon tried again in a different format, becoming one of the founders of the European Union. In 2018 an archive of all speeches made to the Parliamentary Assembly of the Council of Europe by heads of state or government since the Council of Europe's creation in 1949 appeared online, the fruit of a two-year project entitled "Voices of Europe". At the time of its launch, the archive comprised 263 speeches delivered over a 70-year period by some 216 Presidents, Prime Ministers, monarchs and religious leaders from 45 countries - though it continues to expand, as new speeches are added every few months. Some very early speeches by individuals considered to be "founding figures" of the European institutions, even if they were not heads of state or government at the time, are also included (such as Sir Winston Churchill or Robert Schuman). Addresses by eight monarchs appear in the list (such as King Juan Carlos I of Spain, King Albert II of Belgium and Grand Duke Henri of Luxembourg) as well as the speeches given by religious figures (such as Pope John Paul II, and Pope Francis) and several leaders from countries in the Middle East and North Africa (such as Shimon Peres, Yasser Arafat, Hosni Mubarak, Léopold Sédar Senghor or King Hussein of Jordan). The full text of the speeches is given in both English and French, regardless of the original language used. The archive is searchable by country, by name, and chronologically. Article 1(a) of the Statute states that "The aim of the Council of Europe is to achieve a greater unity between its members for the purpose of safeguarding and realising the ideals and principles which are their common heritage and facilitating their economic and social progress." Membership is open to all European states who seek harmony, cooperation, good governance and human rights, accepting the principle of the rule of law and are able and willing to guarantee democracy, fundamental human rights and freedoms. Whereas the member states of the European Union transfer part of their national legislative and executive powers to the European Commission and the European Parliament, Council of Europe member states maintain their sovereignty but commit themselves through conventions/treaties (international law) and co-operate on the basis of common values and common political decisions. Those conventions and decisions are developed by the member states working together at the Council of Europe. Both organisations function as concentric circles around the common foundations for European co-operation and harmony, with the Council of Europe being the geographically wider circle. The European Union could be seen as the smaller circle with a much higher level of integration through the transfer of powers from the national to the EU level. "The Council of Europe and the European Union: different roles, shared values." Council of Europe conventions/treaties are also open for signature to non-member states, thus facilitating equal co-operation with countries outside Europe. The Council of Europe's most famous achievement is the European Convention on Human Rights, which was adopted in 1950 following a report by the Council of Europe's Parliamentary Assembly, and followed on from the United Nations 'Universal Declaration of Human Rights' (UDHR). The Convention created the European Court of Human Rights in Strasbourg. The Court supervises compliance with the European Convention on Human Rights and thus functions as the highest European court. It is to this court that Europeans can bring cases if they believe that a member country has violated their fundamental rights and freedoms. The various activities and achievements of the Council of Europe can be found in detail on its official website. The Council of Europe works in the following areas: The institutions of the Council of Europe are: The CoE system also includes a number of semi-autonomous structures known as "Partial Agreements", some of which are also open to non-member states: The seat of the Council of Europe is in Strasbourg, France. First meetings were held in Strasbourg's University Palace in 1949, but the Council of Europe soon moved into its own buildings. The Council of Europe's eight main buildings are situated in the "Quartier européen", an area in the northeast of Strasbourg spread over the three districts of Le Wacken, La Robertsau and Quartier de l'Orangerie, where are also located the four buildings of the seat of the European Parliament in Strasbourg, the Arte headquarters and the seat of the International Institute of Human Rights. Building in the area started in 1949 with the predecessor of the Palais de l'Europe, the House of Europe (demolished in 1977), and came to a provisional end in 2007 with the opening of the New General Office Building, later named "Agora", in 2008. The Palais de l'Europe (Palace of Europe) and the Art Nouveau Villa Schutzenberger (seat of the European Audiovisual Observatory) are in the Orangerie district, and the European Court of Human Rights, the European Directorate for the Quality of Medicines and the Agora Building are in the Robertsau district. The Agora building has been voted "best international business center real estate project of 2007" on 13 March 2008, at the MIPIM 2008. The European Youth Centre is located in the Wacken district. Besides its headquarters in Strasbourg, the Council of Europe is also present in other cities and countries. The Council of Europe Development Bank has its seat in Paris, the North-South Centre of the Council of Europe is established in Lisbon, Portugal, and the Centre for Modern Languages is in Graz, Austria. There are European Youth Centres in Budapest, Hungary, and in Strasbourg. The European Wergeland Centre, a new Resource Centre on education for intercultural dialogue, human rights and democratic citizenship, operated in cooperation with the Norwegian Government, opened in Oslo, Norway, in February 2009. The Council of Europe has offices in Albania, Armenia, Azerbaijan, Bosnia and Herzegovina, Georgia, Moldova, Montenegro, Serbia, and Ukraine; information offices in Albania, Armenia, Azerbaijan, Bulgaria, Czech Republic, Estonia, Georgia, Hungary, Latvia, Lithuania, Moldova, North Macedonia, Poland, Romania, Russian Federation, Slovakia, Slovenia, and Ukraine; and a projects office in Turkey. All these offices are establishments of the Council of Europe and they share its juridical personality with privileges and immunities. The Council of Europe was founded on 5 May 1949 by Belgium, Denmark, France, Ireland, Italy, Luxembourg, Netherlands, Norway, Sweden and the United Kingdom. Greece joined three months later, and Iceland, Turkey and West Germany the next year. It now has 47 member states, with Montenegro being the latest to join. Article 4 of the Council of Europe Statute specifies that membership is open to any "European" State. This has been interpreted liberally from the beginning, when Turkey was admitted, to include transcontinental states (such as Georgia and Azerbaijan) and states that are geographically Asian but socio-politically European (such as Armenia and Cyprus). Nearly all European states have acceded to the Council of Europe, with the exceptions of Belarus (human rights concerns including active use of the death penalty), Kazakhstan (human rights concerns), and the Vatican City (a theocracy), as well as some of the territories with limited recognition. Besides the status as a full member, the Council of Europe has established other instruments for cooperation and participation of non-member states: observer, applicant, special guest, and partner for democracy. The Council of Europe works mainly through conventions. By drafting conventions or international treaties, common legal standards are set for its member states. However, several conventions have also been opened for signature to non-member states. Important examples are the Convention on Cybercrime (signed for example, by Canada, Japan, South Africa and the United States), the Lisbon Recognition Convention on the recognition of study periods and degrees (signed for example, by Australia, Belarus, Canada, the Holy See, Israel, Kazakhstan, Kyrgyzstan, New Zealand and the United States), the Anti-doping Convention (signed, for example, by Australia, Belarus, Canada and Tunisia) and the Convention on the Conservation of European Wildlife and Natural Habitats (signed for example, by Burkina Faso, Morocco, Tunisia and Senegal as well as the European Community). Non-member states also participate in several partial agreements, such as the Venice Commission, the Group of States Against Corruption (GRECO), the European Pharmacopoeia Commission and the North-South Centre. Invitations to sign and ratify relevant conventions of the Council of Europe on a case-by-case basis are sent to three groups of non-member entities: The Council of Europe is not to be confused with the Council of the European Union (the "Council of Ministers") or the European Council. These belong to the European Union, which is separate from the Council of Europe, although they have shared the same European flag and anthem since the 1980s since they both work for European integration. Nor is the Council of Europe to be confused with the European Union itself. The Council of Europe is an entirely separate body from the European Union. It is not controlled by it. Cooperation between the European Union and the Council of Europe has recently been reinforced, notably on culture and education as well as on the international enforcement of justice and Human Rights. The European Union is expected to accede to the European Convention on Human Rights (the Convention). There are also concerns about consistency in case law – the European Court of Justice (the EU's court in Luxembourg) is treating the Convention as part of the legal system of all EU member states in order to prevent conflict between its judgements and those of the European Court of Human Rights (the court in Strasbourg interpreting the Convention). Protocol No. 14 of the Convention is designed to allow the EU to accede to it and the EU Treaty of Lisbon contains a protocol binding the EU to join. The EU would thus be subject to its human rights law and external monitoring as its member states currently are. The Council of Europe Schools of political studies were established to train future generations of political, economic, social and cultural leaders in countries in transition. With the participation of national and international experts, they run annual series of seminars and conferences on topics such as European integration, democracy, human rights, the rule of law and globalisation. The first School of Political Studies was created in Moscow in 1992. Since then, 20 other schools have been set up along the same lines and now form an Association; a genuine network now covering the whole of Eastern and South-Eastern Europe and the Caucasus, as well as some countries in the Southern Mediterranean region. The Council of Europe Schools of political studies is part of the Education Department which is part of the Directorate of Democratic Participation within the Directorate General of Democracy (“DGII”) of the Council of Europe. The beginning of co-operation between the CoE and the UN started with the agreement signed by the Secretariats of these institutions on 15 December 1951. On 17 October 1989, the General Assembly of the United Nations approved a resolution on granting observer status to the Council of Europe which was proposed by several member states of the CoE. Currently Council of Europe holds observer status with the United Nations and is regularly represented in the UN General Assembly. It has organised the regional UN conferences against racism and on women and co-operates with the United Nations at many levels, in particular in the areas of human rights, minorities, migration and counter-terrorism. In November 2016, the UN General Assembly adopted by consensus Resolution (A/Res/71/17) on Cooperation between the United Nations and the Council of Europe whereby it acknowledged the contribution of Council of Europe to the protection and strengthening of human rights and fundamental freedoms, democracy and the rule of law, welcomed the ongoing co-operation in a variety of fields. Non-governmental organisations (NGOs) can participate in the INGOs Conference of the Council of Europe and become observers to inter-governmental committees of experts. The Council of Europe drafted the European Convention on the Recognition of the Legal Personality of International Non-Governmental Organisations in 1986, which sets the legal basis for the existence and work of NGOs in Europe. Article 11 of the European Convention on Human Rights protects the right to freedom of association, which is also a fundamental norm for NGOs. The rules for Consultative Status for INGOs appended to the resolution (93)38 "On relation between the Council of Europe and non-governmental organisations", adopted by the Committee of Ministers on 18 October 1993 at the 500th meeting of the Ministers' Deputies. On 19 November 2003 the Committee of Ministers changed the consultative status into a participatory status, "considering that it is indispensable that the rules governing the relations between the Council of Europe and NGOs evolve to reflect the active participation of international non-governmental organisations (INGOs) in the Organisation's policy and work programme". On 30 May 2018, the Council of Europe signed a Memorandum of understanding with the European football confederation UEFA. The Council of Europe also signed an agreement with FIFA in which the two agreed to strengthen future cooperation in areas of common interests. The deal which included cooperation between member states in the sport of football and safety and security at football matches, was finalized in October 2018. The General Agreement on Privileges and Immunities of the Council of Europe grants the organisation certain privileges and immunities. The working conditions of staff are governed by the Council's staff regulations, which are public. Salaries and emoluments paid by the Council of Europe to its officials are tax-exempt on the basis of Article 18 of the General Agreement on Privileges and Immunities of the Council of Europe. The Council of Europe created, and has since 1955 used as its official symbol, the European Flag with 12 golden stars arranged in a circle on a blue background. Its musical anthem since 1972, the "European Anthem", is based on the "Ode to Joy" theme from Ludwig van Beethoven's ninth symphony. On 5 May 1964, the 15th anniversary of its founding, the Council of Europe established 5 May as Europe Day. The wide private and public use of the European Flag is encouraged to symbolise a European dimension. To avoid confusion with the European Union which subsequently adopted the same flag in the 1980s, as well as other European institutions, the Council of Europe often uses a modified version with a lower-case "e" surrounding the stars which is referred to as the "Council of Europe Logo". The Council of Europe has been accused of institutional corruption and of not having any meaningful purpose, being superfluous in its aims to other pan-European bodies, including the European Union and the Organization for Security and Cooperation in Europe (OSCE). In 2013 "The Economist" agreed, saying that the "Council of Europe's credibility is on the line". Both Human Rights Watch and the European Stability Initiative have called on the Council of Europe to undertake concrete actions to show that it is willing and able to return to its "original mission to protect and ensure human rights". Issues have been raised regarding Azerbaijan's relationship to the Council of Europe, including allegations that Azerbaijan has, over a sustained period, provided bribes to Council members to vote down criticism of the authoritarian rule of the Aliyev regime and support motions advantageous to Azerbaijan. Azerbaijan joined the Council of Europe in 2001. Since September 2014 Human Rights Watch said that Azerbaijan's "systematic crackdown on human rights defenders and other perceived government critics shows sheer contempt for its commitments to the Council of Europe". In 2017 Council member and Italian politician Luca Volontè was accused by Italian prosecutors of receiving over 2.3 million euros in bribes in exchange for working for Azerbaijan in the parliamentary assembly, and that in 2013 he played a key role in orchestrating the defeat of a highly critical report on the abuse of political prisoners in Azerbaijan. The money was paid to Volontè in monthly instalments of 100,000 euros, starting in 2013, via four anonymous offshore companies. The payments stopped in 2014 when Volontè's bank reported them as suspicious transactions to the Milan prosecutor's office. Arif Mammadov, former head of the Azerbaijan representation at the Council of Europe, has stated that Azerbaijan's delegation at the Council had 25 million dollars available to "bribe members of the delegations and PACE generally". From 2014, Russia's voting rights were temporarily suspended by the Council due to the annexation of Crimea by the Russian Federation from Ukraine. In response, Russia withheld its annual membership dues in the amount of 33 million euros, placing the institution under financial strain. Russia claimed that its suspension by the Council was unfair, and demanded the restoration of voting rights. European Council secretary-general Thorbjørn Jagland organized a special committee to find a compromise with Russia in early 2018, a move that was criticized as giving in to alleged Russian pressure by Council members and academic observers, especially if voting sanctions were lifted. In May 2019, Russia's voting rights were restored after members of the human rights watchdog reached agreement to resolve dispute and the overwhelming majority of the Council voted in favour of the restoration.	The Council of Europe (CoE) ( (CdE), ) is an international organisation whose stated aim is to uphold human rights, democracy and the rule of law in Europe. 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summarize: The word "convection" may have slightly different but related usages in different scientific or engineering contexts or applications. The broader sense is in fluid mechanics, where "convection" refers to the motion of fluid regardless of cause. However, in thermodynamics "convection" often refers specifically to heat transfer by convection. Convection occurs on a large scale in atmospheres, oceans, planetary mantles, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of our sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a hurricane. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of black holes, at speeds which may closely approach that of light. Convective heat transfer is a mechanism of heat transfer occurring because of bulk motion (observable movement) of fluids. Heat is the entity of interest being advected (carried), and diffused (dispersed). This can be contrasted with conductive heat transfer, which is the transfer of energy by vibrations at a molecular level through a solid or fluid, and radiative heat transfer, the transfer of energy through electromagnetic waves. Heat is transferred by convection in numerous examples of naturally occurring fluid flow, such as wind, oceanic currents, and movements within the Earth's mantle. Convection is also used in engineering practices of homes, industrial processes, cooling of equipment, etc. The rate of convective heat transfer may be improved by the use of a heat sink, often in conjunction with a fan. For instance, a typical computer CPU will have a purpose-made fan to ensure its operating temperature is kept within tolerable limits. A convection cell, also known as a Bénard cell is a characteristic fluid flow pattern in many convection systems. A rising body of fluid typically loses heat because it encounters a colder surface. In liquid, this occurs because it exchanges heat with colder liquid through direct exchange. In the example of the Earth's atmosphere, this occurs because it radiates heat. Because of this heat loss the fluid becomes denser than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance, its downward force overcomes the rising force beneath it, and the fluid begins to descend. As it descends, it warms again and the cycle repeats itself. Atmospheric circulation is the large-scale movement of air, and is a means by which thermal energy is distributed on the surface of the Earth, together with the much slower (lagged) ocean circulation system. The large-scale structure of the atmospheric circulation varies from year to year, but the basic climatological structure remains fairly constant. Latitudinal circulation occurs because incident solar radiation per unit area is highest at the heat equator, and decreases as the latitude increases, reaching minima at the poles. It consists of two primary convection cells, the Hadley cell and the polar vortex, with the Hadley cell experiencing stronger convection due to the release of latent heat energy by condensation of water vapor at higher altitudes during cloud formation. Longitudinal circulation, on the other hand, comes about because the ocean has a higher specific heat capacity than land (and also thermal conductivity, allowing the heat to penetrate further beneath the surface ) and thereby absorbs and releases more heat, but the temperature changes less than land. This brings the sea breeze, air cooled by the water, ashore in the day, and carries the land breeze, air cooled by contact with the ground, out to sea during the night. Longitudinal circulation consists of two cells, the Walker circulation and El Niño / Southern Oscillation. Some more localized phenomena than global atmospheric movement are also due to convection, including wind and some of the hydrologic cycle. For example, a foehn wind is a down-slope wind which occurs on the downwind side of a mountain range. It results from the adiabatic warming of air which has dropped most of its moisture on windward slopes. Because of the different adiabatic lapse rates of moist and dry air, the air on the leeward slopes becomes warmer than at the same height on the windward slopes. A thermal column (or thermal) is a vertical section of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation. The Sun warms the ground, which in turn warms the air directly above it. The warmer air expands, becoming less dense than the surrounding air mass, and creating a thermal low. The mass of lighter air rises, and as it does, it cools by expansion at lower air pressures. It stops rising when it has cooled to the same temperature as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward moving exterior is caused by colder air being displaced at the top of the thermal. Another convection-driven weather effect is the sea breeze. Warm air has a lower density than cool air, so warm air rises within cooler air, similar to hot air balloons. Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the water vapor in the rising packet of air to condense. When the moisture condenses, it releases energy known as latent heat of condensation which allows the rising packet of air to cool less than its surrounding air, continuing the cloud's ascension. If enough instability is present in the atmosphere, this process will continue long enough for cumulonimbus clouds to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat). All thunderstorms, regardless of type, go through three stages: the developing stage, the mature stage, and the dissipation stage. The average thunderstorm has a diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through. Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the poles, while cold polar water heads towards the Equator. The surface currents are initially dictated by surface wind conditions. The trade winds blow westward in the tropics, and the westerlies blow eastward at mid-latitudes. This wind pattern applies a stress to the subtropical ocean surface with negative curl across the Northern Hemisphere, and the reverse across the Southern Hemisphere. The resulting Sverdrup transport is equatorward. Because of conservation of potential vorticity caused by the poleward-moving winds on the subtropical ridge's western periphery and the increased relative vorticity of poleward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the cold western boundary current which originates from high latitudes. The overall process, known as western intensification, causes currents on the western boundary of an ocean basin to be stronger than those on the eastern boundary. As it travels poleward, warm water transported by strong warm water current undergoes evaporative cooling. The cooling is wind driven: wind moving over water cools the water and also causes evaporation, leaving a saltier brine. In this process, the water becomes saltier and denser. and decreases in temperature. Once sea ice forms, salts are left out of the ice, a process known as brine exclusion. These two processes produce water that is denser and colder. The water across the northern Atlantic ocean becomes so dense that it begins to sink down through less salty and less dense water. (The convective action is not unlike that of a lava lamp.) This downdraft of heavy, cold and dense water becomes a part of the North Atlantic Deep Water, a southgoing stream. Mantle convection is the slow creeping motion of Earth's rocky mantle caused by convection currents carrying heat from the interior of the earth to the surface. It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface. The Earth's surface is divided into a number of tectonic plates that are continuously being created and consumed at their opposite plate boundaries. Creation (accretion) occurs as mantle is added to the growing edges of a plate. This hot added material cools down by conduction and convection of heat. At the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of subduction at an ocean trench. This subducted material sinks to some depth in the Earth's interior where it is prohibited from sinking further. The subducted oceanic crust triggers volcanism. The Stack effect or chimney effect is the movement of air into and out of buildings, chimneys, flue gas stacks, or other containers due to buoyancy. Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The greater the thermal difference and the height of the structure, the greater the buoyancy force, and thus the stack effect. The stack effect helps drive natural ventilation and infiltration. Some cooling towers operate on this principle; similarly the solar updraft tower is a proposed device to generate electricity based on the stack effect. The convection zone of a star is the range of radii in which energy is transported primarily by convection. Granules on the photosphere of the Sun are the visible tops of convection cells in the photosphere, caused by convection of plasma in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours. A convection oven is an oven that has fans to circulate air around food, using the convection mechanism to cook food faster than a conventional oven. Convection ovens distribute heat evenly around the food, removing the blanket of cooler air that surrounds food when it is first placed in an oven and allowing food to cook more evenly in less time and at a lower temperature than in a conventional oven. A convection oven has a fan with a heating element around it. A small fan circulates the air in the cooking chamber. Convection may happen in fluids at all scales larger than a few atoms. There are a variety of circumstances in which the forces required for natural and forced convection arise, leading to different types of convection, described below. In broad terms, convection arises because of body forces acting within the fluid, such as gravity. The causes of convection are generally described as one of either "natural" ("free") or "forced", although other mechanisms also exist (discussed below). However, the distinction between natural and forced convection is particularly important for convective heat transfer. Natural convection, or free convection, occurs due to temperature differences which affect the density, and thus relative buoyancy, of the fluid. Heavier (denser) components will fall, while lighter (less dense) components rise, leading to bulk fluid movement. Natural convection can only occur, therefore, in a gravitational field. A common example of natural convection is the rise of smoke from a fire. It can be seen in a pot of boiling water in which the hot and less-dense water on the bottom layer moves upwards in plumes, and the cool and more dense water near the top of the pot likewise sinks. Natural convection will be more likely and more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection or a larger distance through the convecting medium. Natural convection will be less likely and less rapid with more rapid diffusion (thereby diffusing away the thermal gradient that is causing the convection) or a more viscous (sticky) fluid. The onset of natural convection can be determined by the Rayleigh number (Ra). Note that differences in buoyancy within a fluid can arise for reasons other than temperature variations, in which case the fluid motion is called gravitational convection (see below). However, all types of buoyant convection, including natural convection, do not occur in microgravity environments. All require the presence of an environment which experiences g-force (proper acceleration). In forced convection, also called heat advection, fluid movement results from external surface forces such as a fan or pump. Forced convection is typically used to increase the rate of heat exchange. Many types of mixing also utilize forced convection to distribute one substance within another. Forced convection also occurs as a by-product to other processes, such as the action of a propeller in a fluid or aerodynamic heating. Fluid radiator systems, and also heating and cooling of parts of the body by blood circulation, are other familiar examples of forced convection. Forced convection may happen by natural means, such as when the heat of a fire causes expansion of air and bulk air flow by this means. In microgravity, such flow (which happens in all directions) along with diffusion is the only means by which fires are able to draw in fresh oxygen to maintain themselves. The shock wave that transfers heat and mass out of explosions is also a type of forced convection. Although forced convection from thermal gas expansion in zero-g does not fuel a fire as well as natural convection in a gravity field, some types of artificial forced convection are far more efficient than free convection, as they are not limited by natural mechanisms. For instance, a convection oven works by forced convection, as a fan which rapidly circulates hot air forces heat into food faster than would naturally happen due to simple heating without the fan. Gravitational convection is a type of natural convection induced by buoyancy variations resulting from material properties other than temperature. Typically this is caused by a variable composition of the fluid. If the varying property is a concentration gradient, it is known as solutal convection. For example, gravitational convection can be seen in the diffusion of a source of dry salt downward into wet soil due to the buoyancy of fresh water in saline. Variable salinity in water and variable water content in air masses are frequent causes of convection in the oceans and atmosphere which do not involve heat, or else involve additional compositional density factors other than the density changes from thermal expansion (see "thermohaline circulation"). Similarly, variable composition within the Earth's interior which has not yet achieved maximal stability and minimal energy (in other words, with densest parts deepest) continues to cause a fraction of the convection of fluid rock and molten metal within the Earth's interior (see below). Gravitational convection, like natural thermal convection, also requires a g-force environment in order to occur. Vibration-induced convection occurs in powders and granulated materials in containers subject to vibration where an axis of vibration is parallel to the force of gravity. When the container accelerates upward, the bottom of the container pushes the entire contents upward. In contrast, when the container accelerates downward, the sides of the container push the adjacent material downward by friction, but the material more remote from the sides is less affected. The net result is a slow circulation of particles downward at the sides, and upward in the middle. If the container contains particles of different sizes, the downward-moving region at the sides is often narrower than the largest particles. Thus, larger particles tend to become sorted to the top of such a mixture. This is one possible explanation of the Brazil nut effect. Ice convection on Pluto is believed to occur in a soft mixture of nitrogen ice and carbon monoxide ice. It has also been proposed for Europa, and other bodies in the outer solar system. Thermomagnetic convection can occur when an external magnetic field is imposed on a ferrofluid with varying magnetic susceptibility. In the presence of a temperature gradient this results in a nonuniform magnetic body force, which leads to fluid movement. A ferrofluid is a liquid which becomes strongly magnetized in the presence of a magnetic field. This form of heat transfer can be useful for cases where conventional convection fails to provide adequate heat transfer, e.g., in miniature microscale devices or under reduced gravity conditions. Capillary action is a phenomenon where liquid spontaneously rises in a narrow space such as a thin tube, or in porous materials. This effect can cause liquids to flow against the force of gravity. It occurs because of inter-molecular attractive forces between the liquid and solid surrounding surfaces; If the diameter of the tube is sufficiently small, then the combination of surface tension and forces of adhesion between the liquid and container act to lift the liquid. The Marangoni effect is the convection of fluid along an interface between dissimilar substances because of variations in surface tension. Surface tension can vary because of inhomogeneous composition of the substances or the temperature-dependence of surface tension forces. In the latter case the effect is known as thermo-capillary convection. A well-known phenomenon exhibiting this type of convection is the "tears of wine". The Weissenberg effect is a phenomenon that occurs when a spinning rod is placed into a solution of liquid polymer. Entanglements cause the polymer chains to be drawn towards the rod instead of being thrown outward as would happen with an ordinary fluid (i.e., water). In a zero-gravity environment, there can be no buoyancy forces, and thus no natural (free) convection possible, so flames in many circumstances without gravity smother in their own waste gases. However, flames may be maintained with any type of forced convection (breeze); or (in high oxygen environments in "still" gas environments) entirely from the minimal forced convection that occurs as heat-induced "expansion" (not buoyancy) of gases allows for ventilation of the flame, as waste gases move outward and cool, and fresh high-oxygen gas moves in to take up the low pressure zones created when flame-exhaust water condenses. Mathematically, convection can be described by the convection–diffusion equation, also known as the generic scalar transport equation. In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system. The relative magnitudes of the Grashof number and the square of the Reynolds number determine which form of convection dominates. If formula_1, forced convection may be neglected, whereas if formula_2, natural convection may be neglected. If the ratio, known as the Richardson number, is approximately one, then both forced and natural convection need to be taken into account.	Convection is the heat transfer due to the bulk movement of molecules within fluids such as gases and liquids, including molten rock (rheid). 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summarize: On a microscopic scale, conduction occurs within a body considered as being stationary; this means that the kinetic and potential energies of the bulk motion of the body are separately accounted for. Internal energy diffuses as rapidly moving or vibrating atoms and molecules interact with neighbouring particles, transferring some of their microscopic kinetic and potential energies, these quantities being defined relative to the bulk of the body considered as being stationary. Heat is transferred by conduction when adjacent atoms or molecules collide, or as several electrons move backwards and forwards from atom to atom in a disorganized way so as not to form a macroscopic electric current, or as photons collide and scatter. Conduction is the most significant means of heat transfer within a solid or between solid objects in thermal contact. Conduction is greater in solids because the network of relatively close fixed spatial relationships between atoms helps to transfer energy between them by vibration. Thermal contact conductance is the study of heat conduction between solid bodies in contact. A temperature drop is often observed at the interface between the two surfaces in contact. This phenomenon is said to be a result of a thermal contact resistance existing between the contacting surfaces. Interfacial thermal resistance is a measure of an interface's resistance to thermal flow. This thermal resistance differs from contact resistance, as it exists even at atomically perfect interfaces. Understanding the thermal resistance at the interface between two materials is of primary significance in the study of its thermal properties. Interfaces often contribute significantly to the observed properties of the materials. The inter-molecular transfer of energy could be primarily by elastic impact, as in fluids, or by free electron diffusion, as in metals, or phonon vibration, as in insulators. In insulators, the heat flux is carried almost entirely by phonon vibrations. Metals (e.g., copper, platinum, gold, etc.) are usually good conductors of thermal energy. This is due to the way that metals bond chemically: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons that transfer thermal energy rapidly through the metal. The "electron fluid" of a conductive metallic solid conducts most of the heat flux through the solid. Phonon flux is still present, but carries less of the energy. Electrons also conduct electric current through conductive solids, and the thermal and electrical conductivities of most metals have about the same ratio. A good electrical conductor, such as copper, also conducts heat well. Thermoelectricity is caused by the interaction of heat flux and electric current. Heat conduction within a solid is directly analogous to diffusion of particles within a fluid, in the situation where there are no fluid currents. In gases, heat transfer occurs through collisions of gas molecules with one another. In the absence of convection, which relates to a moving fluid or gas phase, thermal conduction through a gas phase is highly dependent on the composition and pressure of this phase, and in particular the mean free path of gas molecules relative to the size of the gas gap, as given by the Knudsen number formula_1. To quantify the ease with which a particular medium conducts, engineers employ the thermal conductivity, also known as the conductivity constant or conduction coefficient, "k". In thermal conductivity, "k" is defined as "the quantity of heat, "Q", transmitted in time ("t") through a thickness ("L"), in a direction normal to a surface of area ("A"), due to a temperature difference (Δ"T") [...]". Thermal conductivity is a material "property" that is primarily dependent on the medium's phase, temperature, density, and molecular bonding. Thermal effusivity is a quantity derived from conductivity, which is a measure of its ability to exchange thermal energy with its surroundings. Steady state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant, so that (after an equilibration time), the spatial distribution of temperatures (temperature field) in the conducting object does not change any further. Thus, all partial derivatives of temperature "with respect to space" may either be zero or have nonzero values, but all derivatives of temperature at any point "with respect to time" are uniformly zero. In steady state conduction, the amount of heat entering any region of an object is equal to amount of heat coming out (if this were not so, the temperature would be rising or falling, as thermal energy was tapped or trapped in a region). For example, a bar may be cold at one end and hot at the other, but after a state of steady state conduction is reached, the spatial gradient of temperatures along the bar does not change any further, as time proceeds. Instead, the temperature remains constant at any given cross-section of the rod normal to the direction of heat transfer, and this temperature varies linearly in space in the case where there is no heat generation in the rod. In steady state conduction, all the laws of direct current electrical conduction can be applied to "heat currents". In such cases, it is possible to take "thermal resistances" as the analog to electrical resistances. In such cases, temperature plays the role of voltage, and heat transferred per unit time (heat power) is the analog of electric current. Steady state systems can be modelled by networks of such thermal resistances in series and in parallel, in exact analogy to electrical networks of resistors. See purely resistive thermal circuits for an example of such a network. During any period in which temperatures changes "in time" at any place within an object, the mode of thermal energy flow is termed "transient conduction." Another term is "non steady-state" conduction, referring to time-dependence of temperature fields in an object. Non-steady-state situations appear after an imposed change in temperature at a boundary of an object. They may also occur with temperature changes inside an object, as a result of a new source or sink of heat suddenly introduced within an object, causing temperatures near the source or sink to change in time. When a new perturbation of temperature of this type happens, temperatures within the system change in time toward a new equilibrium with the new conditions, provided that these do not change. After equilibrium, heat flow into the system once again equals the heat flow out, and temperatures at each point inside the system no longer change. Once this happens, transient conduction is ended, although steady-state conduction may continue if heat flow continues. If changes in external temperatures or internal heat generation changes are too rapid for the equilibrium of temperatures in space to take place, then the system never reaches a state of unchanging temperature distribution in time, and the system remains in a transient state. An example of a new source of heat "turning on" within an object, causing transient conduction, is an engine starting in an automobile. In this case, the transient thermal conduction phase for the entire machine is over, and the steady state phase appears, as soon as the engine reaches steady-state operating temperature. In this state of steady-state equilibrium, temperatures vary greatly from the engine cylinders to other parts of the automobile, but at no point in space within the automobile does temperature increase or decrease. After establishing this state, the transient conduction phase of heat transfer is over. New external conditions also cause this process: for example the copper bar in the example steady-state conduction experiences transient conduction as soon as one end is subjected to a different temperature from the other. Over time, the field of temperatures inside the bar reach a new steady-state, in which a constant temperature gradient along the bar is finally set up, and this gradient then stays constant in space. Typically, such a new steady state gradient is approached exponentially with time after a new temperature-or-heat source or sink, has been introduced. When a "transient conduction" phase is over, heat flow may still continue at high power, so long as temperatures do not change. An example of transient conduction that does not end with steady-state conduction, but rather no conduction, occurs when a hot copper ball is dropped into oil at a low temperature. Here, the temperature field within the object begins to change as a function of time, as the heat is removed from the metal, and the interest lies in analyzing this spatial change of temperature within the object over time, until all gradients disappear entirely (the ball has reached the same temperature as the oil). Mathematically, this condition is also approached exponentially; in theory it takes infinite time, but in practice it is over, for all intents and purposes, in a much shorter period. At the end of this process with no heat sink but the internal parts of the ball (which are finite), there is no steady state heat conduction to reach. Such a state never occurs in this situation, but rather the end of the process is when there is no heat conduction at all. The analysis of non steady-state conduction systems is more complex than that of steady-state systems. If the conducting body has a simple shape, then exact analytical mathematical expressions and solutions may be possible (see heat equation for the analytical approach). However, most often, because of complicated shapes with varying thermal conductivities within the shape (i.e., most complex objects, mechanisms or machines in engineering) often the application of approximate theories is required, and/or numerical analysis by computer. One popular graphical method involves the use of Heisler Charts. Occasionally, transient conduction problems may be considerably simplified if regions of the object being heated or cooled can be identified, for which thermal conductivity is very much greater than that for heat paths leading into the region. In this case, the region with high conductivity can often be treated in the lumped capacitance model, as a "lump" of material with a simple thermal capacitance consisting of its aggregate heat capacity. Such regions warm or cool, but show no significant temperature "variation" across their extent, during the process (as compared to the rest of the system). This is due to their far higher conductance. During transient conduction, therefore, the temperature across their conductive regions changes uniformly in space, and as a simple exponential in time. An example of such systems are those that follow Newton's law of cooling during transient cooling (or the reverse during heating). The equivalent thermal circuit consists of a simple capacitor in series with a resistor. In such cases, the remainder of the system with high thermal resistance (comparatively low conductivity) plays the role of the resistor in the circuit. The theory of relativistic heat conduction is a model that is compatible with the theory of special relativity. For most of the last century, it was recognized that the Fourier equation is in contradiction with the theory of relativity because it admits an infinite speed of propagation of heat signals. For example, according to the Fourier equation, a pulse of heat at the origin would be felt at infinity instantaneously. The speed of information propagation is faster than the speed of light in vacuum, which is physically inadmissible within the framework of relativity. Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Heat takes the place of pressure in normal sound waves. This leads to a very high thermal conductivity. It is known as "second sound" because the wave motion of heat is similar to the propagation of sound in air. The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally. Newton's law of cooling is a discrete analogue of Fourier's law, while Ohm's law is the electrical analogue of Fourier's law. The differential form of Fourier's law of thermal conduction shows that the local heat flux density, formula_2, is equal to the product of thermal conductivity, formula_3, and the negative local temperature gradient, formula_4. The heat flux density is the amount of energy that flows through a unit area per unit time. where (including the SI units) The thermal conductivity, formula_3, is often treated as a constant, though this is not always true. While the thermal conductivity of a material generally varies with temperature, the variation can be small over a significant range of temperatures for some common materials. In anisotropic materials, the thermal conductivity typically varies with orientation; in this case formula_3 is represented by a second-order tensor. In non-uniform materials, formula_3 varies with spatial location. For many simple applications, Fourier's law is used in its one-dimensional form. In the "x"-direction, In an isotropic medium, Fourier's law leads to Heat equation: formula_13 with a Fundamental solution famously known as Heat kernel. By integrating the differential form over the material's total surface formula_14, we arrive at the integral form of Fourier's law: where (including the SI units): The above differential equation, when integrated for a homogeneous material of 1-D geometry between two endpoints at constant temperature, gives the heat flow rate as: where This law forms the basis for the derivation of the heat equation. Writing where "U" is the conductance, in W/(m K). Fourier's law can also be stated as: The reciprocal of conductance is resistance, formula_25 is given by: Resistance is additive when several conducting layers lie between the hot and cool regions, because "A" and "Q" are the same for all layers. In a multilayer partition, the total conductance is related to the conductance of its layers by: So, when dealing with a multilayer partition, the following formula is usually used: For heat conduction from one fluid to another through a barrier, it is sometimes important to consider the conductance of the thin film of fluid that remains stationary next to the barrier. This thin film of fluid is difficult to quantify because its characteristics depend upon complex conditions of turbulence and viscosity—but when dealing with thin high-conductance barriers it can sometimes be quite significant. The previous conductance equations, written in terms of extensive properties, can be reformulated in terms of intensive properties. Ideally, the formulae for conductance should produce a quantity with dimensions independent of distance, like Ohm's Law for electrical resistance, formula_29, and conductance, formula_30. From the electrical formula: formula_31, where "ρ" is resistivity, "x" is length, and "A" is cross-sectional area, we have formula_32, where "G" is conductance, "k" is conductivity, "x" is length, and "A" is cross-sectional area. For Heat, where "U" is the conductance. Fourier's law can also be stated as: analogous to Ohm's law, formula_35 or formula_36 The reciprocal of conductance is resistance, "R", given by: analogous to Ohm's law, formula_38 The rules for combining resistances and conductances (in series and in parallel) are the same for both heat flow and electric current. Conduction through cylindrical shells (e.g. pipes) can be calculated from the internal radius, formula_39, the external radius, formula_40, the length, formula_41, and the temperature difference between the inner and outer wall, formula_42. The surface area of the cylinder is formula_43 When Fourier's equation is applied: and rearranged: then the rate of heat transfer is: the thermal resistance is: and formula_48, where formula_49. It is important to note that this is the log-mean radius. The conduction through a spherical shell with internal radius, formula_39, and external radius, formula_40, can be calculated in a similar manner as for a cylindrical shell. The surface area of the sphere is: formula_52 Solving in a similar manner as for a cylindrical shell (see above) produces: formula_53 The heat transfer at an interface is considered a transient heat flow. To analyze this problem, the Biot number is important to understand how the system behaves. The Biot number is determined by: formula_54 The heat transfer coefficient formula_55, is introduced in this formula, and is measured in formula_56. If the system has a Biot number of less than 0.1, the material behaves according to Newtonian cooling, i.e. with negligible temperature gradient within the body. If the Biot number is greater than 0.1, the system behaves as a series solution. The temperature profile in terms of time can be derived from the equation which becomes The heat transfer coefficient, "h", is measured in formula_59, and represents the transfer of heat at an interface between two materials. This value is different at every interface, and is an important concept in understanding heat flow at an interface. The series solution can be analyzed with a nomogram. A nomogram has relative temperature as the "y" coordinate and the Fourier number, which is calculated by The Biot number increases as the Fourier number decreases. There are five steps to determine a temperature profile in terms of time. Splat cooling is a method for quenching small droplets of molten materials by rapid contact with a cold surface. The particles undergo a characteristic cooling process, with the heat profile at formula_62 for initial temperature as the maximum at formula_63 and formula_64 at formula_65 and formula_66, and the heat profile at formula_67 for formula_68 as the boundary conditions. Splat cooling rapidly ends in a steady state temperature, and is similar in form to the Gaussian diffusion equation. The temperature profile, with respect to the position and time of this type of cooling, varies with: formula_69 Splat cooling is a fundamental concept that has been adapted for practical use in the form of thermal spraying. The thermal diffusivity coefficient, represented as formula_70, can be written as formula_71. This varies according to the material. Metal quenching is a transient heat transfer process in terms of the time temperature transformation (TTT). It is possible to manipulate the cooling process to adjust the phase of a suitable material. For example, appropriate quenching of steel can convert a desirable proportion of its content of austenite to martensite, creating a very tough product. To achieve this, it is necessary to quench at the "nose" (or eutectic) of the TTT diagram. Since materials differ in their Biot numbers, the time it takes for the material to quench, or the Fourier number, varies in practice. In steel, the quenching temperature range is generally from 600 °C to 200 °C. To control the quenching time and to select suitable quenching media, it is necessary to determine the Fourier number from the desired quenching time, the relative temperature drop, and the relevant Biot number. Usually, the correct figures are read from a standard nomogram. By calculating the heat transfer coefficient from this Biot number, one can find a liquid medium suitable for the application. One statement of the so-called zeroth law of thermodynamics is directly focused on the idea of conduction of heat. Bailyn (1994) writes that "... the zeroth law may be stated: A diathermal wall is a physical connection between two bodies that allows the passage of heat between them. Bailyn is referring to diathermal walls that exclusively connect two bodies, especially conductive walls. This statement of the 'zeroth law' belongs to an idealized theoretical discourse, and actual physical walls may have peculiarities that do not conform to its generality. For example, the material of the wall must not undergo a phase transition, such as evaporation or fusion, at the temperature at which it must conduct heat. But when only thermal equilibrium is considered and time is not urgent, so that the conductivity of the material does not matter too much, one suitable heat conductor is as good as another. Conversely, another aspect of the zeroth law is that, subject again to suitable restrictions, a given diathermal wall is indifferent to the nature of the heat bath to which it is connected. For example, the glass bulb of a thermometer acts as a diathermal wall whether exposed to a gas or to a liquid, provided they do not corrode or melt it. These differences are amongst the defining characteristics of heat transfer. In a sense, they are symmetries of heat transfer. Thermal conduction property of any gas under standard conditions of pressure and temperature is a fixed quantity. This property of a known reference gas or known reference gas mixtures can, therefore, be used for certain sensory applications, such as the thermal conductivity analyzer. The working of this instrument is by principle based on the Wheatstone bridge containing four filaments whose resistances are matched. Whenever a certain gas is passed over such network of filaments, their resistance changes due to the altered thermal conductivity of the filaments and thereby changing the net voltage output from the Wheatstone Bridge. This voltage output will be correlated with the database to identify the gas sample. The principle of thermal conductivity of gases can also be used to measure the concentration of a gas in a binary mixture of gases. Working: if the same gas is present around the all the Wheatstone bridge filaments, then the same temperature is maintained in all the filaments and hence same resistances are also maintained; resulting in a balanced Wheatstone bridge. However, If dissimilar gas sample (or gas mixture) is passed over one set of two filaments and the reference gas on the other set of two filaments, then the Wheatstone bridge becomes unbalanced. And the resulting net voltage output of the circuit will be correlated with the database to identify the constituents of the sample gas. Using this technique many unknown gas samples can be identified by comparing their thermal conductivity with other reference gas of known thermal conductivity. The most commonly used reference gas is nitrogen; as the thermal conductivity of most common gases (except hydrogen and helium) are similar to that of nitrogen.	Thermal conduction is the transfer of internal energy by microscopic collisions of particles and movement of electrons within a body. The colliding particles, which include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. Conduction takes place in all phases: solid, liquid, and gas. The rate at which energy is conducted as heat between two bodies depends on the temperature difference (and hence temperature gradient) between the two bodies and the properties of the conductive interface through which the heat is transferred.	en	en	102	[ 250004, 250054, 2161, 10, 11948, 12064, 18695, 105994, 4, 158, 77391, 74918, 7, 28032, 10, 14361, 90698, 237, 8035, 29398, 6635, 74, 903, 26950, 450, 70, 200, 86, 9523, 136, 38516, 14579, 7, 111, 70, 11876, 92, 78112, 111, 70, 14361, 621, 84797, 538, 15426, 297, 100, 5, 106745, 141, 48302, 194314, 7, 237, 25545, 538, 98567, 707, 69255, 1916, 34627, 7, 136, 49711, 70838, 78974, 678, 108, 6958, 38648, 214, 2878, 66695, 4, 12302, 2852, 3060, 111, 2363, 11948, 12064, 18695, 200, 86, 9523, 136, 38516, 14579, 7, 4, 6097, 102134, 2449, 8035, 61924, 71, 35845, 47, 70, 11876, 92, 111, 70, 14361, 90698, 237, 8035, 29398, 6635, 5, 1529, 257, 83, 12302, 2822, 390, 158, 77391, 3229, 123594, 16797, 34627, 7, 707, 49711, 70838, 61770, 112, 4, 707, 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summarize: "Central America" may mean different things to various people, based upon different contexts: In the Pre-Columbian era, the northern areas of Central America were inhabited by the indigenous peoples of Mesoamerica. Most notable among these were the Mayans, who had built numerous cities throughout the region, and the Aztecs, who had created a vast empire. The pre-Columbian cultures of eastern El Salvador, eastern Honduras, Caribbean Nicaragua, most of Costa Rica and Panama were predominantly speakers of the Chibchan languages at the time of European contact and are considered by some culturally different and grouped in the Isthmo-Colombian Area. Following the Spanish expedition of Christopher Columbus's voyages to the Americas, the Spanish sent many expeditions to the region, and they began their conquest of Maya territory in 1523. Soon after the conquest of the Aztec Empire, Spanish conquistador Pedro de Alvarado commenced the conquest of northern Central America for the Spanish Empire. Beginning with his arrival in Soconusco in 1523, Alvarado's forces systematically conquered and subjugated most of the major Maya kingdoms, including the K'iche', Tz'utujil, Pipil, and the Kaqchikel. By 1528, the conquest of Guatemala was nearly complete, with only the Petén Basin remaining outside the Spanish sphere of influence. The last independent Maya kingdoms – the Kowoj and the Itza people – were finally defeated in 1697, as part of the Spanish conquest of Petén. In 1538, Spain established the Real Audiencia of Panama, which had jurisdiction over all land from the Strait of Magellan to the Gulf of Fonseca. This entity was dissolved in 1543, and most of the territory within Central America then fell under the jurisdiction of the "Audiencia Real de Guatemala". This area included the current territories of Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Mexican state of Chiapas, but excluded the lands that would become Belize and Panama. The president of the Audiencia, which had its seat in Antigua Guatemala, was the governor of the entire area. In 1609 the area became a captaincy general and the governor was also granted the title of captain general. The Captaincy General of Guatemala encompassed most of Central America, with the exception of present-day Belize and Panama. The Captaincy General of Guatemala lasted for more than two centuries, but began to fray after a rebellion in 1811 which began in the intendancy of San Salvador. The Captaincy General formally ended on 15 September 1821, with the signing of the Act of Independence of Central America. Mexican independence was achieved at virtually the same time with the signing of the Treaty of Córdoba and the Declaration of Independence of the Mexican Empire, and the entire region was finally independent from Spanish authority by 28 September 1821. From its independence from Spain in 1821 until 1823, the former Captaincy General remained intact as part of the short-lived First Mexican Empire. When the Emperor of Mexico abdicated on 19 March 1823, Central America again became independent. On 1 July 1823, the Congress of Central America peacefully seceded from Mexico and declared absolute independence from all foreign nations, and the region formed the Federal Republic of Central America. The Federal Republic of Central America was a representative democracy with its capital at Guatemala City. This union consisted of the provinces of Costa Rica, El Salvador, Guatemala, Honduras, Los Altos, Mosquito Coast, and Nicaragua. The lowlands of southwest Chiapas, including Soconusco, initially belonged to the Republic until 1824, when Mexico annexed most of Chiapas and began its claims to Soconusco. The Republic lasted from 1823 to 1838, when it disintegrated as a result of civil wars. The territory that now makes up Belize was heavily contested in a dispute that continued for decades after Guatemala achieved independence (see History of Belize (1506–1862). Spain, and later Guatemala, considered this land a Guatemalan department. In 1862, Britain formally declared it a British colony and named it British Honduras. It became independent as Belize in 1981. Panama, situated in the southernmost part of Central America on the Isthmus of Panama, has for most of its history been culturally and politically linked to South America. Panama was part of the Province of Tierra Firme from 1510 until 1538 when it came under the jurisdiction of the newly formed "Audiencia Real de Panama". Beginning in 1543, Panama was administered as part of the Viceroyalty of Peru, along with all other Spanish possessions in South America. Panama remained as part of the Viceroyalty of Peru until 1739, when it was transferred to the Viceroyalty of New Granada, the capital of which was located at Santa Fé de Bogotá. Panama remained as part of the Viceroyalty of New Granada until the disestablishment of that viceroyalty in 1819. A series of military and political struggles took place from that time until 1822, the result of which produced the republic of Gran Colombia. After the dissolution of Gran Colombia in 1830, Panama became part of a successor state, the Republic of New Granada. From 1855 until 1886, Panama existed as Panama State, first within the Republic of New Granada, then within the Granadine Confederation, and finally within the United States of Colombia. The United States of Colombia was replaced by the Republic of Colombia in 1886. As part of the Republic of Colombia, Panama State was abolished and it became the Isthmus Department. Despite the many political reorganizations, Colombia was still deeply plagued by conflict, which eventually led to the secession of Panama on 3 November 1903. Only after that time did some begin to regard Panama as a North or Central American entity. By the 1930s the United Fruit Company owned of land in Central America and the Caribbean and was the single largest land owner in Guatemala. Such holdings gave it great power over the governments of small countries. That was one of the factors that led to the coining of the phrase banana republic. After more than two hundred years of social unrest, violent conflict, and revolution, Central America today remains in a period of political transformation. Poverty, social injustice, and violence are still widespread. Nicaragua is the second poorest country in the western hemisphere (only Haiti is poorer). Central America is the tapering isthmus of southern North America, with unique and varied geographic features. The Pacific Ocean lies to the southwest, the Caribbean Sea lies to the northeast, and the Gulf of Mexico lies to the north. Some physiographists define the Isthmus of Tehuantepec as the northern geographic border of Central America, while others use the northwestern borders of Belize and Guatemala. From there, the Central American land mass extends southeastward to the Atrato River, where it connects to the Pacific Lowlands in northwestern South America. Of the many mountain ranges within Central America, the longest are the Sierra Madre de Chiapas, the Cordillera Isabelia and the Cordillera de Talamanca. At, Volcán Tajumulco is the highest peak in Central America. Other high points of Central America are as listed in the table below: Between the mountain ranges lie fertile valleys that are suitable for the raising of livestock and for the production of coffee, tobacco, beans and other crops. Most of the population of Honduras, Costa Rica and Guatemala lives in valleys. Trade winds have a significant effect upon the climate of Central America. Temperatures in Central America are highest just prior to the summer wet season, and are lowest during the winter dry season, when trade winds contribute to a cooler climate. The highest temperatures occur in April, due to higher levels of sunlight, lower cloud cover and a decrease in trade winds. Central America is part of the Mesoamerican biodiversity hotspot, boasting 7% of the world's biodiversity. The Pacific Flyway is a major north–south flyway for migratory birds in the Americas, extending from Alaska to Tierra del Fuego. Due to the funnel-like shape of its land mass, migratory birds can be seen in very high concentrations in Central America, especially in the spring and autumn. As a bridge between North America and South America, Central America has many species from the Nearctic and the Neotropical realms. However the southern countries (Costa Rica and Panama) of the region have more biodiversity than the northern countries (Guatemala and Belize), meanwhile the central countries (Honduras, Nicaragua and El Salvador) have the least biodiversity. The table below shows recent statistics: Over 300 species of the region's flora and fauna are threatened, 107 of which are classified as critically endangered. The underlying problems are deforestation, which is estimated by FAO at 1.2% per year in Central America and Mexico combined, fragmentation of rainforests and the fact that 80% of the vegetation in Central America has already been converted to agriculture. Efforts to protect fauna and flora in the region are made by creating ecoregions and nature reserves. 36% of Belize's land territory falls under some form of official protected status, giving Belize one of the most extensive systems of terrestrial protected areas in the Americas. In addition, 13% of Belize's marine territory are also protected. A large coral reef extends from Mexico to Honduras: the Mesoamerican Barrier Reef System. The Belize Barrier Reef is part of this. The Belize Barrier Reef is home to a large diversity of plants and animals, and is one of the most diverse ecosystems of the world. It is home to 70 hard coral species, 36 soft coral species, 500 species of fish and hundreds of invertebrate species. So far only about 10% of the species in the Belize barrier reef have been discovered. From 2001 to 2010, of forest were lost in the region. In 2010 Belize had 63% of remaining forest cover, Costa Rica 46%, Panama 45%, Honduras 41%, Guatemala 37%, Nicaragua 29%, and El Salvador 21%. Most of the loss occurred in the moist forest biome, with. Woody vegetation loss was partially set off by a gain in the coniferous forest biome with, and a gain in the dry forest biome at. Mangroves and deserts contributed only 1% to the loss in forest vegetation. The bulk of the deforestation was located at the Caribbean slopes of Nicaragua with a loss of of forest in the period from 2001 to 2010. The most significant regrowth of of forest was seen in the coniferous woody vegetation of Honduras. The Central American pine-oak forests ecoregion, in the tropical and subtropical coniferous forests biome, is found in Central America and southern Mexico. The Central American pine-oak forests occupy an area of, extending along the mountainous spine of Central America, extending from the Sierra Madre de Chiapas in Mexico's Chiapas state through the highlands of Guatemala, El Salvador, and Honduras to central Nicaragua. The pine-oak forests lie between elevation, and are surrounded at lower elevations by tropical moist forests and tropical dry forests. Higher elevations above are usually covered with Central American montane forests. The Central American pine-oak forests are composed of many species characteristic of temperate North America including oak, pine, fir, and cypress. Laurel forest is the most common type of Central American temperate evergreen cloud forest, found in almost all Central American countries, normally more than above sea level. Tree species include evergreen oaks, members of the laurel family, and species of "Weinmannia", "Drimys", and "Magnolia". The cloud forest of Sierra de las Minas, Guatemala, is the largest in Central America. In some areas of southeastern Honduras there are cloud forests, the largest located near the border with Nicaragua. In Nicaragua, cloud forests are situated near the border with Honduras, but many were cleared to grow coffee. There are still some temperate evergreen hills in the north. The only cloud forest in the Pacific coastal zone of Central America is on the Mombacho volcano in Nicaragua. In Costa Rica, there are laurel forests in the Cordillera de Tilarán and Volcán Arenal, called Monteverde, also in the Cordillera de Talamanca. The Central American montane forests are an ecoregion of the tropical and subtropical moist broadleaf forests biome, as defined by the World Wildlife Fund. These forests are of the moist deciduous and the semi-evergreen seasonal subtype of tropical and subtropical moist broadleaf forests and receive high overall rainfall with a warm summer wet season and a cooler winter dry season. Central American montane forests consist of forest patches located at altitudes ranging from, on the summits and slopes of the highest mountains in Central America ranging from Southern Mexico, through Guatemala, El Salvador, and Honduras, to northern Nicaragua. The entire ecoregion covers an area of and has a temperate climate with relatively high precipitation levels. Ecoregions are not only established to protect the forests themselves but also because they are habitats for an incomparably rich and often endemic fauna. Almost half of the bird population of the Talamancan montane forests in Costa Rica and Panama are endemic to this region. Several birds are listed as threatened, most notably the resplendent quetzal (Pharomacrus mocinno), three-wattled bellbird (Procnias tricarunculata), bare-necked umbrellabird (Cephalopterus glabricollis), and black guan (Chamaepetes unicolor). Many of the amphibians are endemic and depend on the existence of forest. The golden toad that once inhabited a small region in the Monteverde Reserve, which is part of the Talamancan montane forests, has not been seen alive since 1989 and is listed as extinct by IUCN. The exact causes for its extinction are unknown. Global warming may have played a role, because the development of that frog is typical for this area may have been compromised. Seven small mammals are endemic to the Costa Rica-Chiriqui highlands within the Talamancan montane forest region. Jaguars, cougars, spider monkeys, as well as tapirs, and anteaters live in the woods of Central America. The Central American red brocket is a brocket deer found in Central America's tropical forest. Central America is geologically very active, with volcanic eruptions and earthquakes occurring frequently, and tsunamis occurring occasionally. Many thousands of people have died as a result of these natural disasters. Most of Central America rests atop the Caribbean Plate. This tectonic plate converges with the Cocos, Nazca, and North American plates to form the Middle America Trench, a major subduction zone. The Middle America Trench is situated some off the Pacific coast of Central America and runs roughly parallel to it. Many large earthquakes have occurred as a result of seismic activity at the Middle America Trench. For example, subduction of the Cocos Plate beneath the North American Plate at the Middle America Trench is believed to have caused the 1985 Mexico City earthquake that killed as many as 40,000 people. Seismic activity at the Middle America Trench is also responsible for earthquakes in 1902, 1942, 1956, 1982, 1992, 2001, 2007, 2012, 2014, and many other earthquakes throughout Central America. The Middle America Trench is not the only source of seismic activity in Central America. The Motagua Fault is an onshore continuation of the Cayman Trough which forms part of the tectonic boundary between the North American Plate and the Caribbean Plate. This transform fault cuts right across Guatemala and then continues offshore until it merges with the Middle America Trench along the Pacific coast of Mexico, near Acapulco. Seismic activity at the Motagua Fault has been responsible for earthquakes in 1717, 1773, 1902, 1976, 1980, and 2009. Another onshore continuation of the Cayman Trough is the Chixoy-Polochic Fault, which runs parallel to, and roughly to the north, of the Motagua Fault. Though less active than the Motagua Fault, seismic activity at the Chixoy-Polochic Fault is still thought to be capable of producing very large earthquakes, such as the 1816 earthquake of Guatemala. Managua, the capital of Nicaragua, was devastated by earthquakes in 1931 and 1972. Volcanic eruptions are also common in Central America. In 1968 the Arenal Volcano, in Costa Rica, erupted killing 87 people as the 3 villages of Tabacon, Pueblo Nuevo and San Luis were buried under pyroclastic flows and debris. Fertile soils from weathered volcanic lava have made it possible to sustain dense populations in the agriculturally productive highland areas. The population of Central America is estimated at 47,448,333 as of. With an area of, it has a population density of. Human Development Index values are from the estimates for 2017. The official language majority in all Central American countries is Spanish, except in Belize, where the official language is English. Mayan languages constitute a language family consisting of about 26 related languages. Guatemala formally recognized 21 of these in 1996. Xinca and Garifuna are also present in Central America. This region of the continent is very rich in terms of ethnic groups. The majority of the population is mestizo, with sizable Mayan and African descendent populations present, including Xinca and Garifuna minorities. The immigration of Arabs, Jews, Chinese, Europeans and others brought additional groups to the area. The predominant religion in Central America is Christianity (95.6%). Beginning with the Spanish colonization of Central America in the 16th century, Roman Catholicism became the most popular religion in the region until the first half of the 20th century. Since the 1960s, there has been an increase in other Christian groups, particularly Protestantism, as well as other religious organizations, and individuals identifying themselves as having no religion. Central America is currently undergoing a process of political, economic and cultural transformation that started in 1907 with the creation of the Central American Court of Justice. In 1951 the integration process continued with the signature of the San Salvador Treaty, which created the ODECA, the Organization of Central American States. However, the unity of the ODECA was limited by conflicts between several member states. In 1991, the integration agenda was further advanced by the creation of the Central American Integration System ("Sistema para la Integración Centroamericana", or SICA). SICA provides a clear legal basis to avoid disputes between the member states. SICA membership includes the 7 nations of Central America plus the Dominican Republic, a state that is traditionally considered part of the Caribbean. On 6 December 2008, SICA announced an agreement to pursue a common currency and common passport for the member nations. No timeline for implementation was discussed. Central America already has several supranational institutions such as the Central American Parliament, the Central American Bank for Economic Integration and the Central American Common Market. On 22 July 2011, President Mauricio Funes of El Salvador became the first president "pro tempore" to SICA. El Salvador also became the headquarters of SICA with the inauguration of a new building. Until recently, all Central American countries have maintained diplomatic relations with Taiwan instead of China. President Óscar Arias of Costa Rica, however, established diplomatic relations with China in 2007, severing formal diplomatic ties with Taiwan. After breaking off relations with the Republic of China in 2017, Panama established diplomatic relations with the People's Republic of China. In August 2018, El Salvador also severed ties with Taiwan to formally start recognizing the People's Republic of China as the sole China, a move many considered lacked transparency due to its abruptness and reports of the Chinese government's desires to invest in the department of La Union while also promising to fund the ruling party's reelection campaign. The Central American Parliament (also known as PARLACEN) is a political and parliamentary body of SICA. The parliament started around 1980, and its primary goal was to resolve conflicts in Nicaragua, Guatemala, and El Salvador. Although the group was disbanded in 1986, ideas of unity of Central Americans still remained, so a treaty was signed in 1987 to create the Central American Parliament and other political bodies. Its original members were Guatemala, El Salvador, Nicaragua and Honduras. The parliament is the political organ of Central America, and is part of SICA. New members have since then joined including Panama and the Dominican Republic. Costa Rica is not a member State of the Central American Parliament and its adhesion remains as a very unpopular topic at all levels of the Costa Rican society due to existing strong political criticism towards the regional parliament, since it is regarded by Costa Ricans as a menace to democratic accountability and effectiveness of integration efforts. Excessively high salaries for its members, legal immunity of jurisdiction from any member State, corruption, lack of a binding nature and effectiveness of the regional parliament's decisions, high operative costs and immediate membership of Central American Presidents once they leave their office and presidential terms, are the most common reasons invoked by Costa Ricans against the Central American Parliament. Signed in 2004, the Central American Free Trade Agreement (CAFTA) is an agreement between the United States, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Dominican Republic. The treaty is aimed at promoting free trade among its members. Guatemala has the largest economy in the region. Its main exports are coffee, sugar, bananas, petroleum, clothing, and cardamom. Of its 10.29 billion dollar annual exports, 40.2% go to the United States, 11.1% to neighboring El Salvador, 8% to Honduras, 5.5% to Mexico, 4.7% to Nicaragua, and 4.3% to Costa Rica. The region is particularly attractive for companies (especially clothing companies) because of its geographical proximity to the[United States], very low wages and considerable tax advantages. In addition, the decline in the prices of coffee and other export products and the structural adjustment measures promoted by the international financial institutions have partly ruined agriculture, favouring the emergence of maquiladoras. This sector accounts for 42 per cent of total exports from El Salvador, 55 per cent from Guatemala, and 65 per cent from Honduras. However, its contribution to the economies of these countries is disputed; raw materials are imported, jobs are precarious and low-paid, and tax exemptions weaken public finances. They are also criticised for the working conditions of employees: insults and physical violence, abusive dismissals (especially of pregnant workers), working hours, non-payment of overtime. According to Lucrecia Bautista, coordinator of the"maquilas" sector of the audit firm Coverco,"labour law regulations are regularly violated in maquilas and there is no political will to enforce their application. In the case of infringements, the labour inspectorate shows remarkable leniency. It is a question of not discouraging investors. "Trade unionists are subject to pressure, and sometimes to kidnapping or murder. In some cases, business leaders have used the services of the maras. Finally, black lists containing the names of trade unionists or political activists are circulating in employers' circles. Economic growth in Central America is projected to slow slightly in 2014–15, as country-specific domestic factors offset the positive effects from stronger economic activity in the United States. Tourism in Belize has grown considerably in more recent times, and it is now the second largest industry in the nation. Belizean Prime Minister Dean Barrow has stated his intention to use tourism to combat poverty throughout the country. The growth in tourism has positively affected the agricultural, commercial, and finance industries, as well as the construction industry. The results for Belize's tourism-driven economy have been significant, with the nation welcoming almost one million tourists in a calendar year for the first time in its history in 2012. Belize is also the only country in Central America with English as its official language, making this country a comfortable destination for English-speaking tourists. Costa Rica is the most visited nation in Central America. Tourism in Costa Rica is one of the fastest growing economic sectors of the country, having become the largest source of foreign revenue by 1995. Since 1999, tourism has earned more foreign exchange than bananas, pineapples and coffee exports combined. The tourism boom began in 1987, with the number of visitors up from 329,000 in 1988, through 1.03 million in 1999, to a historical record of 2.43 million foreign visitors and $1.92-billion in revenue in 2013. In 2012 tourism contributed with 12.5% of the country's GDP and it was responsible for 11.7% of direct and indirect employment. Tourism in Nicaragua has grown considerably recently, and it is now the second largest industry in the nation. Nicaraguan President Daniel Ortega has stated his intention to use tourism to combat poverty throughout the country. The growth in tourism has positively affected the agricultural, commercial, and finance industries, as well as the construction industry. The results for Nicaragua's tourism-driven economy have been significant, with the nation welcoming one million tourists in a calendar year for the first time in its history in 2010. The Inter-American Highway is the Central American section of the Pan-American Highway, and spans between Nuevo Laredo, Mexico, and Panama City, Panama. Because of the break in the highway known as the Darién Gap, it is not possible to cross between Central America and South America in an automobile.	Central America (,, "Centroamérica" ) is a region in the southern tip of North America and is sometimes defined as a subregion of the Americas. This region is bordered by Mexico to the north, Colombia to the southeast, the Caribbean Sea to the east and the Pacific Ocean to the west and south. Central America consists of seven countries: El Salvador, Costa Rica, Belize, Guatemala, Honduras, Nicaragua and Panama. 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summarize: The origin of the word Andorra is unknown, although several hypotheses have been formulated. The oldest derivation of the word Andorra is from the Greek historian Polybius ("The Histories" III, 35, 1) who describes the Andosins, an Iberian Pre-Roman tribe, as historically located in the valleys of Andorra and facing the Carthaginian army in its passage through the Pyrenees during the Punic Wars. The word Andosini or Andosins (Ἀνδοσίνοι) may derive from the Basque "handia" whose meaning is "big" or "giant". The Andorran toponymy shows evidence of Basque language in the area. Another theory suggests that the word La Balma de la Margineda, found by archaeologists at Sant Julià de Lòria, was settled in 9,500 BC as a passing place between the two sides of the Pyrenees. The seasonal camp was perfectly located for hunting and fishing by the groups of hunter-gatherers from Ariege and Segre. During the Neolithic Age, a group of people moved to the Valley of Madriu (nowadays Natural Parc located in Escaldes-Engordany declared UNESCO World Heritage Site) as a permanent camp in 6640 BC. The population of The inhabitants of the valleys were traditionally associated with the Iberians and historically located in Andorra as the Iberian tribe Andosins or Andosini (Ἀνδοσίνους) during the 7th and 2nd centuries BC. Influenced by Aquitanias, Basque and Iberian languages, the locals developed some current toponyms. Early writings and documents relating to this group of people goes back to the second century BC by the Greek writer Polybius in his "Histories" during the Punic Wars. Some After the fall of the Roman Empire, Andorra came under the influence of the Visigoths, not remotely from the Kingdom of Toledo, but locally from the Diocese of Urgell. The Visigoths remained in the valleys for 200 years, during which time Christianity spread. When the Muslim Empire and its conquest of most of the Iberian Peninsula replaced the ruling Visigoths, Andorra was sheltered from these invaders by the Franks. Tradition holds that Charles the Great (Charlemagne) granted a charter to the Andorran people for a contingent of five thousand soldiers under the command of Marc Almugaver, in return for fighting against the Moors near Porté-Puymorens Before 1095, Andorra did not have any type of military protection and the Bishop of Urgell, who knew that the count of Urgell wanted to reclaim the Andorran valleys, asked the lord of Caboet for help and protection. In 1095, the Lord of Caboet and the bishop of Urgell signed under oath a declaration of their co-sovereignty over Andorra. Arnalda, daughter of Arnau of Caboet, married the viscount of Castellbò. Their daughter, Ermessenda, married the count of Foix, Roger-Bernard II. Roger-Bernard II and Ermessenda shared ruled over Andorra with the bishop of In 1601 the Tribunal de Corts (High Court of Justice) was created as a result of Huguenot rebellions from France, Inquisition courts coming from Spain and indigenous witchcraft experienced in the country due to the Reformation and Counter-Reformation. With the passage of time, the co-title to Andorra passed to the kings of Navarre. After Henry III of Navarre became king of France, he issued an edict in 1607 that established the head of the French state and the bishop of Urgell as co-princes of Andorra. During 1617, communal councils form the sometent (popular militia or army) to deal with the rise of bandolerisme (brigandage) and the Consell de la Terra was defined and structured in terms of its composition, organization and competences current today. Andorra continued with the same economic system that it had during the 12th–14th centuries with a large production of metallurgy (fargues, a system similar to Farga catalana) and with the introduction of tobacco circa 1692 After the French Revolution in 1809, Napoleon I reestablished the Co-Principate and removed the French medieval title. In 1812–1813, the First French Empire annexed Catalonia during the Peninsular War () and divided the region into four départements, with Andorra as a part of the district of Puigcerdà. In 1814, an imperial decree reestablished the independence and economy of Andorra. During this period, Andorra's late medieval institutions and rural culture remained largely unchanged. In 1866, the syndic Guillem d'Areny-Plandolit led the reformist group in a Council General of 24 members elected by suffrage limited to heads of families. The Council General replaced the aristocratic oligarchy that previously ruled the state. The New Reform () began after ratification by both Co-Princes and established the basis of the constitution and symbols—such as the tricolor flag—of Andorra. A new service economy arose as a demand of the valley inhabitants and began to build infrastructure such as hotels, spa resorts, roads and telegraph lines. The authorities of the Co-Princes banned casinos and betting houses throughout the country. The Andorra declared war on Imperial Germany during World War I, but did not take part directly in the fighting. Some Andorrans volunteered to take part in the conflict as part of the French Legions. It remained in an official state of belligerency until 1958 as it was not included in the Treaty of Versailles. In 1933, France occupied Andorra following social unrest which occurred before elections due to the Revolution of 1933 and the FHASA strikes (Vagues de FHASA); the revolt led by Joves Andorrans (a labour union group related to the Spanish CNT and FAI) called for political reforms, the universal suffrage vote of all Andorrans and acted in defense of the rights of local and foreign workers during the construction of FHASA's hydroelectric power station in Encamp. The 5 April 1933 Joves Andorrans seized the Andorran Parliament. These actions were preceded by the arrival of Colonel René-Jules Baulard with 50 gendarmes and the mobilization of 200 local militias or sometent led by the Síndic Francesc Cairat. On 6 July 1934, adventurer and nobleman Boris Skossyreff, with his promise of freedoms and modernization of the country and wealth through the establishment of Andorra is a parliamentary co-principality with the president of France and the Catholic bishop of Urgell (Catalonia, Spain) as co-princes. This peculiarity makes the president of France, in his capacity as prince of Andorra, an elected monarch, although he is not elected by a popular vote of the Andorran people. The politics of Andorra take place in a framework of a parliamentary representative democracy, whereby the head of government is the chief executive, and of a pluriform multi-party system. The current head of government is Xavier Espot Zamora of the Democrats for Andorra (DA). Executive power is exercised by the government. Legislative power is vested in both government and parliament. The Parliament of Andorra is known as the General Council. The General Council consists of between 28 and 42 councillors. The councillors serve for four-year terms, and elections are held between the 30th and 40th days following the dissolution of the previous Council. Half are elected in equal numbers by each of the seven administrative parishes, and the other half of the councillors are elected in a single national constituency. Fifteen days after the election, the councillors hold their The judiciary is composed of the Magistrates Court, the Criminal Law Court, the High Court of Andorra, and the Constitutional Court. The High Court of Justice is composed of five judges: one appointed by the head of government, one each by the co-princes, one by the Syndic General, and one by the judges and magistrates. It is presided over by the member appointed by the Syndic General and the judges Andorra does not have its own armed forces, although there is a small ceremonial army. Responsibility for defending the nation rests primarily with France and Spain. However, in case of emergencies or natural disasters, the Sometent (an alarm) is called and all able-bodied men between 21 and 60 of Andorran nationality must serve. This is why all Andorrans, and especially the head of each house (usually the eldest able-bodied man of a house) should, by law, keep a rifle, even though the law also states that the police will offer a firearm in case of need. Andorra is a full member of the United Nations (UN), the Organization for Security and Co-operation in Europe (OSCE), and has a special agreement with the European Union (EU). Andorra has a small army, which has historically been raised or reconstituted at various dates, but has never in modern times amounted to a standing army. The basic principle of Andorran defence is that all able-bodied men are available to fight if called upon by the sounding of the Sometent. Being a landlocked country, Andorra has no navy. Before World War I, Andorra maintained an armed force of about 600 part-time militiamen under the supervision of a Captain (Capità or Cap de Sometent) and a Lieutenant (Desener or Lloctinent del Capità). This body was not liable for service outside the principality and was commanded by two officials (veguers) appointed by France and the Bishop of Urgell. Despite not being involved in any fighting during the First World War, Andorra was technically the longest combatant, as the country was left out of the Versailles Peace Conference, technically remaining at war with Germany from its original declaration of war in 1914 until 24 September 1958 when Andorra officially declared peace with Germany. In the modern era, the army has consisted of a very small body of volunteers willing to undertake ceremonial duties. Uniforms and Andorra maintains a small but modern and well-equipped internal police force, with around 240 police officers supported by civilian assistants. The principal services supplied by the corps are uniformed community policing, criminal detection, border control, and traffic policing. There are also small specialist units including police dogs, mountain rescue, and a bomb disposal team. The "Grup d'Intervenció Policia d'Andorra" (GIPA) is a small special forces unit trained in counter-terrorism, and hostage recovery tasks. Although it is the closest in style to an active military force, it is part of the Police Corps, and not the army. As terrorist and hostage situations are a rare threat to the country, the GIPA is commonly assigned to prisoner escort duties, and at other times to routine policing. The Andorran Fire Brigade, with headquarters at Santa Coloma, operates from four modern fire stations, and has a staff of around 120 firefighters. The service is equipped with 16 heavy appliances (fire tenders, turntable ladders, and specialist four-wheel drive vehicles), four light support vehicles (cars and vans) and four ambulances. Historically, the families of the six ancient parishes Andorra consists Due to its location in the eastern Pyrenees mountain range, Andorra consists predominantly of rugged mountains, the highest being the Coma Pedrosa at, and the average elevation of Andorra is. These are dissected by three narrow valleys in a Y Andorra has alpine, continental and oceanic climates, depending on altitude. Its higher elevation means there is, on average, more snow in winter and it is slightly cooler in summer. The diversity of landmarks, the different orientation of the valleys and the irregularity relief typical of the Mediterranean climates make the country have a great diversity of microclimates that hinder the general dominance of the high mountain climate. The great differences of altitude in Tourism, the mainstay of Andorra's tiny, well-to-do economy, accounts for roughly 80% of GDP. An estimated 10.2 million tourists visit annually, attracted by Andorra's duty-free status and by its summer and winter resorts. One of the main sources of income in Andorra is tourism from ski resorts which total over of ski ground. The sport brings in over 7 million visitors annually and an estimated 340 million euros per year, sustaining 2,000 direct and 10,000 indirect jobs at present since 2007. The banking sector, with its tax haven status, also contributes substantially to the economy (the financial and insurance sector accounts for approximately 19% of GDP). The financial system comprises five banking groups, one specialised credit entity, 8 investment undertaking management entities, 3 asset management companies and 29 insurance companies, 14 of which are branches of foreign insurance companies authorised to operate in the principality. Agricultural production is limited; only 5% of the land is arable, and most food has to be imported. Some tobacco is grown locally. The principal livestock activity is domestic sheep raising. Manufacturing output consists mainly of cigarettes, cigars, and furniture. Andorra's natural resources include hydroelectric power, mineral water, timber, iron ore, and The population of Andorra is estimated at (). The Andorrans are a Romance ethnic group of originally Catalan descent. The population has grown from 5,000 in 1900. The historic and official language is Catalan, a Romance language. The Andorran government encourages the use of Catalan. It funds a Commission for Catalan Toponymy in Andorra (Catalan: ), and provides free Catalan classes to assist immigrants. Andorran television and radio stations use Catalan. Because of immigration, historical links, and close geographic proximity, Spanish, The population of Andorra is predominantly (88.2%) Catholic. Their patron saint is Our Lady of Meritxell. Though it is not an official state religion, the constitution acknowledges a special relationship with the Catholic Church, offering some special Children between the ages of 6 and 16 are required by law to have full-time education. Education up to secondary level is provided free of charge by the government. There are three systems of school, Andorran, French and Spanish, which use The Universitat d'Andorra (UdA) is the state public university and is the only university in Andorra. It was established in 1997. The university provides first-level degrees in nursing, computer science, business administration, and educational sciences, in addition to higher professional education courses. The only two graduate schools in Andorra are the Nursing School and the School of Computer Science, the latter having a PhD programme. The geographical complexity of the country as well as the small number of students prevents the University of Andorra from developing a full academic programme, and it serves principally as a centre for virtual studies, connected to Spanish and French universities. The Virtual Studies Centre (Centre d'Estudis Virtuals) at the University runs approximately 20 different academic degrees at both undergraduate and postgraduate levels in fields including tourism, law, Catalan philology, humanities, psychology, political sciences, audiovisual communication, telecommunications engineering, and East Asia studies. The Centre also runs various postgraduate programmes and continuing-education courses for professionals. Until the 20th century, Andorra had very limited transport links to the outside world, and development of the country was affected by its physical isolation. Even now, the nearest major airports at Toulouse and Barcelona are both three hours' drive from Andorra. Andorra has a road network of, of which is unpaved. The two main roads out of Andorra la Vella are the CG-1 to the Spanish border near Sant Julia de Loria, and the CG-2 to the French border via the Envalira Tunnel near El Pas de la Casa. Bus services cover all metropolitan areas and many rural communities, with services on most major routes running half-hourly or more frequently during peak travel times. There are frequent long-distance bus services from Andorra to Barcelona and Toulouse, plus a daily tour from the former city. Bus services mostly are run by private companies, but some local ones are operated by the In Andorra, mobile and fixed telephone and internet services are operated exclusively by the Andorran national telecommunications company, SOM, also known as Andorra Telecom (STA). The same company also manages the technical infrastructure for national broadcasting of digital television and radio. In 2010 Andorra became the first country to provide a direct optical fiber link to all homes (FTTH) and businesses. The first commercial radio station to broadcast was Radio Andorra, which was active from 1939 to 1981. On 12 October 1989, the General Council established radio and television as essential public services creating and The official and historic language is Catalan. Thus the culture is Catalan, with its own specificity. Andorra is home to folk dances like the contrapàs and marratxa, which survive in Sant Julià de Lòria especially. Andorran folk music has similarities to the music of its neighbours, but is especially Catalan in character, especially in the presence of dances such as the sardana. Other Andorran folk dances include contrapàs in Andorra la Vella and Saint Anne's dance in Escaldes-Engordany. Andorra's national holiday is Our Lady of Meritxell Day, 8 September. Among the more important festivals and traditions are the Canólich Gathering in May, the Roser d'Ordino in July, the Meritxell Day (National Day of Andorra), the Andorra la Vella Fair, the Sant Jordi Day, the Santa Llúcia Fair, the Festivity from La Candelera to Canillo, the Carnival of Encamp, the sung of caramelles, the Festivity of Sant Esteve and the Festa del Poble. In popular folklore, the best-known Andorran legends are the legend of Charlemagne, according to which this Frankish King would have founded the country, the White Lady of Auvinyà, the Buner d'Ordino, the legend of Engolasters Lake and the legend of Our Lady of Meritxell. Andorran gastronomy is mainly Catalan, although it has also adopted other elements of French and Italian cuisines. The cuisine of the country has similar characteristics with the neighbors of the Cerdanya and the Alt Urgell, with whom it has a strong cultural ties. Andorra's cuisine is marked by its nature as mountain valleys. Typical dishes of the country are the quince all-i-oli, the duck with winter pear, the lamb in the oven with nuts, pork civet, the massegada cake, the escarole with pear trees, confited duck and mushrooms, escudella, spinach with raisins and pine nuts, jelly marmalade, stuffed murgues (mushrooms) with pork, dandelion salad and the Andorran trout of river. To drink, the mulled wine and beer are also popular. Some of the dishes are very common in the mountainous regions of Catalonia, such as trinxat, embotits, cooked snails, rice with mushrooms, mountain rice and mató. Pre-Romanesque and Romanesque art are one of the most important artistic manifestations and characteristics of the Principality. The Romanesque one allows to know the formation of the parochial communities, the relations of (social and political) power and the national culture. There are a total of forty Romanesque churches that stand out as being small austere ornamentation constructions, as well as bridges, fortresses and manor houses of the same period. Summer solstice fire festivals in the Pyrenees was included as UNESCO Intangible cultural heritage in 2015. Also the Madriu-Perafita-Claror Valley became Andorra's first, and to date its only, UNESCO World Heritage Site in 2004, with a small extension in 2006. Andorra is famous for the practice of winter sports. Andorra has the largest territory of ski slopes in the Pyrenees (3100 hectares and about 350 km of slopes) and two ski resorts. Grandvalira is the largest and most popular resort. Other popular sports played in Andorra include football, rugby union, basketball, and roller hockey. For roller hockey, Andorra usually plays in CERH Euro Cup and in FIRS Roller Hockey World Cup. In 2011, Andorra was the host country to the 2011 European League Final Eight. The country is represented in association football by the Andorra national football team. The team gained its first competitive win in a World Cup qualifier on 11 October 2019, in a European Championship qualifier against Moldova. Football is governed in Andorra by the Andorran Football Federation - founded in 1994, it organizes the national competitions of association football (Primera Divisió, Copa Constitució and Supercopa) and futsal. Andorra was admitted to UEFA and FIFA in the same year, 1996.	Andorra (, ; ), officially the Principality of Andorra (), is a sovereign landlocked microstate on the Iberian Peninsula, in the eastern Pyrenees, bordered by France to the north and Spain to the south. Believed to have been created by Charlemagne, Andorra was ruled by the count of Urgell until 988, when it was transferred to the Roman Catholic Diocese of Urgell. The present principality was formed by a charter in 1278. 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summarize: The city-state of Athens is where western theatre originated. It was part of a broader culture of theatricality and performance in classical Greece that included festivals, religious rituals, politics, law, athletics and gymnastics, music, poetry, weddings, funerals, and "symposia". Participation in the city-state's many festivals—and mandatory attendance at the City Dionysia as an audience member (or even as a participant in the theatrical productions) in particular—was an important part of citizenship. Civic participation also involved the evaluation of the rhetoric of orators evidenced in performances in the law-court or political assembly, both of which were understood as analogous to the theatre and increasingly came to absorb its dramatic vocabulary. The Greeks also developed the concepts of dramatic criticism and theatre architecture. Actors were Western theatre developed and expanded considerably under the Romans. The Roman historian Livy wrote that the Romans first experienced theatre in the 4th century BCE, with a performance by Etruscan actors. Beacham argues that they had been familiar with "pre-theatrical practices" for some time before that recorded contact. The theatre of ancient Rome was a thriving and diverse art form, ranging from festival performances of street The earliest-surviving fragments of Sanskrit drama date from the 1st century CE. The wealth of archeological evidence from earlier periods offers no indication of the existence of a tradition of theatre. The ancient "Vedas" (hymns from between 1500 and 1000 BCE that are among the earliest examples of literature in the world) contain no hint of it (although a small number are composed in a form of dialogue) and the rituals of the Vedic period do not appear to have developed into theatre. The "Mahābhāṣya" by Patañjali contains the The Tang dynasty is sometimes known as "The Age of 1000 Entertainments". During this era, Ming Huang formed an acting school known as The Pear Garden to produce a form of drama that was primarily musical. That is why actors are commonly called "Children of the Pear Garden." During the dynasty of Empress Ling, shadow puppetry first emerged as a recognized form of theatre in China. There were two distinct forms of shadow puppetry, Pekingese (northern) and Cantonese (southern). The two styles were differentiated by the method of making the puppets and the positioning of the rods on the puppets, as opposed to the type of play performed by the puppets. Both styles generally performed plays depicting great adventure and fantasy, rarely was this very stylized form of theatre used for political propaganda. Cantonese shadow puppets were the larger of the two. They were built using thick leather which created more substantial shadows. Symbolic color was also very prevalent; a black face represented honesty, a red one bravery. The rods used to control Cantonese puppets were attached perpendicular to the puppets' heads. Thus, they were not seen by the audience when the shadow was created. Theatre took on many alternate forms in the West between the 15th and 19th centuries, including "commedia dell'arte" and melodrama. The general trend was away from the poetic drama of the Greeks and the Renaissance and toward a more naturalistic prose style of dialogue, especially following the Industrial Revolution. Theatre took a big pause during 1642 and 1660 in England because of the Puritan Interregnum. Viewing theatre as something sinful, the Puritans ordered the closure of London theatres in 1642. This stagnant period ended once Charles II came back to the throne in 1660 in the Restoration. Theatre (among other arts) exploded, with influence from French culture, since Charles had been exiled in France in the years previous to his reign. One of the big changes was the new theatre house. Instead of the type of the Elizabethan era, such as the Globe Theatre, round with The first form of Indian theatre was the Sanskrit theatre. It began after the development of Greek and Roman theatre and before the development of theatre in other parts of Asia. It emerged sometime between the 2nd century BCE and the 1st century CE and flourished between the 1st century CE and the 10th, which was a period of relative peace in the history Drama is the specific mode of fiction represented in performance. The term comes from a Greek word meaning "action", which is derived from the verb δράω, "dráō", "to do" or "to act". The enactment of drama in theatre, performed by actors on a stage before an audience, presupposes collaborative modes of production and a collective form of reception. The structure of dramatic texts, unlike other forms of literature, is directly influenced by this collaborative production and collective reception. The early modern tragedy "Hamlet" (1601) by Shakespeare and the classical Athenian tragedy "Oedipus Rex" (c. 429 BCE) by Sophocles are among the masterpieces of the art of drama. A modern example is "Long Day's Journey into Night" by Eugene O'Neill (1956). Music and theatre have had a close relationship since ancient times—Athenian tragedy, for example, was a form of dance-drama that employed a chorus whose parts were sung (to the accompaniment of an "aulos"—an instrument comparable to the modern clarinet), as were some of the actors' responses and their'solo songs' (monodies). Modern musical theatre is a form of theatre that also combines music, spoken dialogue, and dance. It emerged from comic opera (especially Gilbert and Sullivan), variety, vaudeville, and music hall genres of the late 19th and early 20th century. After Theatre productions that use humour as a vehicle to tell a story qualify as comedies. This may include a modern farce such as "Boeing Boeing" or a Aristotle's phrase "several kinds being found in separate parts of the play" is a reference to the structural origins of drama. In it the spoken parts were written in the Attic dialect whereas the choral (recited or sung) ones in the Doric dialect, these discrepancies reflecting the differing religious origins and poetic metres of the parts that were fused into a new entity, the theatrical "drama". Tragedy refers to a specific tradition of drama that has played a unique and important role historically in the self-definition of Western civilisation. That tradition has been multiple and discontinuous, yet the term has often been used to invoke a powerful effect of Improvisation has been a consistent feature of theatre, with the Commedia dell'arte in the sixteenth century being recognised as the first improvisation form. Popularized by Nobel Prize Winner Dario Fo and troupes such as the Upright Citizens Brigade improvisational theatre continues to evolve with many different streams and philosophies. Keith Johnstone and Viola Spolin are recognized as Having been an important part of human culture for more than 2,500 years, theatre has evolved a wide range of different theories and practices. Some are related to political or spiritual ideologies, while others are based purely on "artistic" concerns. Some processes focus on a story, some on theatre as event, and some on theatre as catalyst for social change. The classical Greek philosopher Aristotle, in his seminal treatise, "Poetics" (c. 335 BCE) is the earliest-surviving example and its arguments have influenced theories of theatre ever since. In it, he offers an account of what he calls "poetry" (a term which in Greek literally means "making" and in this context includes drama—comedy, tragedy, and the satyr play—as well as lyric poetry, epic poetry, and the dithyramb). He examines its "first principles" and identifies its genres and basic elements; his analysis of tragedy constitutes the core of the discussion. Aristotle argues that tragedy consists of six qualitative parts, which are (in order of importance) "mythos" or "plot", "ethos" or "character", "dianoia" or "thought", "lexis" or Theatre presupposes collaborative modes of production and a collective form of reception. The structure of dramatic texts, unlike other forms of literature, is directly influenced by this collaborative production and collective reception. The production of plays usually involves contributions from a playwright, director, a cast of actors, and a technical production team that includes a scenic or set designer, lighting designer, costume designer, sound designer, stage manager, production manager and technical director. Depending on the production, this team may also include a composer, dramaturg, video designer or fight director. Stagecraft is a generic term referring to the technical aspects of theatrical, film, and video production. It includes, but is not limited to, constructing and There are many modern theatre movements which go about producing theatre in a variety of ways. Theatrical enterprises vary enormously in sophistication and purpose. People who are involved vary from novices and hobbyists (in community theatre) to professionals (in Broadway and similar productions). Theatre can be performed with a shoestring budget or on a grand scale with multimillion-dollar budgets. This diversity manifests in the abundance of theatre sub-categories, which include: While most modern theatre companies rehearse one piece of theatre at a time, perform that piece for a set "run", retire the piece, and begin rehearsing a new show, repertory companies rehearse multiple shows at one time. These companies are able to perform these various pieces upon request and often perform works for years before retiring them. In order to put on a piece of theatre, both a theatre company and a theatre venue are needed. When a theatre company is the sole company in residence at a theatre venue, this theatre (and its corresponding theatre company) are called a resident theatre or a producing theatre, because the venue produces its own work. Other theatre companies, as well as dance companies, who do not have their own theatre venue, perform at rental theatres or at presenting theatres. Both rental and presenting theatres have no full-time resident companies. They do, however, sometimes There are many theatre unions including: Actors' Equity Association (for actors and stage managers), the Stage Directors and	Theatre or theater is a collaborative form of performing art that uses live performers, typically actors or actresses, to present the experience of a real or imagined event before a live audience in a specific place, often a stage. The performers may communicate this experience to the audience through combinations of gesture, speech, song, music, and dance. Elements of art, such as painted scenery and stagecraft such as lighting are used to enhance the physicality, presence and immediacy of the experience. The specific place of the performance is also named by the word "theatre" as derived from the Ancient Greek θέατρον (théatron, "a place for viewing"), itself from θεάομαι (theáomai, "to see", "to watch", "to observe").	en	en	148	[ 250004, 250054, 581, 26349, 9, 61340, 111, 94100, 7, 83, 7440, 171827, 163198, 13, 62038, 3674, 5, 1650, 509, 2831, 111, 10, 134744, 56, 29394, 111, 163198, 21533, 2481, 136, 23718, 23, 54704, 289, 200955, 450, 99201, 8395, 7, 4, 167821, 68869, 7, 4, 44951, 7, 4, 27165, 4, 99, 7057, 41637, 136, 195843, 28021, 4, 19612, 4, 30260, 1294, 4, 81141, 7, 4, 211088, 7, 4, 136, 44, 4861, 36624, 3478, 740, 72239, 1363, 23, 70, 26349, 9, 61340, 25, 7, 5941, 8395, 7, 2451, 2940, 81678, 1294, 29966, 7154, 99, 70, 6406, 17893, 299, 3478, 237, 142, 95771, 32786, 15, 748, 3853, 237, 10, 95274, 23, 70, 163198, 21533, 36049, 7, 16, 23, 17311, 2451, 13689, 142, 5526, 2831, 111, 130367, 16070, 5, 167320, 105226, 2843, 75412, 70, 219836, 111, 70, 60971, 3826, 238, 111, 3620, 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summarize: During his lifetime Lotto was a well-respected painter and certainly popular in Northern Italy; he is traditionally included in the Venetian School, but his independent career actually places him outside the Venetian art scene. He was certainly not as highly regarded in Venice as in the other towns where he worked, for he had a stylistic individuality, even an idiosyncratic style (although it fits within the parametres of High Renaissance painting), and, after his death, he gradually became neglected and then almost forgotten. This oblivion could be attributed to the fact that his works now remain in lesser known churches or in provincial museums. Born in Venice, he worked in Treviso (1503–1506); in the Marches (1506–1508); in Rome (1508–1510); in Bergamo (1513–1525); in Venice (1525–1549); in Ancona (1549) and finally, as a Franciscan lay brother, in Loreto (1549–1556). Little is known of his training. As a Venetian he was influenced by Giovanni Bellini as he had a good knowledge of contemporary Venetian painting. Though Bellini was doubtless not his teacher, the influence is clear in his early painting "Virgin and Child with St. Jerome" (1506; National Gallery of Scotland, Edinburgh). However, in his portraits and in his early painting "Allegory of Virtue and Vice" (1505; National Gallery of Art, Washington), he shows the influence of Giorgione's Naturalism. As he grew older his style changed, perhaps evolving, from a detached Giorgionesque classicism, to a more vibrant dramatic setpiece, more reminiscent of his contemporary from Parma, Correggio. Lotto soon left Venice, because there the competition for a young painter would have been too great, with established names such as Giorgione, Palma the Elder and certainly with Titian. Nevertheless, Giorgio Vasari mentions in the third part of his book "Vite" that Lotto was a friend of Palma the Elder. In Treviso, a prospering town within the domain of the republic of Venice, he came under the patronage of bishop Bernardo de' Rossi. The already mentioned painting "Allegory of Virtue and Vice" was intended as an allegorical cover of his portrait (1505) of the bishop (now in National Museum of Capodimonte in Naples), who had survived an assassination attempt. The painting "St. Jerome in the Desert" (1500 or 1506; Louvre, Paris) shows his youthful inexperience as a draughtsman, however the dramatic rocky landscape is accentuated by the red garment of the saint, while at the same time giving an early impression of his skill as a miniaturist. He painted his first altarpieces for the parish church San Cristina al Tiverone (1505) and the baptistery of the Cathedral of Asolo (1506), both still on display in those churches. In 1508 he began the Recanati Polyptych altarpiece for the church of San Domenico; this two-tiered and rather conventionally painted polyptych consists of six panels. His portrait "Young Man against a White Curtain" in the Kunsthistorisches Museum, Vienna (c. 1506) and "Adoration of the Child" (c. 1508) in the National Museum in Kraków with Catherine Cornaro, Queen of Cyprus portraited as Saint Catherine, are paintings from this period. As he became a respected painter, he came to the attention of Bramante, the papal architect, who was passing through Loreto (a pilgrimage site near Recanati). Lotto was invited to Rome to decorate the papal apartments, but nothing survives of this work, as it was destroyed a few years later. This was probably because he had imitated the style of Raphael, a rapidly rising star in the Papal court; indeed he had done it before, in the "Transfiguration" of the Recanati polyptych. In 1511 he was at work for the confraternity of the Buon Gesù in Jesi, painting an "Entombment" (Pinacoteca Civica, Jesi); soon after he was painting altarpieces in Recanati: a "Transfiguration" (c.1512, now in the Pinacoteca Comunale, Recanati and a fresco ("St Vincent Ferrer") for the church of San Domenico. His work in Bergamo, the westernmost town of the Venetian republic, was to prove his best and most productive artistic period, when he received many commissions from wealthy merchants, well educated professionals and local aristocrats. He had become a rich colourist and an experienced draughtsman, who also developed the concept of the psychological portrait that revealed the thoughts and emotions of his subjects. In this he was continuing the tradition begun by Antonello da Messina and a good example would be his "Portrait of a Young Man with a Book" (now in the Accademia, Venice). He began 1513 with a monumental altarpiece: the "Martinengo Altarpiece" in the Dominican church of the Santi Bartolomeo e Stefano in Bergamo. This altarpiece was commissioned by Count Alessandro Martinengo-Colleoni, grandson of the famous condottiere Bartolomeo Colleoni, which would be finished in 1516 and shows us the influence of Bramante and Giorgione. His next assignment was the decoration of the churches of S Bernardino and of Sant'Alessandro in Colonna, with frescoes and distemper paintings. He would finish five more altarpieces between 1521 and 1523. In 1523 he went for a brief stay in the Marches, obtaining there several commissions for altarpieces, which he would paint during his stay in Venice. His next works are mostly wall paintings: in 1524 he painted a series of frescoes with the lives of saints (such as Saint Barbara) in the Suardi Chapel in Trescore (near Bergamo). In the details he depicts scenes of each saint's life, such as in the fresco "Martyrdom of St. Claire". In the same fresco he portrays Christ with vines sprouting from his hands, illustrating the words of the New Testament: "I am the vine, you are the branches". In 1524 he also painted cartoons with Old Testament stories, as models for the intarsia panels for the choir stalls of Santa Maria Maggiore in Bergamo. More than 20 private paintings date from the same period; they are mostly of religious and pious subjects, such as "Madonnas" or a "Deposition", used for worship at home. Though he painted in the Classical tradition, Lotto adds a personal touch to the intense emotions. Using contrasting poses and opposing movement, he breaks the traditional symmetry of the Virgin surrounded by angels and saints. In Venice, Lotto first resided at the Dominican monastery of Santi Giovanni e Paolo, but he was forced to leave after a few months after a conflict with intarsia artist Fra Damiano da Bergamo. To cope with the many commissions he started to receive, he founded a workshop. He shipped five altarpieces for churches in the Marches and another one for the church Santa Maria Assunta in Celano (near Bergamo). Another altarpiece was for the Venetian church of Santa Maria dei Carmini, portraying "St. Nicholas of Bari in Glory". As Venice was a city of great wealth and as popularity increased, he received many orders for private paintings, including ten portraits, among them, "Portrait of a Young Man" (Gemäldegalerie, Berlin). His portrait of "Andrea Odoni" (Royal Art Collection, Hampton Court) (1527) would later influence the portrait of "Jacopo Strada" by Titian (1568) (Kunsthistorisches Museum, Vienna). But in Venice he was overshadowed by Titian, who dominated the artistic scene. In this last period of his life, Lorenzo Lotto would frequently move from town to town, searching for patrons and commissions. In 1532 he went to Treviso. Next he spent about seven years in the Marches (Ancona, Macerata and Jesi), before returning to Venice in 1540. He moved again to Treviso in 1542 and back to Venice in 1545. Finally he went back to Ancona in 1549. This was a productive period in his life, during which he painted several altarpieces and portraits. At the end of his life, Lotto found it difficult to earn a living. Furthermore, in 1550, when he was about 70, one of his works had an unsuccessful auction in Ancona. As recorded in his personal account book, this deeply disillusioned him. As he had always been a deeply religious man, in 1552 he joined the Holy Sanctuary at Loreto, becoming a lay brother. During that time he decorated the basilica of Santa Maria and painted a "Presentation in the Temple" for the Palazzo Apostolico in Loreto. He died in 1556 and was buried, at his request, in a Dominican habit. Giorgio Vasari included Lotto's biography in the third volume of his book "Vite". Lorenzo Lotto himself left many letters and a detailed notebook ("Libro di spese diverse", 1538–1556), giving insight to his life and work. His influence was felt by many painters, including probably Giovanni Busi, and Ercole Ramazzani, born in Arcevia and active near Jesi. Another pupil was Durante Nobili. Thanks to the work of the art historian Bernard Berenson, Lotto was rediscovered at the end of the 19th century. Since then, many monographs and several exhibitions have been dedicated to Lorenzo Lotto, such as the exhibition in Venice in 1953 and one in the National Gallery of Art, Washington, USA, in 1998.	Lorenzo Lotto (c. 1480 – 1556/57) was an Italian painter, draughtsman and illustrator, traditionally placed in the Venetian school, though much of his career was spent in other North Italian cities. He painted mainly altarpieces, religious subjects and portraits. He was active during the High Renaissance and the first half of the Mannerist period, but his work maintained a generally similar High Renaissance style throughout his career, although his nervous and eccentric posings and distortions represented a transitional stage to the Florentine and Roman Mannerists.	en	en	96	[ 250004, 250054, 133698, 1919, 6897, 6032, 185632, 509, 10, 5299, 9, 177981, 297, 249, 10433, 136, 68782, 5700, 23, 182688, 98848, 74, 764, 83, 89160, 538, 99201, 23, 70, 30337, 55283, 19188, 4, 1284, 1919, 41371, 80997, 20653, 44677, 4049, 50782, 70, 30337, 55283, 4927, 28302, 5, 1529, 509, 68782, 959, 237, 103210, 28601, 297, 23, 2609, 3466, 237, 23, 70, 3789, 59444, 7, 7440, 764, 79786, 4, 100, 764, 1902, 10, 182352, 1771, 11651, 2481, 4, 3853, 142, 6, 57840, 12654, 15182, 9523, 20623, 15, 289, 197271, 442, 11177, 7, 28032, 70, 39850, 90, 111, 19694, 231119, 178829, 247, 136, 4, 7103, 1919, 47219, 4, 764, 128839, 538, 100512, 124789, 89829, 136, 7068, 39555, 240764, 5, 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summarize: Color, made up of hue, saturation, and value, dispersed over a surface is the essence of painting, just as pitch and rhythm are the essence of music. Color is highly subjective, but has observable psychological effects, although these can differ from one culture to the next. Black is associated with mourning in the West, but in the East, white is. Some painters, theoreticians, writers and scientists, including Goethe, Kandinsky, and Newton, have written their own color theory. Moreover, the use of language is only an abstraction for a color equivalent. The word "red", for example, can cover a wide range of variations from the pure red of the visible spectrum of light. Modern artists have extended the practice of painting considerably to include, as one example, collage, which began with Cubism and is not painting in the strict sense. Some modern painters incorporate different materials such as metal, plastic, sand, Jean Metzinger's mosaic-like Divisionist technique had its parallel in literature; a characteristic of the alliance between Symbolist writers and Neo-Impressionist artists: I ask of divided brushwork not the objective rendering of light, but iridescences and certain aspects of color still foreign to painting. I make a kind of chromatic versification and for syllables I use strokes which, variable in quantity, cannot differ in dimension without modifying the rhythm of a pictorial phraseology destined to translate the diverse emotions aroused by nature. (Jean Metzinger, circa 1907) Rhythm, for artists such as Piet Mondrian, is important in painting as it is in music. If one defines rhythm as "a pause incorporated into a sequence", then there can be rhythm in paintings. These pauses allow creative force to intervene and add new creations—form, melody, coloration. The distribution of form, or any kind of information is of crucial importance in the given work of art, and it directly affects The oldest known paintings are at the Grotte Chauvet in France, which some historians believe are about 32,000 years old. They are engraved and painted using red ochre and black pigment, and they show horses, rhinoceros, lions, buffalo, mammoth, abstract designs and what are possibly partial human figures. However, the earliest evidence of the act of painting has been discovered in two rock-shelters in Arnhem Land, in northern Australia. In the lowest layer of material at these sites, there are used pieces of ochre estimated to be 60,000 years old. Archaeologists have also found a fragment of rock painting preserved in a limestone rock-shelter in the Kimberley region of North-Western Australia, that is dated 40,000 years old. There are examples of cave paintings all over the world—in Italy, France, Spain, Portugal, China, Australia, Mexico, etc. In Western cultures, oil painting and watercolor painting have rich and complex traditions in style Aesthetics is the study of art and beauty; it was an important issue for 18th- and 19th-century philosophers such as Kant and Hegel. Classical philosophers like Plato and Aristotle also theorized about art and painting in particular. Plato disregarded painters (as well as sculptors) in his philosophical system; he maintained that painting cannot depict the truth—it is a copy of reality (a shadow of the world of ideas) and is nothing but a craft, similar to shoemaking or iron casting. By the time of Leonardo, painting had become a closer representation of the truth than painting was in Ancient Greece. Leonardo da Vinci, on the contrary, said that "" (""). Kant distinguished between Beauty and the Sublime, in terms that clearly gave priority to the former. Although he did not refer to painting in particular, this concept was taken up by painters such as J.M.W. Turner and Caspar David Friedrich. Hegel recognized the failure of attaining a universal concept of beauty and, in his aesthetic essay, wrote Different types of paint are usually identified by the medium that the pigment is suspended or embedded in, which determines the general working characteristics of the paint, such as viscosity, miscibility, solubility, drying time, etc. Oil painting is the process of painting with pigments that are bound with a medium of drying oil, such as linseed oil, which was widely used in early modern Europe. Often the oil was boiled with a resin such as pine resin Pastel is a painting medium in the form of a stick, consisting of pure powdered pigment and a binder. The pigments used in pastels are the same as those used to produce all colored art media, including oil paints; the binder is of a neutral hue and low saturation. The color effect of pastels is closer to the natural Acrylic paint is fast drying paint containing pigment suspension in acrylic polymer emulsion. Acrylic paints can be diluted with water, but become water-resistant when dry. Depending on how much the paint is diluted (with water) or modified with acrylic gels, media, or pastes, the finished acrylic painting can Watercolor is a painting method in which the paints are made of pigments suspended in a water-soluble vehicle. The traditional and most common support for watercolor paintings is paper; other supports include papyrus, bark papers, plastics, vellum or leather, fabric, wood and Ink paintings are done with a liquid that contains pigments and/or dyes and is used to color a surface to produce an image, text, or design. Ink is used for drawing with a pen, Encaustic painting, also known as hot wax painting, involves using heated beeswax to which colored pigments are added. The liquid/paste is then applied to a surface—usually prepared wood, though canvas and other materials are often used. The simplest encaustic mixture can be made from adding pigments to beeswax, but there are several other recipes that can be used—some containing other types of waxes, damar resin, linseed oil, Fresco is any of several related mural painting types, done on plaster on walls or ceilings. The word fresco comes from the Italian word "affresco", which derives from the Latin word for "fresh". Frescoes were often made during the Renaissance and other early time Gouache is a water-based paint consisting of pigment and other materials designed to be used in an opaque painting method. Gouache differs from watercolor in that the particles Enamels are made by painting a substrate, typically metal, with powdered glass; minerals called color oxides provide coloration. After firing at a temperature of 750–850 degrees Celsius (1380–1560 degrees Fahrenheit), the result is a fused lamination of glass and metal. Unlike most painted techniques, the surface can be handled and wetted Enamels have traditionally been Aerosol paint (also called spray paint) is a type of paint that comes in a sealed pressurized container and is released in a fine spray mist when depressing a valve button. A form of spray painting, aerosol paint leaves a smooth, evenly coated surface. Standard sized cans are portable, inexpensive and easy to store. Aerosol primer can be applied directly to bare metal and many Tempera, also known as egg tempera, is a permanent, fast-drying painting medium consisting of colored pigment mixed with a water-soluble binder medium (usually a glutinous material such as egg yolk or some other size). Tempera also refers to the paintings done in this medium. Water miscible oil paints (also called "water soluble" or "water-mixable") is a modern variety of oil paint engineered to be thinned and cleaned up with water, rather than having to use chemicals such as turpentine. It can be mixed and Digital painting is a method of creating an art object (painting) digitally and/or a technique for making digital art in the computer. As a method of creating an art object, it adapts traditional painting medium such as acrylic paint, oils, ink, watercolor, etc. and applies the pigment to traditional carriers, such as woven canvas cloth, paper, polyester etc. by means of computer software driving industrial robotic or office machinery "Style" is used in two senses: It can refer to the distinctive visual elements, techniques and methods that typify an "individual" artist's work. It can also refer to the movement or school that an artist is associated with. This can stem from an actual group that the artist was consciously involved with or it can be a category in which art historians have placed the painter. The word'style' in the latter sense has fallen out of favor in academic discussions about contemporary painting, though it continues to be used in popular contexts. Such movements or classifications include the following: Modernism describes both a set of cultural tendencies and an array of associated cultural movements, originally arising from wide-scale and far-reaching changes to Western society in the late 19th century and early 20th century. Modernism was a revolt against the conservative values of realism. The term encompasses the activities and output of those who felt the "traditional" forms of art, architecture, literature, religious faith, social organization and daily life were becoming outdated in the new economic, social and political conditions of an emerging fully industrialized world. A salient characteristic of modernism is self-consciousness. This often led to experiments with form, and work that draws attention to the processes and materials used (and to the further tendency of abstraction). Allegory is a figurative mode of representation conveying meaning other than the literal. Allegory communicates its message by means of symbolic figures, actions or symbolic representation. Allegory is generally treated as a figure of rhetoric, but In Spanish art, a bodegón is a still life painting depicting pantry items, such as victuals, game, and drink, often arranged on a simple stone slab, and also a painting with one or more figures, but significant still life elements, typically set in a kitchen or tavern. Starting in the Baroque period, such paintings became popular in Spain in the second quarter A figure painting is a work of art in any of the painting media with the primary subject being the human figure, whether clothed or nude. Figure painting may also refer to the Illustration paintings are those used as illustrations in books, magazines, and theater or movie posters and comic books. Today, there is a growing interest in collecting and admiring the original artwork. Various museum exhibitions, magazines and art galleries have devoted space to the Landscape painting is a term that covers the depiction of natural scenery such as mountains, valleys, trees, rivers, and forests, and especially art where the main subject is a wide view, with its elements arranged into a coherent composition. In other works landscape backgrounds for figures can still Portrait paintings are representations of a person, in which the face and its expression is predominant. The intent is to display the likeness, personality, and even the mood of the person. The art of the A still life is a work of art depicting mostly inanimate subject matter, typically commonplace objects—which may be either natural (food, flowers, plants, rocks, or shells) or man-made (drinking glasses, books, vases, jewelry, coins, pipes, and so on). With origins in the Middle Ages and Ancient Greek/Roman art, A veduta is a highly detailed, usually large-scale painting of a cityscape or some other vista. This genre of landscape originated in Flanders, where artists such as Paul Bril painted "vedute" as early as the 16th	Painting is the practice of applying paint, pigment, color or other medium to a solid surface (called the "matrix" or "support"). The medium is commonly applied to the base with a brush, but other implements, such as knives, sponges, and airbrushes, can be used. 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summarize: "Yen" derives from the Japanese word, which borrows its phonetic reading from Chinese yuan, similar to North Korean won and South Korean won. Originally, the Chinese had traded silver in mass called sycees and when Spanish and Mexican silver coins arrived, the Chinese called them "silver rounds" () for their circular shapes. The coins and the name also appeared in Japan. While the Chinese eventually replaced with, the Japanese continued to use the same word, which was given the shinjitai form in reforms at the end of World War II. The spelling and pronunciation "yen" is standard in English because when Japan was first encountered by Europeans around the 16th century, Japanese () and () both had been pronounced and Portuguese missionaries had spelled them "ye". By the middle of the 18th century, and came to be pronounced as in modern Japanese, although some regions retain the pronunciation. Walter Henry Medhurst, who had neither been to Japan nor met any Japanese, having consulted mainly a Japanese-Dutch dictionary, spelled some "e"s as "ye" in his "An English and Japanese, and Japanese and English Vocabulary" (1830). In the early Meiji era, James Curtis Hepburn, following Medhurst, spelled all "e"s as "ye" in his "A Japanese and English dictionary" (1867); in Japanese, "e" and "i" are slightly palatalized, somewhat as in Russian. That was the first full-scale Japanese-English/English-Japanese dictionary, which had a strong influence on Westerners in Japan and probably prompted the spelling "yen". Hepburn revised most "ye"s to "e" in the 3rd edition (1886) to mirror the contemporary pronunciation, except "yen". This was probably already fixed and has remained so ever since. In the 19th century, silver Spanish dollar coins were common throughout Southeast Asia, the China coast, and Japan. These coins had been introduced through Manila over a period of two hundred and fifty years, arriving on ships from Acapulco in Mexico. These ships were known as the Manila galleons. Until the 19th century, these silver dollar coins were actual Spanish dollars minted in the new world, mostly at Mexico City. But from the 1840s, they were increasingly replaced by silver dollars of the new Latin American republics. In the later half of the 19th century, some local coins in the region were made in the resemblance of the Mexican peso. The first of these local silver coins was the Hong Kong silver dollar coin that was minted in Hong Kong between the years 1866 and 1869. The Chinese were slow to accept unfamiliar coinage and preferred the familiar Mexican dollars, and so the Hong Kong government ceased minting these coins and sold the mint machinery to Japan. The Japanese then decided to adopt a silver dollar coinage under the name of 'yen', meaning 'a round object'. The yen was officially adopted by the Meiji government in an Act signed on June 27, 1871. The new currency was gradually introduced beginning from July of that year. The yen was therefore basically a dollar unit, like all dollars, descended from the Spanish Pieces of eight, and up until the year 1873, all the dollars in the world had more or less the same value. The yen replaced Tokugawa coinage, a complex monetary system of the Edo period based on the mon. The "New Currency Act" of 1871, stipulated the adoption of the decimal accounting system of "yen" (1, ),'(, ), and'(, ), with the coins being round and manufactured using Western machinery. The yen was legally defined as 0.78 troy ounces (24.26 g) of pure silver, or 1.5 grams of pure gold (as recommended by the European Congress of Economists in Paris in 1867; the 5-yen coin was equivalent to the Argentine 5 peso fuerte coin), hence putting it on a bimetallic standard. Following the silver devaluation of 1873, the yen devalued against the U.S. dollar and the Canadian dollar (since those two countries adhered to a gold standard), and by the year 1897, the yen was worth only about US$0.50. In that year, Japan adopted a gold exchange standard and hence froze the value of the yen at $0.50. This exchange rate remained in place until Japan left the gold standard in December 1931, after which the yen fell to $0.30 by July 1932 and to $0.20 by 1933. It remained steady at around $0.30 until the start of the Pacific War on December 7, 1941, at which time it fell to $0.23. The sen and the rin were eventually taken out of circulation at the end of 1953. No true exchange rate existed for the yen between December 7, 1941, and April 25, 1949; wartime inflation reduced the yen to a fraction of its pre-war value. After a period of instability, on April 25, 1949, the U.S. occupation government fixed the value of the yen at ¥360 per US$1 through a United States plan, which was part of the Bretton Woods System, to stabilize prices in the Japanese economy. That exchange rate was maintained until 1971, when the United States abandoned the gold standard, which had been a key element of the Bretton Woods System, and imposed a 10 percent surcharge on imports, setting in motion changes that eventually led to floating exchange rates in 1973. By 1971, the yen had become undervalued. Japanese exports were costing too little in international markets, and imports from abroad were costing the Japanese too much. This undervaluation was reflected in the current account balance, which had risen from the deficits of the early 1960s, to a then-large surplus of US$5.8 billion in 1971. The belief that the yen, and several other major currencies, were undervalued motivated the United States' actions in 1971. Following the United States' measures to devalue the dollar in the summer of 1971, the Japanese government agreed to a new, fixed exchange rate as part of the Smithsonian Agreement, signed at the end of the year. This agreement set the exchange rate at ¥308 per US$1. However, the new fixed rates of the Smithsonian Agreement were difficult to maintain in the face of supply and demand pressures in the foreign-exchange market. In early 1973, the rates were abandoned, and the major nations of the world allowed their currencies to float. In the 1970s, Japanese government and business people were very concerned that a rise in the value of the yen would hurt export growth by making Japanese products less competitive and would damage the industrial base. The government therefore continued to intervene heavily in foreign-exchange marketing (buying or selling dollars), even after the 1973 decision to allow the yen to float. Despite intervention, market pressures caused the yen to continue climbing in value, peaking temporarily at an average of ¥271 per US$1 in 1973, before the impact of the 1973 oil crisis was felt. The increased costs of imported oil caused the yen to depreciate to a range of ¥290 per US$1 to ¥300 per US$1 between 1974 and 1976. The re-emergence of trade surpluses drove the yen back up to ¥211 in 1978. This currency strengthening was again reversed by the second oil shock in 1979, with the yen dropping to ¥227 per US$1 by 1980. During the first half of the 1980s, the yen failed to rise in value even though current account surpluses returned and grew quickly. From ¥221 per US$1 in 1981, the average value of the yen actually dropped to ¥239 per US$1 in 1985. The rise in the current account surplus generated stronger demand for yen in foreign-exchange markets, but this trade-related demand for yen was offset by other factors. A wide differential in interest rates, with United States interest rates much higher than those in Japan, and the continuing moves to deregulate the international flow of capital, led to a large net outflow of capital from Japan. This capital flow increased the supply of yen in foreign-exchange markets, as Japanese investors changed their yen for other currencies (mainly dollars) to invest overseas. This kept the yen weak relative to the dollar and fostered the rapid rise in the Japanese trade surplus that took place in the 1980s. In 1985, a dramatic change began. Finance officials from major nations signed an agreement (the Plaza Accord) affirming that the dollar was overvalued (and, therefore, the yen undervalued). This agreement, and shifting supply and demand pressures in the markets, led to a rapid rise in the value of the yen. From its average of ¥239 per US$1 in 1985, the yen rose to a peak of ¥128 in 1988, virtually doubling its value relative to the dollar. After declining somewhat in 1989 and 1990, it reached a new high of ¥123 to US$1 in December 1992. In April 1995, the yen hit a peak of under 80 yen per dollar, temporarily making Japan's economy nearly the size of that of the US. The yen declined during the Japanese asset price bubble and continued to do so afterwards, reaching a low of ¥134 to US$1 in February 2002. The Bank of Japan's policy of zero interest rates has discouraged yen investments, with the carry trade of investors borrowing yen and investing in better-paying currencies (thus further pushing down the yen) estimated to be as large as $1 trillion. In February 2007, "The Economist" estimated that the yen was 15% undervalued against the dollar, and as much as 40% undervalued against the euro. However, this trend of depreciation reversed after the global economic crisis of 2008. Other major currencies, except the Swiss franc, have been declining relative to the yen. On April 4, 2013, the Bank of Japan announced that they would expand their Asset Purchase Program by $1.4 trillion in two years. The Bank of Japan hopes to bring Japan from deflation to inflation, aiming for 2% inflation. The amount of purchases is so large that it is expected to double the money supply. But this move has sparked concerns that the authorities in Japan are deliberately devaluing the yen in order to boost exports. However, the commercial sector in Japan worried that the devaluation would trigger an increase in import prices, especially for energy and raw materials. Coins were introduced in 1870. There were silver 5-, 10-, 20- and 50-sen and 1-yen, and gold 2-, 5-, 10- and 20-yen. Gold 1-yen were introduced in 1871, followed by copper 1-rin, -, 1- and 2-sen in 1873. Cupronickel 5-sen coins were introduced in 1889. In 1897, the silver 1-yen coin was demonetized and the sizes of the gold coins were reduced by 50%, with 5-, 10- and 20-yen coins issued. In 1920, cupro-nickel 10-sen coins were introduced. Production of silver coins ceased in 1938, after which a variety of base metals were used to produce 1-, 5- and 10-sen coins during the Second World War. Clay 5- and 10-sen coins were produced in 1945, but not issued for circulation. After the war, brass 50-sen, 1- and 5-yen were introduced between 1946 and 1948. In 1949, the current type of holed 5-yen was introduced, followed by bronze 10-yen (of the type still in circulation) in 1951. Coins in denominations of less than 1-yen became invalid on December 31, 1953, following enforcement of the. In 1955, the current type of aluminium 1-yen was introduced, along with unholed, nickel 50-yen. In 1957, silver 100-yen pieces were introduced, followed by the holed 50-yen coin in 1959. These were replaced in 1967 by the current cupro-nickel type, along with a smaller 50-yen coin. In 1982, the first 500-yen coins were introduced. The date (expressed as the year in the reign of the emperor at the time the coin was stamped) is on the reverse of all coins, and, in most cases, country name (through 1945, ; after 1945, and the value in kanji is on the obverse, except for the present 5-yen coin where the country name is on the reverse. Alongside with the 5-Swiss franc coin and the rarely used 5-Cuban convertible peso coin, the 500-yen coin is one of the highest-valued coin to be used regularly in the world, with value of US$4.5. Because of this high face value, the 500-yen coin has been a favorite target for counterfeiters; it was counterfeited to such an extent, that in 2000, a new series of coins was issued with various security features, but counterfeiting continued. The 1-yen coin is made out of 100% aluminium and can float on water if placed correctly. On various occasions, commemorative coins are minted, often in gold and silver with face values up to 100,000 yen. The first of these were silver ¥100 and ¥1000 Summer Olympic coins issued on the occasion of the 1964 games. Recently this practice is undertaken with the 500-yen coin, the first two types were issued in 1985, in commemoration of the science and technology exposition in Tsukuba and the 100th anniversary of the Governmental Cabinet system. The current commemorative 500- and 1000-yen coin series honouring the 47 prefectures of Japan commenced in 2008, with 47 unique designs planned for each denomination. Only one coin per customer is available from banks in each prefecture. 100,000 of each 1000-yen silver coin have been minted. Even though all commemorative coins can be spent like ordinary (non-commemorative) coins, they are not seen often in typical daily use and normally do not circulate. Instead of displaying the Gregorian calendar year of mintage like most nations' coins, yen coins instead display the year of the current emperor's reign. For example, a coin minted in 2009, would bear the date Heisei 21 (the 21st year of Emperor Akihito's reign). Due to the great differences in style, size, weight and the pattern present on the edge of the coin they are very easy for people with visual impairments to tell apart from one another. The issuance of the yen banknotes began in 1872, two years after the currency was introduced. Throughout its history, the denominations have ranged from 10 yen to 10,000 yen; since 1984, the lowest-valued banknote is the 1,000 yen note. Before and during World War II, various bodies issued banknotes in yen, such as the Ministry of Finance and the Imperial Japanese National Bank. The Allied forces also issued some notes shortly after the war. Since then, the Bank of Japan has been the exclusive note issuing authority. The bank has issued five series after World War II. Series E, the current series introduced in 2004, consists of ¥1000, ¥5000, and ¥10,000 notes. The EURion constellation pattern is present in the designs. Japan is generally considered a cash-based society, with 38% of payments in Japan made by cash in 2014. Possible explanations are that cash payments protect one's privacy, merchants do not have to wait for payment, and it does not carry any negative connotation like credit. On April 9, 2019, Finance Minister Tarō Asō announced new designs for the ¥1000, ¥5000, and ¥10,000 notes, for use beginning in 2024. The ¥1000 bill will feature Kitasato Shibasaburō and The Great Wave off Kanagawa, the ¥5000 bill will feature Tsuda Umeko and wisteria flowers, and the ¥10,000 bill will feature Shibusawa Eiichi and Tokyo Station. Beginning in December 1931, Japan gradually shifted from the gold standard system to the managed currency system. The relative value of the yen is determined in foreign exchange markets by the economic forces of supply and demand. The supply of the yen in the market is governed by the desire of yen holders to exchange their yen for other currencies to purchase goods, services, or assets. The demand for the yen is governed by the desire of foreigners to buy goods and services in Japan and by their interest in investing in Japan (buying yen-denominated real and financial assets). Since the 1990s, the Bank of Japan, the country's central bank, has kept interest rates low in order to spur economic growth. Short-term lending rates have responded to this monetary relaxation and fell from 3.7% to 1.3% between 1993 and 2008. Low interest rates combined with a ready liquidity for the yen prompted investors to borrow money in Japan and invest it in other countries (a practice known as carry trade). This has helped to keep the value of the yen low compared to other currencies. The special drawing rights (SDR) valuation is an IMF basket of currencies, including the Japanese yen. The SDR is linked to a basket of five different currencies, with 41.73% for the U.S. dollar, 30.93% for the Euro, 10.92% for the Chinese renminbi, 8.33% for the Japanese yen, and 8.09% for the pound sterling (as of 2016). The percentage for the yen has, however, declined from 18% in 2000. The exchange rate for the Japanese yen is expressed in terms of currency units per U.S. dollar; other rates are expressed as U.S. dollars per currency unit. The SDR currency value is calculated daily and the valuation basket is reviewed and adjusted every five years. The SDR was created in 1969, to support the fixed exchange system. Before the war commenced, the yen traded on an average of 3.6 yen to the dollar. During the war, because of overprinting and inflation as the Empire occupied more territory, the yen went as low as 600 yen to the USD. When McArthur and the US forces entered Japan in 1945, they decreed an official conversion rate of 15 yen to the USD. Within 1945-1946: the rate tanked to 50 yen to the USD because of the ongoing inflation. During the first half of 1946, the rate fluctuated to 66 yen to the USD and eventually plummeting to 600 yen to the dollar by 1947 because of the failure of the economic remedies. Eventually, the peg was officially moved to 270 yen to the dollar in 1948 before being adjusted again from 1949–1971 to 360 yen to the dollar. The table below shows the monthly average of the U.S. dollar–yen spot rate (JPY per USD) at 17:00 JST:	Zoology () is the branch of biology that studies the animal kingdom, including the structure, embryology, evolution, classification, habits, and distribution of all animals, both living and extinct, and how they interact with their ecosystems. The term is derived from Ancient Greek ζῷον, "zōion", i.e. "animal" and λόγος, "logos", i.e. "knowledge, study".	en	en	78	[ 250004, 250054, 44, 1723, 33, 58, 122, 60877, 1295, 70, 148926, 2565, 4, 3129, 3017, 15555, 7, 6863, 24089, 9523, 16454, 1295, 76438, 6, 132053, 4, 21373, 47, 23924, 133915, 23742, 136, 25134, 133915, 23742, 5, 34525, 538, 4, 70, 76438, 1902, 52350, 71, 115392, 23, 46889, 35839, 954, 329, 90, 136, 3229, 195374, 136, 181815, 115392, 43780, 7, 174920, 4, 70, 76438, 35839, 2856, 44, 10801, 814, 68807, 7, 58, 15, 16, 100, 2363, 115339, 115700, 7, 5, 581, 43780, 7, 136, 70, 9351, 2843, 118775, 23, 15758, 5, 51404, 70, 76438, 155605, 91995, 71, 678, 4, 70, 148926, 136475, 47, 4527, 70, 5701, 2565, 4, 3129, 509, 34475, 70, 6544, 6942, 5686, 3173, 23, 17690, 7, 99, 70, 3564, 111, 6661, 5550, 1995, 5, 581, 10010, 2069, 136, 92217, 1363, 44, 12222, 58, 83, 5570, 23, 14941, 6637, 3229, 15758, 509, 5117, 190647, 297, 390, 28811, 7, 10932, 70, 611, 927, 142642, 4, 148926, 15, 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summarize: The name "England" is derived from the Old English name "Englaland", which means "land of the Angles". The Angles were one of the Germanic tribes that settled in Great Britain during the Early Middle Ages. The Angles came from the Anglia peninsula in the Bay of Kiel area (present-day German state of Schleswig–Holstein) of the Baltic Sea. The earliest recorded use of the term, as "Engla londe", is in the late-ninth-century translation into Old English of Bede's "Ecclesiastical History of the English People". The term was then used in a different sense to the modern one, meaning "the land inhabited by the English", and it included English people in what is now south-east Scotland but was then part of the English kingdom of Northumbria. The "Anglo-Saxon Chronicle" recorded that the Domesday Book of 1086 covered the whole of England, meaning the English kingdom, but a few years later the "Chronicle" stated that The earliest known evidence of human presence in the area now known as England was that of "Homo antecessor", dating to approximately 780,000 years ago. The oldest proto-human bones discovered in England date from 500,000 years ago. Modern humans are known to have inhabited the area during the Upper Paleolithic period, though permanent settlements were only established within the last 6,000 years. After the last ice age only large mammals such as mammoths, bison and woolly rhinoceros remained. Roughly 11,000 years ago, when the ice sheets began to recede, humans repopulated the area; genetic research suggests they came from the northern part of the Iberian Peninsula. Roman military withdrawals left Britain open to invasion by pagan, seafaring warriors from north-western continental Europe, chiefly the Saxons, Angles, Jutes and Frisians who had long raided the coasts of the Roman province. These groups then began to settle in increasing numbers over the course of the fifth and sixth centuries, initially in the eastern part of the country. Their advance was contained for some decades after the Britons' victory at the Battle of Mount Badon, but subsequently resumed, over-running the fertile lowlands of Britain and reducing the area under Brittonic control to a series of separate enclaves in the more rugged country to the west by the end of the 6th century. Contemporary texts describing this period are extremely scarce, giving rise to its description as a Dark Age. The nature and During the Tudor period, the Renaissance reached England through Italian courtiers, who reintroduced artistic, educational and scholarly debate from classical antiquity. England began to develop naval skills, and exploration to the West intensified. Henry VIII broke from communion with the Catholic Church, over issues relating to his divorce, under the Acts of Supremacy in 1534 which proclaimed the monarch head of the Church of England. In contrast with much of European Protestantism, the roots of the split were more political than theological. He also legally incorporated his ancestral land Wales into the Kingdom of England with the 1535–1542 acts. There were internal religious conflicts during the reigns of Henry's daughters, Mary I and Elizabeth I. The former took the country back to Catholicism Under the newly formed Kingdom of Great Britain, output from the Royal Society and other English initiatives combined with the Scottish Enlightenment to create innovations in science and engineering, while the enormous growth in British overseas trade protected by the Royal Navy paved the way for the establishment of the British Empire. Domestically it drove the Industrial Revolution, a period of profound change in the socioeconomic and cultural conditions of England, resulting in industrialised agriculture, manufacture, engineering and mining, as well as new and pioneering road, rail and water networks to facilitate their expansion and development. The opening As part of the United Kingdom, the basic political system in England is a constitutional monarchy and parliamentary system. There has not been a government of England since 1707, when the Acts of Union 1707, putting into effect the terms of the Treaty of Union, joined England and Scotland to form the Kingdom of Great Britain. Before the union England was ruled by its monarch and the Parliament of England. Today England is governed directly by the Parliament of the United Kingdom, although other countries of the United Kingdom have devolved governments. In the House of Commons which is the lower house of the British Parliament based at the Palace of Westminster, there are 532 Members of Parliament (MPs) for constituencies in England, out of the 650 total. As of the 2019 United Kingdom general election, The English law legal system, developed over the centuries, is the basis of common law legal systems used in most Commonwealth countries and the United States (except Louisiana). Despite now being part of the United Kingdom, the legal system of the Courts of England and Wales continued, under the Treaty of Union, as a separate legal system from the one used in Scotland. The general essence of English law is that it is made by judges sitting in courts, applying their common sense and knowledge of legal precedent – "stare decisis" – to the facts before them. The subdivisions of England consist of up to four levels of subnational division controlled through a variety of types of administrative entities created for the purposes of local government. The highest tier of local government were the nine regions of England: North East, North West, Yorkshire and the Humber, East Midlands, West Midlands, East, South East, South West, and London. These were created in 1994 as Government Offices, used by the UK government to deliver a wide range of policies and programmes regionally, but there are no elected bodies at this level, except in London, and in 2011 the regional government offices were abolished. After devolution began to take place in other parts of the United Kingdom it was planned that referendums for the regions of England would take place for their own elected regional assemblies as a counterweight. London accepted in 1998: the London Assembly was created two years later. However, when the proposal was rejected by the 2004 North East England devolution referendum in the North East, further referendums were cancelled. The regional assemblies outside London were abolished in Geographically England includes the central and southern two-thirds of the island of Great Britain, plus such offshore islands as the Isle of Wight and the Isles of Scilly. It is bordered by two other countries of the United Kingdom: to the north by Scotland and to the west by Wales. England is closer than any other part of mainland Britain to the European continent. It is separated from France (Hauts-de-France) by a sea gap, though the two countries are connected by the Channel Tunnel near Folkestone. England also has shores on the Irish Sea, North Sea and Atlantic Ocean. The ports of London, Liverpool, and Newcastle lie on the tidal rivers Thames, Mersey and Tyne respectively. At, the Severn is the longest river flowing through England. It empties into the Bristol Channel and is notable for its Severn Bore (a tidal bore), which can reach in height. However, the longest river entirely in England is the Thames, which is in length. There are many lakes in England; the largest is Windermere, within the aptly named Lake District. Most of England's landscape England has a temperate maritime climate: it is mild with temperatures not much lower than in winter and not much higher than in summer. The weather is damp relatively frequently and is changeable. The coldest months are January and February, the latter particularly on the English coast, while July is normally the warmest month. Months with mild to warm weather are The Greater London Built-up Area is by far the largest urban area in England and one of the busiest cities in the world. It is considered a global city and has a population larger than other countries in the United Kingdom besides England itself. Other urban areas of considerable size and influence England's economy is one of the largest in the world, with an average GDP per capita of £28,100 or $36,000. Usually regarded as a mixed market economy, it has adopted many free market principles, yet maintains an advanced social welfare infrastructure. The official currency in England is the pound sterling, whose ISO 4217 code is GBP. Taxation in England is quite competitive when compared to much of the rest of Europe – the basic rate of personal tax is 20% on taxable income up to £31,865 above the personal tax-free allowance (normally £10,000), and 40% on any additional earnings above that amount. The economy of England is the largest part of the UK's economy, which has the 18th highest GDP PPP per capita in the world. England is a leader in the chemical and pharmaceutical sectors and in key technical industries, particularly aerospace, the arms industry, and the manufacturing side of the software industry. London, home to the London Stock Exchange, the United Kingdom's main stock exchange and the largest in Europe, is England's financial centre, with 100 of Europe's 500 largest corporations being based there. London is the largest financial centre in Europe, and is the second largest in the world. The Bank of England, founded in 1694 by Scottish banker William Paterson, is the United Kingdom's central bank. Originally established as private banker to the government of England, since 1946 it has been a state-owned institution. The bank has a monopoly on the issue of banknotes in England and Wales, although not in other parts of the United Kingdom. The government has devolved responsibility to the bank's Monetary Policy Committee for managing the monetary policy of the country and setting interest rates. England is highly industrialised, but since the 1970s there has been a decline in traditional heavy and manufacturing industries, and an increasing emphasis on a more service industry oriented economy. Tourism has become a significant industry, attracting millions of visitors to England each year. The export part of the economy is dominated by pharmaceuticals, cars (although many English marques are now foreign-owned, such as Land Rover, Lotus, Jaguar and Bentley), crude oil and petroleum from the English parts of North Sea oil along with Wytch Farm, aircraft engines and alcoholic beverages. Most of the UK's £30 billion aerospace industry is primarily based in England. The global market opportunity for UK aerospace manufacturers over the next two decades is estimated at £3.5 trillion. GKN Aerospace – an expert in metallic and composite aerostructures is involved in almost every civil and military fixed and rotary wing aircraft in production is based in Redditch. BAE Systems makes large sections of the Typhoon Eurofighter at its sub-assembly plant in Salmesbury and assembles the aircraft for the RAF at its Warton plant, near Preston. It is also a principal subcontractor on the F35 Joint Strike Fighter – the world's largest single defence project – for which it designs and manufactures a range of components including the aft fuselage, vertical and horizontal tail and wing tips and fuel system. It also manufactures the Hawk, the world's most successful jet training aircraft. Rolls-Royce PLC is the world's second-largest aero-engine manufacturer. Its engines power more than 30 types of commercial aircraft, and it has more 30,000 engines currently in service across both the civil and defence sectors. With a workforce of over 12,000 people, Derby has the largest concentration of Rolls-Royce employees in the UK. Rolls-Royce also produces low-emission power systems for ships; makes critical equipment and safety systems for the nuclear industry and powers offshore platforms and major pipelines for the oil and gas industry. Much of the UK's space industry is centred on EADS Astrium, based in Stevenage and Portsmouth. The company builds the buses – the underlying structure onto which the payload and propulsion systems are built – for most of the European Space Agency's spacecraft, as well as commercial satellites. The world leader in compact satellite systems, Surrey Satellite Technology, is also part of Astrium. Reaction Engines Limited, the company planning to build Skylon, a single-stage-to-orbit spaceplane using their SABRE rocket engine, a combined-cycle, air-breathing rocket propulsion system is based Culham. Agriculture is intensive and highly mechanised, producing 60% of food needs with only 2% of the labour force. Two-thirds of production is devoted to livestock, the other to arable crops. National Health England (NHS England) is the publicly funded healthcare system responsible for providing the majority of healthcare in the country. The NHS began on 5 July 1948, putting into effect the provisions of the National Health Service Act 1946. It was based on the findings of the Beveridge Report, prepared by economist and social reformer William Beveridge. The NHS is largely funded from general taxation including National Insurance payments, and it provides most of its services free at the point of use, although there are charges for some people for eye tests, dental care, prescriptions and aspects of personal care. The government department responsible for the With over 53 million inhabitants, England is by far the most populous country of the United Kingdom, accounting for 84% of the combined total. England taken as a unit and measured against international states has the fourth largest population in the European Union and would be the 25th largest country by population in the world. With a density of 424 people per square kilometre, it would be the second most densely populated country in the European Union after Malta. The English people are a British people. Some genetic evidence suggests that 75–95% descend in the paternal line from prehistoric settlers who originally came from the Iberian Peninsula, as well as a 5% contribution from Angles and Saxons, and a significant Scandinavian (Viking) element. However, other geneticists place the Germanic estimate up to half. Over time, various cultures have been influential: Prehistoric, Brythonic, Roman, Anglo-Saxon, Viking (North Germanic), Gaelic cultures, as well as a large influence from Normans. There is an English diaspora in former parts of the British Empire; especially As its name suggests, the English language, today spoken by hundreds of millions of people around the world, originated as the language of England, where it remains the principal tongue spoken by 98% of the population. It is an Indo-European language in the Anglo-Frisian branch of the Germanic family. After the Norman conquest, the Old English language was displaced and confined to the lower social classes as Norman French and Latin were used by the aristocracy. By the 15th century, English was back in fashion among all classes, though much changed; the Middle English form showed many signs of French influence, both in vocabulary and spelling. During the English Renaissance, many words were coined from Latin and Greek origins. Modern English has extended this custom of flexibility when it comes to incorporating words from different languages. Thanks in large part to the British Empire, the English language is the world's unofficial "lingua franca". English language learning and teaching is an important economic In the 2011 census, 59.4% of the population of England specified their religion as Christian, 24.7% answered that they had no religion, 5% specified that they were Muslim, while 3.7% of the population belongs to other religions and 7.2% did not give an answer. Christianity is the most widely practised religion in England, as it has been since the Early Middle Ages, although it was first introduced much earlier in Gaelic and Roman times. This Celtic Church was gradually joined to the Catholic hierarchy following the 6th-century Gregorian mission The Department for Education is the government department responsible for issues affecting people in England up to the age of 19, including education. State-run and state-funded schools are attended by approximately 93% of English schoolchildren. Of these, a minority are faith schools (primarily Church of England or Roman Catholic schools). Children who are between the ages of 3 and 5 attend nursery or an Early Years Foundation Stage reception unit within a primary school. Children between the ages of 5 and 11 attend primary school, and secondary school is attended by those aged between 11 and 16. After finishing compulsory education, students take GCSE examinations. Students may then opt to continue into further education for two years. Further education colleges (particularly sixth form colleges) often form part of a secondary school site. A-level examinations are sat by a large number of further education students, and often form the basis of an application to university. Although most English secondary schools are comprehensive, in some areas there are selective intake grammar schools, to which entrance is subject to passing the eleven-plus exam. Around 7.2% of English schoolchildren attend private schools, which are funded by private sources. Standards in state schools are monitored by Many ancient standing stone monuments were erected during the prehistoric period; amongst the best known are Stonehenge, Devil's Arrows, Rudston Monolith and Castlerigg. With the introduction of Ancient Roman architecture there was a development of basilicas, baths, amphitheaters, triumphal arches, villas, Roman temples, Roman roads, Roman forts, stockades and aqueducts. It was the Romans who founded the first cities and towns such as London, Bath, York, Chester and St Albans. Perhaps the best-known example is Hadrian's Wall stretching right across northern England. Another well-preserved example is the Roman Baths at Bath, Somerset. Early Medieval architecture's secular buildings were simple constructions mainly using timber with thatch for roofing. Ecclesiastical architecture ranged from a synthesis of Hiberno–Saxon monasticism, to Early Christian basilica and architecture characterised by pilaster-strips, blank arcading, baluster shafts and triangular headed openings. After the Norman conquest in 1066 various Castles in England English folklore developed over many centuries. Some of the characters and stories are present across England, but most belong to specific regions. Common folkloric beings include pixies, giants, elves, bogeymen, trolls, goblins and dwarves. While many legends and folk-customs are thought to be ancient, for instance the tales featuring Offa of Angel and Wayland the Smith, others date from after the Norman invasion; Robin Hood and his Merry Men of Sherwood and their battles with the Sheriff of Nottingham being, perhaps, the best known. During the High Middle Ages tales originating from Brythonic traditions entered English folklore and developed into the Arthurian myth. These were derived from Anglo-Norman, Welsh and French sources, featuring King Arthur, Camelot, Excalibur, Merlin and the Knights of the Round Table such as Lancelot. These stories are most centrally brought together within Geoffrey of Monmouth's "Historia Regum Britanniae" ("History of the Kings Since the early modern period the food of England has historically been characterised by its simplicity of approach and a reliance on the high quality of natural produce. During the Middle Ages and through the Renaissance period, English cuisine enjoyed an excellent reputation, though a decline began during the Industrial Revolution with the move away from the land and increasing urbanisation of the populace. The cuisine of England has, however, recently undergone a revival, which has been recognised by food critics with some good ratings in "Restaurant"s best restaurant in the world charts. An early book of English recipes is the "Forme of Cury" from the royal court of Richard II. Traditional examples of English food include the Sunday roast, featuring a roasted joint (usually beef, lamb, chicken or pork) served with assorted vegetables, Yorkshire pudding and The earliest known examples are the prehistoric rock and cave art pieces, most prominent in North Yorkshire, Northumberland and Cumbria, but also feature further south, for example at Creswell Crags. With the arrival of Roman culture in the 1st century, various forms of art such as statues, busts, glasswork and mosaics were the norm. There are numerous surviving artefacts, such as those at Lullingstone and Aldborough. During the Early Middle Ages the style favoured sculpted crosses and ivories, manuscript painting, gold and enamel jewellery, demonstrating a love of intricate, interwoven designs such as in the Staffordshire Hoard discovered in 2009. Some of these blended Gaelic and Anglian styles, such as the Lindisfarne Gospels and Vespasian Psalter. Later Gothic art was popular at Winchester and Canterbury, examples survive Early authors such as Bede and Alcuin wrote in Latin. The period of Old English literature provided the epic poem "Beowulf" and the secular prose of the "Anglo-Saxon Chronicle", along with Christian writings such as "Judith", Cædmon's "Hymn" and hagiographies. Following the Norman conquest Latin continued amongst the educated classes, as well as an Anglo-Norman literature. Middle English literature emerged with Geoffrey Chaucer, author of "The Canterbury Tales", along with Gower, the Pearl Poet and Langland. William of Ockham and Roger Bacon, who were Franciscans, were major philosophers of the Middle Ages. Julian of Norwich, who wrote "Revelations of Divine Love", was a prominent Christian mystic. With the English Renaissance literature in the Early Modern English style appeared. William Shakespeare, whose works include "Hamlet", "Romeo and Juliet", "Macbeth", and "A Midsummer Night's Dream", remains one of the most championed authors in English literature. Christopher Marlowe, Edmund Spenser, Philip Sydney, Thomas Kyd, John Donne, and Ben Jonson are other established authors of The traditional folk music of England is centuries old and has contributed to several genres prominently; mostly sea shanties, jigs, hornpipes and dance music. It has its own distinct variations and regional peculiarities. Wynkyn de Worde printed ballads of Robin Hood from the 16th century are an important artefact, as are John Playford's "The Dancing Master" and Robert Harley's "Roxburghe Ballads" collections. Some of the best-known songs are "Greensleeves", "Pastime with Good Company", "Maggie May" and "Spanish Ladies" amongst others. Many nursery rhymes are of English England (and the UK as a whole) has had a considerable influence on the history of the cinema, producing some of the greatest actors, directors and motion pictures of all time, including Alfred Hitchcock, Charlie Chaplin, David Lean, Laurence Olivier, Vivien Leigh, John Gielgud, Peter Sellers, Julie Andrews, Michael Caine, Gary Oldman, Helen Mirren, Kate Winslet and Daniel Day-Lewis. Hitchcock and Lean are among the most critically acclaimed filmmakers. Hitchcock's first thriller, "" (1926), helped shape the thriller genre in film, while his 1929 film, "Blackmail", is often regarded as the first British feature film. Major film studios in England include Pinewood, Elstree and Shepperton. Some of the most commercially successful films of all time have been produced in England, including two of the highest-grossing film franchises ("Harry Potter" and "James Bond"). Ealing Studios in London has a claim to being the oldest English Heritage is a governmental body with a broad remit of managing the historic sites, artefacts and environments of England. It is currently sponsored by the Department for Culture, Media and Sport. The charity National Trust for Places of Historic Interest or Natural Beauty holds a contrasting role. 17 of the 25 United Kingdom UNESCO World Heritage Sites fall within England. Some of the best-known of these are: Hadrian's Wall, Stonehenge, Avebury and Associated Sites, Tower of London, Jurassic Coast, Saltaire, Ironbridge Gorge, Studley Royal Park and various others. England has a strong sporting heritage, and during the 19th century codified many sports that are now played around the world. Sports originating in England include association football, cricket, rugby union, rugby league, tennis, boxing, badminton, squash, rounders, hockey, snooker, billiards, darts, table tennis, bowls, netball, thoroughbred horseracing, greyhound racing and fox hunting. It has helped the development of golf, sailing and Formula One. Football is the most popular of these sports. The England national football team, whose home venue is Wembley Stadium, played Scotland in the first ever international football match in 1872. Referred to as the "home of football" by FIFA, England hosted the 1966 FIFA World Cup, and won the tournament by defeating West Germany 4–2 in the final, with Geoff Hurst scoring a hat-trick. With a British television audience peak of 32.30 million viewers, the final is the most watched television event ever in the UK. At club level, England is recognised by FIFA as the birthplace of club football, due to Sheffield F.C. founded in 1857 being the world's oldest club. The Football Association is the oldest governing body in the sport, with the rules of football first drafted in 1863 by Ebenezer Cobb Morley. The FA Cup and The Football League were the first cup and league competitions respectively. In the modern day, the Premier League is the world's most-watched football league, most lucrative, and amongst the elite. As is the case throughout the UK, football in England is notable for the rivalries between clubs and the passion of the supporters, which includes a tradition of football chants. The European Cup (now UEFA Champions League) has been won by several English clubs. The most successful English football team in the European Cup/UEFA Champions League is Liverpool F.C. who have won the competition on six occasions. Other English success has come from Manchester United F.C., winning the competition on 3 occasions; Nottingham Forest F.C. on 2 occasions, Aston Villa F.C. and Chelsea F.C. have both won the trophy once. Cricket is generally thought to have been developed in the early medieval period among the farming and metalworking communities of the Weald. The England cricket team is a composite England and Wales, team. One of the game's top rivalries is The Ashes series between England and Australia, contested since 1882. The climax of the 2005 Ashes was viewed by 7.4 million as it was available on terrestrial television. England has hosted five Cricket World Cups (1975, 1979, 1983, 1999 and 2019), winning the 2019 edition in a final regarded as one of the greatest one day internationals ever played. They hosted the ICC World Twenty20 in 2009, winning this format in 2010 beating rivals Australia in the final. In the domestic competition, the County Championship, Yorkshire are by far the most successful club having won the competition 32 times outright and sharing it on 1 other occasion. Lord's Cricket Ground situated in London is sometimes referred to as the "Mecca of Cricket". William Penny Brookes was prominent in organising the format for the modern Olympic Games. In 1994, then President of the IOC, Juan Antonio Samaranch, laid a wreath on Brooke's grave, and said, "I came to pay homage and tribute to Dr Brookes, who really was the founder of the modern Olympic Games". London has hosted the Summer Olympic Games three times, in 1908, 1948, and 2012. England competes in the Commonwealth Games, held every four years. Sport England is the governing body responsible for distributing funds and providing strategic guidance for sporting activity in England. Rugby union originated in Rugby School, Warwickshire in the early 19th century. The England rugby union team won the 2003 Rugby World Cup, with Jonny Wilkinson The St George's Cross has been the national flag of England since the 13th century. Originally the flag was used by the maritime Republic of Genoa. The English monarch paid a tribute to the Doge of Genoa from 1190 onwards so that English ships could fly the flag as a means of protection when entering the Mediterranean. A red cross was a symbol for many Crusaders in the 12th and 13th centuries. It became associated with Saint George, along with countries and cities, which claimed him as their patron saint and used his cross as a banner. Since 1606 the St George's Cross has formed part of the design of the Union Flag, a Pan-British flag designed by King James I. During the English Civil War and Interregnum, the New Model Army's standards and the Commonwealth's Great Seal both incorporated the flag of Saint George. There are numerous other symbols and symbolic artefacts, both official and unofficial, including the Tudor rose, the nation's floral emblem, and the Three Lions featured on the Royal Arms of England. The Tudor rose was adopted as a national emblem of England around the time of the Wars of the Roses as a symbol of peace. It is a syncretic symbol in that it merged the white rose of the Yorkists and the red rose of the Lancastrians—cadet branches of the Plantagenets who went to war over control of the nation. It is also known as the "Rose of England". The oak tree is a symbol of England, representing strength and endurance. The Royal Oak symbol and Oak Apple Day commemorate the escape of King Charles II from the grasp of the parliamentarians after his father's execution: he hid in an oak tree to avoid detection before safely reaching exile. The Royal Arms of England, a national coat of arms featuring three lions, originated with its adoption by Richard the Lionheart in 1198. It is blazoned as "gules, three lions passant guardant or" and it provides one of the most prominent symbols of England; it is similar to the traditional arms of Normandy. England does not have an official designated national anthem, as the United Kingdom as a whole has "God Save the Queen". However, the following are often considered unofficial English national anthems: "Jerusalem", "Land of Hope and Glory" (used for England during the 2002 Commonwealth Games), and "I Vow to Thee, My Country". England's National Day is 23 April which is St George's Day: St George is the patron saint of England.	England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest of England and the Celtic Sea to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain, which lies in the North Atlantic, and includes over 100 smaller islands, such as the Isles of Scilly and the Isle of Wight. 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summarize: Most liquids freeze by crystallization, formation of crystalline solid from the uniform liquid. This is a first-order thermodynamic phase transition, which means that as long as solid and liquid coexist, the temperature of the whole system remains very nearly equal to the melting point due to slow removal of heat when in contact with air, which is a poor heat conductor. Because of the latent heat of fusion, the freezing is greatly slowed and the temperature will not drop any more once the freezing starts but will continue dropping once it finishes. Crystallization consists of two major events, nucleation and crystal growth. Nucleation is the step wherein the molecules start to gather into clusters, on the nanometer scale, arranging in a defined and periodic manner that defines the crystal structure. The crystal growth is the subsequent growth of the nuclei that succeed in achieving the critical cluster size. In spite of the second law of thermodynamics, crystallization of pure liquids usually begins at a lower temperature than the melting point, due to high activation energy of homogeneous nucleation. The creation of a nucleus implies the formation of an interface at the boundaries of the new phase. Some energy is expended to form this interface, based on the surface energy of each phase. If a hypothetical nucleus is too small, the energy that would be released by forming its volume is not enough to create its surface, and nucleation does not proceed. Freezing does not start until the temperature is low enough to provide enough energy to form stable nuclei. In presence of irregularities on the surface of the containing vessel, solid or gaseous impurities, pre-formed solid crystals, or other nucleators, heterogeneous nucleation may occur, where some energy is released by the partial destruction of the previous interface, raising the supercooling point to be near or equal to the melting point. The melting point of water at 1 atmosphere of pressure is very close to 0 °C (32 °F, 273.15 K), and in the presence of nucleating substances the freezing point of water is close to the melting point, but in the absence of nucleators water can supercool to −40 °C (−40 °F, 233 K) before freezing. Under high pressure (2,000 atmospheres) water will supercool to as low as −70 °C (−94 °F, 203 K) before freezing. Freezing is almost always an exothermic process, meaning that as liquid changes into solid, heat and pressure are released. This is often seen as counter-intuitive, since the temperature of the material does not rise during freezing, except if the liquid were supercooled. But this can be understood since heat must be continually removed from the freezing liquid or the freezing process will stop. The energy released upon freezing is a latent heat, and is known as the enthalpy of fusion and is exactly the same as the energy required to melt the same amount of the solid. Low-temperature helium is the only known exception to the general rule. Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative enthalpy of fusion below 0.8 K. This means that, at appropriate constant pressures, heat must be "added" to these substances in order to freeze them. Certain materials, such as glass and glycerol, may harden without crystallizing; these are called amorphous solids. Amorphous materials, as well as some polymers, do not have a freezing point, as there is no abrupt phase change at any specific temperature. Instead, there is a gradual change in their viscoelastic properties over a range of temperatures. Such materials are characterized by a glass transition that occurs at a glass transition temperature, which may be roughly defined as the "knee" point of the material's density vs. temperature graph. Because vitrification is a non-equilibrium process, it does not qualify as freezing, which requires an equilibrium between the crystalline and liquid state. Some substances, such as water and bismuth, expand when frozen. Many living organisms are able to tolerate prolonged periods of time at temperatures below the freezing point of water. Most living organisms accumulate cryoprotectants such as anti-nucleating proteins, polyols, and glucose to protect themselves against frost damage by sharp ice crystals. Most plants, in particular, can safely reach temperatures of −4 °C to −12 °C. Certain bacteria, notably "Pseudomonas syringae", produce specialized proteins that serve as potent ice nucleators, which they use to force ice formation on the surface of various fruits and plants at about −2 °C. The freezing causes injuries in the epithelia and makes the nutrients in the underlying plant tissues available to the bacteria. Three species of bacteria, "Carnobacterium pleistocenium", as well as "Chryseobacterium greenlandensis" and "Herminiimonas glaciei", have reportedly been revived after surviving for thousands of years frozen in ice. Many plants undergo a process called hardening, which allows them to survive temperatures below 0 °C for weeks to months. The nematode "Haemonchus contortus" can survive 44 weeks frozen at liquid nitrogen temperatures. Other nematodes that survive at temperatures below 0 °C include "Trichostrongylus colubriformis" and "Panagrolaimus davidi". Many species of reptiles and amphibians survive freezing. See cryobiology for a full discussion. Human gametes and 2-, 4- and 8-cell embryos can survive freezing and are viable for up to 10 years, a process known as cryopreservation. Experimental attempts to freeze human beings for later revival are known as cryonics. Freezing is a common method of food preservation that slows both food decay and the growth of micro-organisms. Besides the effect of lower temperatures on reaction rates, freezing makes water less available for bacteria growth.	Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. 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summarize: "Nucleate boiling" is characterized by the growth of bubbles or pops on a heated surface, which rises from discrete points on a surface, whose temperature is only slightly above the temperature of the liquid. In general, the number of nucleation sites is increased by an increasing surface temperature. An irregular surface of the boiling vessel (i.e., increased surface roughness) or additives to the fluid (i.e., surfactants and/or nanoparticles) facilitate nucleate boiling over a broader temperature range, while an exceptionally smooth surface, such as plastic, lends itself to superheating. Under these conditions, a heated liquid may show boiling delay and the temperature may go somewhat above the boiling point without boiling. "Critical heat flux (CHF)" describes the thermal limit of a phenomenon where a phase change occurs during heating (such as bubbles forming on a metal surface used to heat water), which suddenly decreases the efficiency of heat transfer, thus causing localised overheating of the heating surface. As the boiling surface is heated above a critical temperature, a film of vapor forms on the surface. Since this vapor film is much less capable of carrying heat away from the surface, the temperature rises very rapidly beyond this point into the transition boiling regime. The point at which this occurs is dependent on the characteristics of boiling fluid and the heating surface in question. "Transition boiling" may be defined as the unstable boiling, which occurs at surface temperatures between the maximum attainable in nucleate and the minimum attainable in film boiling. The formation of bubbles in a heated liquid is a complex physical process which often involves cavitation and acoustic effects, such as the broad-spectrum hiss one hears in a kettle not yet heated to the point where bubbles boil to the surface. If a surface heating the liquid is significantly hotter than the liquid then film boiling will occur, where a thin layer of vapor, which has low thermal conductivity, insulates the surface. This condition of a vapor film insulating the surface from the liquid characterizes "film boiling". The boiling point of an element at a given pressure is a characteristic attribute of the element. This is also true for many simple compounds including water and simple alcohols. Once boiling has started and provided that boiling remains stable and the pressure is constant, the temperature of the boiling liquid remains constant. This attribute led to the adoption of boiling points as the definition of 100°C. Mixtures of volatile liquids have a boiling point specific to that mixture producing vapour with a constant mix of components - the constant boiling mixture. This attribute allows mixtures of liquids to be separated or partly separated by boiling and is best known as a means of separating ethanol from water. Most types of refrigeration and some type of air-conditioning work by compressing a gas so that it becomes liquid and then allowing it to boil. This adsorbs heat from the surroundings cooling the 'fridge or freezer or cooling the air entering a building. Typical liquids include propane, ammonia, carbon dioxide or nitrogen. As a method of disinfecting water, bringing it to its boiling point at, is the oldest and most effective way since it does not affect the taste, it is effective despite contaminants or particles present in it, and is a single step process which eliminates most microbes responsible for causing intestine related diseases. The boiling point of water is at sea level and at normal barometric pressure. In places having a proper water purification system, it is recommended only as an emergency treatment method or for obtaining potable water in the wilderness or in rural areas, as it cannot remove chemical toxins or impurities. The elimination of micro-organisms by boiling follows first-order kinetics—at high temperatures, it is achieved in less time and at lower temperatures, in more time. The heat sensitivity of micro-organisms varies, at, Giardia species (causes Giardiasis) can take ten minutes for complete inactivation, most intestine affecting microbes and "E. coli" (gastroenteritis) take less than a minute; at boiling point, "Vibrio cholerae" (cholera) takes ten seconds and hepatitis A virus (causes the symptom of jaundice), one minute. Boiling does not ensure the elimination of all micro-organisms; the bacterial spores Clostridium can survive at but are not water-borne or intestine affecting. Thus for human health, complete sterilization of water is not required. The traditional advice of boiling water for ten minutes is mainly for additional safety, since microbes start getting eliminated at temperatures greater than and bringing it to its boiling point is also a useful indication that can be seen without the help of a thermometer, and by this time, the water is disinfected. Though the boiling point decreases with increasing altitude, it is not enough to affect the disinfecting process. "Boiling" is the method of cooking food in boiling water or other water-based liquids such as stock or milk. Simmering is gentle boiling, while in poaching the cooking liquid moves but scarcely bubbles. The boiling point of water is typically considered to be. Pressure and a change in the composition of the liquid may alter the boiling point of the liquid. High elevation cooking generally takes longer since boiling point is a function of atmospheric pressure. At an elevations of about, water boils at approximately 95 °C or 203 °F. Depending on the type of food and the elevation, the boiling water may not be hot enough to cook the food properly. Similarly, increasing the pressure as in a pressure cooker raises the temperature of the contents above the open air boiling point. Also known as "boil-in-bag", this involves heating or cooking ready-made foods sealed in a thick plastic bag. The bag containing the food, often frozen, is submerged in boiling water for a prescribed time. The resulting dishes can be prepared with greater convenience as no pots or pans are dirtied in the process. Such meals are available for camping as well as home dining. At any given temperature, all the molecules in a liquid do not have the same kinetic energy. Some high energy particles on the liquid surface may have enough energy to escape the intermolecular forces of attraction of the liquid and become a gas. This is called evaporation. Evaporation only happens on the surface while boiling happens throughout the liquid. When a liquid reaches its boiling point bubbles of gas form in it which rise into the surface and burst into the air. This process is called boiling. If the boiling liquid is heated more strongly the temperature does not rise but the liquid boils more quickly. This distinction is exclusive to the liquid-to-gas transition; any transition directly from solid to gas is always referred to as sublimation regardless of whether it is at its boiling point or not.	Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. There are two main types of boiling: nucleate boiling where small bubbles of vapour form at discrete points, and critical heat flux boiling where the boiling surface is heated above a certain critical temperature and a film of vapor forms on the surface. Transition boiling is an intermediate, unstable form of boiling with elements of both types. 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summarize: A "saturated liquid" contains as much thermal energy as it can without boiling (or conversely a "saturated vapor" contains as little thermal energy as it can without condensing). Saturation temperature means "boiling point". The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition. If the pressure in a system remains constant (isobaric), a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy (heat) is removed. Similarly, a liquid at saturation temperature and pressure will boil into its vapor phase as additional thermal energy is applied. The boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the surrounding environmental pressure. Thus, the boiling point is dependent on the pressure. Boiling points may be published with respect to the NIST, USA standard pressure of 101.325 kPa (or 1 atm), or the IUPAC standard pressure of 100.000 kPa. At higher elevations, where the atmospheric pressure is much lower, the boiling point is also lower. The boiling point increases with increased pressure up to the critical point, where the gas and liquid properties become identical. The boiling point cannot be increased beyond the critical point. Likewise, the boiling point decreases with decreasing pressure until the triple point is reached. The boiling point cannot be reduced below the triple point. If the heat of vaporization and the vapor pressure of a liquid at a certain temperature are known, the boiling point can be calculated by using the Clausius–Clapeyron equation, thus: where: Saturation pressure is the pressure for a corresponding saturation temperature at which a liquid boils into its vapor phase. Saturation pressure and saturation temperature have a direct relationship: as saturation pressure is increased, so is saturation temperature. If the temperature in a system remains constant (an "isothermal" system), vapor at saturation pressure and temperature will begin to condense into its liquid phase as the system pressure is increased. Similarly, a liquid at saturation pressure and temperature will tend to flash into its vapor phase as system pressure is decreased. There are two conventions regarding the "standard boiling point of water": The "normal boiling point" is at a pressure of 1 atm (i.e., 101.325 kPa). The IUPAC recommended "standard boiling point of water" at a standard pressure of 100 kPa (1 bar) is. For comparison, on top of Mount Everest, at elevation, the pressure is about and the boiling point of water is. The Celsius temperature scale was defined until 1954 by two points: 0 °C being defined by the water freezing point and 100 °C being defined by the water boiling point at standard atmospheric pressure. The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point (i.e., the boiling point at atmospheric pressure) of the liquid. The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids. As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points. For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−24.2 °C), which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure. The critical point of a liquid is the highest temperature (and pressure) it will actually boil at. See also Vapour pressure of water. The element with the lowest boiling point is helium. Both the boiling points of rhenium and tungsten exceed 5000 K at standard pressure; because it is difficult to measure extreme temperatures precisely without bias, both have been cited in the literature as having the higher boiling point. As can be seen from the above plot of the logarithm of the vapor pressure vs. the temperature for any given pure chemical compound, its normal boiling point can serve as an indication of that compound's overall volatility. A given pure compound has only one normal boiling point, if any, and a compound's normal boiling point and melting point can serve as characteristic physical properties for that compound, listed in reference books. The higher a compound's normal boiling point, the less volatile that compound is overall, and conversely, the lower a compound's normal boiling point, the more volatile that compound is overall. Some compounds decompose at higher temperatures before reaching their normal boiling point, or sometimes even their melting point. For a stable compound, the boiling point ranges from its triple point to its critical point, depending on the external pressure. Beyond its triple point, a compound's normal boiling point, if any, is higher than its melting point. Beyond the critical point, a compound's liquid and vapor phases merge into one phase, which may be called a superheated gas. At any given temperature, if a compound's normal boiling point is lower, then that compound will generally exist as a gas at atmospheric external pressure. If the compound's normal boiling point is higher, then that compound can exist as a liquid or solid at that given temperature at atmospheric external pressure, and will so exist in equilibrium with its vapor (if volatile) if its vapors are contained. If a compound's vapors are not contained, then some volatile compounds can eventually evaporate away in spite of their higher boiling points. In general, compounds with ionic bonds have high normal boiling points, if they do not decompose before reaching such high temperatures. Many metals have high boiling points, but not all. Very generally—with other factors being equal—in compounds with covalently bonded molecules, as the size of the molecule (or molecular mass) increases, the normal boiling point increases. When the molecular size becomes that of a macromolecule, polymer, or otherwise very large, the compound often decomposes at high temperature before the boiling point is reached. Another factor that affects the normal boiling point of a compound is the polarity of its molecules. As the polarity of a compound's molecules increases, its normal boiling point increases, other factors being equal. Closely related is the ability of a molecule to form hydrogen bonds (in the liquid state), which makes it harder for molecules to leave the liquid state and thus increases the normal boiling point of the compound. Simple carboxylic acids dimerize by forming hydrogen bonds between molecules. A minor factor affecting boiling points is the shape of a molecule. Making the shape of a molecule more compact tends to lower the normal boiling point slightly compared to an equivalent molecule with more surface area. Most volatile compounds (anywhere near ambient temperatures) go through an intermediate liquid phase while warming up from a solid phase to eventually transform to a vapor phase. By comparison to boiling, a sublimation is a physical transformation in which a solid turns directly into vapor, which happens in a few select cases such as with carbon dioxide at atmospheric pressure. For such compounds, a sublimation point is a temperature at which a solid turning directly into vapor has a vapor pressure equal to the external pressure. In the preceding section, boiling points of pure compounds were covered. Vapor pressures and boiling points of substances can be affected by the presence of dissolved impurities (solutes) or other miscible compounds, the degree of effect depending on the concentration of the impurities or other compounds. The presence of non-volatile impurities such as salts or compounds of a volatility far lower than the main component compound decreases its mole fraction and the solution's volatility, and thus raises the normal boiling point in proportion to the concentration of the solutes. This effect is called boiling point elevation. As a common example, salt water boils at a higher temperature than pure water. In other mixtures of miscible compounds (components), there may be two or more components of varying volatility, each having its own pure component boiling point at any given pressure. The presence of other volatile components in a mixture affects the vapor pressures and thus boiling points and dew points of all the components in the mixture. The dew point is a temperature at which a vapor condenses into a liquid. Furthermore, at any given temperature, the composition of the vapor is different from the composition of the liquid in most such cases. In order to illustrate these effects between the volatile components in a mixture, a boiling point diagram is commonly used. Distillation is a process of boiling and [usually] condensation which takes advantage of these differences in composition between liquid and vapor phases.	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summarize: Values are usually quoted in J/mol or kJ/mol (molar enthalpy of vaporization), although kJ/kg or J/g (specific heat of vaporization), and older units like kcal/mol, cal/g and Btu/lb are sometimes still used, among others. The enthalpy of condensation (or heat of condensation) is by definition equal to the enthalpy of vaporization with the opposite sign: enthalpy changes of vaporization are always positive (heat is absorbed by the substance), whereas enthalpy changes of condensation are always negative (heat is released by the substance). The enthalpy of vaporization can be written as It is equal to the increased internal energy of the vapor phase compared with the liquid phase, plus the work done against ambient pressure. The increase in the internal energy can be viewed as the energy required to overcome the intermolecular interactions in the liquid (or solid, in the case of sublimation). Hence helium has a particularly low enthalpy of vaporization, 0.0845 kJ/mol, as the van der Waals forces between helium atoms are particularly weak. On the other hand, the molecules in liquid water are held together by relatively strong hydrogen bonds, and its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C ("c" = 75.3 J Kmol). Care must be taken, however, when using enthalpies of vaporization to "measure" the strength of intermolecular forces, as these forces may persist to an extent in the gas phase (as is the case with hydrogen fluoride), and so the calculated value of the bond strength will be too low. This is particularly true of metals, which often form covalently bonded molecules in the gas phase: in these cases, the enthalpy of atomization must be used to obtain a true value of the bond energy. An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop in entropy when a gas condenses to a liquid. As the liquid and gas are in equilibrium at the boiling point ("T"), Δ"G" = 0, which leads to: As neither entropy nor enthalpy vary greatly with temperature, it is normal to use the tabulated standard values without any correction for the difference in temperature from 298 K. A correction must be made if the pressure is different from 100 kPa, as the entropy of a gas is proportional to its pressure (or, more precisely, to its fugacity): the entropies of liquids vary little with pressure, as the compressibility of a liquid is small. These two definitions are equivalent: the boiling point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. As a given quantity of matter always has a higher entropy in the gas phase than in a condensed phase (formula_6 is always positive), and from the Gibbs free energy change falls with increasing temperature: gases are favored at higher temperatures, as is observed in practice. Estimation of the enthalpy of vaporization of electrolyte solutions can be simply carried out using equations based on the chemical thermodynamic models, such as Pitzer model or TCPC model. The vaporization of metals is a key step in metal vapor synthesis, which exploits the increased reactivity of metal atoms or small particles relative to the bulk elements. Enthalpies of vaporization of common substances, measured at their respective standard boiling points:	The enthalpy of vaporization, (symbol ) also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance, to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.	en	en	68	[ 250004, 250054, 190060, 7, 621, 56104, 66747, 71, 23, 821, 64, 17965, 707, 472, 1375, 64, 17965, 15, 432, 320, 22, 56680, 6493, 111, 101319, 47691, 247, 102971, 472, 1375, 64, 8517, 707, 821, 64, 177, 15, 159975, 80097, 111, 101319, 47691, 247, 136, 114210, 25072, 7, 1884, 158805, 64, 17965, 4, 6510, 64, 177, 136, 335, 458, 64, 48543, 621, 68018, 7464, 11814, 4, 54940, 27060, 5, 581, 22, 56680, 6493, 111, 188171, 1363, 15, 748, 80097, 111, 188171, 1363, 16, 83, 390, 80934, 105950, 47, 70, 22, 56680, 6493, 111, 101319, 47691, 678, 70, 198274, 24092, 12, 22, 56680, 6493, 65572, 111, 101319, 47691, 621, 11343, 24491, 15, 156253, 83, 57622, 297, 390, 70, 161451, 247, 7440, 162, 22, 56680, 6493, 65572, 111, 188171, 1363, 621, 11343, 40907, 15, 156253, 83, 121447, 390, 70, 161451, 194, 581, 22, 56680, 6493, 111, 101319, 47691, 831, 186, 59121, 237, 1650, 83, 105950, 47, 70, 124735, 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summarize: Solid carbon dioxide (dry ice) sublimes everywhere along the line below the triple point (e.g., at the temperature of −78.5 °C (194.65 K, ) at atmospheric pressure, whereas its melting into liquid CO can occur only along the line at pressures and temperatures above the triple point (i.e., 5.2 atm, −56.4 °C). Snow and ice sublime, although more slowly, at temperatures below the freezing/melting point temperature line at 0 °C for most pressures; see line below triple point. In freeze-drying, the material to be dehydrated is frozen and its water is allowed to sublime under reduced pressure or vacuum. The loss of snow from a snowfield during a cold spell is often caused by sunshine acting directly on the upper layers of the snow. Ablation is a process that includes sublimation and erosive wear of glacier ice. Naphthalene, an organic compound commonly found in pesticides such as mothballs, sublimes easily because it is made of non-polar molecules that are held together only by van der Waals intermolecular forces. Naphthalene is a solid that sublimes at standard atmospheric temperature with the sublimation point at around 80°C or 176°F. At low temperature, its vapour pressure is high enough, 1mmHg at 53°C, to make the solid form of naphthalene evaporate into gas. On cool surfaces, the naphthalene vapours will solidify to form needle-like crystals. Iodine produces fumes on gentle heating. It is possible to obtain liquid iodine at atmospheric pressure by controlling the temperature at just above the melting point of iodine. In forensic science, iodine vapor can reveal latent fingerprints on paper. Arsenic can also sublime at high temperatures. Cadmium and zinc are not suitable materials for use in vacuum because they sublime much more than other common materials. Sublimation is a technique used by chemists to purify compounds. A solid is typically placed in a sublimation apparatus and heated under vacuum. Under this reduced pressure, the solid volatilizes and condenses as a purified compound on a cooled surface (cold finger), leaving a non-volatile residue of impurities behind. Once heating ceases and the vacuum is removed, the purified compound may be collected from the cooling surface. For even higher purification efficiencies, a temperature gradient is applied, which also allows for the separation of different fractions. Typical setups use an evacuated glass tube that is heated gradually in a controlled manner. The material flow is from the hot end, where the initial material is placed, to the cold end that is connected to a pump stand. By controlling temperatures along the length of the tube, the operator can control the zones of re-condensation, with very volatile compounds being pumped out of the system completely (or caught by a separate cold trap), moderately volatile compounds re-condensing along the tube according to their different volatilities, and non-volatile compounds remaining in the hot end. Vacuum sublimation of this type is also the method of choice for purification of organic compounds for use in the organic electronics industry, where very high purities (often > 99.99%) are needed to satisfy the standards for consumer electronics and other applications. In ancient alchemy, a protoscience that contributed to the development of modern chemistry and medicine, alchemists developed a structure of basic laboratory techniques, theory, terminology, and experimental methods. "Sublimation" was used to refer to the process in which a substance is heated to a vapor, then immediately collects as sediment on the upper portion and neck of the heating medium (typically a retort or alembic), but can also be used to describe other similar non-laboratory transitions. It was mentioned by alchemical authors such as Basil Valentine and George Ripley, and in the "Rosarium philosophorum", as a process necessary for the completion of the magnum opus. Here, the word "sublimation" was used to describe an exchange of "bodies" and "spirits" similar to laboratory phase transition between solids and gases. Valentine, in his "Le char triomphal de l'antimoine" (Triumphal Chariot of Antimony, published 1646) made a comparison to spagyrics in which a vegetable sublimation can be used to separate the spirits in wine and beer. Ripley used language more indicative of the mystical implications of sublimation, indicating that the process has a double aspect in the spiritualization of the body and the corporalizing of the spirit. He writes: <poem> And Sublimations we make for three causes, The first cause is to make the body spiritual. The second is that the spirit may be corporeal, And become fixed with it and consubstantial. The third cause is that from its filthy original. It may be cleansed, and its saltiness sulphurious May be diminished in it, which is infectious. </poem> The enthalpy of sublimation has commonly been predicted using the equipartition theorem. If the lattice energy is assumed to be approximately half the packing energy, then the following thermodynamic corrections can be applied to predict the enthalpy of sublimation. Assuming a 1 molar ideal gas gives a correction for the thermodynamic environment (pressure and volume) in which pV = RT, hence a correction of 1RT. Additional corrections for the vibrations, rotations and translation then need to be applied. From the equipartition theorem gaseous rotation and translation contribute 1.5RT each to the final state, therefore a +3RT correction. Crystalline vibrations and rotations contribute 3RT each to the initial state, hence −6RT. Summing the RT corrections; −6RT + 3RT + RT = −2RT. This leads to the following approximate sublimation enthalpy. A similar approximation can be found for the entropy term if rigid bodies are assumed. formula_1 Dye-sub printing is a digital printing technology using full color artwork that works with polyester and polymer-coated substrates. Also referred to as digital sublimation, the process is commonly used for decorating apparel, signs and banners, as well as novelty items such as cell phone covers, plaques, coffee mugs, and other items with sublimation-friendly surfaces. The process uses the science of sublimation, in which heat and pressure are applied to a solid, turning it into a gas through an endothermic reaction without passing through the liquid phase. In sublimation printing, unique sublimation dyes are transferred to sheets of “transfer” paper via liquid gel ink through a piezoelectric print head. The ink is deposited on these high-release inkjet papers, which are used for the next step of the sublimation printing process. After the digital design is printed onto sublimation transfer sheets, it is placed on a heat press along with the substrate to be sublimated. In order to transfer the image from the paper to the substrate, it requires a heat press process that is a combination of time, temperature and pressure. The heat press applies this special combination, which can change depending on the substrate, to “transfer” the sublimation dyes at the molecular level into the substrate. The most common dyes used for sublimation activate at 350 degrees Fahrenheit. However, a range of 380 to 420 degrees Fahrenheit is normally recommended for optimal color. The end result of the sublimation process is a nearly permanent, high resolution, full color print. Because the dyes are infused into the substrate at the molecular level, rather than applied at a topical level (such as with screen printing and direct to garment printing), the prints will not crack, fade or peel from the substrate under normal conditions.	Sublimation is the transition of a substance directly from the solid to the gas state, without passing through the liquid state. Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation is deposition or desublimation, in which a substance passes directly from a gas to a solid phase. Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition). While a transition from liquid to gas is described as evaporation if it occurs below the boiling point of the liquid, and as boiling if it occurs at the boiling point, there is no such distinction within the solid-to-gas transition, which is always described as sublimation.	en	en	161	[ 250004, 250054, 95823, 44603, 6, 143961, 13, 15, 48855, 6, 2980, 16, 117584, 90, 219743, 33233, 70, 13315, 35064, 70, 162738, 6275, 15, 13, 5, 177, 5, 4, 99, 70, 52768, 111, 48768, 966, 107944, 16207, 441, 5173, 115459, 758, 341, 4, 1388, 99, 99, 840, 94266, 1771, 81147, 4, 7440, 162, 6863, 21501, 1916, 3934, 41931, 8244, 831, 74918, 4734, 33233, 70, 13315, 99, 81147, 7, 136, 52768, 7, 36917, 70, 162738, 6275, 15, 14, 5, 13, 5, 4, 97608, 99, 39, 4, 48768, 13683, 5, 617, 16207, 441, 194, 76935, 136, 6, 2980, 117584, 13, 4, 102971, 1286, 191975, 4, 99, 52768, 7, 35064, 70, 4092, 35401, 64, 76681, 214, 6275, 52768, 13315, 99, 757, 16207, 441, 100, 2684, 81147, 7, 74, 1957, 13315, 35064, 162738, 6275, 5, 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summarize: Sebastiano del Piombo was probably born in Venice, though there is no certainty as to his background. His birthdate is extrapolated from Vasari's statement that he was 62 at his death in 1547. That he was first known as a musician and singer may suggest an upper-middle-class background; the extent to which his playing on the lute and other instruments was professional is unclear. Like his contemporary Raphael, his career was marked by his ability to get on well with both other artists and patrons. He began to train as a painter at a relatively late age, probably 18 or 20, so around 1503–05, becoming a pupil of Giovanni Bellini and probably afterwards of Giorgione, both of whose influence is apparent in his works; Vasari's mention of their relationship is rather vague: ""si acconciò con Giorgione"". No signed or firmly documented works survive from his period painting in Venice, and many attributions are disputed. As with other artists, some of Sebastiano's works have long been confused with Giorgione's. Like Titian, he may have completed work left unfinished at Giorgione's death in 1510; Marcantonio Michiel says he finished "The Three Philosophers". The earliest significant work attributed to him is a portrait of a girl in Budapest, of about 1505. He is now usually assigned the unfinished and reworked "Judgement of Solomon" now at Kingston Lacy. This dramatic and imposing picture, "one of the masterpieces of Venetian narrative painting", was also long attributed to Giorgione; it may have been abandoned about 1508, though the estimated dates vary in the period 1505–1510. After extensive restoration in the 1980s, removing later overpainting, the painting is now left with traces of the three different compositions visible; still more can be seen with infra-red reflectography. Still over 2 × 3 metres, it seems originally to have been even larger, with some 40 cm lost along the left edge. There are two versions of the elaborate architectural background, which was a recurrent interest of Sebastiano's Venetian period. The last setting is in a basilica, which may reflect a "more learned" picture intended for a building holding courts of justice. The figure at the front of the executioner, left without clothes or the baby, is clearly drawn from classical sculpture. Four standing figures of saints in niches on the organ-shutters of San Bartolomeo, Venice, now in the Gallerie dell'Accademia in Venice, date from c. 1508–09, and are "very Giorgionesque", especially the pair on the insides. They were painted at the same time as Giorgione's frescos for the Fondaco dei Tedeschi (now lost) just by the church, which was the German's church in Venice, and at this time also held Albrecht Dürer's "Madonna of the Rose-Garlands" of 1506. The outside pair of shutters also show what Sebastiano had learnt from Bellini. Their technique has developed "from the earlier smooth surface to the application of paint in heavy brushstrokes", and the figure of Saint Sebastian shows awareness of classical sculpture. The main altarpiece for San Giovanni Crisostomo, Venice of 1510–11 shows the patron saint, Saint John Chrysostom reading aloud at a desk, a Mary Magdalene looking out at the viewer, and two other female and three male saints. The organ-shutters for the church were also painted. The style shows developments "towards a new fullness of form and breadth of movement" that may have been influenced by the Florentine painter Fra Bartolommeo, who was in Venice in 1508. Aspects of the composition were also innovative, and later copied by Venetian painters, including even Titian. In 1511 the Papal banker Agostino Chigi was the richest man in Rome, and a generous patron of the arts. Early in the year he was sent to Venice by Pope Julius II to buy Venetian support for the papacy in the War of the League of Cambrai. When he returned to Rome after a stay of some six months, he brought Sebastiano with him; Sebastiano was to remain based in Rome for the rest of his life. Sebastiano began by painting mythological subjects in lunettes in the "Sala di Galatea" in Chigi's Villa Farnesina, under a ceiling just done by Baldassarre Peruzzi. In these he already shows an adaption to Roman style, especially that of Michelangelo, whose Sistine Chapel ceiling had just been completed. Probably the next year, he added a large "Polyphemus". It is possible that Raphael's famous "Galatea" of 1514, which is in the next bay and now dominates the room, replaced a fresco by Sebastiano. A larger cycle on the lower walls was apparently intended, but abandoned, for reasons that are not clear. Sebastiano had also been producing easel paintings from soon after his arrival, showing the development of his new style. A "Death of Adonis" in the Uffizi dates to about 1512–13, and shows that he "had achieved a working dialectic of Roman and Venetian classical styles", in which he "enlarged the proportion of his figures into an almost bulking massiveness, ponderous and sensuously splendid: idealizations, but of sensuous existence". By about 1515, Sebastiano had befriended and allied himself with Michelangelo, who recruited him "as a kind of deputy for him in painting", he having returned to his backlog of promised projects in sculpture. Michelangelo's intention was for Sebastiano to "contest Raphael's first place" in painting in Rome, using at least in part ideas and designs supplied by Michelangelo, whose rivalry with Raphael had become intense. The intention may have been for a closer relationship than actually resulted, as in 1516 Michelangelo returned to Florence, only returning occasionally to Rome for several years after. The first result of this collaboration was one of Sebastiano's most important paintings, a "Pietà" in Viterbo. Here the composition is highly unusual for this common subject (which Michelangelo had famously sculpted in 1498–99), with Christ lying across the bottom of the picture space, at the feet of a Virgin looking up to Heaven, so that the two figures do not actually touch. Though no drawing survives, this was Michelangelo's conception, where "an idea of high tragic power is expressed with extreme simplicity in a structure of severe geometric rigour". The back of the panels have large sketches in charcoal that seem to be by both artists. In 1516 he painted a similar subject, the "Lamentation of Jesus" (now Hermitage Museum) using his own composition, and showing his awareness of Raphael's handling of groups of figures. These led a Florentine friend of Michelangelo, Pierfrancesco Borgherini, to commission Sebastiano to decorate a chapel in San Pietro in Montorio in Rome; he no doubt hoped to get significant input from Michelangelo. There is a Michelangelo drawing of 1516 for the "Flagellation of Jesus" in the British Museum, and other sketches; the final design survives only in a copy by Giulio Clovio after another Michelangelo drawing (Royal Collection). In the event there were a series of interruptions and Sebastiano did not complete the chapel until early 1524. The "Flagellation" is painted in oil on plaster. This was a method first practiced by Domenico Veneziano, and afterwards by other artists; but according to Vasari only Sebastiano succeeded in preventing the colours eventually blackening. The last major work of the period was the "Raising of Lazarus", now in the National Gallery, London, which was commissioned in 1516 by Cardinal Giulio de Medici, archbishop of Narbonne in southern France, and the future Pope Clement VII, in blatant competition, engineered by Michelangelo, with a painting of the same size by Raphael, the "Transfiguration". Both were supposed to hang in Narbonne Cathedral. Michelangelo supplied at least drawings for the figure of Lazarus and the two men supporting him (British Museum), but probably did not do any work on the painting itself, if only because he was only briefly in Rome during the time it was painted. When the two paintings were hung together in the Vatican, just after Raphael's death in 1520, both were praised, but the Raphael generally preferred, as has remained the case ever since. In the early 1520s Sebastiano completed the Borgherini Chapel with a "Transfiguration" in the semi-dome above his "Flagellation". The combination shows the influence of the "Apocalipsis Nova", a contemporary text that prophesied the coming of an "Angelic Pastor" who would bring a new age of peace. Michelangelo was among many reformist Catholics interested in the text. The "Flagellation" represents "the current, corrupted state of Christianity and the Transfiguration the glorious future to come". The death of Raphael in 1520, immediately before the exhibition of the two rival paintings intended for Narbonne, left Sebastiano clearly the leading painter operating in Rome. As his letters show, he immediately attempted to secure for himself the "Sala dei Pontefici", Raphael's next Vatican project, but was frustrated by Raphael's workshop, armed with the master's drawings, and his own inability to enlist Michelangelo's help, as the pope had told him to work exclusively on the long-promised Tomb of Pope Julius II. In the following years Sebastiano mostly avoided very large commissions for churches, and concentrated on portraits, where he had a considerable reputation, and religious easel paintings, such as his "Visitation" for France (1518–19, now Louvre), and his "Madonna of the Veil" (c. 1525), a very successful adaptation of Raphael's "Madonna di Loreto". To both of these types he brought his refined monumental classicism. His career in the decade was greatly impacted by outside events. In 1522 there was plague in Rome, and he may have left Rome for a long period; there is little evidence of his activity for over a year. In 1523 Giulio de Medici became Pope Clement VII, and thereafter Sebastiano seems to have been a part of Vatican court life. He painted a number of portraits of the pope, and other paintings for him. In 1527 he seems to have remained with the pope all through the horrors of the Sack of Rome and his nervous retreat to Orvieto, though he seems to have spent time in Venice in 1528 and perhaps 1529, his first known return there since 1511. This catastrophe brought to an end the High Renaissance epoch in Rome, scattering Raphael's workshop and the emerging Roman Mannerists, and largely destroying the confidence of patrons. In 1531 the death of the previous holder allowed Sebastiano to press Pope Clement for the lucrative office of the ""piombatore"", which he obtained after promising to pay a fixed sum of 300 scudi annually to the other main contender, Giovanni da Udine, who was also a painter, from Raphael's workshop. To hold the position he had to take vows as a friar, despite having a wife and two children. After this his paintings, which are more often signed than dated, carry signatures such as "F(rater) Sebastianus Ven(etus)". Sebastiano's artistic output reduced after taking the court role, though possibly not by as much as Vasari suggests. Large projects, even of a single painting, could take many years to complete, as with a "Pieta" for Spain. This was the last piece where Michelangelo helped him with a drawing. Vasari, probably much influenced by Michelangelo, places great emphasis on Sebastiano's turning away from art for a comfortable life as a well-paid courtier from this point, but may overstate the reality. His friendship with Michelangelo came to an end in 1534, after a disagreement over the latter's "Last Judgment" in the Sistine Chapel. Sebastiano encouraged the pope to insist that this picture should be executed in oil on plaster, the technique he had developed and used. The enormous wall was prepared with the smooth plaster needed for this, with Michelangelo apparently acquiescent. There may even have been the idea floated that Sebastiano might do the painting to Michelangelo's designs. Michelangelo may also have tried painting in oils on the smooth surface. It is clear that several months after the idea of using oils first appeared, Michelangelo finally and furiously rejected it, and insisted that the whole wall be re-plastered in the rough "arriccio" needed as a base for fresco. It was on this occasion that he famously said that oil painting was "an art for women and for leisurely and idle people like Fra Sebastiano". Two late projects for churches were never finished by Sebastiano. A large altarpiece of the "Birth of the Virgin", still in Santa Maria del Popolo, Rome, was begun in the late 1530s but had to be finished after his death by Francesco Salviati. Before his death in 1541, the executor of Agostino Chigi's estate commissioned a large "Visitation" as a memorial, in Santa Maria della Pace, Rome. It was still half-finished at Sebastiano's death in 1547, and was eventually removed in the 17th century. Fragments with some of the over life-size main figures are at Alnwick Castle, in a style of impressive simplicity, the end point of a "tendency to over-generalize appearances and pictorial structures so that they verged on an effect of geometrical abstraction" that had been increasing apparent in his work since his early years in Rome. Vasari records that he died after a short illness on 14 June 1547, at the age of 62. His will directed that he be buried very simply in Santa Maria del Popolo, with the savings from not having an elaborate burial given to the poor. After efforts by Daniele da Volterra his remains were moved in 1561 to the predecessor of the Rome Accademia di San Luca. Sebastiano was trained in the Venetian tradition of rich, subtly varying, colours in oil painting. In the "Raising of Lazarus" (1517–1519) he used a very wide range of pigments, often in complicated mixtures, and the painting can be seen as a display of Venetian skill for the Roman critics, attempting to achieve "the greatest and most subtly varied range of colours ever seen in a single painting". He became less interested in colour as his career progressed, and many later works are rather sombre, with touches of bright colour. His early works generally use the Venetian technique of freehand underdrawing on the surface to be painted, no doubt following a relatively approximate sketch, as was his technique for the Kingston Lacy "Judgement of Solomon". But after some years in Rome he began to use full-size cartoons for frescos, which were pricked along the lines and then soot "pounced" through, to give dotted lines on the surface for the artist to follow. This technique, normal in Florence and Rome, was used in the fresco "Transfiguration" of the Borgherini Chapel, for which some pricked sheets survive. However, this was his last work in fresco. From early on he was innovative and ready to experiment in compositional details as well as technique, with a special interest in painting in oils on new surfaces, whether plaster, stone, alabaster or slate. Though tending to be dark, several of his works with these unorthodox backings have survived well. Though he often covered the whole surface, leaving no indication of the support, some of his paintings on mineral sheets leave the background unpainted. This is the case with a small head of Clement VII in Naples, wearing the beard he always had as a penance after the Sack of Rome. He made excellent drawings, nearly all as compositional sketches. He continued to prefer to draw on light blue paper in black chalk with white highlights, a Venetian habit. Few if any early ones survive, and he may have changed his methods to use more precise sketches under the influence of Michelangelo and Raphael. Few survive for his portraits. A British Museum "curator's comment" on one of their late drawings notes: "As so often with Sebastiano's drawings, the first impression is one of unrhythmic dryness; but the suggestion of atmosphere, the sensitively drawn contemplative faces and the subtle use of reflected lights and tonal transitions leave no doubt that [this] is from his own hand. Sebastiano seems to have followed Michelangelo in painting with "no more than merely mechanical assistance" from a studio, and had no significant pupils formed in his style. Whether this was a cause or result of his avoidance of large compositions and his court office from the 1530s we cannot know. The main sources for his personality and habits are Vasari and surviving letters, mostly to and from Michelangelo. Vasari knew Sebastiano, but probably not very well; although he had been compiling material for some time, the first edition of his "Lives" did not appear until 1550, after Sebastiano's death, and it is not clear if he had specifically discussed the biography with Sebastiano. He knew Michelangelo rather better, and his description of Sebastiano is probably heavily influenced by the hostile attitude Michelangelo had towards Sebastiano after 1534. Vasari takes up much of his "Life" bemoaning Sebastiano's supposed indolence and neglect of his artistic talent for a comfortable and convivial life, at least after 1531. Vasari says that in later life he lived in a fine house near the Piazza del Popolo, keeping a very good table, and often entertaining regular friends as well as visitors. He says he was always cheerful and humorous, and very good company. He became red-faced and rather fat, as the bearded portrait in the "Lives" suggests. As described above, he had become close to Michelangelo by about 1515. Though they eventually fell out, few people were able to remain on good terms with Michelangelo for a period of nearly twenty years. In 1519 Michelangelo became godfather to Sebastiano's first son, Luciano, after which Sebastiano addressed his letters to "My dearest "compare"" ("godfather"). The relationship suffered a dip in 1520 when Sebastiano asked Michelangelo to write to Cardinal Bibbiena, a close friend of Pope Leo X, recommending Sebastiano for projects in the Vatican after Raphael's death. Michelangelo sent the letter a month or so later, which Sebastiano presented to the cardinal, without reading it. The letter was in very flippant terms, and Sebastianio complained that it became "practically the only topic of conversation at the Palace, and it makes everyone laugh". Nor did it work in getting Vatican commissions. In 1521 he acted as Michelangelo's agent in the installation of the "Risen Christ" or "Cristo della Minerva" in Rome, which was botched by the assistant Michelangelo had sent. From 1525 there is a draft for an emotional letter by Michelangelo passing on praise for Sebastiano by one "Captain Cuio", who he had dined with. In 1531 Sebastiano writes a despondent letter describing how "I still don't feel I am the same Bastiano that I was before the Sack; I still don't feel in my right mind." The relationship never recovered from the argument over the "Last Judgement" in 1534, described above.	Sebastiano del Piombo (; c. 1485 – 21 June 1547) was an Italian painter of the High Renaissance and early Mannerist periods famous as the only major artist of the period to combine the colouring of the Venetian school in which he was trained with the monumental forms of the Roman school. He belongs both to the painting school of his native city, Venice, where he made significant contributions before he left for Rome in 1511, and that of Rome, where he stayed for the rest of his life, and whose style he thoroughly adopted.	en	en	104	[ 250004, 250054, 58685, 31, 146, 3065, 34298, 509, 31895, 103122, 23, 2609, 3466, 4, 21208, 2685, 83, 110, 24233, 939, 237, 47, 1919, 76615, 5, 18763, 127319, 17489, 83, 4173, 5877, 27686, 1295, 142654, 14, 25, 7, 63805, 450, 764, 509, 10031, 99, 1919, 47219, 23, 423, 13330, 5, 9925, 764, 509, 5117, 51529, 237, 10, 19612, 3378, 136, 5367, 56, 1543, 42459, 142, 1407, 56, 9, 22000, 19298, 9, 67413, 76615, 74, 70, 192961, 47, 3129, 1919, 75169, 98, 70, 3480, 67, 136, 3789, 13984, 7, 509, 23182, 83, 51, 119488, 5, 18852, 1919, 158, 99736, 6635, 242466, 4, 1919, 80997, 509, 94419, 390, 1919, 81273, 47, 2046, 98, 5299, 678, 15044, 3789, 22104, 7, 136, 32926, 7, 5, 1529, 80723, 47, 25550, 237, 10, 249, 10433, 99, 10, 35845, 538, 72399, 32070, 4, 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summarize: Modern flambéing became popular in the 19th century. The English Christmas pudding was served flaming in Charles Dickens' 1843 novel, "A Christmas Carol": "the pudding... blazing in half of half-a-quarter of ignited brandy". The most common flambé dish appears to have been sweet omelette with rum or kirsch; for example, Alexis Soyer's 1846 cookbook, "The Gastronomic Regenerator", gives a recipe for "Omelette au Rhum": "...the moment of going to table pour three glasses of rum round and set it on fire". Ida Joscelyne's book, "The Marvellous Little Housekeepers" (1880), mentions both rum and kirsch; another recipe appears in A.G. Payne's English cookbook, "Choice Dishes at Small Cost", of 1882: "Make a sweet omelet, and heat a tablespoonful of kirsch, by holding a light under the spoon. As soon as the spirit catches fire pour it round the omelet, and serve flaming." Perhaps the most famous flambé dish, Crêpe Suzette, was supposedly invented in 1895 as an accident. Cognac, rum, or other flavorful liquors that are about 40% alcohol (80 USA proof) are considered ideal for flambé. Wines and beers have too little alcohol and will not flambé. High-alcohol liquors, such as Bacardi 151 or Everclear, are highly flammable and considered too dangerous by professional cooks. Cinnamon is sometimes added not only for flavor but for show, as the powder ignites when added. The alcoholic beverage must be heated before lighting it on fire. This is because at room temperature, the liquid is still below the flash point, and there are not enough alcoholic vapors to ignite. By heating it, the vapor pressure increases, releasing enough vapors to catch fire from the match. Flambéing reduces the alcohol content of the food modestly. In one experimental model, about 25% of the alcohol was boiled off. The effects of the flames are also modest: although the temperature within the flame may be quite high (over 500 °C), the temperature at the surface of the pan is lower than that required for a Maillard browning reaction or for caramelization. Whether or not there is a change in flavor as result of flambéing is unclear. Some claim that because the flame is above the food, and since hot gases rise, it cannot significantly affect the flavor. Indeed, experimental work shows that most people cannot tell the difference. That said, in an informal taste test conducted by the "Los Angeles Times" of two batches of caramelized apples (one flambéed and one simmered), one tester declared the "flambéed dish was for adults, the other for kids". Others, however, dispute this and quote celebrated French chefs who claim that flambéing is strictly a show-biz aspect of restaurant business that ruins food but is done to create an impressive visual presentation at a dramatic point in the preparation of a meal. For safety, it is recommended that alcohol not be added to a pan on a burner, and that the cook use a long fireplace match to ignite the pan. Examples of popular flambé dishes include:	Flambé (, ; also spelled flambe) is a cooking procedure in which alcohol is added to a hot pan to create a burst of flames. 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summarize: While it is possible to safely preserve many kinds of foodstuffs, home canning can expose consumers to botulism and other kinds of food poisoning if done incorrectly. The most common source of food-borne botulism is home-canned foods prepared in an unsafe manner. Safety measures must be taken when performing home canning, since ingestion of toxin in food produced by "Clostridium botulinum" can cause death. Because of the high risk of illness or death associated with improper canning techniques, the United States Department of Agriculture (USDA) considers it critical that consumers who intend to can at home obtain proper and current information from a reliable source. At the basis of these recommendations is the balance between bringing the food to a high enough temperature for a long enough time that spoilage and disease-producing microorganisms are killed, while not heating the food so much that it loses nutritive value or palatability. In North America, home canning is usually done in Mason jars, which have thicker walls than single-use commercial glass jars. Unless the food being preserved has a high acid content (pH <4.6) or salt or sugar content resulting in water availability <0.85, such as pickles or jellies, the filled jars are also processed under pressure in a canner, a specialized type of pressure cooker. Ordinary pressure cookers are not recommended for canning as their smaller size and the reduced thickness of the cooker wall will not allow for the correct building up and reducing time of pressure, which is factored into the overall processing time and therefore will not destroy all the harmful microorganisms. The goal in using a pressure canner is to achieve a "botulinum cook" of 121 °C for 3 minutes, throughout the entire volume of canned product. Canners often incorporate racks to hold Mason jars, and pressure canners are capable of achieving the elevated temperatures needed to prevent spoilage. The most common configuration is a Mason jar with a flat lid and screw ring. The lid is generally made of plated or painted steel, with an elastomeric washer or gasket bonded to the underside of the rim. The lid also incorporates a slightly dimpled shape, which acts as an indicator of the vacuum (or lack thereof) inside a sealed jar. A newer reusable lid is now available that uses a flat plastic disk with a reusable rubber gasket. The ring threads onto the top of the jar over the lid to hold it in place while the jar cools after processing; the ring can be removed once a vacuum has been established in the jar. Jars are commonly in either pint or quart capacities, with two opening diameters, known as "standard" and "wide mouth". When a jar has cooled and is properly sealed, pressing the dimple on the lid will not make any sound. An improperly sealed jar will allow the dimple to move up and down, sometimes making a popping noise. Lack of this noise does not necessarily indicate that the food in the jar is properly preserved. Typically, during the cooling process, a properly sealed lid will pop once as the pressure inside the jar is reduced enough that atmospheric pressure pushes the lid inward. Older variations had a ceramic seal inside a one-piece zinc lid. Another method that is no longer recommended was the use of layer of hot paraffin wax poured directly over the top of the food (especially jams and jellies) to seal it from air, thus reducing growth of aerobic microorganisms like mold. In the United Kingdom home bottling is done with Kilner jars in a similar way to the Mason jars in the US, and although old-style Kilner jars have a glass lid without a "dimple" more recent varieties do. Most home bottling is done using the "open kettle method", with hot food ladled into hot jars and lids placed on jars, with no water bath sterilization processing of the product afterward. In Australia the most popular home canning system is Fowler's Vacola. This system uses glass jars, single use seals, metal lids, and a water bath canning sterilization process. During the canning process the lids are secured by metal tension clips which are removed once a vacuum seal has formed. Fowler's Vacola products are still produced and are available from some hardware stores. Used equipment is frequently sold on online auction sites and in opportunity shops. In Germany the most popular home canning system is Weck jar. This system uses glass jars (80ml-2.5l) and glass bottles (200ml-1l), reusable rubber seals, glass lids, and a water bath canning sterilization process. During the canning process the lids are secured by steel tension clips which can be removed once a vacuum seal has formed. During storage the vertical position of the rubber seal's external tongue indicates the status of the sealing. Weck products are still produced and are available from German hardware stores. Used equipment is frequently sold on online auction sites and in opportunity shops. They can be used for water bath canning and pressure canning. For water bath canning use two steel tension clips and for pressure canning use three steel tension clips. Remove them after vacuum has formed. United States: Metric:	Home canning or bottling, also known colloquially as putting up or processing, is the process of preserving foods, in particular, fruits, vegetables, and meats, by packing them into glass jars and then heating the jars to create a vacuum seal and kill the organisms that would create spoilage.	en	en	56	[ 250004, 250054, 51404, 442, 83, 7722, 47, 46002, 538, 479, 86687, 5941, 8562, 7, 111, 15381, 271, 21493, 7, 4, 5368, 831, 592, 831, 172554, 107222, 7, 47, 337, 130266, 39, 136, 3789, 8562, 7, 111, 15381, 5737, 31, 592, 2174, 16940, 214552, 538, 5, 581, 2684, 39210, 31344, 111, 15381, 9, 3422, 86, 337, 130266, 39, 83, 5368, 9, 4398, 14534, 15381, 7, 133888, 23, 142, 51, 115840, 144996, 5, 147715, 72350, 7, 8110, 186, 39958, 3229, 51339, 214, 5368, 831, 592, 4, 16792, 23, 141933, 111, 169577, 23, 15381, 181653, 390, 44, 441, 365, 7655, 28483, 337, 3766, 37211, 58, 831, 22304, 47219, 5, 88949, 111, 70, 11192, 10512, 111, 202711, 707, 47219, 137272, 678, 60418, 1264, 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summarize: The vacuum flask was designed and invented by Scottish scientist Sir James Dewar in 1892 as a result of his research in the field of cryogenics and is sometimes called a Dewar flask in his honour. While performing experiments in determining the specific heat of the element palladium, Dewar made a brass chamber that he enclosed in another chamber to keep the palladium at its desired temperature. He evacuated the air between the two chambers, creating a partial vacuum to keep the temperature of the contents stable. Through the need for this insulated container James Dewar created the vacuum flask, which became a significant tool for chemical experiments and also became a common household item. The flask was later developed using new materials such as glass and aluminum; however, Dewar refused to patent his invention. Dewar's design was quickly transformed into a commercial item in 1904 as two German glassblowers, Reinhold Burger and Albert Aschenbrenner, discovered that it could be used to keep cold drinks cold and warm drinks warm and invented a more robust flask design, which was suited for everyday use. The Dewar flask design had never been patented but the German men who discovered the commercial use for the product named it "Thermos", and subsequently claimed both the rights to the commercial product and the trademark to the name. In his subsequent attempt to claim the rights to the invention, Dewar instead lost a court case to the company. The manufacturing and performance of the Thermos bottle was significantly improved and refined by the Viennese inventor and merchant Gustav Robert Paalen, who designed various types for domestic use, which he also patented, and distributed widely, through the Thermos Bottle Companies in the United States, Canada and the UK, which bought licences for respective national markets. The American Thermos Bottle Company built up a mass production in Norwich, CT, which brought prices down and enabled the wide distribution of the product for at-home use. Over time, the company expanded the size, shapes and materials of these consumer products, primarily used for carrying coffee on the go and carrying liquids on camping trips to keep them either hot or cold. Eventually other manufacturers produced similar products for consumer use. The name later became a genericized trademark after the term "thermos" became the household name for such a vacuum-insulated container for liquids. The vacuum flask went on to be used for many different types of scientific experiments and the commercial "Thermos" was transformed into a common item. "Thermos" remains a registered trademark in some countries, but it was declared a genericized trademark by court action in the United States in 1963, since it had become colloquially synonymous with vacuum flasks in general. However, there are other vacuum flasks. The vacuum flask consists of two vessels, one placed within the other and joined at the neck. The gap between the two vessels is partially evacuated of air, creating a partial-vacuum which reduces heat conduction or convection. Heat transfer by thermal radiation may be minimized by silvering flask surfaces facing the gap but can become problematic if the flask's contents or surroundings are very hot; hence vacuum flasks usually hold contents below the boiling point of water. Most heat transfer occurs through the neck and opening of the flask, where there is no vacuum. Vacuum flasks are usually made of metal, borosilicate glass, foam or plastic and have their opening stoppered with cork or polyethylene plastic. Vacuum flasks are often used as insulated shipping containers. Extremely large or long vacuum flasks sometimes cannot fully support the inner flask from the neck alone, so additional support is provided by "spacers" between the interior and exterior shell. These spacers act as a thermal bridge and partially reduce the insulating properties of the flask around the area where the spacer contacts the interior surface. Several technological applications, such as NMR and MRI machines, rely on the use of double vacuum flasks. These flasks have two vacuum sections. The inner flask contains liquid helium and the outer flask contains liquid nitrogen, with one vacuum section in between. The loss of precious helium is limited in this way. Other improvements to the vacuum flask include the "vapour-cooled radiation shield" and the "vapour-cooled neck", both of which help to reduce evaporation from the flask. In laboratories and industry, vacuum flasks are often used to hold liquefied gases (often LN2) for flash freezing, sample preparation and other processes where maintaining an extreme low temperature is desired. Larger vacuum flasks store liquids that become gaseous at well below ambient temperature, such as oxygen and nitrogen; in this case the leakage of heat into the extremely cold interior of the bottle results in a slow boiling-off of the liquid so that a narrow unstoppered opening, or a stoppered opening protected by a pressure relief valve, is necessary to prevent pressure from building up and eventually shattering the flask. The insulation of the vacuum flask results in a very slow "boil" and thus the contents remain liquid for long periods without refrigeration equipment. Vacuum flasks have been used to house standard cells and ovenized Zener diodes, along with their printed circuit board, in precision voltage-regulating devices used as electrical standards. The flask helped with controlling the Zener temperature over a long time span and was used to reduce variations of the output voltage of the Zener standard owing to temperature fluctuation to within a few parts per million. One notable use was by Guildline Instruments, of Canada, in their Transvolt, model 9154B, saturated standard cell, which is an electrical voltage standard. Here a silvered vacuum flask was encased in foam insulation and, using a large glass vacuum plug, held the saturated cell. The output of the device was 1.018 volts and was held to within a few parts per million. The principle of the vacuum flask makes it ideal for storing certain types of rocket fuel, and NASA used it extensively in the propellant tanks of the Saturn launch vehicles in the 1960s and 1970s. The design and shape of the Dewar flask was used as a model for optical experiments based on the idea that the shape of the two compartments with the space in between is similar to the way the light hits the eye. The vacuum flask has also been part of experiments using it as the capacitor of different chemicals in order to keep them at a consistent temperature. The industrial Dewar flask is the base for a device used to passively insulate medical shipments. Most vaccines are sensitive to heat and require a cold chain system to keep them at stable, near freezing temperatures. The Arktek device uses eight one-litre ice blocks to hold vaccines at under 10 °C. Vacuum flasks are at risk of implosion hazard, and glass vessels under vacuum, in particular, may shatter unexpectedly. Chips, scratches or cracks can be a starting point for dangerous vessel failure, especially when the vessel temperature changes rapidly (when hot or cold liquid is added). Proper preparation of the Dewar vacuum flask by tempering prior to use is advised to maintain and optimize the functioning of the unit. Glass vacuum flasks are usually fitted into a metal base with the cylinder contained in or coated with mesh, aluminum or plastic to aid in handling, protect it from physical damage, and contain fragments should they break. In addition, cryogenic storage dewars are usually pressurized, and they may explode if pressure relief valves are not used. The rate of heat (energy) loss through a vacuum flask can be analyzed thermodynamically, starting from the second relation: Assuming constant pressure throughout the process, Rearranging the equation in terms of the temperature of the outside surface of the vacuum flask's inner wall, Where Now consider the general expression for heat loss due to radiation: In the case of the vacuum flask, Substituting our earlier expression for "T", Where Assuming that the outer surface of the inner wall and the inner surface of the outer wall of the vacuum flask are coated with polished silver to minimize heat loss due to radiation, we can say that the rate of heat absorption by the inner surface of the outer wall is equal to the absorptivity of polished silver times the heat radiated by the outer surface of the inner wall, In order for energy balance to be maintained, the heat lost through the outer surface of the outer wall must be equal to the heat absorbed by the inner surface of the outer wall, Since the absorptivity of polished silver is the same as its emissivity, we can write We must also consider the rate of heat loss through the lid of the vacuum flask (assuming it is made of polypropylene, a common plastic) where there is no vacuum inside the material. In this area, the three heat transfer modes of conduction, convection, and radiation are present. Therefore, the rate of heat loss through the lid is, Where Now we have an expression for the total rate of heat loss, which is the sum of the rate of heat loss through the walls of the vacuum flask and the rate of heat loss through the lid, where we substitute each of the expressions for each component into the equation. The rate of entropy generation of this process can also be calculated, starting from entropy balance: Written in rate form, Assuming a steady-state process, Since there is no heat added to the system,	A vacuum flask (also known as a Dewar flask, Dewar bottle or thermos) is an insulating storage vessel that greatly lengthens the time over which its contents remain hotter or cooler than the flask's surroundings. Invented by Sir James Dewar in 1892, the vacuum flask consists of two flasks, placed one within the other and joined at the neck. The gap between the two flasks is partially evacuated of air, creating a near-vacuum which significantly reduces heat transfer by conduction or convection.	en	en	92	[ 250004, 250054, 581, 241433, 56055, 92, 509, 82775, 136, 26868, 297, 390, 50695, 4745, 172647, 10868, 14631, 262, 4205, 23, 151278, 237, 10, 16750, 111, 1919, 25188, 23, 70, 44457, 111, 91190, 62976, 28021, 136, 83, 68018, 35839, 10, 262, 4205, 56055, 92, 23, 1919, 3486, 34639, 5, 51404, 51339, 214, 28007, 7, 23, 72694, 214, 70, 29458, 80097, 111, 70, 12830, 110586, 28483, 4, 262, 4205, 7228, 10, 70910, 7, 1608, 26278, 450, 764, 22, 155648, 71, 23, 15700, 1608, 26278, 47, 13695, 70, 110586, 28483, 99, 6863, 104851, 71, 52768, 5, 1529, 166499, 3674, 70, 1831, 17721, 70, 6626, 1608, 26278, 7, 4, 105233, 10, 2878, 289, 241433, 47, 13695, 70, 52768, 111, 70, 10941, 7, 144142, 5, 194397, 70, 3871, 100, 903, 125001, 3674, 116419, 14631, 262, 4205, 75935, 70, 241433, 56055, 92, 4, 3129, 100512, 10, 88551, 55516, 100, 165045, 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summarize: The term kinematic is the English version of A.M. Ampère's "cinématique", which he constructed from the Greek "kinema" ("movement, motion"), itself derived from "kinein" ("to move"). Kinematic and cinématique are related to the French word cinéma, but neither are directly derived from it. However, they do share a root word in common, as cinéma came from the shortened form of cinématographe, "motion picture projector and camera," once again from the Greek word for movement and from the Greek "grapho" ("to write"). Particle kinematics is the study of the trajectory of particles. The position of a particle is defined as the coordinate vector from the origin of a coordinate frame to the particle. For example, consider a tower 50 m south from your home, where the coordinate frame is centered at your home, such that east is in the direction of the x-axis and north is in the direction of the y-axis, then the coordinate vector to the base of the tower is r = (0, −50, 0). If the tower is 50 m high, and this height is measured along the z-axis, then the coordinate vector to the top of the tower is r = (0, −50, 50). In the most general case, a three-dimensional coordinate system is used to define the position of a particle. However, if the particle is constrained to move within a plane, a two-dimensional coordinate system is sufficient. All observations in physics are incomplete without being described with respect to a reference frame. The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin. In three dimensions, the position of point "P" can be expressed as where formula_2, formula_3, and formula_4 are the Cartesian coordinates and formula_5, formula_6 and formula_7 are the unit vectors along the formula_8, formula_9, and formula_10 coordinate axes, respectively. The magnitude of the position vector formula_11 gives the distance between the point formula_12 and the origin. The direction cosines of the position vector provide a quantitative measure of direction. It is important to note that the position vector of a particle isn't unique. The position vector of a given particle is different relative to different frames of reference. The "trajectory" of a particle is a vector function of time, formula_14, which defines the curve traced by the moving particle, given by where the coordinates "x", "y", and "z" are each functions of time. The velocity of a particle is a vector quantity that describes the magnitude as well as direction of motion of the particle. More mathematically, the rate of change of the position vector of a point, with respect to time is the velocity of the point. Consider the ratio formed by dividing the difference of two positions of a particle by the time interval. This ratio is called the average velocity over that time interval and is defined as Velocity=displacement/time taken where ΔP is the change in the position vector over the time interval Δ"t". In the limit as the time interval Δ"t" becomes smaller and smaller, the average velocity becomes the time derivative of the position vector, Thus, velocity is the time rate of change of position of a point, and the dot denotes the derivative of those functions x, y, and z with respect to time. Furthermore, the velocity is tangent to the trajectory of the particle at every position the particle occupies along its path. Note that in a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The speed of an object is the magnitude \|V\| of its velocity. It is a scalar quantity: where "s" is the arc-length measured along the trajectory of the particle. This arc-length traveled by a particle over time is a non-decreasing quantity. Hence, "ds"/"dt" is non-negative, which implies that speed is also non-negative. The velocity vector can change in magnitude and in direction or both at once. Hence, the acceleration accounts for both the rate of change of the magnitude of the velocity vector and the rate of change of direction of that vector. The same reasoning used with respect to the position of a particle to define velocity, can be applied to the velocity to define acceleration. The acceleration of a particle is the vector defined by the rate of change of the velocity vector. The average acceleration of a particle over a time interval is defined as the ratio. where ΔV is the difference in the velocity vector and Δ"t" is the time interval. The acceleration of the particle is the limit of the average acceleration as the time interval approaches zero, which is the time derivative, or Thus, acceleration is the first derivative of the velocity vector and the second derivative of the position vector of that particle. Note that in a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The magnitude of the acceleration of an object is the magnitude \|A\| of its acceleration vector. It is a scalar quantity: A relative position vector is a vector that defines the position of one point relative to another. It is the difference in position of the two points. The position of one point "A" relative to another point "B" is simply the difference between their positions formula_23 which is the difference between the components of their position vectors. If point "A" has position components formula_24 If point "B" has position components formula_25 then the position of point "A" relative to point "B" is the difference between their components: formula_26 The velocity of one point relative to another is simply the difference between their velocities formula_27 which is the difference between the components of their velocities. If point "A" has velocity components formula_28 and point "B" has velocity components formula_29 then the velocity of point "A" relative to point "B" is the difference between their components: formula_30 Alternatively, this same result could be obtained by computing the time derivative of the relative position vector R. In the case where the velocity is close to the speed of light "c" (generally within 95%), another scheme of relative velocity called rapidity, that depends on the ratio of V to c, is used in special relativity. The acceleration of one point "C" relative to another point "B" is simply the difference between their accelerations. formula_31 which is the difference between the components of their accelerations. If point "C" has acceleration components formula_32 and point "B" has acceleration components formula_33 then the acceleration of point "C" relative to point "B" is the difference between their components: formula_34 Alternatively, this same result could be obtained by computing the second time derivative of the relative position vector P. Assuming that the initial conditions of the position, formula_35, and velocity formula_36 at time formula_37 are known, the first integration yields the velocity of the particle as a function of time. A second integration yields its path (trajectory), Additional relations between displacement, velocity, acceleration, and time can be derived. Since the acceleration is constant, A relationship between velocity, position and acceleration without explicit time dependence can be had by solving the average acceleration for time and substituting and simplifying where ∘ denotes the dot product, which is appropriate as the products are scalars rather than vectors. The dot can be replaced by the cosine of the angle formula_45 between the vectors and the vectors by their magnitudes, in which case: In the case of acceleration always in the direction of the motion and the direction of motion should be in positive or nagetive, the angle between the vectors (formula_45) is 0, so formula_48, and This can be simplified using the notation for the magnitudes of the vectors formula_50 where formula_51 can be any curvaceous path taken as the constant tangential acceleration is applied along that path, so This reduces the parametric equations of motion of the particle to a cartesian relationship of speed versus position. This relation is useful when time is unknown. We also know that formula_53 or formula_51 is the area under a v, t graph. We can take formula_51 by adding the top area and the bottom area. The bottom area is a rectangle, and the area of a rectangle is the formula_56 where formula_57 is the width and formula_58 is the height. In this case formula_59 and formula_60 (note that the formula_57 here is different from the acceleration formula_62). This means that the bottom area is formula_63. Now let's find the top area (a triangle). The area of a trangle is formula_64 where formula_58 is the base and formula_66 is the height. In this case, formula_67 & formula_68 or formula_69. Adding formula_63 and formula_71 results in the equation formula_72 results in the equation formula_73. This equation is very useful when the final velocity formula_74 is unknown. It is often convenient to formulate the trajectory of a particle P(t) = (X(t), Y(t) and Z(t)) using polar coordinates in the "X"–"Y" plane. In this case, its velocity and acceleration take a convenient form. Recall that the trajectory of a particle "P" is defined by its coordinate vector P measured in a fixed reference frame "F". As the particle moves, its coordinate vector P(t) traces its trajectory, which is a curve in space, given by: where "i", "j", and "k" are the unit vectors along the "X", "Y" and "Z" axes of the reference frame "F", respectively. Consider a particle "P" that moves only on the surface of a circular cylinder R(t)=constant, it is possible to align the "Z" axis of the fixed frame "F" with the axis of the cylinder. Then, the angle θ around this axis in the "X"–"Y" plane can be used to define the trajectory as, The cylindrical coordinates for P(t) can be simplified by introducing the radial and tangential unit vectors, and their time derivatives from elementary calculus: Using this notation, P(t) takes the form, where "R" is constant in the case of the particle moving only on the surface of a cylinder of radius "R". In general, the trajectory P(t) is not constrained to lie on a circular cylinder, so the radius "R" varies with time and the trajectory of the particle in cylindrical-polar coordinates becomes: Where R, theta, and Z might be continuously differentiable functions of time and the function notation is dropped for simplicity. The velocity vector V is the time derivative of the trajectory P(t), which yields: Similarly, the acceleration A, which is the time derivative of the velocity V, is given by: The term formula_86 acts toward the center of curvature of the path at that point on the path, is commonly called the centripetal acceleration. The term formula_87 is called the Coriolis acceleration. If the trajectory of the particle is constrained to lie on a cylinder, then the radius "R" is constant and the velocity and acceleration vectors simplify. The velocity of V is the time derivative of the trajectory P(t), The acceleration vector becomes: A special case of a particle trajectory on a circular cylinder occurs when there is no movement along the "Z" axis: where "R" and "Z" are constants. In this case, the velocity V is given by: where is the angular velocity of the unit vector around the "z" axis of the cylinder. The acceleration A of the particle "P" is now given by: The components are called, respectively, the "radial" and "tangential components" of acceleration. The notation for angular velocity and angular acceleration is often defined as so the radial and tangential acceleration components for circular trajectories are also written as The movement of components of a mechanical system are analyzed by attaching a reference frame to each part and determining how the various reference frames move relative to each other. If the structural stiffness of the parts are sufficient, then their deformation can be neglected and rigid transformations can be used to define this relative movement. This reduces the description of the motion of the various parts of a complicated mechanical system to a problem of describing the geometry of each part and geometric association of each part relative to other parts. Geometry is the study of the properties of figures that remain the same while the space is transformed in various ways—more technically, it is the study of invariants under a set of transformations. These transformations can cause the displacement of the triangle in the plane, while leaving the vertex angle and the distances between vertices unchanged. Kinematics is often described as applied geometry, where the movement of a mechanical system is described using the rigid transformations of Euclidean geometry. The coordinates of points in a plane are two-dimensional vectors in R (two dimensional space). Rigid transformations are those that preserve the distance between any two points. The set of rigid transformations in an "n"-dimensional space is called the special Euclidean group on R, and denoted "SE(n)." The position of one component of a mechanical system relative to another is defined by introducing a reference frame, say "M", on one that moves relative to a fixed frame, "F," on the other. The rigid transformation, or displacement, of "M" relative to "F" defines the relative position of the two components. A displacement consists of the combination of a rotation and a translation. The set of all displacements of "M" relative to "F" is called the configuration space of "M." A smooth curve from one position to another in this configuration space is a continuous set of displacements, called the motion of "M" relative to "F." The motion of a body consists of a continuous set of rotations and translations. The combination of a rotation and translation in the plane R can be represented by a certain type of 3x3 matrix known as a homogeneous transform. The 3x3 homogeneous transform is constructed from a 2x2 rotation matrix A(φ) and the 2x1 translation vector d=(d, d), as: These homogeneous transforms perform rigid transformations on the points in the plane z=1, that is on points with coordinates p=(x, y, 1). In particular, let p define the coordinates of points in a reference frame "M" coincident with a fixed frame "F." Then, when the origin of "M" is displaced by the translation vector d relative to the origin of "F" and rotated by the angle φ relative to the x-axis of "F", the new coordinates in "F" of points in "M" are given by: Homogeneous transforms represent affine transformations. This formulation is necessary because a translation is not a linear transformation of R. However, using projective geometry, so that R is considered a subset of R, translations become affine linear transformations. If a rigid body moves so that its reference frame "M" does not rotate (∅=0) relative to the fixed frame "F", the motion is called pure translation. In this case, the trajectory of every point in the body is an offset of the trajectory d(t) of the origin of "M," that is: Thus, for bodies in pure translation, the velocity and acceleration of every point "P" in the body are given by: where the dot denotes the derivative with respect to time and V and A are the velocity and acceleration, respectively, of the origin of the moving frame "M". Recall the coordinate vector p in "M" is constant, so its derivative is zero. Rotational or angular kinematics is the description of the rotation of an object. The description of rotation requires some method for describing orientation. Common descriptions include Euler angles and the kinematics of turns induced by algebraic products. In what follows, attention is restricted to simple rotation about an axis of fixed orientation. The "z"-axis has been chosen for convenience. The description of rotation then involves these three quantities: The equations of translational kinematics can easily be extended to planar rotational kinematics for constant angular acceleration with simple variable exchanges: Here "θ" and "θ" are, respectively, the initial and final angular positions, "ω" and "ω" are, respectively, the initial and final angular velocities, and "α" is the constant angular acceleration. Although position in space and velocity in space are both true vectors (in terms of their properties under rotation), as is angular velocity, angle itself is not a true vector. Important formulas in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space. This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations. In order to define these formulas, the movement of a component "B" of a mechanical system is defined by the set of rotations [A(t)] and translations d(t) assembled into the homogeneous transformation [T(t)]=[A(t), d(t)]. If p is the coordinates of a point "P" in "B" measured in the moving reference frame "M", then the trajectory of this point traced in "F" is given by: This notation does not distinguish between P = (X, Y, Z, 1), and P = (X, Y, Z), which is hopefully clear in context. This equation for the trajectory of "P" can be inverted to compute the coordinate vector p in "M" as: This expression uses the fact that the transpose of a rotation matrix is also its inverse, that is: The velocity of the point "P" along its trajectory P(t) is obtained as the time derivative of this position vector, The dot denotes the derivative with respect to time; because p is constant, its derivative is zero. This formula can be modified to obtain the velocity of "P" by operating on its trajectory P(t) measured in the fixed frame "F". Substituting the inverse transform for p into the velocity equation yields: The matrix [S] is given by: where is the angular velocity matrix. Multiplying by the operator [S], the formula for the velocity V takes the form: where the vector ω is the angular velocity vector obtained from the components of the matrix [Ω]; the vector is the position of "P" relative to the origin "O" of the moving frame "M"; and is the velocity of the origin "O". The acceleration of a point "P" in a moving body "B" is obtained as the time derivative of its velocity vector: This equation can be expanded firstly by computing and The formula for the acceleration A can now be obtained as: or where α is the angular acceleration vector obtained from the derivative of the angular velocity matrix; is the relative position vector (the position of "P" relative to the origin "O" of the moving frame "M"); and is the acceleration of the origin of the moving frame "M". Kinematic constraints are constraints on the movement of components of a mechanical system. Kinematic constraints can be considered to have two basic forms, (i) constraints that arise from hinges, sliders and cam joints that define the construction of the system, called holonomic constraints, and (ii) constraints imposed on the velocity of the system such as the knife-edge constraint of ice-skates on a flat plane, or rolling without slipping of a disc or sphere in contact with a plane, which are called non-holonomic constraints. The following are some common examples. A kinematic coupling exactly constrains all 6 degrees of freedom. An object that rolls against a surface without slipping obeys the condition that the velocity of its center of mass is equal to the cross product of its angular velocity with a vector from the point of contact to the center of mass: For the case of an object that does not tip or turn, this reduces to formula_135. This is the case where bodies are connected by an idealized cord that remains in tension and cannot change length. The constraint is that the sum of lengths of all segments of the cord is the total length, and accordingly the time derivative of this sum is zero. A dynamic problem of this type is the pendulum. Another example is a drum turned by the pull of gravity upon a falling weight attached to the rim by the inextensible cord. An "equilibrium" problem (i.e. not kinematic) of this type is the catenary. Reuleaux called the ideal connections between components that form a machine kinematic pairs. He distinguished between higher pairs which were said to have line contact between the two links and lower pairs that have area contact between the links. J. Phillips shows that there are many ways to construct pairs that do not fit this simple classification. A lower pair is an ideal joint, or holonomic constraint, that maintains contact between a point, line or plane in a moving solid (three-dimensional) body to a corresponding point line or plane in the fixed solid body. There are the following cases: Generally speaking, a higher pair is a constraint that requires a curve or surface in the moving body to maintain contact with a curve or surface in the fixed body. For example, the contact between a cam and its follower is a higher pair called a "cam joint". Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints. Rigid bodies ("links") connected by kinematic pairs ("joints") are known as "kinematic chains." Mechanisms and robots are examples of kinematic chains. The degree of freedom of a kinematic chain is computed from the number of links and the number and type of joints using the mobility formula. This formula can also be used to enumerate the topologies of kinematic chains that have a given degree of freedom, which is known as "type synthesis" in machine design. The planar one degree-of-freedom linkages assembled from "N" links and "j" hinged or sliding joints are: For larger chains and their linkage topologies, see R. P. Sunkari and L. C. Schmidt, "Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm", "Mechanism and Machine Theory" #41, pp. 1021–1030 (2006).	Kinematics is a subfield of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. 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191060, 939, 173, 18770, 5, 581, 83080, 197108, 1830, 111, 10, 915, 26147, 645, 10, 1733, 51514, 83, 61924, 71, 237, 70, 70460, 5, 7440, 6732, 856, 83, 70, 60212, 23, 70, 191060, 939, 173, 18770, 136, 6732, 58, 18, 58, 83, 70, 1733, 51514, 5, 581, 197108, 1830, 111, 70, 915, 26147, 83, 70, 17475, 111, 70, 83080, 197108, 1830, 237, 70, 1733, 51514, 51515, 90, 45234, 4, 3129, 83, 70, 1733, 30057, 4935, 4, 707, 12613, 7, 4, 197108, 1830, 83, 70, 5117, 30057, 4935, 111, 70, 191060, 939, 173, 18770, 136, 70, 17932, 30057, 4935, 111, 70, 19069, 173, 18770, 111, 450, 915, 26147, 5, 18622, 450, 23, 10, 351, 9, 109645, 1916, 123789, 111, 91067, 4, 70, 30057, 42991, 111, 70, 176866, 13, 48225, 7, 621, 959, 90698, 237, 2363, 48225, 7, 136, 101668, 90, 621, 53697, 7, 5, 581, 101668, 13, 111, 70, 197108, 1830, 111, 142, 36746, 83, 70, 101668, 13, 6, 58745, 284, 58745, 111, 6863, 197108, 1830, 173, 18770, 5, 1650, 83, 10, 146232, 42, 102134, 939, 12, 62, 35845, 19069, 173, 18770, 83, 10, 173, 18770, 450, 61924, 7, 70, 19069, 111, 1632, 6275, 35845, 47, 15700, 5, 1650, 83, 70, 60212, 23, 19069, 111, 70, 6626, 26847, 5, 581, 19069, 111, 1632, 6275, 44, 284, 58, 35845, 47, 15700, 6275, 44, 571, 58, 83, 42856, 70, 60212, 17721, 2363, 19069, 7, 26168, 454, 3742, 3129, 83, 70, 60212, 17721, 70, 82761, 7, 111, 2363, 19069, 22834, 22230, 5, 4263, 6275, 44, 284, 58, 1556, 19069, 82761, 7, 26168, 454, 2357, 4263, 6275, 44, 571, 58, 1556, 19069, 82761, 7, 26168, 454, 2588, 7068, 70, 19069, 111, 6275, 44, 284, 58, 35845, 47, 6275, 44, 571, 58, 83, 70, 60212, 17721, 2363, 82761, 7, 12, 26168, 454, 4046, 581, 191060, 939, 111, 1632, 6275, 35845, 47, 15700, 83, 42856, 70, 60212, 17721, 2363, 191060, 2449, 26168, 454, 3768, 3129, 83, 70, 60212, 17721, 70, 82761, 7, 111, 2363, 191060, 2449, 5, 4263, 6275, 44, 284, 58, 1556, 191060, 939, 82761, 7, 26168, 454, 3882, 136, 6275, 44, 571, 58, 1556, 191060, 939, 82761, 7, 26168, 454, 4235, 7068, 70, 191060, 939, 111, 6275, 44, 284, 58, 35845, 47, 6275, 44, 571, 58, 83, 70, 60212, 17721, 2363, 82761, 7, 12, 26168, 454, 1197, 103905, 538, 4, 903, 5701, 16750, 5809, 186, 113054, 297, 390, 242122, 70, 1733, 30057, 4935, 111, 70, 35845, 19069, 173, 18770, 627, 5, 360, 70, 7225, 7440, 70, 191060, 939, 83, 20903, 47, 70, 38352, 111, 22729, 44, 238, 58, 15, 180300, 538, 28032, 59653, 247, 15700, 150370, 111, 35845, 191060, 939, 35839, 25545, 2481, 4, 450, 56566, 7, 98, 70, 70460, 111, 310, 47, 501, 4, 83, 11814, 23, 5361, 90816, 939, 5, 581, 197108, 1830, 111, 1632, 6275, 44, 441, 58, 35845, 47, 15700, 6275, 44, 571, 58, 83, 42856, 70, 60212, 17721, 2363, 197108, 17514, 5, 26168, 454, 5016, 3129, 83, 70, 60212, 17721, 70, 82761, 7, 111, 2363, 197108, 17514, 5, 4263, 6275, 44, 441, 58, 1556, 197108, 1830, 82761, 7, 26168, 454, 6460, 136, 6275, 44, 571, 58, 1556, 197108, 1830, 82761, 7, 26168, 454, 9185, 7068, 70, 197108, 1830, 111, 6275, 44, 441, 58, 35845, 47, 6275, 44, 571, 58, 83, 70, 60212, 17721, 2363, 82761, 7, 12, 26168, 454, 10289, 103905, 538, 4, 903, 5701, 16750, 5809, 186, 113054, 297, 390, 242122, 70, 17932, 1733, 30057, 4935, 111, 70, 35845, 19069, 173, 18770, 436, 5, 62, 66596, 214, 450, 70, 61475, 27289, 111, 70, 19069, 4, 26168, 454, 5843, 4, 136, 191060, 939, 26168, 454, 8659, 99, 1733, 26168, 454, 10945, 621, 51529, 4, 70, 5117, 157353, 11180, 19388, 7, 70, 191060, 939, 111, 70, 915, 26147, 237, 10, 32354, 111, 1733, 5, 62, 17932, 157353, 11180, 19388, 7, 6863, 60875, 15, 1517, 75161, 30675, 247, 29117, 14, 43315, 91582, 17721, 2837, 23935, 674, 4, 191060, 939, 4, 197108, 1830, 4, 136, 1733, 831, 186, 16406, 4126, 5, 66016, 70, 197108, 1830, 83, 53697, 4, 62, 76755, 17721, 191060, 939, 4, 19069, 136, 197108, 1830, 15490, 143726, 1733, 6, 215131, 831, 186, 1902, 390, 3115, 6496, 70, 83080, 197108, 1830, 100, 1733, 136, 161740, 214, 136, 112892, 18929, 214, 7440, 6, 248823, 8, 157, 1636, 70, 20633, 12996, 4, 3129, 83, 95307, 237, 70, 38742, 621, 146232, 4295, 43257, 3501, 22834, 22230, 5, 581, 20633, 831, 186, 91995, 71, 390, 70, 552, 14186, 111, 70, 55291, 26168, 454, 4633, 17721, 70, 22834, 22230, 136, 70, 22834, 22230, 390, 2363, 101668, 90, 4, 23, 3129, 7225, 12, 360, 70, 7225, 111, 197108, 1830, 11343, 23, 70, 48225, 111, 70, 78112, 136, 70, 48225, 111, 78112, 5608, 186, 23, 24491, 707, 24, 429, 4935, 4, 70, 55291, 17721, 70, 22834, 22230, 15, 2472, 19908, 454, 129507, 83, 757, 4, 221, 26168, 454, 9285, 4, 136, 3293, 831, 186, 112892, 1029, 297, 17368, 70, 110, 22062, 100, 70, 101668, 90, 111, 70, 22834, 22230, 26168, 454, 2525, 7440, 26168, 454, 11703, 831, 186, 2499, 130661, 329, 10821, 60875, 39958, 237, 70, 53697, 25269, 80973, 197108, 1830, 83, 190659, 33233, 450, 60875, 4, 221, 3293, 34390, 7, 70, 121, 186518, 28, 13722, 5256, 111, 78112, 111, 70, 915, 26147, 47, 10, 129912, 3378, 76755, 111, 38352, 119475, 19069, 5, 3293, 41911, 83, 80234, 3229, 1733, 83, 51, 69723, 19, 5, 1401, 2843, 3714, 450, 26168, 454, 14226, 707, 26168, 454, 11703, 83, 70, 16128, 1379, 10, 81, 4, 808, 6, 41382, 5, 1401, 831, 5646, 26168, 454, 11703, 390, 154107, 70, 2663, 16128, 136, 70, 103136, 16128, 5, 581, 103136, 16128, 83, 10, 148734, 449, 133, 4, 136, 70, 16128, 111, 10, 148734, 449, 133, 83, 70, 26168, 454, 13683, 7440, 26168, 454, 12243, 83, 70, 6, 146984, 136, 26168, 454, 10057, 83, 70, 155955, 5, 360, 903, 7225, 26168, 454, 12975, 136, 26168, 454, 4598, 15, 48345, 450, 70, 26168, 454, 12243, 3688, 83, 12921, 1295, 70, 197108, 1830, 26168, 454, 10837, 194, 3293, 26950, 450, 70, 103136, 16128, 83, 26168, 454, 15748, 5, 14240, 2633, 25, 7, 7413, 70, 2663, 16128, 15, 11, 1927, 109217, 194, 581, 16128, 111, 10, 8369, 133, 83, 26168, 454, 13307, 7440, 26168, 454, 10057, 83, 70, 3647, 136, 26168, 454, 14604, 83, 70, 155955, 5, 360, 903, 7225, 4, 26168, 454, 18197, 619, 26168, 454, 16028, 707, 26168, 454, 14212, 5, 62, 59725, 26168, 454, 15748, 136, 26168, 454, 15770, 50339, 23, 70, 28, 5490, 2320, 26168, 454, 12825, 50339, 23, 70, 28, 5490, 2320, 26168, 454, 13574, 5, 3293, 28, 5490, 2320, 83, 4552, 80234, 3229, 70, 2704, 191060, 939, 26168, 454, 16360, 83, 51, 69723, 19, 5, 1650, 83, 27983, 142267, 47, 26168, 67, 70, 182418, 30675, 111, 10, 915, 26147, 436, 132, 18, 16, 2203, 15, 1542, 132, 18, 247, 990, 132, 18, 16, 136, 567, 132, 18, 16, 16, 17368, 160, 320, 176866, 90, 23, 70, 44, 1542, 58, 1104, 58, 1723, 58, 47880, 5, 360, 903, 7225, 4, 6863, 191060, 939, 136, 197108, 1830, 5646, 10, 142267, 3173, 5, 853, 85763, 450, 70, 182418, 30675, 111, 10, 915, 26147, 44, 683, 58, 83, 61924, 71, 390, 6863, 176866, 13, 173, 18770, 436, 72350, 71, 23, 10, 188347, 91067, 123789, 44, 919, 740, 1301, 70, 915, 26147, 25813, 7, 4, 6863, 176866, 13, 173, 18770, 436, 132, 18, 16, 144851, 7, 6863, 182418, 30675, 4, 3129, 83, 10, 9709, 272, 23, 32628, 4, 34475, 390, 12, 7440, 44, 14, 830, 44, 170, 830, 136, 44, 92, 58, 621, 70, 25072, 22834, 22230, 33233, 70, 44, 1542, 830, 44, 1723, 58, 136, 44, 1511, 58, 10, 31195, 111, 70, 91067, 123789, 44, 919, 830, 107013, 538, 5, 137399, 10, 915, 26147, 44, 683, 58, 450, 25813, 7, 4734, 98, 70, 71579, 111, 10, 115339, 19932, 104532, 627, 132, 18, 16, 1369, 2271, 42539, 4, 442, 83, 7722, 47, 6, 143420, 70, 44, 1511, 58, 10, 33102, 111, 70, 188347, 123789, 44, 919, 58, 678, 70, 10, 33102, 111, 70, 19932, 104532, 5, 47009, 4, 70, 55291, 30691, 10932, 903, 10, 33102, 23, 70, 44, 1542, 58, 1104, 58, 1723, 58, 47880, 831, 186, 11814, 47, 61924, 70, 182418, 30675, 237, 4, 581, 19932, 150, 29887, 6827, 176866, 90, 100, 436, 132, 18, 16, 831, 186, 112892, 1029, 297, 390, 39864, 214, 70, 4567, 289, 136, 25269, 80973, 25072, 22834, 22230, 4, 136, 2363, 1733, 30057, 42991, 1295, 131830, 53, 44805, 223, 12, 345, 6953, 903, 110, 22062, 4, 436, 132, 18, 16, 51776, 70, 3173, 4, 7440, 44, 1052, 58, 83, 53697, 23, 70, 7225, 111, 70, 915, 26147, 98567, 4734, 98, 70, 71579, 111, 10, 19932, 104532, 111, 4567, 223, 44, 1052, 740, 360, 4537, 4, 70, 182418, 30675, 436, 132, 18, 16, 83, 959, 158, 9297, 122009, 47, 28127, 98, 10, 115339, 19932, 104532, 4, 221, 70, 4567, 223, 44, 1052, 58, 41110, 7, 678, 1733, 136, 70, 182418, 30675, 111, 70, 915, 26147, 23, 19932, 150, 29887, 6827, 9, 771, 320, 176866, 90, 24209, 7, 12, 78662, 627, 4, 70, 102, 4, 136, 567, 13648, 186, 19686, 79850, 99710, 2886, 32354, 7, 111, 1733, 136, 70, 32354, 110, 22062, 83, 36069, 20051, 100, 134381, 939, 5, 581, 191060, 939, 173, 18770, 310, 83, 70, 1733, 30057, 4935, 111, 70, 182418, 30675, 436, 132, 18, 247, 3129, 11180, 19388, 7, 12, 209683, 538, 4, 70, 197108, 1830, 62, 4, 3129, 83, 70, 1733, 30057, 4935, 111, 70, 191060, 939, 310, 4, 83, 34475, 390, 12, 581, 13579, 26168, 454, 15276, 27992, 7, 154732, 70, 27585, 111, 130661, 6644, 111, 70, 60875, 99, 450, 6275, 98, 70, 60875, 4, 83, 39210, 538, 35839, 70, 69514, 5408, 289, 197108, 1830, 5, 581, 13579, 26168, 454, 19308, 83, 35839, 70, 5631, 846, 4086, 197108, 1830, 5, 4263, 70, 182418, 30675, 111, 70, 915, 26147, 83, 158, 9297, 122009, 47, 28127, 98, 10, 19932, 104532, 4, 7068, 70, 4567, 223, 44, 1052, 58, 83, 53697, 136, 70, 191060, 939, 136, 197108, 1830, 22834, 22230, 112892, 18929, 5, 581, 191060, 939, 111, 310, 83, 70, 1733, 30057, 4935, 111, 70, 182418, 30675, 436, 132, 18, 247, 581, 197108, 1830, 173, 18770, 24209, 7, 12, 62, 5361, 7225, 111, 10, 915, 26147, 182418, 30675, 98, 10, 115339, 19932, 104532, 74918, 7, 3229, 2685, 83, 110, 112664, 33233, 70, 44, 1511, 58, 10, 33102, 12, 7440, 44, 1052, 58, 136, 44, 1511, 58, 621, 53697, 7, 5, 360, 903, 7225, 4, 70, 191060, 939, 310, 83, 34475, 390, 12, 7440, 83, 70, 348, 35975, 191060, 939, 111, 70, 25072, 173, 18770, 10932, 70, 44, 169, 58, 10, 33102, 111, 70, 19932, 104532, 5, 581, 197108, 1830, 62, 111, 70, 915, 26147, 44, 683, 58, 83, 5036, 34475, 390, 12, 581, 82761, 7, 621, 35839, 4, 107013, 538, 4, 70, 44, 10541, 289, 58, 136, 44, 14525, 80973, 82761, 7, 58, 111, 197108, 1830, 5, 581, 110, 22062, 100, 348, 35975, 191060, 939, 136, 348, 35975, 197108, 1830, 83, 27983, 61924, 71, 237, 221, 70, 4567, 289, 136, 25269, 80973, 197108, 1830, 82761, 7, 100, 115339, 182418, 31, 10484, 621, 2843, 59121, 237, 581, 112664, 111, 82761, 7, 111, 10, 135969, 289, 5426, 621, 7968, 53, 64807, 390, 243, 934, 214, 10, 91067, 123789, 47, 12638, 2831, 136, 72694, 214, 3642, 70, 67842, 91067, 2674, 90, 25813, 35845, 47, 12638, 3789, 5, 4263, 70, 118990, 141, 13629, 4902, 7432, 111, 70, 63920, 621, 6, 129980, 4, 7068, 2363, 8, 5037, 2320, 831, 186, 124789, 89829, 136, 128652, 167201, 7, 831, 186, 11814, 47, 61924, 903, 35845, 112664, 5, 3293, 34390, 7, 70, 76811, 111, 70, 78112, 111, 70, 67842, 63920, 111, 10, 96704, 297, 135969, 289, 5426, 47, 10, 2967, 111, 28852, 23709, 70, 700, 87739, 53, 111, 12638, 2831, 136, 84183, 238, 125413, 111, 12638, 2831, 35845, 47, 3789, 63920, 5, 2206, 87739, 53, 83, 70, 35187, 111, 70, 183871, 111, 26366, 7, 450, 47143, 70, 5701, 12960, 70, 32628, 83, 27198, 297, 23, 67842, 48322, 2451, 17678, 121392, 538, 4, 442, 83, 70, 35187, 111, 23, 162591, 7, 1379, 10, 5423, 111, 167201, 7, 5, 32255, 167201, 7, 831, 22304, 70, 2837, 23935, 674, 111, 70, 1927, 109217, 23, 70, 47880, 4, 12960, 137802, 70, 493, 24371, 55291, 136, 70, 62488, 7, 17721, 95378, 5170, 51, 152028, 71, 5, 95662, 47148, 7, 83, 27983, 151552, 237, 190659, 700, 87739, 53, 4, 7440, 70, 112664, 111, 10, 135969, 289, 5426, 83, 151552, 17368, 70, 128652, 167201, 7, 111, 5177, 34937, 130265, 700, 87739, 53, 5, 581, 176866, 90, 111, 26847, 23, 10, 47880, 621, 6626, 9, 157955, 22834, 22230, 23, 627, 15, 55547, 6, 157955, 32628, 194, 129956, 532, 167201, 7, 621, 8382, 450, 479, 86687, 70, 62488, 17721, 2499, 6626, 26847, 5, 581, 5423, 111, 128652, 167201, 7, 23, 142, 44, 19, 58, 9, 157955, 32628, 83, 35839, 70, 5361, 5177, 34937, 130265, 21115, 98, 627, 4, 136, 8, 157, 3674, 44, 9127, 132, 19, 194, 58, 581, 19069, 111, 1632, 82761, 111, 10, 135969, 289, 5426, 35845, 47, 15700, 83, 61924, 71, 390, 39864, 214, 10, 91067, 123789, 4, 5154, 44, 594, 830, 98, 1632, 450, 25813, 7, 35845, 47, 10, 188347, 123789, 4, 44, 919, 4, 58, 98, 70, 3789, 5, 581, 128652, 167201, 4, 707, 2837, 23935, 674, 4, 111, 44, 594, 58, 35845, 47, 44, 919, 58, 61924, 7, 70, 35845, 19069, 111, 70, 6626, 82761, 7, 5, 62, 2837, 23935, 674, 58055, 7, 111, 70, 162515, 111, 10, 2062, 22062, 136, 10, 153648, 5, 581, 5423, 111, 756, 2837, 23935, 9035, 111, 44, 594, 58, 35845, 47, 44, 919, 58, 83, 35839, 70, 180346, 32628, 111, 44, 594, 1242, 62, 156100, 9709, 272, 1295, 1632, 19069, 47, 15700, 23, 903, 180346, 32628, 83, 10, 62005, 223, 5423, 111, 2837, 23935, 9035, 4, 35839, 70, 78112, 111, 44, 594, 58, 35845, 47, 44, 919, 1242, 581, 78112, 111, 10, 14361, 58055, 7, 111, 10, 62005, 223, 5423, 111, 47014, 5256, 136, 153648, 7, 5, 581, 162515, 111, 10, 2062, 22062, 136, 153648, 23, 70, 47880, 627, 831, 186, 33636, 297, 390, 10, 24233, 10644, 111, 138, 425, 363, 50944, 425, 51529, 237, 10, 12840, 15292, 10821, 27198, 5, 581, 138, 425, 363, 12840, 15292, 10821, 27198, 83, 64549, 297, 1295, 10, 116, 425, 304, 2062, 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summarize: The English expression "deep-fried" is attested from the early 20th century. Frying food in olive oil is attested in Classical Greece from about the 5th century BCE. The late Roman cookbook of "Apicius" (c. 400), appears to list the ancient Romans' first use of deep frying to prepare Pullum Frontonianum, a chicken dish. The practice of deep frying spread to other parts of Europe and Arabia in the following centuries. Deep-fried foods such as funnel cakes arrived in northern Europe by the 13th century, and deep-fried fish recipes have been found in cookbooks in Spain and Portugal at around the same time. Falafel arrived in the Middle East from population migrations from Egypt as soon as the 14th century. Evidence of potato frying can be found as early as the late 17th century in Europe. French fries, invented in the late 18th century, became popular in the early 19th century western Europe. In 1860 Joseph Malin combined deep fried fish with chips (french fries) to open the first fish and chip shop in London. Modern deep frying in the United States began in the 19th century with the growing popularity of cast iron, particularly around the American South which led to the development of many modern deep-fried dishes. Doughnuts were invented in the mid-19th century, with foods such as onion rings, deep-fried turkey, and corn dogs all being invented in the early 20th century. In recent years, the growth of fast food has expanded the reach of deep-fried foods, especially French fries. Deep frying food is defined as a process where food is completely submerged in hot oil at temperatures typically between and. One common method for preparing food for deep frying involves adding multiple layers of batter around the food, such as cornmeal, flour, or tempura; breadcrumbs may also be used. After the food is submerged in oil, the surface of it begins to dehydrate and it undergoes Maillard reactions which break down sugars and proteins, creating the golden brown exterior of the food. Once the surface is dehydrated, it forms a crust which prevents further oil absorption. The heat conducts throughout the food causing proteins to denature, starches to undergo starch gelatinization, and dietary fiber to soften. While most foods need batter coatings for protection, it is not as necessary for cooked noodles and potatoes because their high starch content enables them to hold more moisture and resist shrinking. Meats may be cooked before deep frying to ensure that they are done inside while keeping juiciness. When performed properly, deep frying does not make food excessively greasy, because the moisture in the food repels the oil. The hot oil heats the water within the food, steaming it; oil cannot go against the direction of this powerful flow because (due to its high temperature) the water vapor pushes the bubbles toward the surface. As long as the oil is hot enough and the food is not immersed in the oil for too long, oil penetration will be confined to the outer surface. Foods deep-fried at proper temperatures typically absorb "no more than a couple of tablespoons per cups of oil" used. This oil absorption rate is around the same as occurs with shallow frying, such as in a pan. However, if the food is cooked in the oil for too long, much of the water will be lost and the oil will begin to penetrate the food. The correct frying temperature depends on the thickness and type of food, but in most cases it lies between. An informal test for a temperature close to this range involves adding a tiny amount of flour into the oil and watching to see if it sizzles without immediately burning. A second test involves adding one piece of food to deep fry and watching it sink somewhat and rise back up. Sinking without resurfacing indicates that the oil is too cold; not sinking at all indicates that the oil is too hot. It is recommended that deep fryers be cleaned often to prevent contamination. The process of cooking with oil can also contaminate nearby surfaces as oil may splatter on adjacent areas. Oil vapors can also condense on more distant surfaces such as walls and ceilings. Supplies such as dish detergent and baking soda can effectively clean affected surfaces. Deep frying is done with a deep fryer, a pan such as a wok or chip pan, a Dutch oven, or a cast-iron pot. Additional tools include fry baskets, which are used to contain foods in a deep fryer and to strain foods when removed from the oil, and cooking thermometers, used to gauge oil temperature. Tongs, slotted spoons, wooden spoons, and sieves may be used to remove or separate foods from the hot oil. Japanese deep frying tools include long metal chopsticks; the "agemono-nabe" deep frying pot, which is heavy for retaining heat and deep for holding oil; the "ami-shakushi" net ladle used for scooping out batter debris; and the "abura-kiri" oil drying rack pan. Deep-fried foods are common in many countries, and have also been described as "a staple of almost all street cuisines on all continents". There are hundreds of dishes that are associated with deep frying as most foods can be deep-fried. Examples of food that can be deep-fried include meat, poultry, fish and vegetables. Fish and chips, for instance, combines deep-fried fish and deep-fried potatoes. French fries, doughnuts, onion rings, and hushpuppies are common deep-fried foods. Other common deep-fried foods include Chinese "You Bing" deep-fried pancakes, Southeast Asian Jin deui, and Japanese tempura. Less common deep-fried foods include maple leaves, peanut butter and jelly sandwiches, pizza, and Snickers bars. In the United States, the "Chicago Tribune" notes that "you can deep fry almost anything". The American South has been noted as a modern center of innovation in the area of deep-fried food. According to the owner of a deep frying restaurant in the South, "If something is edible, you can bet that someone south of the Mason-Dixon line has tried to cook it in oil". In Northern Africa, deep-fried dishes are a part of the cuisine. A common food in this region is the deep-fried fritter, also referred to as "sponges". In East Africa deep fried food is common, cooked in cast iron or earthenware pots. Frying in batter is common. A Ugandan speciality is a kind of doughnut called Mandazi. In areas of Southern Africa, street foods include deep-fried potato and cassava chips. Deep-fried foods in the country of South Africa include fish and chips, "vetkoek" and "koeksisters", among others. Japanese tempura is a popular deep-fried food that generally consists of battered and fried seafood and vegetables. Japanese deep-fried dishes, or Agemono, include other styles besides tempura, such as Karaage, Korokke, Kushikatsu, and Tonkatsu. In areas of Southeast Asia such as Thailand, insects are commonly deep-fried for human consumption. Western-style fast food items such as donuts, deep-fried chicken, and deep-fried potatoes are also becoming popular in Asia. Deep-fried fish, tofu, and'are commonly eaten in Vietnamese cuisine. Deep frying is also used to make several kinds of ', including'(fried rice ball),'(sesame ball),'(hollow doughnut),'(sweet potato pancake),'(banana fritter), Hồ Tây–style'(shrimp fritter), and "" (pillow cake). Deep-fried sticks of dough, known as youtiao in Chinese, are eaten in many East and Southeast Asian cuisines. In Hong Kong, is a popular food. In South Asia, popular deep fried snacks are samosa, jalebi, and pakora. Many countries in Europe use pure or hydrogenated rapeseed oil for deep-frying. The deep-fried Mars bar originated in Scotland, with The Carron Fish Bar in Stonehaven claiming to have invented it in the early 1990s. Fish and chips is a very popular deep-fried dish in England since it originated in London in the 19th century and became popular among the working class. Its popularity continues with 229 million portions of fish and chips being sold annually in England. There is an annual trade fair devoted to deep-fried foods called the International Symposium on Deep-Fat Frying which features discussions on deep fat frying as well as exhibitions by companies involved with the process. Belgian tradition requires French fries to be deep-fried in filtered fat of cattle, locally called "blanc de boeuf" or "ossewit". In the United States, soybean oil is often used for deep-frying. Beignets, originally a French dish, are a popular deep-fried pastry in the U.S. city of New Orleans. Deep-fried food has been a core part of the culture of the American South with many restaurants solely serving deep-fried foods. The owner of one such restaurant has said that the deep-fried food, "in the South it's a way of life". Fast food is one of the most common ways to consume deep-fried food in North America. Novelty deep-fried foods are popular today in American fairs, especially those in the American South. Hundreds of items are served at these fairs. Some of them include deep-fried beer, butter, and bubblegum. Additionally, deep frying can be used as a form of artwork by frying non-edible objects, such as electronics. Artists such as Henry Hargreaves have deep-fried replicas of electronic items such as iPads, Game Boys, and laptops. Deep-fried food contests are frequently held at fairs such as the Texas State Fair, where they hold an annual contest for the most creative deep-fried food. Notable past winners have included fried Coke and deep-fried butter, both invented by Abel Gonzales. Since 2013, an American reality competition show called "deep-fried Masters", produced by Discovery Networks, holds deep frying competitions at several state fairs across the country. Milk bars in Australia may purvey several types of deep-fried foods, along with other food types. The buñuelo, a fried dough ball popular in Central America and Greece, is a popular deep-fried snack and street food in South America. Picarone, a Peruvian dessert originated in the colonial period, are deep-fried cakes made with pumpkin and sweet potatoes, popular in Peru and Chile, especially during harvest festivals. Deep fat frying involves heating oil to temperatures in excess of 180 °C in the presence of moisture and air. These conditions can induce a series of complex chemical reactions which may impact the quality of both the food and the oil it is cooked in. Examples of different chemical reactions include the production of free radicals, oxidation, hydrolysis, isomerization and polymerization. The exact reactions are dependent upon factors such as the oil type, frying conditions, and food being cooked. When frying, water can attack the ester linkage of triacylglycerols, resulting in di- and monoglycerols, glycerol, and free fatty acids (a type of hydrolysis reaction). The aforementioned hydrolysis reaction is enhanced by the produced fatty acids and other low molecular weight acid compounds. Overheating or over-using the frying oil leads to formation of rancid-tasting products of oxidation, polymerization, and other deleterious, unintended or even toxic compounds such as acrylamide (from starchy foods). Recent research suggests fat deterioration may be worse when fat or oil is fried with food than when fat or oil is tested on its own in a laboratory. Deep-frying under vacuum helps to significantly reduce acrylamide formation, but this process is not widely used in the food industry due to the high investment cost involved. Some useful tests and indicators of excessive oil deterioration are the following: Instruments that indicate total polar compounds, currently the best single gauge of how deep-fried an object is, are available with sufficient accuracy for restaurant and industry use. Cooking oil is flammable, and fires may be caused by it igniting at too high a temperature. Further, attempts to extinguish an oil fire with water cause an extremely dangerous condition, a boilover, as they cause the water to flash into steam due to the high heat of the oil, in turn sending the burning oil in all directions and thus aggravating the fire. This is the leading cause of house fires in the United Kingdom. Instead, oil fires must be extinguished with a non-water fire extinguisher or by smothering. Other means of extinguishing an oil fire include application of dry powder (e.g., baking soda, salt) or fire fighting foam. Most commercial deep fryers are equipped with automatic fire suppression systems using foam. Spilled hot cooking oil can also cause severe third degree burns, In the worst-case scenario, severe burns can be fatal. The higher temperatures and tendency of oil to stick to the skin make spilled hot cooking oil far more dangerous than spilled hot water. Children can accidentally place their hands on top of the stove, playing with the materials while being cooked, or accidentally pull the pot down, which can cause significant injury. The utmost care should be used when deep frying when children are present, to protect their safety at all times. Deep frying produces large amounts of waste oil, which must be disposed of properly. Waste oil can contribute to the creation of fatbergs, overflow sewage systems, bind to the walls of sewage pipes, and interfere with sewage treatment. Waste oil from deep frying is increasingly being recycled and refined into biodiesel. Potatoes that are stored in artificially humidified warehouses contain more water, which makes the time required to deep fry them into chips longer. This increases the carbon dioxide footprint of commercially producing chips because more energy is required for frying over a longer time. According to one source, an average home appliance deep fryer draws 2,000 watts. The process of deep frying food is generally detrimental to its nutritional value. The oils that foods absorb in their batter typically contain large amounts of fats, especially saturated fats and trans fats. Consumption of large amounts of saturated and trans fats has been linked to a higher risk for some cancers including prostate cancer. Eating deep-fried foods has also been linked to higher cholesterol levels, obesity, heart attacks, and diabetes. Deep-fried foods cooked at certain temperatures can also contain acrylamide, a possible carcinogen. Additionally, fat degradation processes (lipid peroxidation) during deep frying results in the loss of nutritional value in deep-fried foods. Cooking oil that has been used for too long may in addition cause blood pressure elevation and vascular hypertrophy. Trans fats are used in shortenings for deep-frying in restaurants, as they can be used for longer than most conventional oils before becoming rancid. In the early 21st century, non-hydrogenated vegetable oils that have lifespans exceeding that of the frying shortenings became available. As fast-food chains routinely use different fats in different locations, trans fat levels in fast food can have large variations. Some studies have found that deep frying in olive and sunflower oils has been found to be less of a detriment to health and in some cases have positive effects on insulin levels. Oil can be reused a few times after original use after straining out solids. However, excessive use of the same oil can cause it to break down and release compounds into the food that may be carcinogenic, affect liver health, or influence the body's ability to absorb vitamins. Some European countries have set public health standards for the safety of frying oil.	Deep frying (also referred to as deep fat frying) is a cooking method in which food is submerged in hot fat, most commonly oil, as opposed to the shallow oil used in conventional frying done in a frying pan. Normally, a deep fryer or chip pan is used for this; industrially, a pressure fryer or vacuum fryer may be used. Deep frying may also be performed using oil that is heated in a pot. Deep frying is classified as hot-fat cooking method. 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summarize: In 1679, French physicist Denis Papin, better known for his studies on steam, invented the "steam digester" in an attempt to reduce the cooking time of food. His airtight cooker used steam pressure to raise the water's boiling point, thus cooking food more quickly. In 1681 Papin presented his invention to the Royal Society of London as a scientific study; he was later elected as a member. In 1864, Georg Gutbrod of Stuttgart began manufacturing pressure cookers made of tinned cast iron. In 1918, Spain granted a patent for the pressure cooker to José Alix Martínez from Zaragoza. Martínez named it the "olla exprés", literally "express cooking pot", under patent number 71143 in the "Boletín Oficial de la Propiedad Industrial". In 1924, the first pressure cooking pot recipe book was published, written by José Alix and titled "360 fórmulas de cocina Para guisar con la 'olla expres'", or "360 recipes for cooking with a pressure cooker". In 1938, Alfred Vischer presented his invention, the "Flex-Seal Speed Cooker", in New York City. Vischer's pressure cooker was the first designed for home use, and its success led to competition among American and European manufacturers. At the 1939 New York World's Fair, the National Pressure Cooker Company, later renamed National Presto Industries, introduced its own pressure cooker. Also known as "old type" pressure cookers, these operate with a weight-modified or "jiggler" valve, which releases pressure during operation. Some people consider them loud because the valve rattles as excess steam is released. Older pressure cookers typically offered only one pressure level, but from the 1960s onwards some allow the operator to change the weight of the valve, thus changing the pressure. Today, most pressure cookers are variations on the first-generation cookers, with the addition of new safety features such as a mechanism that prevents the cooker from being opened until it is entirely depressurized. These operate with a spring-loaded valve that is often hidden from view in a proprietary mechanism. This generation is characterized by two or more pressure settings. Some of these pressure cookers do not release any steam during operation (non-venting) and instead use a rising indicator with markings to show the pressure level. These only release steam when the pan is opened, or as a safety precaution if the heat source is not reduced enough when the pan reaches the required cooking pressure. Others use a dial that the operator can advance by a few clicks (which alters the spring tension) to change the pressure setting or release pressure; these release steam during operation (venting). After the stove-top pressure cookers, in 1991 came the electric pressure cookers, called the "third generation" pressure cookers. These include an electric heat source that is automatically regulated to maintain the operating pressure. They also include a spring-loaded valve (as described above). This type of pressure cooker cannot be opened with a cold water quick-release method and should be operated with caution when releasing vapour through the valve, especially while cooking foamy foods and liquids (lentils, beans, grains, milk, gravy, etc.) An electric pressure cooker integrates a timer. Depending on cooking control capability, there are three generations of electric pressure cookers: Some cookers are multifunctional (multicookers): pressure cooker, saute/browning, slow cooker, rice cooker, yogurt maker, steamer, sous vide and stockpot warmer that can also be used to keep cooked food warm. In an ordinary, non-pressurized cooking vessel, the boiling point of water is at standard pressure. Once the temperature in the vessel reaches the boiling point of water, excess heat causes the water to vaporize into steam. In a sealed pressure cooker, however, the boiling point of water increases with increasing pressure. As the temperature increases, so does the pressure, resulting in superheated water. When the pressure reaches 1 bar or above the existing atmospheric pressure, the water will have reached a temperature of. Pressure cookers employ a regulator to limit the pressure, thereby maintaining a precise temperature. Once the desired pressure and temperature are reached, the heat can be lowered somewhat to minimize excess release of steam, saving energy. Some recipes require browning to develop flavors during roasting or frying. Browning occurs via the Maillard reaction, under temperatures higher than the roughly 250 deg F achieved in pressure cooking. One may brown foods by searing them either in the open pressure cooker or another pan beforehand. A pressure cooker can be used to compensate for lower atmospheric pressure at high elevations. The boiling point of water drops by approximately 1°C per every 294 metres of altitude, causing the boiling point of water to be significantly below the at standard pressure. For example, on the summit of Everest (8,848m), the boiling point of water would be 30°C. Without the use of a pressure cooker, boiled foods may be undercooked, as described in Charles Darwin's "The Voyage of the Beagle" (chapter XV, March 20, 1835): At higher altitudes, the boiling point of liquid is somewhat lower than it would be at sea level. When pressure cooking at high altitudes, cooking times need to be increased by approximately 5% for every above elevation. Since the regulators work off the pressure differential between interior and ambient pressure, the absolute pressure in the interior of a pressure cooker will always be lower at higher altitudes. Weight is a concern with backpackers, so mountaineering pressure cookers are designed to operate at a lower differential pressure than stove-top units. This enables them to use thinner, and therefore lighter materials. Generally, the goal is to raise the cooking temperature enough to make cooking possible and to conserve fuel by reducing heat lost through boiling. Lightweight pressure cookers as small as weighing are available for mountain climbers. Sherpas often use pressure cookers in base camp. Some food toxins can be reduced by pressure cooking. A Korean study of aflatoxins in rice (associated with "Aspergillus" fungus) showed that pressure cooking was capable of reducing aflatoxin concentrations to 32 percent of the amount in the uncooked rice, compared to 77 percent from ordinary cooking. Some foods are not recommended for pressure cooking. Foods such as noodles, pasta, cranberries, cereals and oatmeal can expand too much, froth and sputter, potentially blocking the steam vent and creating an unsafe condition. Pressure cookers are available in different capacities for cooking larger or smaller amounts, with 6 litres' capacity being common. The maximum capacity of food is less than the advertised capacity because pressure cookers can only be filled up to 2/3 full, depending on ingredients and liquid (see Safety features section). Pressure cookers are typically made of aluminum (aluminium) or stainless steel. Aluminum pressure cookers may be stamped, polished, or anodized, but all are unsuitable for the dishwasher. They are cheaper, but the aluminum is reactive to acidic foods, whose flavors are changed in the reactions, and less durable than stainless steel pressure cookers. Higher-quality stainless steel pressure cookers are made with heavy, three-layer, or copper-clad bottoms (heat spreader) for uniform heating because stainless steel has lower thermal conductivity. Most modern stainless steel cookers are dishwasher safe, although some manufacturers may recommend washing by hand. Some pressure cookers have a non-stick interior. A gasket or sealing ring, made from either rubber or silicone, forms a gas-tight seal that does not allow air or steam to escape between the lid and pan. Normally, the only way steam can escape is through a regulator on the lid while the cooker is pressurized. If the regulator becomes blocked, a safety valve provides a backup escape route for steam. To seal the gasket there are several main methods used. Each determines the design of the pressure cooker: Because of the forces that pressure cookers must withstand, they are usually heavier than conventional pots of similar size. Early pressure cookers equipped with only a primary safety valve risked explosion from food blocking the release valve. On modern pressure cookers, food residues blocking the steam vent or the liquid boiling dry will trigger additional safety devices. Modern pressure cookers sold from reputable manufacturers have sufficient safety features to prevent the pressure cooker itself from exploding. When excess pressure is released by a safety mechanism, debris of food being cooked may also be ejected with the steam, which is loud and forceful. This can be avoided if the pressure cooker is regularly cleaned and maintained in accordance with the manufacturer's instructions and never overfilled with food and/or liquid. Modern pressure cookers typically have two or three redundant safety valves and additional safety features, such as an interlock lid that prevents the user from opening the lid when the internal pressure exceeds atmospheric pressure, preventing accidents from a sudden release of hot liquid, steam and food. If safety mechanisms are not correctly in place, the cooker will not pressurize the contents. Pressure cookers should be operated only after reading the instruction manual, to ensure correct usage. Pressure cooker failure is dangerous: a large quantity of scalding steam and water will be forcefully ejected and if the lid separates it may be propelled with considerable force. Some cookers with an internally fitted lid may be particularly dangerous upon failure as the lid fits tighter with increasing pressure, preventing the lid from deforming and venting around the edges. Due to these dangers pressure cookers are generally over-engineered in a safety regard and some countries even have regulations to prevent the sale of non-compliant cookers. For first generation pressure cookers with a weighted valve or "jiggler", the primary safety valve or regulator is usually a weighted stopper, commonly called "the rocker" or "vent weight". This weighted stopper is lifted by the steam pressure, allowing excess pressure to be released. There is a backup pressure release mechanism that releases pressure quickly if the primary pressure release mechanism fails (e.g., food jams the steam discharge path). One such method is a hole in the lid that is blocked by a low melting point alloy plug and another is a rubber grommet with a metal insert at the center. At a sufficiently high pressure, the grommet will distort and the insert will blow out of its mounting hole to release pressure. If the pressure continues to increase, the grommet itself will blow out to release pressure. These safety devices usually require replacement when activated by excess pressure. Newer pressure cookers may have a self-resettable spring device, fixed onto the lid, that releases excess pressure. On second generation pressure cookers, a common safety feature is the gasket, which expands to release excess pressure downward between the lid and the pot. This release of excess pressure is forceful and sufficient to extinguish the flame of a gas stove. Pressure cookers sold in the European Union (EU) must comply with the Pressure Equipment Directive. The recommended maximum fill levels of food/liquid avoids blockage of the steam valve or developing excess pressure: two-thirds full with solid food, half full for liquids and foods that foam and froth (e.g., rice, pasta); adding a tablespoon of cooking oil minimizes foaming., and no more than one-third full for pulses (e.g., lentils). Pressure cooking always requires liquid. Pressure cooking cannot be used for cooking methods that produce little steam such as roasting, pan frying, or deep frying. Thick sauces do not contain enough liquid to vaporize and create pressure, so they usually burn onto the interior base of the pressure cooker after prolonged heating. Sauces should be thickened after pressure cooking. The inner pot of a pressure cooker should never be filled more than halfway when cooking beans. Food is placed inside the pressure cooker with a small amount of water or other liquid such as stock. Food is either cooked in the liquid or above the liquid to be steamed; the latter method prevents the transfer of flavors from the liquid. The lid is closed, the pressure setting is chosen and the pressure cooker is placed on a stove on the highest heat (less than high for induction cooking to allow air to be vented). Once the cooker reaches full pressure, the heat is lowered to maintain pressure; timing the recipe begins at this point. Recipes for foods using raising agents such as steamed puddings call for gentle pre-steaming, without pressure, in order to activate the raising agents prior to cooking and achieve a light, fluffy texture. It takes several minutes for the pressure cooker to reach the selected pressure level. It can take around 10 minutes or longer depending on: the quantity of food, the temperature of the food (cold or frozen food delays pressurization), the amount of liquid, the power of the heat source and the size of the pressure cooker. A common mistake is for the user to start timing when a colored pop-up indicator rises, which happens when there is the slightest increase in pressure, instead of waiting for the cooker to reach its selected pressure level. The typical pop-up indicator only shows that the cooker has pressure inside, which does not reliably signal that the cooker has reached the selected pressure. This pop-up indicator often acts as an interlock, preventing the lid from being opened while there is internal pressure. Manufacturers may use their own terminology for it, such as calling it a ""locking indicator."" As the internal temperature rises, the pressure also rises until it reaches the design gauge pressure. Timing the recipe begins when the selected pressure is reached. With first generation designs, the pressure regulator weight begins levitating above its nozzle, allowing excess steam to escape. In second generation pressure cookers, either a relief valve subsequently opens, releasing steam to prevent the pressure from rising any further or a rod rises with markers to indicate the pressure level, without constantly venting steam. At this stage, the heat source is reduced to the lowest possible heat that still maintains pressure, as extra heat wastes energy and increases liquid loss. Before the pressure cooker lid is sealed airtight, the internal air has to be mostly replaced by steam. Steam has a much higher specific heat than air, and the presence of steam rather than air inside the pressure cooker is how it is able to transfer sufficient heat into the parts of the food that are not submerged in liquid, such as a pot roast. If the lid is sealed before enough air has been removed, not enough heat can be transferred to the food, and food may be undercooked; the presence of air would make the food cook more like it is in an oven than a pressure cooker. To remove the air, steam is vented for several minutes to replace the volume of air inside the cooker. This is why a pressure cooker takes about 10 minutes to reach pressure. For pressure cookers with a weight, the weight is placed over the steam vent pipe while steam is being emitted to ensure the air inside has escaped. The newer generation pressure cookers, which have no weights, automatically expel air from inside for several minutes before a coloured pop-up indicator pin rises to seal the lid airtight; pressure then builds in the now airtight cooker. If the pressure cooker is already hot or a stovetop pressure cooker is placed on a very strong heat source, such as induction on too high a setting, the lid can seal airtight too quickly before the air inside has been removed. In these situations, a slightly lower heat setting can be used to allow the water to boil slower in order to vent the air. Small containers such as plastic pudding containers can be used in a pressure cooker, if the containers (and any covering used) can withstand temperatures of and are not placed directly on the interior base. The containers can be used for cooking foods that are prone to burning on the base of the pressure cooker. A lid for the container may be used if the lid allows some steam to come into contact with the food and the lid is securely fitted; an example is foil or greaseproof paper, pleated in the center and tied securely with string. Containers that are cracked or have otherwise sustained damage are not suitable. Cooking time is longer when using covered containers because the food is not in direct contact with the steam. Since non-metal containers are poorer heat conductors, the type of container material stated in the recipe cannot be substituted without affecting the outcome. For example, if the recipe time is calculated using a stainless steel container and a plastic container is used instead, the recipe will be undercooked, unless the cooking time is increased. Containers with thicker sides, e.g., oven-proof glass or ceramic containers, which are slower to conduct heat, will add about 10 minutes to the cooking time. Liquid can be added inside the container when pressure cooking foods such as rice, which need to absorb liquid in order to cook properly. The flavor of some foods, such as meat and onions, can be improved by gently cooking with a little pre-heated cooking oil, butter or other fat in the open pressure cooker over medium heat for stove-top models (unless the manufacturer advises against this) before pressure cooking, while avoiding overheating the empty pressure cooker not heating the empty cooker with the lid and gasket in place to avoid damage. Electric pressure cookers usually have a "saute" or "brown" option for frying ingredients. The pressure cooker needs to cool briefly before adding liquid; otherwise some of the liquid will evaporate instantly, possibly leaving insufficient liquid for the entire pressure cooking time; if deglazing the pan, more liquid may need to be added. After cooking, there are three ways of releasing the pressure, either quickly or slowly, before the lid can be opened. Recipes for pressure cookers state which release method is required at the end of the cooking time for proper results. Failure to follow the recommendation may result in food that is under-cooked or over-cooked. To avoid opening the pressure cooker too often while cooking different vegetables with varying cooking times, the vegetables that take longer to cook can be cut into smaller pieces and vegetables that cook faster can be cut into thicker pieces. This method is sometimes called a "quick release," not to be confused with the cold water release (mentioned below). It involves the quick release of vapor by gradually lifting (or removing) the valve, pushing a button, or turning a dial. It is most suitable to interrupt cooking to add food that cooks faster than what is already in the cooker. For example, since meat takes longer to cook than vegetables, it is necessary to add vegetables to stew later so that it will cook only for the last few minutes. Unlike the cold water release method, this release method does not cool down the pressure cooker. Releasing the steam with care avoids the risk of being scalded by the rapid release of hot steam. This release method is not suitable for foods that foam and froth while cooking; the hot contents might spray outwards due to the pressure released from the steam vent. This release method takes about two minutes to release the pressure before the lid can be opened. The natural release method allows the pressure to drop slowly; this is achieved by removing the pressure cooker from the heat source and allowing the pressure to lower without action. It takes approximately 10 to 15 minutes (possibly longer) for the pressure to disappear before the lid can be opened. On many pressure cookers, a coloured indicator pin will drop when the pressure has gone. This natural release method is recommended for foods that foam and froth during cooking, such as rice, legumes, or recipes with raising agents such as steamed puddings. The texture and tenderness of meat cooked in a pressure cooker can be improved by using the natural release method. The natural release method finishes cooking foods or recipes that have longer cooking times because the inside of the pressure cooker stays hot. This method is not recommended for foods that require very short cooking times, otherwise the food overcooks. This method is the fastest way of releasing pressure with portable pressure cookers, but can be dangerous if performed incorrectly. It is therefore safer to release pressure by following the other methods. The manufacturer's instruction book may advise against the cold water release or require it to be performed differently. The cold water release method involves using slow running cold tap water, over the edge of the pressure cooker lid, being careful to avoid the steam vent or any other valves or outlets and never immersing the pressure cooker under water, otherwise steam can be ejected from under the lid, which could cause scalding injury to the user; also the pressure cooker lid can be permanently damaged by an internal vacuum if water gets sucked into the pressure cooker, since the incoming water blocks the inrush of air. The cold water release is most suitable for foods with short cooking times. It takes about 20 seconds for the cooker to cool down enough to lower the pressure so that it can be safely opened. This method is not suitable for electric pressure cookers, as they are not immersible. The cold water release method is not recommended when cooking pulses e.g. red kidney beans, as the sudden release of pressure can cause the bean to burst its skin. Most pressure cookers have a cooking (operating) pressure setting between 0.8–1 bar (11.6–15 psi) (gauge) so the pressure cooker operates at 1.8 to 2.0 bar (absolute). The standard cooking pressure of 15 psi gauge was determined by the United States Department of Agriculture in 1917. At this pressure, water boils at (described in vapour pressure of water article). The higher temperature causes food to cook faster; cooking times can typically be reduced to one-third of the time for conventional cooking methods. The actual cooking time also depends on the pressure release method used after timing "(see Pressure release methods for details)" and the thickness and density of the food, since thicker (and denser) foods take longer to cook. Meat joints and some other foods like sponge puddings and Christmas puddings are typically timed according to their weight. Frozen foods need extra cooking time to allow for thawing. When pressure cooking at 1 bar/15 psi (gauge), approximate cooking times are one minute for shredded cabbage, seven minutes for boiled potatoes (if cut small, not diced) and three minutes for fresh green beans. If the pressure is released naturally after timing "(see Pressure release methods for details)," cooking times are even shorter. Food cooks more quickly when cut into smaller pieces. Some recipes may require cooking at lower than 1 bar/15 psi (gauge) e.g. fresh vegetables, as these can easily overcook. Many pressure cookers have 2 or more selectable pressure settings or weights. Some pressure cookers have a lower or higher "maximum" pressure than 1 bar/15 psi (gauge) or can be adjusted to different pressures for some recipes; cooking times will increase or decrease accordingly. This is typically done by having different regulator weights or different pressure settings. If the recipe is devised for a higher pressure and the pressure cooker does not reach that pressure, the cooking time can be increased slightly to compensate. Electric pressure cookers operate at lower pressures than stovetop pressure cookers. Foods cook much faster with pressure cooking than with other methods (except for small quantities in microwave ovens). Food is cooked more quickly in a pressure cooker because at the higher pressure (1 bar/15 psi), the boiling point of water rises from 100 °C (212 °F) to 121 °C (250 °F). The hotter steam is able to transmit its thermal energy to the food at around 4 times the rate of conventional boiling. Pressure cooking requires much less water than conventional boiling, so food can be ready sooner. Less energy is required than that of boiling, steaming, or oven cooking. Since less water or liquid has to be heated, the food reaches its cooking temperature faster. Using more liquid than necessary wastes energy because it takes longer to heat up; the liquid quantity is stated in the recipe. Pressure cookers can use much less liquid than the amount required for boiling or steaming in an ordinary saucepan. It is not necessary to immerse food in water. The minimum quantity of water or liquid used in the recipe to keep the pressure cooker filled with steam is sufficient. With sealed pressure cookers, steam isn't continually escaping, thus evaporation losses are non existent once it has reached pressure. Overall, energy used by pressure cookers can be as much as 70% lower than used by cooking in a pan. Because of this, vitamins and minerals are not leached (dissolved) away by water, as they would be if food were boiled in large amounts of water. Due to the shorter cooking time, vitamins are preserved relatively well during pressure cooking. Several foods can be cooked together in the pressure cooker, either for the same amount of time or added later for different times. Manufacturers provide steamer baskets to allow more foods to be cooked together inside the pressure cooker. Not only is this steam energy transmitted quickly to food, it is also transmitted rapidly to any micro-organisms that are present, easily killing even the deadliest types that are able to survive at the boiling point. Because of this enhanced germ killing ability, a pressure cooker can be used as an effective sterilizer for jam pots, glass baby bottles, or for water while camping. In fact, the autoclave, used in hospitals to sterilize surgical instruments, is really just a more precise and technical version of the ordinary pressure cooker. The appliance has been adapted as a crude type of bomb, which has been used in terrorist attacks. An "autoclave" is a type of pressure cooker used by laboratories and hospitals to sterilize equipment. Large pressure cookers are often called "pressure canners" in the United States, because of their capacity to hold jars used in canning. Pressure canners are specifically designed for home canning, whereas ordinary pressure cookers are not recommended for canning due to the risk of botulism poisoning, because pressure canners hold heat and pressure for much longer than ordinary pressure cookers; these factors are a critical part of the total processing time required to destroy harmful microbes. "Pressure fryers" are used for deep fat frying under pressure, because ordinary pressure cookers are not suitable for pressure frying. A "pressure air fryer" (not to be confused with a "pressure fryer") is a recent combination of a pressure cooker and an air fryer, with two separate lids, one for pressure cooking and one for air frying. The air frying lid has a convection fan in it that allows it to air fry foods, similar to an air fryer oven. This innovation was popularized by the Ninja Foodi Pressure Cooker, marketed as the first pressure cooker that can crisp and air fry. A "pressure oven" is a recent combination of an oven and pressure cooker, usually as a countertop convection oven. They operate at low pressures,, compared to other pressure cookers. Their main function is as an enhanced oven or broiler for meat and poultry, avoiding drying. As such, they often include a rotisserie. Although having insufficient pressure for most conventional pressure cooking functions, they do also have non-pressure oven modes.	Pressure cooking is the process of cooking food at high pressure, employing water or a water-based cooking liquid, in a sealed vessel known as a "pressure cooker". 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summarize: Generally speaking, researchers involved in dynamics study how a physical system might develop or alter over time and study the causes of those changes. In addition, Newton established the fundamental physical laws which govern dynamics in physics. By studying his system of mechanics, dynamics can be understood. In particular, dynamics is mostly related to Newton's second law of motion. However, all three laws of motion are taken into account because these are interrelated in any given observation or experiment. The study of dynamics falls under two categories: linear and rotational. Linear dynamics pertains to objects moving in a line and involves such quantities as force, mass/inertia, displacement (in units of distance), velocity (distance per unit time), acceleration (distance per unit of time squared) and momentum (mass times unit of velocity). Rotational dynamics pertains to objects that are rotating or moving in a curved path and involves such quantities as torque, moment of inertia/rotational inertia, angular displacement (in radians or less often, degrees), angular velocity (radians per unit time), angular acceleration (radians per unit of time squared) and angular momentum (moment of inertia times unit of angular velocity). Very often, objects exhibit linear and rotational motion. For classical electromagnetism, Maxwell's equations describe the kinematics. The dynamics of classical systems involving both mechanics and electromagnetism are described by the combination of Newton's laws, Maxwell's equations, and the Lorentz force. From Newton, force can be defined as an exertion or pressure which can cause an object to accelerate. The concept of force is used to describe an influence which causes a free body (object) to accelerate. It can be a push or a pull, which causes an object to change direction, have new velocity, or to deform temporarily or permanently. Generally speaking, force causes an object's state of motion to change. Newton described force as the ability to cause a mass to accelerate. His three laws can be summarized as follows: Newton's Laws of Motion are valid only in an inertial frame of reference.	Dynamics is the branch of classical mechanics concerned with the study of forces and their effects on motion. 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summarize: Mammal classification has been through several iterations since Carl Linnaeus initially defined the class. No classification system is universally accepted; McKenna & Bell (1997) and Wilson & Reader (2005) provide useful recent compendiums. George Gaylord Simpson's "Principles of Classification and a Classification of Mammals" (AMNH "Bulletin" v. 85, 1945) provides systematics of mammal origins and relationships that were universally taught until the end of the 20th century. Since Simpson's classification, the paleontological record has been recalibrated, and the intervening years have seen much debate and progress concerning the theoretical underpinnings of systematization itself, partly through the new concept of cladistics. Though field work gradually made Simpson's classification outdated, it remains the closest thing to an official classification of mammals. Most mammals, including the six most species-rich orders, belong to the placental group. The three largest orders in numbers of species are Rodentia: mice, rats, porcupines, beavers, capybaras and other gnawing mammals; Chiroptera: bats; and Soricomorpha: shrews, moles and solenodons. The next three biggest orders, depending on the biological classification scheme used, are the Primates including the apes, monkeys and lemurs; the Cetartiodactyla including whales and even-toed ungulates; and the Carnivora which includes cats, dogs, weasels, bears, seals and allies. According to "Mammal Species of the World", 5,416 species were identified in 2006. These were grouped into 1,229 genera, 153 families and 29 orders. In 2008, the International Union for Conservation of Nature (IUCN) completed a five-year Global Mammal Assessment for its IUCN Red List, which counted 5,488 species. According to research published in the "Journal of Mammalogy" in 2018, the number of recognized mammal species is 6,495 including 96 recently extinct. The word "mammal" is modern, from the scientific name "Mammalia" coined by Carl Linnaeus in 1758, derived from the Latin "mamma" ("teat, pap"). In an influential 1988 paper, Timothy Rowe defined Mammalia phylogenetically as the crown group of mammals, the clade consisting of the most recent common ancestor of living monotremes (echidnas and platypuses) and therian mammals (marsupials and placentals) and all descendants of that ancestor. Since this ancestor lived in the Jurassic period, Rowe's definition excludes all animals from the earlier Triassic, despite the fact that Triassic fossils in the Haramiyida have been referred to the Mammalia since the mid-19th century. In 1997, the mammals were comprehensively revised by Malcolm C. McKenna and Susan K. Bell, which has resulted in the McKenna/Bell classification. Their 1997 book, "Classification of Mammals above the Species Level", is a comprehensive work on the systematics, relationships and occurrences of all mammal taxa, living and extinct, down As of the early 21st century, molecular studies based on DNA analysis have suggested new relationships among mammal families. Most of these findings have been independently validated by retrotransposon presence/absence data. Classification systems based on molecular studies reveal three major groups or lineages of placental mammals—Afrotheria, Xenarthra and Boreoeutheria—which diverged in the Cretaceous. The relationships between these three lineages is contentious, and all three Synapsida, a clade that contains mammals and their extinct relatives, originated during the Pennsylvanian subperiod (~323 million to ~300 million The first fully terrestrial vertebrates were amniotes. Like their amphibious tetrapod predecessors, they had lungs and limbs. Amniotic eggs, however, have internal membranes that allow the developing embryo to breathe but keep water in. Hence, amniotes can lay eggs on dry land, while amphibians generally need to lay their eggs in water. The first amniotes apparently arose in the Pennsylvanian subperiod of the Carboniferous. They descended from earlier reptiliomorph amphibious tetrapods, which lived on land that was already inhabited by insects and other invertebrates as well as ferns, mosses and other plants. Within a few million years, two important amniote lineages became distinct: the The Permian–Triassic extinction event about 252 million years ago, which was a prolonged event due to the accumulation of several extinction pulses, ended the dominance of carnivorous therapsids. In the early Triassic, most medium to large land carnivore niches were taken over by archosaurs which, over an extended period (35 million years), came to include the crocodylomorphs, the pterosaurs and the dinosaurs; however, large cynodonts like "Trucidocynodon" and traversodontids still occupied large sized carnivorous and herbivorous niches respectively. By the Jurassic, the dinosaurs had come to dominate the large terrestrial herbivore niches as well. The first mammals (in Kemp's sense) appeared in the Late Triassic epoch (about 225 million years ago), 40 million years after the first therapsids. They expanded out of their nocturnal insectivore niche from the mid-Jurassic onwards; The Jurassic "Castorocauda", for example, was a close relative of true mammals that had adaptations for swimming, digging and catching fish. Most, if not all, are thought to have remained nocturnal (the nocturnal bottleneck), accounting for much of the typical mammalian traits. The majority of the mammal species that existed in the Mesozoic Era were multituberculates, eutriconodonts and spalacotheriids. The "Hadrocodium", whose fossils date from approximately 195 million years ago, in the early Jurassic, provides the first clear evidence of a jaw joint formed solely by the squamosal and dentary bones; there is no space in the jaw for the articular, a bone involved in the jaws of all early synapsids. The earliest clear evidence of hair or fur is in fossils of "Castorocauda" and "Megaconus", from 164 million years ago in the mid-Jurassic. In the 1950s, it was suggested that the foramina (passages) in the maxillae and premaxillae (bones in the front of the upper jaw) of cynodonts were channels which supplied blood vessels and nerves to vibrissae (whiskers) and so were evidence of hair or fur; it was soon pointed out, however, that foramina do not necessarily show that an animal had vibrissae, as the modern lizard "Tupinambis" has foramina that are almost identical to those found in the nonmammalian cynodont "Thrinaxodon". Therian mammals took over the medium- to large-sized ecological niches in the Cenozoic, after the Cretaceous–Paleogene extinction event approximately 66 million years ago emptied ecological space once filled by non-avian dinosaurs and other groups of reptiles, as well as various other mammal groups, and underwent an exponential increase in body size (megafauna). Then mammals diversified very quickly; both birds and mammals show an exponential rise in diversity. For example, the earliest known bat dates from about 50 million years ago, only 16 million years after the extinction of the non-avian dinosaurs. Molecular phylogenetic studies Living mammal species can be identified by the presence of sweat glands, including those that are specialized to produce milk to nourish their young. In classifying fossils, however, other features must be used, since soft tissue The majority of mammals have seven cervical vertebrae (bones in the neck), including bats, giraffes, whales and humans. The exceptions are the manatee and the two-toed sloth, which have just six, and the three-toed sloth which has nine cervical vertebrae. All mammalian brains possess a neocortex, a brain region unique to mammals. Placental mammals have a corpus callosum, unlike monotremes and marsupials. The lungs of mammals are spongy and honeycombed. Breathing is mainly achieved with the diaphragm, which divides the thorax from the abdominal cavity, forming a dome convex to the thorax. Contraction of the diaphragm flattens the dome, increasing the volume of the lung cavity. Air enters through the oral and nasal cavities, and travels through the larynx, trachea and bronchi, and expands the alveoli. Relaxing the diaphragm has the opposite effect, decreasing the volume of the lung cavity, causing air to be pushed out of the lungs. During exercise, the abdominal wall contracts, increasing pressure on the diaphragm, which forces air out quicker and more forcefully. The rib As in all other tetrapods, mammals have a larynx that can quickly open and close to produce sounds, and a supralaryngeal vocal tract which filters this sound. The lungs and surrounding musculature provide the air stream and pressure required to phonate. The larynx controls the pitch and volume of sound, but the strength the lungs exert to exhale also contributes to volume. More primitive mammals, such as the echidna, can only hiss, as sound is achieved solely through exhaling through a partially closed larynx. Other mammals phonate using vocal folds, as opposed to the vocal cords seen in birds and reptiles. The movement or tenseness of the vocal folds can result in many sounds such as purring and screaming. Mammals can change the position of the larynx, allowing them to breathe through the nose while swallowing through the mouth, and to form both oral and nasal sounds; nasal sounds, such as a dog whine, are generally soft sounds, and oral sounds, such as a dog bark, are generally loud. Some mammals have a large larynx and thus a low-pitched voice, namely the hammer-headed The primary function of the fur of mammals is thermoregulation. Others include protection, sensory purposes, waterproofing, and camouflage. Different types of fur serve different purposes: Hair length is not a factor in thermoregulation: for example, some tropical mammals such as sloths have the same length of fur length as some arctic mammals but with less insulation; and, conversely, other tropical mammals with short hair have the same insulating value as arctic mammals. The denseness of fur can increase an animal's insulation value, and Mammalian coats are colored for a variety of reasons, the major selective pressures including camouflage, sexual selection, communication, and thermoregulation. Coloration in both the hair and skin of mammals is mainly determined by the type and amount of melanin; eumelanins for brown and black colors and pheomelanin for a range of yellow to reddish-brown colors, giving mammals an earth tone. Some mammals, like the mandrill, have more vibrant colors due to structural coloration. Many sloths appear green because their fur hosts green algae; this may be a symbiotic relation that affords camouflage to the sloths. Camouflage is a powerful influence in a large number of mammals, as it helps to conceal individuals from predators or prey. In arctic and subarctic mammals such as the arctic fox ("Alopex lagopus"), collared lemming ("Dicrostonyx groenlandicus"), stoat In male placentals, the penis is used both for urination and copulation. Depending on the species, an erection may be fueled by blood flow into vascular, spongy tissue or by muscular action. A penis may be contained in a prepuce when not erect, and some placentals also have a penis bone (baculum). Marsupials typically have forked penises, while the echidna penis generally has four heads with only two functioning. The testes of most mammals descend into the scrotum which is typically posterior to the penis but is often anterior in marsupials. Female mammals generally have a clitoris, labia majora and Nearly all mammals are endothermic ("warm-blooded"). Most mammals also have hair to help keep them warm. Like birds, mammals can forage or hunt in weather and climates too cold for ectothermic ("cold-blooded") reptiles and insects. Endothermy Among mammals, species maximum lifespan varies significantly (for example the shrew has a lifespan of two years, whereas the oldest bowhead whale is recorded to be 211 years). Although the underlying basis for these lifespan differences is still uncertain, numerous studies indicate that the ability to repair DNA damage is an important determinant of mammalian lifespan. In a 1974 study by Hart and Setlow, it was found that DNA excision repair Most vertebrates—the amphibians, the reptiles and some mammals such as humans and bears—are plantigrade, walking on the whole of the underside of the foot. Many mammals, such as cats and dogs, are digitigrade, walking on their toes, the greater stride length allowing more speed. Digitigrade mammals are also often adept at quiet movement. Some animals such as horses are unguligrade, walking on the tips of their toes. This even further increases their stride length and thus their speed. A few mammals, namely the great apes, are also known to walk on their knuckles, at least for their front legs. Giant anteaters and platypuses are also knuckle-walkers. Some mammals are bipeds, using only two limbs for locomotion, which can be seen in, for example, humans and the great apes. Bipedal species have a larger field of vision than quadrupeds, Arboreal animals frequently have elongated limbs that help them cross gaps, reach fruit or other resources, test the firmness of support ahead and, in some cases, to brachiate (swing between trees). Many arboreal species, such as tree porcupines, silky anteaters, spider monkeys, and possums, use prehensile tails to grasp branches. In the spider monkey, the tip of the tail has either a bare patch or adhesive pad, which provides increased friction. Claws can be used to interact with rough substrates and reorient the direction of forces the animal applies. This is what allows squirrels to climb tree trunks that are so large to be essentially flat from the perspective of such a small animal. However, claws can interfere with an animal's ability to grasp very small branches, as they may wrap too Bats are the only mammals that can truly fly. They fly through the air at a constant speed by moving their wings up and down (usually with some fore-aft movement as well). Because the animal is in motion, there is some airflow relative to its body which, combined with the velocity of the wings, generates a faster airflow moving over the wing. This generates a lift force vector pointing forwards and upwards, and a drag force vector pointing rearwards and upwards. The upwards components of these counteract gravity, keeping the body in the air, while the forward component provides thrust to counteract both the drag A fossorial (from Latin "fossor", meaning "digger") is an animal adapted to digging which lives primarily, but not solely, underground. Some examples are badgers, and naked mole-rats. Many rodent species are also considered fossorial because they live in burrows for most but not all of the day. Species that live exclusively underground are subterranean, and those with limited adaptations to a fossorial lifestyle sub-fossorial. Some organisms are fossorial to aid in temperature regulation while others use the underground habitat for protection from predators or for food storage. Fossorial mammals have a fusiform body, thickest at the shoulders and tapering off at the tail and Fully aquatic mammals, the cetaceans and sirenians, have lost their legs and have a tail fin to propel themselves through the water. Flipper movement is continuous. Whales swim by moving their tail fin and lower body up and down, propelling themselves through vertical movement, while their flippers are mainly used for steering. Their skeletal anatomy allows them to be fast swimmers. Most species have a dorsal fin to prevent themselves from turning upside-down in the water. The flukes of sirenians are raised up and down in long strokes to move the animal forward, and can be twisted to turn. The forelimbs are paddle-like flippers which aid in turning and slowing. Semi-aquatic mammals, like pinnipeds, have two Many mammals communicate by vocalizing. Vocal communication serves many purposes, including in mating rituals, as warning calls, to indicate food sources, and for social purposes. Males often call during mating rituals to ward off other males and to attract females, as in the roaring of lions and red deer. The songs of the humpback whale may be signals to females; they have different dialects in different regions of the ocean. Social vocalizations include the territorial calls of gibbons, and the use of frequency in greater spear-nosed bats to distinguish between groups. The vervet monkey gives a distinct alarm call for each of at least four different predators, and the reactions of other monkeys vary according to the call. For To maintain a high constant body temperature is energy expensive—mammals therefore need a nutritious and plentiful diet. While the earliest mammals were probably predators, different species have since adapted to meet their dietary requirements in a variety of ways. Some eat other animals—this is a carnivorous diet (and includes insectivorous diets). Other mammals, called herbivores, eat plants, which contain complex carbohydrates such as cellulose. An herbivorous diet includes subtypes such as granivory (seed eating), folivory (leaf eating), frugivory (fruit eating), nectarivory (nectar eating), gummivory (gum eating) and mycophagy (fungus eating). The digestive tract of an herbivore is host to bacteria that ferment these complex substances, and make them available for digestion, which are either In intelligent mammals, such as primates, the cerebrum is larger relative to the rest of the brain. Intelligence itself is not easy to define, but indications of intelligence include the ability to learn, matched with behavioral flexibility. Rats, for example, are considered to be highly intelligent, as they can learn and perform new tasks, an ability that may be important when they first colonize a fresh habitat. In some mammals, food gathering appears to be related to intelligence: a deer feeding on plants has a brain smaller than a cat, which must think to outwit its prey. Tool use by animals may indicate different levels of learning and cognition. The sea otter uses rocks as essential and regular parts of its foraging behaviour (smashing abalone from rocks or breaking open shells), with some populations spending 21% of their time making tools. Other tool use, such as chimpanzees using twigs to "fish" for termites, may be developed by watching Eusociality is the highest level of social organization. These societies have an overlap of adult generations, the division of reproductive labor and cooperative caring of young. Usually insects, such as bees, ants and termites, have eusocial behavior, but it is demonstrated in two rodent species: the naked mole-rat and the Damaraland mole-rat. Presociality is when animals exhibit more than just sexual interactions with members of the same species, but fall short of qualifying as eusocial. That is, presocial animals can display communal living, cooperative care of young, or primitive division of reproductive labor, but they do not display all of the three essential traits of eusocial animals. Humans and some species of Callitrichidae (marmosets and tamarins) are unique among primates in their degree Non-human mammals play a wide variety of roles in human culture. They are the most popular of pets, with tens of millions of dogs, cats and other animals including rabbits and mice kept by families around the world. Mammals such as mammoths, horses and deer are among the earliest subjects of art, being found in Upper Paleolithic cave paintings such as at Lascaux. Domestic mammals form a large part of the livestock raised for meat across the world. They include (2009) around 1.4 billion cattle, 1 billion sheep, 1 billion domestic pigs, and (1985) over 700 million rabbits. Working domestic animals including cattle and horses have been used for work and transport from the origins of agriculture, their numbers declining with the arrival of mechanised transport and agricultural machinery. In 2004 they still provided some 80% of the power for the mainly small farms in the third world, and some 20% of the world's transport, again mainly in rural areas. In mountainous regions unsuitable for wheeled vehicles, pack animals continue to transport goods. Mammal skins provide leather for shoes, clothing and upholstery. Wool from mammals including sheep, Hybrids are offspring resulting from the breeding of two genetically distinct individuals, which usually will result in a high degree of heterozygosity, though hybrid and heterozygous are not synonymous. The deliberate or accidental hybridizing of two or more species of closely related animals through captive breeding is a human activity which has been in existence for millennia and has grown for economic purposes. Hybrids between different subspecies within a species (such as between the Bengal tiger and Siberian tiger) are known as intra-specific hybrids. Hybrids between different species within the same genus (such as between lions and tigers) are known as interspecific hybrids or crosses. Hybrids between different genera (such as between sheep and goats) are known as intergeneric hybrids. Natural hybrids will occur in hybrid zones, where two populations of species within the same genera or species living in the same or adjacent areas will interbreed with each other. Some hybrids have been recognized The loss of species from ecological communities, defaunation, is primarily driven by human activity. This has resulted in empty forests, ecological communities depleted of large vertebrates. In the Quaternary extinction event, the mass die-off of megafaunal variety coincided with the appearance of humans, suggesting a human influence. One hypothesis is that humans hunted large mammals, such as the woolly mammoth, into extinction. The 2019 "Global Assessment Report on Biodiversity and Ecosystem Services" by IPBES states that the total biomass of wild mammals has declined by 82 percent since the beginning of human civilization. Various species are predicted to become extinct in the near future, among them the rhinoceros, primates, pangolins, and giraffes. Hunting alone threatens hundreds of mammalian species around the world. Scientists claim that the growing demand for meat is contributing to biodiversity loss as this is a significant driver of deforestation and habitat destruction; species-rich habitats, such as significant portions of the Amazon rainforest, are being converted to agricultural land for meat production. According to the World Wildlife	Mammals (from Latin "mamma" "breast") are vertebrate animals constituting the class Mammalia (), and characterized by the presence of mammary glands which in females (and sometimes males) produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or hair, and three middle ear bones. These characteristics distinguish them from reptiles and birds, from which they diverged in the late Carboniferous, approximately 300 million years ago. Around 6,400 extant species of mammals have been described. The largest orders are the rodents, bats and Eulipotyphla (hedgehogs, moles, shrews, and others). 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summarize: Energy is a scalar quantity and the mechanical energy of a system is the sum of the potential energy (which is measured by the position of the parts of the system) and the kinetic energy (which is also called the energy of motion): The potential energy, "U", depends on the position of an object subjected to a conservative force. It is defined as the object's ability to do work and is increased as the object is moved in the opposite direction of the direction of the force. If "F" represents the conservative force and "x" the position, the potential energy of the force between the two positions "x" and "x" is defined as the negative integral of "F" from "x" to "x": The kinetic energy, "K", depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them. It is defined as one half the product of the object's mass with the square of its speed, and the total kinetic energy of a system of objects is the sum of the kinetic energies of the respective objects: The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path. On the contrary, when a non-conservative force acts upon an object, the work done by the non-conservative force is dependent of the path. According to the principle of conservation of mechanical energy, the mechanical energy of an isolated system remains constant in time, as long as the system is free of friction and other non-conservative forces. In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. Though energy cannot be created or destroyed in an isolated system, it can be converted to another form of energy. In a mechanical system like a swinging pendulum subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible, energy passes back and forth between kinetic and potential energy but never leaves the system. The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points. However, when taking the frictional forces into account, the system loses mechanical energy with each swing because of the negative work done on the pendulum by these non-conservative forces. That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that comprise matter. This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision, mechanical energy is conserved – the sum of the mechanical energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the mechanical energy of the system will have changed. Usually, the mechanical energy before the collision is greater than the mechanical energy after the collision. In inelastic collisions, some of the mechanical energy of the colliding objects is transformed into kinetic energy of the constituent particles. This increase in kinetic energy of the constituent particles is perceived as an increase in temperature. The collision can be described by saying some of the mechanical energy of the colliding objects has been converted into an equal amount of heat. Thus, the total energy of the system remains unchanged though the mechanical energy of the system has reduced. A satellite of mass formula_4 at a distance formula_5 from the centre of Earth possesses both kinetic energy, formula_6, (by virtue of its motion) and gravitational potential energy, formula_7, (by virtue of its position within the Earth's gravitational field; Earth's mass is formula_8). Hence, mechanical energy formula_9 of the satellite-Earth system is given by If the satellite is in circular orbit, the energy conservation equation can be further simplified into since in circular motion, Newton's 2nd Law of motion can be taken to be Today, many technological devices convert mechanical energy into other forms of energy or vice versa. These devices can be placed in these categories: The classification of energy into different types often follows the boundaries of the fields of study in the natural sciences. Notes Citations Bibliography	In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. It is the macroscopic energy associated with a system. The principle of conservation of mechanical energy states that in an isolated system that is only subject to conservative forces, the mechanical energy is constant. If an object moves in the opposite direction of a conservative net force, the potential energy will increase; and if the speed (not the velocity) of the object changes, the kinetic energy of the object also changes. In all real systems, however, nonconservative forces, such as frictional forces, will be present, but if they are of negligible magnitude, the mechanical energy changes little and its conservation is a useful approximation. In elastic collisions, the mechanical energy is conserved, but in inelastic collisions some mechanical energy is converted into thermal energy. 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summarize: The idea of a simple machine originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the Archimedean simple machines: lever, pulley, and screw. He discovered the principle of mechanical advantage in the lever. Archimedes' famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth," () expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to calculate their (ideal) mechanical advantage. For example, Heron of Alexandria (c. 10–75 AD) in his work "Mechanics" lists five mechanisms that can "set a load in motion"; lever, windlass, pulley, wedge, and screw, and describes their fabrication and uses. However the Greeks' understanding was limited to the statics of simple machines (the balance of forces), and did not include dynamics, the tradeoff between force and distance, or the concept of work. During the Renaissance the dynamics of the "Mechanical Powers", as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in "Le Meccaniche" ("On Mechanics"), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create energy, only transform it. The classic rules of sliding friction in machines were discovered by Leonardo da Vinci (1452–1519), but were unpublished and merely documented in his notebooks, and were based on pre-Newtonian science such as believing friction was an ethereal fluid. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785). If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions. Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force formula_1 is applied to the device at one point, and it does work moving a load, formula_2 at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage that can be calculated from the machine's geometry and friction. Simple machines do not contain a source of energy, so they cannot do more work than they receive from the input force. A simple machine with no friction or elasticity is called an "ideal machine". Due to conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time formula_4 is equal to the power input formula_5 The power output equals the velocity of the load formula_7 multiplied by the load force formula_8. Similarly the power input from the applied force is equal to the velocity of the input point formula_9 multiplied by the applied force formula_10. Therefore, So the mechanical advantage of an ideal machine formula_12 is equal to the "velocity ratio", the ratio of input velocity to output velocity The "velocity ratio" is also equal to the ratio of the distances covered in any given period of time Therefore the mechanical advantage of an ideal machine is also equal to the "distance ratio", the ratio of input distance moved to output distance moved This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the lever is equal to the ratio of its lever arms. The mechanical advantage can be greater or less than one: In the screw, which uses rotational motion, the input force should be replaced by the torque, and the velocity by the angular velocity the shaft is turned. All real machines have friction, which causes some of the input power to be dissipated as heat. If formula_19 is the power lost to friction, from conservation of energy The mechanical efficiency formula_21 of a machine (where formula_22) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses As above, the power is equal to the product of force and velocity, so Therefore, So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency "η". So a machine that includes friction will not be able to move as large a load as a corresponding ideal machine using the same input force. A "compound machine" is a machine formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a bench vise consists of a lever (the vise's handle) in series with a screw, and a simple gear train consists of a number of gears (wheels and axles) connected in series. The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is Because the output force of each machine is the input of the next, formula_27, this mechanical advantage is also given by Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it In many simple machines, if the load force "F" on the machine is high enough in relation to the input force "F", the machine will move backwards, with the load force doing work on the input force. So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called ""reversible"", ""non-locking"" or ""overhauling"" machines, and the backward motion is called ""overhauling"". However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a ""self-locking"", ""nonreversible"", or ""non-overhauling"" machine. These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left. Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the screw, inclined plane, and wedge: A machine will be self-locking if and only if its efficiency "η" is below 50%: Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio "d/d" (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock. When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work formula_32 is equal to the sum of the work done on the load force formula_33 and the work lost to friction formula_34 If the efficiency is below 50% formula_35 From When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction formula_34 is the same So the output work is Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force Machines are studied as mechanical systems consisting of actuators and mechanisms that transmit forces and movement, monitored by sensors and controllers. The components of actuators and mechanisms consist of links and joints that form kinematic chains. Simple machines are elementary examples of kinematic chains that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint. Two levers, or cranks, are combined into a planar four-bar linkage by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a six-bar linkage or in series to form a robot. The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines. However, a more successful strategy was identified by Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface. This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the revolute joint, sliding joint, cam joint and gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints. The design of mechanisms to perform required movement and force transmission is known as kinematic synthesis. This is a collection of geometric techniques for the mechanical design of linkages, cam and follower mechanisms and gears and gear trains.	A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. 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summarize: Before the invention of the refrigerator, icehouses were used to provide cool storage for most of the year. Placed near freshwater lakes or packed with snow and ice during the winter, they were once very common. Natural means are still used to cool foods today. On mountainsides, runoff from melting snow is a convenient way to cool drinks, and during the winter one can keep milk fresh much longer just by keeping it outdoors. The word "refrigeratory" was used at least as early as the 17th century The history of artificial refrigeration began when Scottish professor William Cullen designed a small refrigerating machine in 1755. Cullen used a pump to create a partial vacuum over a container of diethyl ether, which then boiled, absorbing heat from the surrounding air. The experiment even created a small amount of ice, but had no practical application at that time. In 1805, American inventor Oliver Evans described a closed vapor-compression refrigeration cycle for the production of ice by ether under vacuum. In 1820, the British scientist Michael Faraday liquefied ammonia and other gases by using high pressures and low temperatures, and in 1834, an American expatriate in Great Britain, Jacob Perkins, built the first working vapor-compression refrigeration system. It was a closed-cycle device that could operate continuously. A similar attempt was made in 1842, by American physician, John Gorrie, who built a working prototype, but it was a commercial failure. American engineer Alexander Twining took out a British patent in 1850 for a vapor compression system that used ether. The first practical vapor compression refrigeration system was built by James Harrison, a Scottish Australian. His 1856 patent was for a vapor compression system using ether, alcohol or ammonia. He built a mechanical ice-making machine in 1851 on the banks of the Barwon River at Rocky Point in Geelong, Victoria, and his first commercial ice-making machine followed in 1854. Harrison also introduced commercial vapor-compression refrigeration to breweries and meat packing houses, and by 1861, a dozen of his systems were in operation. The first gas absorption refrigeration system using gaseous ammonia dissolved in water (referred to as "aqua ammonia") was developed by Ferdinand Carré of France in 1859 and patented in 1860. Carl von Linde, an engineering professor at the Technological University Munich in Germany, patented an improved method of liquefying gases in 1876. His new process made possible the use of gases such as ammonia (NH), sulfur dioxide (SO) and methyl chloride (CHCl) as refrigerants and they were widely used for that purpose until the late 1920s. Commercial refrigerator and freezer units, which go by many other names, were in use for almost 40 years prior to the common home models. They used gas systems such as ammonia (R-717) or sulfur dioxide (R-764), which occasionally leaked, making them unsafe for home use. Practical household refrigerators were introduced in 1915 and gained wider acceptance in the United States in the 1930s as prices fell and non-toxic, non-flammable synthetic refrigerants such as Freon-12 (R-12) were introduced. However, R-12 damaged the ozone layer, causing governments to issue a ban on its use in new refrigerators and air-conditioning systems in 1994. The less harmful replacement for R-12, R-134a (tetrafluoroethane), has been in common use since 1990, but R-12 is still found in many old systems today. A common commercial refrigerator is the glass fronted beverage cooler. These type of appliances are typically designed for specific re-load conditions meaning that they generally have a larger cooling system. This ensures that they are able to cope with a large throughput of drinks and frequent door opening. As a result, it is common for these types of commercial refrigerators to have energy consumption of >4 kWh/day. In 1913, refrigerators for home and domestic use were invented by Fred W. Wolf of Fort Wayne, Indiana, with models consisting of a unit that was mounted on top of an ice box. In 1914, engineer Nathaniel B. Wales of Detroit, Michigan, introduced an idea for a practical electric refrigeration unit, which later became the basis for the Kelvinator. A self-contained refrigerator, with a compressor on the bottom of the cabinet was invented by Alfred Mellowes in 1916. Mellowes produced this refrigerator commercially but was bought out by William C. Durant in 1918, who started the Frigidaire company to mass-produce refrigerators. In 1918, Kelvinator company introduced the first refrigerator with any type of automatic control. The absorption refrigerator was invented by Baltzar von Platen and Carl Munters from Sweden in 1922, while they were still students at the Royal Institute of Technology in Stockholm. It became a worldwide success and was commercialized by Electrolux. Other pioneers included Charles Tellier, David Boyle, and Raoul Pictet. Carl von Linde was the first to patent and make a practical and compact refrigerator. These home units usually required the installation of the mechanical parts, motor and compressor, in the basement or an adjacent room while the cold box was located in the kitchen. There was a 1922 model that consisted of a wooden cold box, water-cooled compressor, an ice cube tray and a compartment, and cost $714. (A 1922 Model-T Ford cost about $450.) By 1923, Kelvinator held 80 percent of the market for electric refrigerators. Also in 1923 Frigidaire introduced the first self-contained unit. About this same time porcelain-covered metal cabinets began to appear. Ice cube trays were introduced more and more during the 1920s; up to this time freezing was not an auxiliary function of the modern refrigerator. The first refrigerator to see widespread use was the General Electric "Monitor-Top" refrigerator introduced in 1927, so-called, by the public, because of its resemblance to the gun turret on the ironclad warship USS "Monitor" of the 1860s. The compressor assembly, which emitted a great deal of heat, was placed above the cabinet, and enclosed by a decorative ring. Over a million units were produced. As the refrigerating medium, these refrigerators used either sulfur dioxide, which is corrosive to the eyes and may cause loss of vision, painful skin burns and lesions, or methyl formate, which is highly flammable, harmful to the eyes, and toxic if inhaled or ingested. The introduction of Freon in the 1920s expanded the refrigerator market during the 1930s and provided a safer, low-toxicity alternative to previously used refrigerants. Separate freezers became common during the 1940s; the popular term at the time for the unit was a "deep freeze". These devices, or "appliances", did not go into mass production for use in the home until after World War II. The 1950s and 1960s saw technical advances like automatic defrosting and automatic ice making. More efficient refrigerators were developed in the 1970s and 1980s, even though environmental issues led to the banning of very effective (Freon) refrigerants. Early refrigerator models (from 1916) had a cold compartment for ice cube trays. From the late 1920s fresh vegetables were successfully processed through freezing by the Postum Company (the forerunner of General Foods), which had acquired the technology when it bought the rights to Clarence Birdseye's successful fresh freezing methods. In the early 1950s most refrigerators were white, but from the mid-1950s through present day designers and manufacturers put color onto refrigerators. In the late-1950s/early-1960s, pastel colors like turquoise and pink became popular, and brushed chrome-plating (similar to stainless finish) was available on some models. In the late 1960s and throughout the 1970s, earth tone colors were popular, including Harvest Gold, Avocado Green and almond. In the 1980s, black became fashionable. In the late 1990s stainless steel came into vogue, and in 2009, one manufacturer introduced multi-color designs. Since 1961 the Color Marketing Group has attempted to coordinate the colors of appliances and other consumer goods. Freezer units are used in households and in industry and commerce. Food stored at or below is safe indefinitely. Most household freezers maintain temperatures from, although some freezer-only units can achieve and lower. Refrigerator freezers generally do not achieve lower than, since the same coolant loop serves both compartments: Lowering the freezer compartment temperature excessively causes difficulties in maintaining above-freezing temperature in the refrigerator compartment. Domestic freezers can be included as a separate compartment in a refrigerator, or can be a separate appliance. Domestic freezers may be either upright units resembling a refrigerator, or chests (with the lid or door on top, sacrificing convenience for efficiency and partial immunity to power outages). Many modern upright freezers come with an ice dispenser built into their door. Some upscale models include thermostat displays and controls, and sometimes flat screen televisions as well. Home freezers as separate compartments (larger than necessary just for ice cubes), or as separate units, were introduced in the United States in 1940. Frozen foods, previously a luxury item, became commonplace. The following table shows worldwide production of household refrigerator units as of 2005. A vapor compression cycle is used in most household refrigerators, refrigerator–freezers and freezers. In this cycle, a circulating refrigerant such as R134a enters a compressor as low-pressure vapor at or slightly below the temperature of the refrigerator interior. The vapor is compressed and exits the compressor as high-pressure superheated vapor. The superheated vapor travels under pressure through coils or tubes that make up the "condenser"; the coils or tubes are passively cooled by exposure to air in the room. The condenser cools the vapor, which liquefies. As the refrigerant leaves the condenser, it is still under pressure but is now only slightly above room temperature. This liquid refrigerant is forced through a metering or throttling device, also known as an expansion valve (essentially a pin-hole sized constriction in the tubing) to an area of much lower pressure. The sudden decrease in pressure results in explosive-like flash evaporation of a portion (typically about half) of the liquid. The latent heat absorbed by this flash evaporation is drawn mostly from adjacent still-liquid refrigerant, a phenomenon known as "auto-refrigeration". This cold and partially vaporized refrigerant continues through the coils or tubes of the evaporator unit. A fan blows air from the compartment ("box air") across these coils or tubes and the refrigerant completely vaporizes, drawing further latent heat from the box air. This cooled air is returned to the refrigerator or freezer compartment, and so keeps the box air cold. Note that the cool air in the refrigerator or freezer is still warmer than the refrigerant in the evaporator. Refrigerant leaves the evaporator, now fully vaporized and slightly heated, and returns to the compressor inlet to continue the cycle. Modern domestic refrigerators are extremely reliable because motor and compressor are integrated within a welded container, "sealed unit", with greatly reduced likelihood of leakage or contamination. By comparison, externally-coupled refrigeration compressors, such as those in automobile air conditioning, inevitably leak fluid and lubricant past the shaft seals. This leads to a requirement for periodic recharging and, if ignored, possible compressor failure. Refrigerators with two compartments need special design to control the cooling of refrigerator or freezer compartments. Typically, the compressors and condenser coils are mounted at the top of the cabinet, with a single fan to cool them both. This arrangement has a few downsides: each compartment cannot be controlled independently and the more humid refrigerator air is mixed with the dry freezer air. A few manufacturers offer dual compressor models. These models have separate freezer and refrigerator compartments that operate independently of each other, sometimes mounted within a single cabinet. Each has its own separate compressor, condenser and evaporator coils, insulation, thermostat, and door. A hybrid between the two designs is using a separate fan for each compartment, the Dual Fan approach. Doing so allows for separate control and airflow on a single compressor system. An absorption refrigerator works differently from a compressor refrigerator, using a source of heat, such as combustion of liquefied petroleum gas, solar thermal energy or an electric heating element. These heat sources are much quieter than the compressor motor in a typical refrigerator. A fan or pump might be the only mechanical moving parts; reliance on convection is considered impractical. Other uses of an absorption refrigerator (or "chiller") include large systems used in office buildings or complexes such as hospitals and universities. These large systems are used to chill a brine solution that is circulated through the building. The Peltier effect uses electricity to pump heat directly; refrigerators employing this system are sometimes used for camping, or in situations where noise is not acceptable. They can be totally silent (if a fan for air circulation is not fitted) but are less energy-efficient than other methods. "Ultra-cold" or "ultra-low temperature (ULT)" (typically −80C) freezers, as used for storing biological samples, also generally employ two stages of cooling, but in cascade. The lower temperature stage uses methane, or a similar gas, as a refrigerant, with its condenser kept at around −40C by a second stage which uses a more conventional refrigerant. Well known brands include Forma and Revco (both now Thermo Scientific) and Thermoline. For much lower temperatures (around −196C), laboratories usually purchase liquid nitrogen, kept in a Dewar flask, into which the samples are suspended. Alternatives to the vapor-compression cycle not in current mass production include: Many modern refrigerator/freezers have the freezer on top and the refrigerator on the bottom. Most refrigerator-freezers—except for manual defrost models or cheaper units—use what appears to be two thermostats. Only the refrigerator compartment is properly temperature controlled. When the refrigerator gets too warm, the thermostat starts the cooling process and a fan circulates the air around the freezer. During this time, the refrigerator also gets colder. The freezer control knob only controls the amount of air that flows into the refrigerator via a damper system. Changing the refrigerator temperature will inadvertently change the freezer temperature in the opposite direction. Changing the freezer temperature will have no effect on the refrigerator temperature. The freezer control may also be adjusted to compensate for any refrigerator adjustment. This means the refrigerator may become too warm. However, because only enough air is diverted to the refrigerator compartment, the freezer usually re-acquires the set temperature quickly, unless the door is opened. When a door is opened, either in the refrigerator or the freezer, the fan in some units stops immediately to prevent excessive frost build up on the freezer's evaporator coil, because this coil is cooling two areas. When the freezer reaches temperature, the unit cycles off, no matter what the refrigerator temperature is. Modern computerized refrigerators do not use the damper system. The computer manages fan speed for both compartments, although air is still blown from the freezer. Newer refrigerators may include: These older freezer compartments were the main cooling body of the refrigerator, and only maintained a temperature of around, which is suitable for keeping food for a week. Later advances included automatic ice units and self compartmentalized freezing units. Domestic refrigerators and freezers for food storage are made in a range of sizes. Among the smallest is a 4 L Peltier refrigerator advertised as being able to hold 6 cans of beer. A large domestic refrigerator stands as tall as a person and may be about 1 m wide with a capacity of 600 L. Some models for small households fit under kitchen work surfaces, usually about 86 cm high. Refrigerators may be combined with freezers, either stacked with refrigerator or freezer above, below, or side by side. A refrigerator without a frozen food storage compartment may have a small section just to make ice cubes. Freezers may have drawers to store food in, or they may have no divisions (chest freezers). Refrigerators and freezers may be free-standing, or built into a kitchen. Three distinct classes of refrigerator are common: Other specialized cooling mechanisms may be used for cooling, but have not been applied to domestic or commercial refrigerators. In a house without air-conditioning (space heating and/or cooling) refrigerators consumed more energy than any other home device. In the early 1990s a competition was held among the major manufacturers to encourage energy efficiency. Current US models that are Energy Star qualified use 50% less energy than the average models made in 1974. The most energy-efficient unit made in the US consumes about half a kilowatt-hour per day (equivalent to 20 W continuously). But even ordinary units are quite efficient; some smaller units use less than 0.2 kWh per day (equivalent to 8 W continuously). Larger units, especially those with large freezers and icemakers, may use as much as 4 kW·h per day (equivalent to 170 W continuously). The European Union uses a letter-based mandatory energy efficiency rating label instead of the Energy Star; thus EU refrigerators at the point of sale are labelled according to how energy-efficient they are. For US refrigerators, the Consortium on Energy Efficiency (CEE) further differentiates between Energy Star qualified refrigerators. Tier 1 refrigerators are those that are 20% to 24.9% more efficient than the Federal minimum standards set by the National Appliance Energy Conservation Act (NAECA). Tier 2 are those that are 25% to 29.9% more efficient. Tier 3 is the highest qualification, for those refrigerators that are at least 30% more efficient than Federal standards. About 82% of the Energy Star qualified refrigerators are Tier 1, with 13% qualifying as Tier 2, and just 5% at Tier 3. Besides the standard style of compressor refrigeration used in normal household refrigerators and freezers, there are technologies such as absorption refrigeration and magnetic refrigeration. Although these designs generally use a much larger amount of energy compared to compressor refrigeration, other qualities such as silent operation or the ability to use gas can favor these refrigeration units in small enclosures, a mobile environment or in environments where unit failure would lead to devastating consequences. Many refrigerators made in the 1930s and 1940s were far more efficient than most that were made later. This is partly attributable to the addition of new features, such as auto-defrost, that reduced efficiency. Additionally, after World War 2, refrigerator style became more important than efficiency. This was especially true in the US in the 1970s, when side-by-side models (known as American fridgefreezers outside of the US) with ice dispensers and water chillers became popular. However, the reduction in efficiency also arose partly from reduction in the amount of insulation to cut costs. Because of the introduction of new energy efficiency standards, refrigerators made today are much more efficient than those made in the 1930s; they consume the same amount of energy while being three times as large. The efficiency of older refrigerators can be improved by defrosting (if the unit is manual defrost) and cleaning them regularly, replacing old and worn door seals with new ones, adjusting the thermostat to accommodate the actual contents (a refrigerator needn't be colder than to store drinks and non-perishable items) and also replacing insulation, where applicable. Some sites recommend cleaning condenser coils every month or so on units with coils on the rear, to add life to the coils and not suffer an unnoticeable deterioration in efficiency over an extended period, the unit should be able to ventilate or "breathe" with adequate spaces around the front, back, sides and above the unit. If the refrigerator uses a fan to keep the condenser cool, then this must be cleaned or serviced, at per individual manufactures recommendations. Frost-free refrigerators or freezers use electric fans to cool the appropriate compartment. This could be called a "fan forced" refrigerator, whereas manual defrost units rely on colder air lying at the bottom, versus the warm air at the top to achieve adequate cooling. The air is drawn in through an inlet duct and passed through the evaporator where it is cooled, the air is then circulated throughout the cabinet via a series of ducts and vents. Because the air passing the evaporator is supposedly warm and moist, frost begins to form on the evaporator (especially on a freezer's evaporator). In cheaper and/or older models, a defrost cycle is controlled via a mechanical timer. This timer is set to shut off the compressor and fan and energize a heating element located near or around the evaporator for about 15 to 30 minutes at every 6 to 12 hours. This melts any frost or ice build up and allows the refrigerator to work normally once more. It is believed that frost free units have a lower tolerance for frost, due to their air-conditioner like evaporator coils. Therefore, if a door is left open accidentally (especially the freezer), the defrost system may not remove all frost, in this case, the freezer (or refrigerator) must be defrosted. If the defrosting system melts all the ice before the timed defrosting period ends, then a small device (called a defrost limiter) acts like a thermostat and shuts off the heating element to prevent too large a temperature fluctuation, it also prevents hot blasts of air when the system starts again, should it finish defrosting early. On some early frost-free models, the defrost limiter also sends a signal to the defrost timer to start the compressor and fan as soon as it shuts off the heating element before the timed defrost cycle ends. When the defrost cycle is completed, the compressor and fan are allowed to cycle back on. Frost-free refrigerators, including some early frost free refrigerator/freezers that used a cold plate in their refrigerator section instead of airflow from the freezer section, generally don't shut off their refrigerator fans during defrosting. This allows consumers to leave food in the main refrigerator compartment uncovered, and also helps keep vegetables moist. This method also helps reduce energy consumption, because the refrigerator is above freeze point and can pass the warmer-than-freezing air through the evaporator or cold plate to aid the defrosting cycle. With the advent of digital inverter compressors, the energy consumption is even further reduced than a single-speed induction motor compressor, and thus contributes far less in the way of greenhouse gases. The energy consumption of a refrigerator is also dependent on the type of refrigeration being done. For instance, Inverter Refrigerators consume comparatively less energy than a typical non-inverter refrigerator. In an inverter refrigerator, the compressor is used conditionally on requirement basis. For instance, an inverter refrigerator might use less energy during the winters than it does during the summers. This is because the compressor works for a shorter time than it does during the summers. The phycial design of refrigerators also plays a large part in its energy efficiency. The most efficient is the chest-style freezer, as its top-opening design minimizes convection when opening the doors, reducing the amount of warm moist air entering the freezer. On the other hand, in-door ice dispensers cause more heat leakage, contributing to an increase in energy consumption. The refrigerator allows the modern family to keep food fresh for longer than before. The most notable improvement is for meat and other highly perishable wares, which needed to be refined to gain anything resembling shelf life. (On the other hand, refrigerators and freezers can also be stocked with processed, quick-cook foods that are less healthy.) Refrigeration in transit makes it possible to enjoy food from distant places. Dairy products, meats, fish, poultry and vegetables can be kept refrigerated in the same space within the kitchen (although raw meat should be kept separate from other food for reasons of hygiene). Freezers allow people to buy food in bulk and eat it at leisure, and bulk purchases save money. Ice cream, a popular commodity of the 20th century, could previously only be obtained by traveling to where the product was made and eating it on the spot. Now it is a common food item. Ice on demand not only adds to the enjoyment of cold drinks, but is useful for first-aid, and for cold packs that can be kept frozen for picnics or in case of emergency. The capacity of a refrigerator is measured in either liters or cubic feet. Typically the volume of a combined refrigerator-freezer is split with 1/3rds to 1/4th of the volume allocated to the freezer although these values are highly variable. Temperature settings for refrigerator and freezer compartments are often given arbitrary numbers by manufacturers (for example, 1 through 9, warmest to coldest), but generally is ideal for the refrigerator compartment and for the freezer. Some refrigerators must be within certain external temperature parameters to run properly. This can be an issue when placing units in an unfinished area, such as a garage. Some refrigerators are now divided into four zones to store different types of food: European freezers, and refrigerators with a freezer compartment, have a four star rating system to grade freezers. Although both the three and four star ratings specify the same storage times and same minimum temperature of, only a four star freezer is intended for freezing fresh food, and may include a "fast freeze" function (runs the compressor continually, down to as low as ) to facilitate this. Three (or fewer) stars are used for frozen food compartments that are only suitable for storing frozen food; introducing fresh food into such a compartment is likely to result in unacceptable temperature rises. This difference in categorization is shown in the design of the 4-star logo, where the "standard" three stars are displayed in a box using "positive" colours, denoting the same normal operation as a 3-star freezer, and the fourth star showing the additional fresh food/fast freeze function is prefixed to the box in "negative" colours or with other distinct formatting. Most European refrigerators include a moist cold refrigerator section (which does require (automatic) defrosting at irregular intervals) and a (rarely frost free) freezer section. An increasingly important environmental concern is the disposal of old refrigerators—initially because freon coolant damages the ozone layer—but as older generation refrigerators wear out, the destruction of CFC-bearing insulation also causes concern. Modern refrigerators usually use a refrigerant called HFC-134a (1,1,1,2-Tetrafluoroethane), which does not deplete the ozone layer, instead of Freon. A R-134a is now becoming very uncommon in Europe. Newer refrigerants are being used instead. The main refrigerant now used is R-600a, or isobutane which has a smaller effect on the atmosphere if released. There have been reports of refrigerators exploding if the refrigerant leaks isobutane in the presence of a spark. If the coolant leaks into the fridge, at times when the door is not being opened (such as overnight) the concentration of coolant in the air within the fridge can build up to form an explosive mixture that can be ignited either by a spark from the thermostat or when the light comes on as the door is opened, resulting in documented cases of serious property damage and injury or even death from the resulting explosion. Disposal of discarded refrigerators is regulated, often mandating the removal of doors for safety reasons. Children playing hide-and-seek have been asphyxiated while hiding inside discarded refrigerators, particularly older models with latching doors, in a phenomenon called refrigerator death. Since 2 August 1956, under U.S. federal law, refrigerator doors are no longer permitted to latch so they cannot be opened from the inside. Modern units use a magnetic door gasket that holds the door sealed but allows it to be pushed open from the inside. This gasket was invented, developed and manufactured by Max Baermann (1903–1984) of Bergisch Gladbach/Germany. Regarding total life-cycle costs, many governments offer incentives to encourage recycling of old refrigerators. One example is the Phoenix refrigerator program launched in Australia. This government incentive picked up old refrigerators, paying their owners for "donating" the refrigerator. The refrigerator was then refurbished, with new door seals, a thorough cleaning and the removal of items, such as the cover that is strapped to the back of many older units. The resulting refrigerators, now over 10% more efficient, were then distributed to low income families.	A refrigerator (colloquially fridge) consists of a thermally insulated compartment and a heat pump (mechanical, electronic or chemical) that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the room temperature. Refrigeration is an essential food storage technique in developed countries. The lower temperature lowers the reproduction rate of bacteria, so the refrigerator reduces the rate of spoilage. A refrigerator maintains a temperature a few degrees above the freezing point of water. Optimum temperature range for perishable food storage is. A similar device that maintains a temperature below the freezing point of water is called a freezer. 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summarize: The order Carnivora belongs to a group of mammals known as Laurasiatheria, which also includes other groups such as bats and ungulates. Within this group the carnivorans are placed in the clade Ferae. Ferae includes the closest extant relative of carnivorans, the pangolins, as well as several extinct groups of mostly Paleogene carnivorous placentals such as the creodonts, the arctocyonians, and mesonychians. The creodonts were originally thought of as the sister taxon to the carnivorans, perhaps even ancestral to, based on the presence of the carnassial teeth. but the nature of the carnassial teeth is different between the two groups. In carnivorans the carnassials are positioned near the front of the molar row, while in the creodonts they are positioned near the back of the molar row. and this suggests a separate evolutionary history and an order-level distinction. In addition recent phylogenetic analysis suggests that creodonts are more closely related to pangolins while mesonychians might be the sister group to carnivorans and their stem-relatives. The closest stem-carnivorans are the miacoids. The miacoids include the families Viverravidae and Miacidae, and together the Carnivora and Miacoidea form the stem-clade Carnivoramorpha. The miacoids were small, gennet-like carnivoramorphs that occupy a variety of niches such as terrestrial and arboreal habitats. Recent studies have shown a supporting amount of evidence that Miacoidea is an evolutionary grade of canivoramorphs that, while viverravids are monophyletic basal group, the miacids are paraphyletic in respect to Carnivora (as shown in the phylogeny below). Carnivoramorpha as a whole first appeared in the Paleocene of North America about 60 million years ago. Crowned carnivorans first appeared around 42 million years ago in the Middle Eocene. Their molecular phylogeny shows the extant Carnivora are a monophyletic group, the crown group of the Carnivoramorpha. From there carnivorans have split into two clades based on the composition of the bony structures that surround the middle ear of the skull, the cat-like feliforms and the dog-like caniforms. In feliforms, the auditory bullae are double-chambered, composed of two bones joined by a septum. Caniforms have single-chambered or partially divided auditory bullae, composed of a single bone. Initially the early representatives of carnivorans were small as the creodonts dominated the niches as top apex predators, but by the Miocene most of the extant carnivoran families have diversified and successfully out-competed the creodonts. The phylogenetic relationships of the carnivorans are shown in the following cladogram: In 1758 the Swedish botanist Carl Linnaeus placed all the carnivorans that was known at the time in the group Ferae (not to be confused with the modern concept of Ferae which also include pangolins) in the tenth edition of his book "Systema Naturae". He recognized six genera: "Canis" (canids and hyaenids), "Phoca" (pinnipeds), "Felis" (felids), "Viverra" (viverrids, herpestids, and mephitids), "Mustela" (non-badger mustelids), "Ursus" (ursids, large species of mustelids, and procyonids). It wasn't until in 1821 when the English writer and traveler Thomas Edward Bowdich gave the group its modern and accepted name. Initially the modern concept of Carnivora was divided into two suborders: the terrestrial Fissipedia and the marine Pinnipedia. Below is the classification of how the extant families were related to each other after American paleontologist George Gaylord Simpson in 1945: Since then, however, the methods in which mammalogists use to assess the phylogenetic relationships among the carnivoran families has been improved with using more complicated and intensive incorporation of genetics, morphology and the fossil record. Research into Carnivora phylogeny since 1945 has found Fisspedia to be paraphlyetic in respect to Pinnipedia, with pinnipeds being either more closely related to bears or to weasels. The small carnivoran families Viverridae, Procyonidae, and Mustelidae have found to be polyphyletic: Below is a table chart of the extant carnivoran families and number of extant species recognized by various authors of the first and fourth volumes of "Handbook of the Mammals of the World" published in 2009 and 2014 respectively: The canine teeth are usually large and conical. The canines are thick and incredibly stress resistant. All of the terrestrial species of carnivorans have three incisors on the top and bottom row of the dentition (the exception being is the sea otter ("Enhydra lutris") which only has two lower incisor teeth). The third molar has been lost. The carnassial pair is made up by the fourth upper premolar and the first lower molar teeth. Like most mammals the dentition is heterodont in nature, though in some species like the aardwolf ("Proteles cristata") the teeth have been greatly reduced and the cheek teeth are specialised for eating insects. In pinnipeds the teeth are homodont as they have evolved to grasp or to catch fish, and the cheek teeth are often lost. In bears and raccoons the carnassial pair is secondarily reduced. The skulls are heavily built with a strong zygomatic arch. Often a sagittal crest is present, sometimes more evident in sexual dimorphic species like sea lions and fur seals, though it has also been greatly reduced seen in some small carnivorans. The braincase is enlarged and the frontoparietal is position at the front of it. In most species the eyes are position at the front of the face. In caniforms the rostrum is usually longer with many teeth, where in comparison with felifoms the rostrum is shorter and have fewer teeth. The carnassial teeth in feliforms, however is more sectional. The turbinates are large and complex in comparison to other mammals, providing a large surface area for olfactory receptors. Aside from an accumulation of characteristics in the dental and cranial features, not much of their overall anatomy unites them as a group. All species of carnivorans have quadrupedal limbs with usually five digits at the front feet and four digits at the back feet. In terrestrial carnivorans the feet have soft pads. The feet can either be digitigrade seen in cats, hyenas and dogs or plantigrade seen in bears, skunks, raccoons, weasels, civets and mongooses. In pinnipeds the limbs have been modified into flippers. Unlike other marine mammals, such as cetaceans and sirenians which have fully functional tails to help them swim, pinnipeds use their limbs underwater for locomotion. In earless seals they use their back flippers; sea lions and fur seals use their front flippers, and the walrus use all of their limbs. This resulted in pinnipeds having significantly shorter tails. Aside from the pinnipeds, dogs, bears, hyenas, and cats have distinct and recognizable appearances. Dogs are usually cursorial mammals and are gracile in appearance, often relying on their teeth to hold to prey; bears are much larger and rely on their physical strength to forage for food. Cats in comparison to dogs and bears have much longer and stronger frontlimbs armed with retractable claws to hold on to prey. Hyenas are dog-like feliforms that have sloping backs due to their front legs being longer than their hindlegs. The raccoon family as well as the red panda are small, bear-like carnivorans with long tails. The other small carnivoran families Nandiniidae, Prionodontidae, Viverridae, Herpestidae, Eupleridae, Mephitidae and Mustelidae have through convergent evolution maintained the small, ancestral appearance of the miacoids, though there is some variation seen such as the robust and stout physicality of badgers and the wolverine ("Gulo gulo"). Male carnivorans usually have bacula, though they are absent in hyenas and binturongs. Depending on the environment the species is, the length and density of their fur varies. In warm climate species the fur is often short in length and lighter. In comparison to cold climate species the fur is either dense or long, often with an oily substance to keep them warm. The pelage coloration comes in many colors, often including black, white, orange, yellow, red, and many shades of gray and brown. There can be colored patterns too, such striped, spotted, blotched, banded, or otherwise boldly patterned. There seems to be a correlation between habitat and color pattern as for example spotted or banded species tend to be found in heavily forested environments. Some species like the grey wolf is a polymorphic species with different individual variation in colors. The arctic fox ("Vulpes lagopus") and the stoat ("Mustela erminea") the fur goes from white and dense in the winter to brown and sparse in the summer. In pinnipeds, polar bears, and sea otters have a thick insulating layer of blubber to help maintain their body temperature.	Carnivora is an order of placental mammals that have specialized in primarily eating flesh. Its members are formally referred to as carnivorans, though some species are omnivorous, like raccoons and bears, and quite a few species like pandas are specialized herbivores. The word 'carnivore' is derived from Latin "carō" (stem "carn-") "flesh" and "vorāre" "to devour", it refers to any meat-eating organism. The order Carnivora is the fifth largest order of mammals and one of the more successful members of the group; it comprises at least 279 species living on every major landmass and in a variety of habitats, ranging the cold polar regions to the hyper-arid region of the Sahara Desert to the open seas. They come in a huge array of different body plans in contrasting shapes and sizes. The smallest carnivoran is the least weasel ("Mustela nivalis") with a body length of about and a weight of about. The largest is the southern elephant seal ("Mirounga leonina"), with adult males weighing up to and measuring up to. All species of carnivorans are descended from a group of mammals which were related to today's pangolins, having appeared in North America 6 million years after the Cretaceous–Paleogene extinction event. These early ancestors of carnivorans would have resembled small weasel or genet-like mammals, occupying a nocturnal shift on the forest floor or in the trees, as other groups of mammals like the mesonychians and creodonts were occupying the top faunivorous niche. 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summarize: The study of fluid mechanics goes back at least to the days of ancient Greece, when Archimedes investigated fluid statics and buoyancy and formulated his famous law known now as the Archimedes' principle, which was published in his work "On Floating Bodies"—generally considered to be the first major work on fluid mechanics. Rapid advancement in fluid mechanics began with Leonardo da Vinci (observations and experiments), Evangelista Torricelli (invented the barometer), Isaac Newton (investigated viscosity) and Blaise Pascal (researched hydrostatics, formulated Pascal's law), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in "Hydrodynamica" (1739). Inviscid flow was further analyzed by various mathematicians (Jean le Rond d'Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace, Siméon Denis Poisson) and viscous flow was explored by a multitude of engineers including Jean Léonard Marie Poiseuille and Gotthilf Hagen. Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl, Theodore von Kármán), while various scientists such as Osborne Reynolds, Andrey Kolmogorov, and Geoffrey Ingram Taylor advanced the understanding of fluid viscosity and turbulence. Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to some aspects of geophysics and astrophysics (for example, in understanding plate tectonics and anomalies in the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow—the science of liquids and gases in motion. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and movements on aircraft, determining the mass flow rate of petroleum through pipelines, predicting evolving weather patterns, understanding nebulae in interstellar space and modeling explosions. Some fluid-dynamical principles are used in traffic engineering and crowd dynamics. Fluid mechanics is a subdiscipline of continuum mechanics, as illustrated in the following table. In a mechanical view, a fluid is a substance that does not support shear stress; that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress. The assumptions inherent to a fluid mechanical treatment of a physical system can be expressed in terms of mathematical equations. Fundamentally, every fluid mechanical system is assumed to obey: For example, the assumption that mass is conserved means that for any fixed control volume (for example, a spherical volume)—enclosed by a control surface—the rate of change of the mass contained in that volume is equal to the rate at which mass is passing through the surface from "outside" to "inside", minus the rate at which mass is passing from "inside" to "outside". This can be expressed as an equation in integral form over the control volume. The is an idealization of continuum mechanics under which fluids can be treated as continuous, even though, on a microscopic scale, they are composed of molecules. Under the continuum assumption, macroscopic (observed/measurable) properties such as density, pressure, temperature, and bulk velocity are taken to be well-defined at "infinitesimal" volume elements—small in comparison to the characteristic length scale of the system, but large in comparison to molecular length scale. Fluid properties can vary continuously from one volume element to another and are average values of the molecular properties. The continuum hypothesis can lead to inaccurate results in applications like supersonic speed flows, or molecular flows on nano scale. Those problems for which the continuum hypothesis fails can be solved using statistical mechanics. To determine whether or not the continuum hypothesis applies, the Knudsen number, defined as the ratio of the molecular mean free path to the characteristic length scale, is evaluated. Problems with Knudsen numbers below 0.1 can be evaluated using the continuum hypothesis, but molecular approach (statistical mechanics) can be applied for all ranges of Knudsen numbers. The Navier–Stokes equations (named after Claude-Louis Navier and George Gabriel Stokes) are differential equations that describe the force balance at a given point within a fluid. For an incompressible fluid with vector velocity field formula_1, the Navier–Stokes equations are These differential equations are the analogues for deformable materials to Newton's equations of motion for particles – the Navier–Stokes equations describe changes in momentum (force) in response to pressure formula_3 and viscosity, parameterized by the kinematic viscosity formula_4 here. Occasionally, body forces, such as the gravitational force or Lorentz force are added to the equations. Solutions of the Navier–Stokes equations for a given physical problem must be sought with the help of calculus. In practical terms, only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow in which the Reynolds number is small. For more complex cases, especially those involving turbulence, such as global weather systems, aerodynamics, hydrodynamics and many more, solutions of the Navier–Stokes equations can currently only be found with the help of computers. This branch of science is called computational fluid dynamics. An inviscid fluid has no viscosity, formula_5. In practice, an inviscid flow is an idealization, one that facilitates mathematical treatment. In fact, purely inviscid flows are only known to be realized in the case of superfluidity. Otherwise, fluids are generally viscous, a property that is often most important within a boundary layer near a solid surface, where the flow must match onto the no-slip condition at the solid. In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then matching its solution onto that for a thin laminar boundary layer. For fluid flow over a porous boundary, the fluid velocity can be discontinuous between the free fluid and the fluid in the porous media (this is related to the Beavers and Joseph condition). Further, it is useful at low subsonic speeds to assume that gas is incompressible—that is, the density of the gas does not change even though the speed and static pressure change. A Newtonian fluid (named after Isaac Newton) is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means regardless of the forces acting on a fluid, it "continues to flow". For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. (Compare friction). Important fluids, like water as well as most gases, behave—to good approximation—as a Newtonian fluid under normal conditions on Earth. By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time—this behavior is seen in materials such as pudding, oobleck, or sand (although sand isn't strictly a fluid). Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" (this is seen in non-drip paints). There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property—for example, most fluids with long molecular chains can react in a non-Newtonian manner. The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation to describe incompressible Newtonian fluid behavior is where For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure, not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress (in Cartesian coordinates) is where If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is where formula_19 is the second viscosity coefficient (or bulk viscosity). If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic. In some applications, another rough broad division among fluids is made: ideal and non-ideal fluids. An ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. One example of this is the flow far from solid surfaces. In many cases, the viscous effects are concentrated near the solid boundaries (such as in boundary layers) while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid (ideal flow). When the viscosity is neglected, the term containing the viscous stress tensor formula_20 in the Navier–Stokes equation vanishes. The equation reduced in this form is called the Euler equation.	Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. 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summarize: A "solid" is a material that can support a substantial amount of shearing force over a given time scale during a natural or industrial process or action. This is what distinctly distinguishes solids from fluids, because fluids also support "normal forces" which are those forces that are directed perpendicular to the material plane across from which they act and "normal stress" is the normal force per unit area of that material plane. "Shearing forces" in contrast with "normal forces", act parallel rather than perpendicular to the material plane and the shearing force per unit area is called "shear stress". Therefore, solid mechanics examines the shear stress, deformation and the failure of solid materials and structures. The most common topics covered in solid mechanics include: As shown in the following table, solid mechanics inhabits a central place within continuum mechanics. The field of rheology presents an overlap between solid and fluid mechanics. A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity. This region of deformation is known as the linearly elastic region. It is most common for analysts in solid mechanics to use linear material models, due to ease of computation. However, real materials often exhibit non-linear behavior. As new materials are used and old ones are pushed to their limits, non-linear material models are becoming more common. These are basic models that describe how a solid responds to an applied stress:	Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.	en	en	48	[ 250004, 250054, 62, 44, 97281, 58, 83, 10, 4912, 450, 831, 8060, 10, 193984, 41170, 111, 2412, 101098, 37772, 645, 10, 34475, 1733, 105994, 20271, 10, 6083, 707, 25297, 9433, 707, 22631, 5, 3293, 83, 2367, 117781, 538, 157167, 114942, 18652, 7, 1295, 79552, 7, 4, 6637, 79552, 7, 2843, 8060, 44, 33176, 84616, 58, 3129, 621, 8382, 84616, 450, 621, 8951, 297, 117, 40930, 25667, 47, 70, 4912, 47880, 36880, 1295, 3129, 1836, 27992, 136, 44, 33176, 11405, 58, 83, 70, 3638, 37772, 117, 25072, 16128, 111, 450, 4912, 47880, 5, 44, 72859, 101098, 84616, 58, 23, 69822, 678, 44, 33176, 84616, 830, 27992, 95103, 43257, 3501, 117, 40930, 25667, 47, 70, 4912, 47880, 136, 70, 2412, 101098, 37772, 117, 25072, 16128, 83, 35839, 44, 7, 90431, 11405, 740, 228072, 4, 18652, 135969, 7, 160477, 7, 70, 2412, 147, 11405, 4, 8, 5037, 2320, 136, 70, 137578, 111, 18652, 76319, 136, 45646, 7, 5, 581, 2684, 39210, 28451, 7, 127918, 23, 18652, 135969, 7, 26698, 12, 1301, 127887, 23, 70, 25632, 23180, 4, 18652, 135969, 7, 23, 54815, 933, 10, 9879, 3687, 28032, 19686, 316, 135969, 7, 5, 581, 44457, 111, 60971, 25443, 13379, 7, 142, 645, 6324, 17721, 18652, 136, 79552, 135969, 7, 5, 62, 4912, 1556, 10, 10588, 115700, 136, 6863, 115700, 8, 17365, 7, 16065, 1295, 70, 10588, 115700, 4743, 47, 11405, 5, 581, 41170, 111, 8, 2500, 6644, 1295, 10588, 115700, 83, 35839, 8, 5037, 2320, 4, 70, 123875, 111, 8, 5037, 2320, 47, 7311, 13267, 83, 35839, 177488, 5, 4263, 70, 190659, 11405, 83, 6, 129980, 538, 27226, 15, 748, 70, 566, 144429, 177488, 83, 19336, 20174, 247, 39555, 756, 18652, 76319, 186, 68991, 23, 6044, 10, 3917, 450, 70, 177488, 83, 105237, 123875, 289, 47, 70, 11405, 74, 70, 552, 13, 24500, 45964, 111, 70, 123875, 83, 35839, 70, 17055, 223, 111, 128766, 2481, 5, 3293, 10776, 111, 8, 5037, 2320, 83, 51529, 237, 70, 192617, 538, 128766, 10776, 5, 1650, 83, 2684, 39210, 100, 60822, 933, 23, 18652, 135969, 7, 47, 4527, 192617, 4912, 115774, 4, 4743, 47, 28, 6991, 111, 181135, 1363, 5, 33306, 4, 2773, 76319, 27983, 80788, 18, 351, 9, 2256, 147, 123166, 5, 1301, 3525, 76319, 621, 11814, 136, 10332, 64333, 621, 25944, 297, 47, 2363, 17475, 7, 4, 351, 9, 2256, 147, 4912, 115774, 621, 141753, 1286, 39210, 5, 32255, 621, 62822, 115774, 450, 98363, 3642, 10, 18652, 35644, 7, 47, 142, 190659, 11405, 12, 2 ]	[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ]	[ 250004, 95823, 135969, 7, 4, 2843, 51529, 237, 135969, 7, 111, 18652, 7, 4, 83, 70, 32845, 206, 111, 19686, 316, 135969, 7, 450, 96335, 70, 123166, 111, 18652, 76319, 4, 41866, 2363, 78112, 136, 8, 5037, 2320, 1379, 70, 22631, 111, 84616, 4, 52768, 65572, 4, 93402, 65572, 4, 136, 3789, 173591, 707, 70796, 97957, 5, 2 ]
summarize: The name "Belarus" is closely related with the term "Belaya Rus", i.e., "White Rus'". There are several claims to the origin of the name "White Rus'." An ethno-religious theory suggests that the name used to describe the part of old Ruthenian lands within the Grand Duchy of Lithuania that had been populated mostly by Slavs who had been Christianized early, as opposed to Black Ruthenia, which was predominantly inhabited by pagan Balts. An alternate explanation for the name comments on the white clothing worn by the local Slavic population. A third theory suggests that the old Rus' lands that were not conquered by the Tatars (i.e., Polotsk, Vitebsk and Mogilev) had been referred to as "White Rus'". The name "Rus" is often conflated with its Latin forms "Russia" and "Ruthenia", thus Belarus is often referred to as "White Russia" or "White Ruthenia". The name first appeared in German and Latin medieval literature; the chronicles of Jan of Czarnków mention the imprisonment of Lithuanian grand duke Jogaila and his mother at "" in 1381. In some languages, including German, Afrikaans and Dutch, the country is generally called "White Russia" to this day (' and'respectively). The Latin term "Alba Russia" was used again by Pope Pius VI in 1783 to recognize the Society of Jesus there, exclaiming "." The first known use of "White Russia" to refer to Belarus was in the late-16th century by Englishman Sir Jerome Horsey, who was known for his close contacts with the Russian Royal Court. During the 17th century, the Russian tsars used "White Rus" to describe the lands added From 5000 to 2000 BC, Bandkeramik cultures predominated. In addition, remains from the Dnieper-Donets culture were found in Belarus and parts of Ukraine. Cimmerians and other pastoralists roamed through the area by 1,000 BC, and by 500 AD, Slavs had taken up residence, which was circumscribed by the Scythians who roamed its outskirts. Invaders from Asia, among whom were the Huns and Avars, swept through c. 400–600 AD, but were unable to dislodge the Slavic presence. The region that is now Belarus was first settled by Baltic tribes in the 3rd century. Around the 5th century, the area was taken over by Slavic tribes. The takeover was partially due to the lack of military coordination of the Balts but the gradual assimilation of the Balts into Slavic culture was peaceful in nature. In the 9th century the territory of On 2 February 1386, the Grand Duchy of Lithuania and the Kingdom of Poland were joined in a personal union through a marriage of their rulers. This union set in motion the developments that eventually resulted in the formation of the Polish–Lithuanian Commonwealth, created in 1569 by the Union of Lublin. The Lithuanian nobles were forced to go for rapprochement because of the threat coming from Muscovy. To strengthen the independence in the format of the union, three editions of the Statutes of Lithuania were issued in the 16th century. The third Article of the Statute establishes that all lands of Grand Duchy of Lithuania will be eternally in Grand Duchy of Lithuania and never enter as The union between Poland and Lithuania ended in 1795 with the Third Partition of Poland by Imperial Russia, Prussia, and Austria. The Belarusian territories acquired by the Russian Empire under the reign of Catherine II were included into the Belarusian Governorate () in 1796 and held until their occupation by the German Empire during World War I. Under Nicholas I and Alexander III the national cultures were repressed. Policies of Polonization changed by Russification, which included the return to Orthodox Christianity of Belorusian Uniates. Belarusian language was banned in schools while in neighboring Samogitia primary school education with Samogitian literacy was allowed. The Belarusian People's Republic was the first attempt to create an independent Belarusian state under name "Belarus". Despite significant efforts the state ceased to exist, primarily because the territory was continually dominated by the German Imperial Army and the Imperial Russian Army in The Republic of Central Lithuania was a short-lived political entity, which was the last attempt to restore Lithuania in the historical confederacy state (it was also supposed to create Lithuania Upper and Lithuania Lower). The republic was created in 1920 following the staged rebellion of soldiers of the 1st Lithuanian–Belarusian Division of the Polish Army under Lucjan Żeligowski. Centered on the historical capital of the Grand Duchy of Lithuania, Vilna A part of Belarus under Russian rule emerged as the Byelorussian Soviet Socialist Republic (Byelorussian SSR) in 1919. Soon thereafter it merged to form the Lithuanian-Byelorussian SSR. The contested lands were divided between Poland and the Soviet Union after the war ended in 1921, and the Byelorussian SSR became a founding member of the Union of Soviet Socialist Republics in 1922. The western part of modern Belarus remained part of Poland. In the 1920s and 1930s, Soviet agricultural and economic policies, including collectivization and five-year plans for the national economy, led to In March 1990, elections for seats in the Supreme Soviet of the Byelorussian SSR took place. Though the pro-independence Belarusian Popular Front took only 10% of the seats, the populace was content with the selection of the delegates. Belarus declared itself sovereign on 1990 by issuing the Declaration of State Sovereignty of the Belarusian Soviet Socialist Republic. Two-round elections for the presidency on ( 1994 and 1994) catapulted the formerly unknown Alexander Lukashenko into national prominence. He garnered 45% of the vote in the first round and 80% in the second, defeating Vyacheslav Kebich who received 14% of the vote. Lukashenko was re-elected in 2001, in 2006, in 2010 and again in 2015. Western governments, Amnesty International, and Human Rights Watch have criticized Lukashenko's authoritarian style of government. Since 2014, following years of embrace of Russian influence in the country, Lukashenko has pressed a revival of Belarusian identity, following the Russian annexation of Crimea and military intervention in Eastern Ukraine. Belarus lies between latitudes 51° and 57° N, and longitudes 23° and 33° E. Its extension from north to south is, from west to east is. It is landlocked, relatively flat, and contains large tracts of marshy land. About 40% of Belarus is covered by forests. Many streams and 11,000 lakes are found in Belarus. Three major rivers run through the country: the Neman, the Pripyat, and the Dnieper. The Neman flows westward towards the Baltic sea and the Pripyat flows eastward to the Dnieper; the Dnieper flows southward towards the Black Sea. The highest point is Dzyarzhynskaya Hara (Dzyarzhynsk Hill) at, and the lowest point is on the Neman River at. The average elevation of Belarus is above sea level. The climate features mild to cold winters, with Belarus is a presidential republic, governed by a president and the National Assembly. The term for each presidency is five years. Under the 1994 constitution, the president could serve for only two terms as president, but a change in the constitution in 2004 eliminated term limits. Alexander Lukashenko has been the president of Belarus since 1994. In 1996, Lukashenko called for a controversial vote to extend the presidential term from five to seven years, and as a result the election that was supposed to occur in 1999 was pushed back to 2001. The referendum on the extension was denounced as a "fantastic" fake by the chief electoral officer, Viktar Hanchar, who was removed from the office for official matters only during the campaign. The National Assembly is a bicameral parliament comprising the 110-member House of Representatives (the lower house) and the 64-member Council of the Republic (the upper house). The House of Representatives has the power to appoint the prime minister, make constitutional amendments, call for a vote of confidence on the prime minister, and make suggestions on foreign and domestic policy. The Council of the Republic has the power to select various government officials, conduct an impeachment trial of the president, and accept or reject the bills passed by the House of Representatives. Each chamber has the ability to veto any law passed by local officials if it is contrary to the constitution. The government includes a Council of Ministers, headed by the prime minister and five deputy prime ministers. The members of this council need not be members of the legislature and are appointed by the president. The judiciary comprises the Supreme Court and specialized courts such as the Constitutional Court, which deals with specific issues related to constitutional and business law. The judges of national courts are appointed by the president and confirmed by the Council of the Republic. For criminal cases, the highest court of appeal is the Supreme Court. The Belarusian Constitution forbids the use of special extrajudicial courts. In the 2012 parliamentary election, 105 of the 110 members elected to the House of Representatives were not affiliated with any political party. The Communist Party of Belarus won 3 seats, and the Agrarian Party and Republican Party of Labour and Justice, one each. Most non-partisans represent a wide scope of social organizations such as workers' collectives, public associations, and civil society organizations, similar to the composition of the Soviet legislature. In 2014 the share of manufacturing in GDP was 37%, more than two thirds of this amount falls on manufacturing industries. The number of people employed in industry is 32.7% of the working population. The growth rate is much lower than for the economy as a whole – about 1.9% in 2014. At the time of the dissolution of the Soviet Union in 1991, Belarus was one of the world's most industrially developed states by percentage of GDP as well as the richest CIS member-state. In 2015, 39.3% of Belarusians were employed by state-controlled companies, 57.2% were employed by private companies (in which the government has a 21.1% stake) and 3.5% were employed by foreign companies. The country relies According to the National Statistical Committee,, the population is 9.49 million. Ethnic Belarusians constitute 83.7% of Belarus's total population. The next largest ethnic groups are: Russians (8.3%), Poles (3.1%), and Ukrainians (1.7%). Belarus has a population density of about 50 people per square kilometer (127 per sq mi); 70% of its total population is concentrated in urban areas. Minsk, the nation's capital and largest city, was home to 1,937,900 residents. Gomel, with a population of 481,000, is the second-largest city and serves as the capital of the Homiel Voblast. Other large cities are Mogilev (365,100), Vitebsk (342,400), Hrodna (314,800) and Brest (298,300). Like many other eastern European countries, Belarus has a negative population growth rate and a negative natural growth rate. In 2007, Belarus's population declined by 0.41% and its fertility rate was 1.22, well below the replacement rate. Its net migration rate is +0.38 per 1,000, indicating that Belarus experiences slightly more immigration than emigration., 69.9% of Belarus's population is aged 14 to 64; 15.5% is under 14, and 14.6% is 65 or older. Its population is also aging; the median age of 30–34 is estimated to rise to between 60 and 64 in 2050. There are about 0.87 males per female in Belarus. The average life expectancy is 72.15 (66.53 years for men and 78.1 years for women). Over 99% of Belarusians aged 15 and older are literate. Belarus's two official languages are Russian and Belarusian; Russian is the most common language used at home, used by 70% of the population, while Belarusian, the official first According to the census of, 58.9% of all Belarusians adhere to some kind of religion; out of those, Eastern Orthodoxy (Belarusian Exarchate of the Russian Orthodox Church) makes up about 82%. Roman Catholicism is practiced mostly in the western regions, and there are also different denominations of Protestantism. Minorities also practice Greek Catholicism, Judaism, Islam and Neopaganism. Overall, 48.3% of the population is Orthodox Christian, 41.1% is not religious, 7.1% is Catholic and 3.3% follows other religions. Belarus's Catholic minority is concentrated in the western part of the country, The Belarusian government sponsors annual cultural festivals such as the Slavianski Bazaar in Vitebsk, which showcases Belarusian performers, artists, writers, musicians, and actors. Several state holidays, such as Independence Day and Victory Day, draw big crowds and often include displays such as fireworks and military parades, especially in Vitebsk and Minsk. The government's Ministry of Culture finances events promoting Belarusian arts and culture both inside and outside the country. Belarusian literature began with 11th- to 13th-century religious scripture, such as the 12th-century poetry of Cyril of Turaw. By the 16th century, Polotsk resident Francysk Skaryna translated the Bible into Belarusian. It was published in Prague and Vilnius sometime between 1517 and 1525, making it the first book printed in Belarus or anywhere in Eastern Europe. The modern era of Belarusian literature began in the late 19th century; one prominent writer was Yanka Kupala. Many Belarusian writers of the time, such as Uładzimir Žyłka, Kazimir Svayak, Yakub Kolas, Źmitrok Biadula, and Maksim Haretski, wrote for "Nasha Niva", a Belarusian-language paper published that was previously published in Vilnius but now is published in Minsk. After Belarus was incorporated into the Soviet Union, the Soviet government took control of the Republic's cultural affairs. At first, a policy of "Belarusianization" was followed in the newly formed Byelorussian SSR. This policy was reversed in the 1930s, and the majority of prominent Belarusian intellectuals and nationalist advocates were either exiled or killed in Stalinist purges. The free development of literature occurred only The traditional Belarusian dress originates from the Kievan Rus' period. Due to the cool climate, clothes were designed to preserve body heat and were usually made from flax or wool. They were Belarusian cuisine consists mainly of vegetables, meat (particularly pork), and bread. Foods are usually either slowly cooked or stewed. Typically, Belarusians eat a light breakfast and two hearty meals Belarus has competed in the Olympic Games since the 1994 Winter Olympics. Its National Olympic Committee has been headed by President Lukashenko since 1997. Receiving heavy sponsorship from the government, ice hockey is the nation's second most popular sport after football. The national football team has never qualified for a major tournament; however, BATE Borisov has played in the Champions League. The national hockey team finished fourth at the 2002 Salt Lake City Olympics following a memorable upset win over Sweden in the quarterfinals, and regularly competes in the World Championships, often making the quarterfinals. Numerous Belarusian players are present in the Kontinental Hockey League in Eurasia, particularly for Belarusian club HC Dinamo Minsk, and several have also played in the National The state telecom monopoly, Beltelecom, holds the exclusive interconnection with Internet providers outside of Belarus. Beltelecom owns all the backbone Belarus has four UNESCO-designated World Heritage Sites: the Mir Castle Complex, the In May 2020 it was reported that the country had one of Europe's highest per capita infection rates in the COVID-19 pandemic. President Lukashenko, campaigning for the August presidential election, had repeatedly	Belarus (;, ), officially the Republic of Belarus (, ), formerly known by its Russian name Byelorussia or Belorussia (), is a landlocked country in Eastern Europe. It is bordered by Russia to the northeast, Ukraine to the south, Poland to the west, and Lithuania and Latvia to the northwest. Its capital and most populous city is Minsk. Over 40% of its is forested. Its major economic sectors are service industries and manufacturing. 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summarize: Many physical processes are Temperature scales differ in two ways: the point chosen as zero degrees, and the magnitudes of incremental units or degrees on the scale. The Celsius scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale that was developed by a historical progress, which led to its zero point being defined by the freezing point of water, and additional degrees defined so that was the boiling point of water, both at sea-level atmospheric pressure. Because At the absolute zero of temperature, no more energy can be removed from matter as heat, a fact expressed in the third law of thermodynamics. At this temperature, matter contains no macroscopic thermal energy, but still has quantum-mechanical zero-point energy as predicted by the uncertainty principle. Referring to the Boltzmann constant, to the Maxwell–Boltzmann distribution, and to the Boltzmann statistical mechanical definition of entropy, as distinct from the Gibbs definition, for independently moving microscopic particles, disregarding interparticle potential energy, by international agreement, a temperature scale is defined and said to be absolute because it is independent of the characteristics of particular thermometric substances and thermometer mechanisms. Apart from the absolute zero, it does not have a reference temperature. It is known as the Kelvin scale, widely used in science and technology. The kelvin (the word is spelled with a lower-case Many scientific measurements use the Kelvin temperature scale (unit symbol: K), named in honor of the physicist who first defined it. It is an absolute scale. Its numerical zero point,, is at the absolute zero of temperature. Since May, Since May 2019, the magnitude of the kelvin is defined in relation to microscopic phenomena, characterized in terms of statistical mechanics. Previously, since 1954, the International System of Units defined a scale and unit for the kelvin as a thermodynamic temperature, by There is a variety of kinds of temperature scale. It may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century. Empirically based temperature scales rely directly on measurements of simple macroscopic physical properties of materials. For example, the length of a column of mercury, confined in a glass-walled capillary tube, is dependent largely on temperature, and is the basis of the very useful mercury-in-glass thermometer. Such scales are valid only within convenient ranges of temperature. For example, above the boiling point of mercury, a mercury-in-glass thermometer is impracticable. Most materials expand with temperature increase, but some materials, such Theoretically based temperature scales are based directly on theoretical arguments, especially those of kinetic theory and thermodynamics. They are more or less ideally realised in practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers. In physics, the internationally agreed conventional temperature scale is called the Kelvin scale. It is calibrated through the internationally agreed and prescribed value of the Boltzmann constant, referring to motions of microscopic particles, such as atoms, molecules, and electrons, constituent in the body whose temperature is to be measured. In contrast with the thermodynamic temperature scale invented by Kelvin, the presently conventional Kelvin temperature is not defined through comparison with the temperature of a reference state of a standard body, nor in terms of macroscopic thermodynamics. Apart from the absolute zero Historically, till May 2019, the definition of the Kelvin scale was that invented by Kelvin, based on a ratio of quantities of energy in processes in an ideal Carnot engine, entirely in terms of macroscopic thermodynamics. That Carnot engine was to work between two temperatures, that of the body A material on which a macroscopically defined temperature scale may be based is the ideal gas. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature ranges that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today. The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. In contrast to real materials, the ideal gas does not liquefy or solidify, no matter how cold it is. Alternatively thinking, the ideal gas law, refers to the limit of infinitely high temperature and zero pressure; these conditions guarantee non-interactive motions of the constituent molecules. The magnitude of the kelvin is now defined in terms of kinetic theory, derived from the value of Boltzmann's constant. Kinetic theory provides a microscopic account of temperature for some bodies of material, especially gases, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena through the classical mechanics of the microscopic particles. The equipartition theorem of kinetic theory asserts that each classical degree of freedom of a freely moving particle has an average kinetic energy of where denotes Boltzmann's constant. The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate, the average translational kinetic energy of a freely moving particle in a system with temperature will be. Molecules, such as oxygen (O), have more degrees of freedom than Temperature is one of the principal quantities in the study of thermodynamics. Formerly, the magnitude of the kelvin was defined in thermodynamic terms, but nowadays, as mentioned above, it is defined in terms of kinetic theory. The thermodynamic temperature is said to be absolute for two reasons. One is that its formal character is independent of the properties of particular materials. The other reason is that its zero is, in a sense, absolute, in that it indicates absence of microscopic classical motion of the constituent particles of matter, so that they have a limiting specific heat of zero for zero temperature, according to the third law of thermodynamics. Nevertheless, a thermodynamic temperature does in fact have a definite numerical value that has been arbitrarily chosen by tradition and is dependent on the property of a particular materials; it is simply less arbitrary than relative "degrees" scales such as Celsius and Fahrenheit. Being an absolute scale with one fixed point (zero), there is only one degree of freedom left to arbitrary choice, rather than two as in relative scales. For the Kelvin scale since May 2019, by international convention, the choice has been made to use knowledge of modes of operation of various thermometric devices, relying on microscopic kinetic theories about molecular motion. The numerical scale is settled by a conventional definition of the value of the Boltzmann constant, which relates macroscopic temperature to average microscopic kinetic energy of particles such as molecules. Its numerical value is arbitrary, and an alternate, less widely used absolute temperature scale exists called the Rankine scale, made to be aligned with the Fahrenheit scale as Kelvin is with Celsius. The thermodynamic definition of temperature is due to Kelvin. It is framed in terms of an idealized device called a Carnot engine, imagined to run in a fictive continuous cycle of successive processes that traverse a cycle of states of its working body. The engine takes in a quantity of heat from a hot reservoir and passes out a lesser quantity of heat to a cold reservoir. The difference in energy is passed, as thermodynamic work, to a work reservoir, and is considered to be the output of the engine. The cycle is imagined to run so slowly that at each point of the cycle the working body is in a state of thermodynamic equilibrium. The successive processes the cycle are thus imagined to run reversibly with no entropy production. Then the quantity of entropy taken in from the hot reservoir when the working body is heated is equal to that passed to the cold reservoir when the working body is cooled. Then the absolute or thermodynamic temperatures, and, of the reservoirs are defined so that to be such that The zeroth law of thermodynamics allows this definition to be used to measure the absolute or thermodynamic temperature of an arbitrary body of interest, by making the other heat reservoir have the same temperature as the body of interest. Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before the formulation of the first law of thermodynamics. Carnot had no sound understanding of heat, and no specific concept of entropy. He wrote of 'caloric', and said that all the caloric that passed from the hot reservoir was passed into the cold reservoir. Kelvin wrote in his 1848 paper that his scale was absolute in the sense that it was defined "independently of the properties of any particular kind of matter". His definitive publication, which sets out the definition just stated, was printed in 1853, a paper read in 1851. Numerical details were formerly settled by making one of the heat reservoirs a cell at the triple point of water, which was defined to have an absolute temperature of 273.16 K. Nowadays, the numerical value is instead obtained from measurement through the microscopic statistical mechanical international definition, as above. Temperature is a measure of a quality of a state of a material. The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called "hotness" by some writers. The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness varies from place to place. It is not necessarily the case that a material in a particular place is in a state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or temperature. Hotness may be represented abstractly as a one-dimensional manifold. Every valid temperature scale has its own one-to-one map into the hotness manifold. When two systems in thermal contact are at the same temperature no heat transfers between them. When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system until they are in thermal equilibrium. Such heat transfer occurs by conduction or by thermal radiation. Experimental physicists, for example Galileo and Newton, found that there are indefinitely many empirical temperature scales. Nevertheless, the zeroth law of thermodynamics says that they all measure the same quality. This means that for a body in its own state of internal thermodynamic equilibrium, every correctly calibrated thermometer, of whatever kind, that measures the temperature of the body, records one and the same temperature. For a body that is not in its own state of internal thermodynamic equilibrium, different thermometers can record different temperatures, depending respectively on the mechanisms of operation of the thermometers. For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature. This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic. A definite sense of greater hotness can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of thermal While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though When a body is not in a steady state, then the notion of temperature becomes even For axiomatic treatment of thermodynamic equilibrium, since the 1930s, it has become customary to refer to a zeroth law of thermodynamics. The customarily stated minimalist version of such a law postulates only that all bodies, which when thermally connected would be in thermal equilibrium, should be said to have the same temperature by definition, but by itself does not establish temperature as a quantity expressed as a real number on a scale. A more physically informative version of such a law views empirical temperature as a chart When an energy transfer to or from a body is only as heat, the state of the body changes. Depending on the surroundings and the walls separating them from the body, various changes are possible in the body. They include chemical reactions, increase of pressure, increase of temperature, and phase change. For each kind of change under specified conditions, the heat capacity is the ratio of the quantity of heat transferred to the magnitude of Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use in the United States for non-scientific applications. Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for Belize, Myanmar, Liberia and the United States), the Celsius scale is used for most temperature measuring purposes. Most scientists measure temperature using the Celsius scale and thermodynamic temperature using the Kelvin scale, which is the Celsius scale offset so that its null point is =, or absolute zero. Many engineering fields in the US, notably high-tech and US federal specifications (civil and military), also use the Kelvin and Celsius scales. Other engineering fields in the US also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion. The basic unit of temperature in the International System of Units (SI) is the Kelvin. It has the symbol K. For everyday applications, it is often convenient to use the Celsius scale, in which corresponds very closely to the freezing point of water and is its boiling point at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, is better defined as the melting point of ice. In this scale a temperature difference of 1 degree Celsius is the same as a increment, but the scale is offset by the temperature at which ice melts (). By international agreement, until May 2019, the Kelvin and Celsius scales were defined by two fixing points: absolute zero and the triple point of Vienna Standard Mean Ocean Water, which is water specially prepared with a specified blend of The following table shows the temperature The field of plasma physics deals with phenomena of electromagnetic nature that involve very high temperatures. It is customary to express temperature as energy in units of electronvolts (eV) or kiloelectronvolts (keV). The energy, which has a different dimension from temperature, is then calculated as the product of the Boltzmann constant and temperature, formula_2. Then, 1eV corresponds to. In the study of QCD matter one routinely encounters temperatures of the order of a few hundred MeV, equivalent to about. Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the kinetic theory of gases which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on statistical physics and quantum mechanics. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature. Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using natural units, temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern metric system of units, the macroscopic and the microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy. The microscopic description in statistical mechanics is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or quantum-mechanical oscillators and considers the system as a statistical ensemble of microstates. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called kinetic energy, of the particles, whether in solids, liquids, gases, or plasmas. The kinetic energy, a concept of classical mechanics, is half the mass of a particle times its speed squared. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monatomic perfect gases and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the thermodynamic limit, meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model. The kinetic energy is also considered as a component of thermal energy. The thermal energy may be partitioned into independent components attributed to the degrees of freedom of the particles or to the modes of oscillators in a thermodynamic system. In general, the number of these degrees of freedom that are available for the equipartitioning of energy depends on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas, the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, vibrational and rotational motions also contribute degrees of freedom. Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases. This theory also explains the ideal gas law and the observed heat capacity of monatomic (or 'noble') gases. The ideal gas law is based on observed empirical relationships between pressure ("p"), volume ("V"), and temperature ("T"), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws). The ideal gas law states: where "n" is the number of moles of gas and is the gas constant. This relationship gives us our first hint that there is an absolute zero on the temperature scale, because it only holds if the temperature is measured on an absolute scale such as Kelvin's. The ideal gas law allows one to measure temperature on this absolute scale using the gas thermometer. The temperature in kelvins can be defined as the pressure in pascals of one mole of gas in a container When two otherwise isolated bodies are connected together by a rigid physical path impermeable to matter, there is spontaneous transfer of energy as heat from the hotter to the colder of them. Eventually, they reach a state of mutual thermal equilibrium, in which heat transfer has ceased, and the bodies' respective state variables have settled to become unchanging. One statement of the zeroth law of thermodynamics is that if two systems are each in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This statement As an alternative to considering or defining the zeroth law of thermodynamics, it was the historical development in thermodynamics to define temperature in terms of the second law of thermodynamics which deals with entropy. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. For example, in a series of coin tosses, a perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means the outcome is always 100% the same result. In contrast, many mixed ("disordered") outcomes are possible, and their number increases with each toss. Eventually, the combinations of ~50% heads and ~50% tails dominate and obtaining an outcome significantly different from 50/50 becomes increasingly unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy. As temperature governs the transfer of heat between two systems and the universe tends to progress toward a maximum of entropy, it is expected that there is some relationship between temperature and entropy. A heat engine is a device for converting thermal energy into mechanical energy, resulting in the performance of work. and analysis of the Carnot heat engine provides the necessary relationships. The work from a heat engine corresponds to the difference between the heat put into the system at high temperature, "q" and the heat extracted at the Statistical mechanics defines temperature based on a system's fundamental degrees of freedom. Eq.(10) It is possible to extend the definition of temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration-space ensembles given in statistical mechanics in the case of thermal and particle exchange between On the empirical temperature scales that are not referenced to absolute zero, a negative temperature is one below the zero-point of the scale used. For example, dry ice has a sublimation temperature of which is equivalent to. On the absolute kelvin scale this temperature is. No body can be brought to exactly (the temperature of the ideally coldest possible body) by any finite practicable process; this is a consequence of the third law of thermodynamics. The international kinetic theory temperature of a body cannot take negative values. The thermodynamic temperature scale, however, is not so constrained. For a body of matter, there can sometimes be conceptually defined, in terms of microscopic degrees of freedom, namely particle spins, a subsystem, with a temperature other than that of the whole body. When the body is in its own state of internal thermodynamic equilibrium, the temperatures of the whole body and of the subsystem must be	Temperature is a physical property of matter that quantitatively expresses hot and cold. 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summarize: The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles (objects with negligible size). The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it. Each of these parameters is discussed in turn. In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of "very" small particles, such as the electron, is more accurately described by quantum mechanics.) Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom, e.g., a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made of a large number of collectively acting point particles. The center of mass of a composite object behaves like a point particle. Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as location in space and speed. Non-relativistic mechanics also assumes that forces act instantaneously (see also Action at a distance). The "position" of a point particle is defined in relation to a coordinate system centered on an arbitrary fixed reference point in space called the origin "O". A simple coordinate system might describe the position of a particle "P" with a vector notated by an arrow labeled r that points from the origin "O" to point "P". In general, the point particle does not need to be stationary relative to "O". In cases where "P" is moving relative to "O", r is defined as a function of "t", time. In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval that is observed to elapse between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space. The "velocity", or the rate of change of position with time, is defined as the derivative of the position with respect to time: In classical mechanics, velocities are directly additive and subtractive. For example, if one car travels east at 60 km/h and passes another car traveling in the same direction at 50 km/h, the slower car perceives the faster car as traveling east at. However, from the perspective of the faster car, the slower car is moving 10 km/h to the west, often denoted as -10 km/h where the sign implies opposite direction. Velocities are directly additive as ; they must be dealt with using vector analysis. Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector and the velocity of the second object by the vector, where "u" is the speed of the first object, "v" is the speed of the second object, and d and e are unit vectors in the directions of motion of each object respectively, then the velocity of the first object as seen by the second object is Similarly, the first object sees the velocity of the second object as When both objects are moving in the same direction, this equation can be simplified to Or, by ignoring direction, the difference can be given in terms of speed only: The "acceleration", or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time): Acceleration represents the velocity's change over time. Velocity can change in either magnitude or direction, or both. Occasionally, a decrease in the magnitude of velocity ""v"" is referred to as "deceleration", but generally any change in the velocity over time, including deceleration, is simply referred to as acceleration. While the position, velocity and acceleration of a particle can be described with respect to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames. An inertial frame is an idealized frame of reference within which an object has no external force acting upon it. Because there is no external force acting upon it, the object has a constant velocity; that is, it is either at rest or moving uniformly in a straight line. A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that do not accelerate with respect to distant stars (an extremely distant point) are regarded as good approximations to inertial frames. Non-inertial reference frames accelerate in relation to an existing inertial frame. They form the basis for Einstein's relativity. Due to the relative motion, particles in the non-inertial frame appear to move in ways not explained by forces from existing fields in the reference frame. Hence, it appears that there are other forces that enter the equations of motion solely as a result of the relative acceleration. These forces are referred to as fictitious forces, inertia forces, or pseudo-forces. Consider two reference frames "S" and S'. For observers in each of the reference frames an event has space-time coordinates of ("x","y","z","t") in frame "S" and (x',y',z',t') in frame S'. Assuming time is measured the same in all reference frames, and if we require when, then the relation between the space-time coordinates of the same event observed from the reference frames S' and "S", which are moving at a relative velocity of "u" in the "x" direction is: This set of formulas defines a group transformation known as the Galilean transformation (informally, the "Galilean transform"). This group is a limiting case of the Poincaré group used in special relativity. The limiting case applies when the velocity "u" is very small compared to "c", the speed of light. The transformations have the following consequences: For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one can either keep a mapping to a convenient inertial frame, or introduce additionally a fictitious centrifugal force and Coriolis force. A force in physics is any action which causes an object's velocity to change; that is, to accelerate. A force originates from within a field, such as an electro-static field (caused by static electrical charges), electro-magnetic field (caused by moving charges), or gravitational field (caused by mass), among others. Newton was the first to mathematically express the relationship between force and momentum. Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law": The quantity "m"v is called the (canonical) momentum. The net force on a particle is thus equal to the rate of change of the momentum of the particle with time. Since the definition of acceleration is, the second law can be written in the simplified and more familiar form: So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the "equation of motion". As an example, assume that friction is the only force acting on the particle, and that it may be modeled as a function of the velocity of the particle, for example: where "λ" is a positive constant, the negative sign states that the force is opposite the sense of the velocity. Then the equation of motion is This can be integrated to obtain where v is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the particle is absorbed by friction (which converts it to heat energy in accordance with the conservation of energy), and the particle is slowing down. This expression can be further integrated to obtain the position r of the particle as a function of time. Important forces include the gravitational force and the Lorentz force for electromagnetism. In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle "A" exerts a force F on another particle "B", it follows that "B" must exert an equal and opposite "reaction force", −F, on "A". The strong form of Newton's third law requires that F and −F act along the line connecting "A" and "B", while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces. If a constant force F is applied to a particle that makes a displacement Δr, the "work done" by the force is defined as the scalar product of the force and displacement vectors: More generally, if the force varies as a function of position as the particle moves from r to r along a path "C", the work done on the particle is given by the line integral If the work done in moving the particle from r to r is the same no matter what path is taken, the force is said to be conservative. Gravity is a conservative force, as is the force due to an idealized spring, as given by Hooke's law. The force due to friction is non-conservative. The kinetic energy "E" of a particle of mass "m" travelling at speed "v" is given by For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles. The work–energy theorem states that for a particle of constant mass "m", the total work "W" done on the particle as it moves from position r to r is equal to the change in kinetic energy "E" of the particle: Conservative forces can be expressed as the gradient of a scalar function, known as the potential energy and denoted "E": If all the forces acting on a particle are conservative, and "E" is the total potential energy (which is defined as a work of involved forces to rearrange mutual positions of bodies), obtained by summing the potential energies corresponding to each force The decrease in the potential energy is equal to the increase in the kinetic energy This result is known as "conservation of energy" and states that the total energy, is constant in time. It is often useful, because many commonly encountered forces are conservative. Classical mechanics also describes the more complex motions of extended non-pointlike objects. Euler's laws provide extensions to Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. The rocket equation extends the notion of rate of change of an object's momentum to include the effects of an object "losing mass". There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics. These, and other modern formulations, usually bypass the concept of "force", instead referring to other physical quantities, such as energy, speed and momentum, for describing mechanical systems in generalized coordinates. The expressions given above for momentum and kinetic energy are only valid when there is no significant electromagnetic contribution. In electromagnetism, Newton's second law for current-carrying wires breaks down unless one includes the electromagnetic field contribution to the momentum of the system as expressed by the Poynting vector divided by "c", where "c" is the speed of light in free space. Many branches of classical mechanics are simplifications or approximations of more accurate forms; two of the most accurate being general relativity and relativistic statistical mechanics. Geometric optics is an approximation to the quantum theory of light, and does not have a superior "classical" form. When both quantum mechanics and classical mechanics cannot apply, such as at the quantum level with many degrees of freedom, quantum field theory (QFT) is of use. QFT deals with small distances and large speeds with many degrees of freedom as well as the possibility of any change in the number of particles throughout the interaction. When treating large degrees of freedom at the macroscopic level, statistical mechanics becomes useful. Statistical mechanics describes the behavior of large (but countable) numbers of particles and their interactions as a whole at the macroscopic level. Statistical mechanics is mainly used in thermodynamics for systems that lie outside the bounds of the assumptions of classical thermodynamics. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. In case that objects become extremely heavy (i.e. their Schwarzschild radius is not negligibly small for a given application), deviations from Newtonian mechanics become apparent and can be quantified by using the Parameterized post-Newtonian formalism. In that case, General relativity (GR) becomes applicable. However, until now there is no theory of Quantum gravity unifying GR and QFT in the sense that it could be used when objects become extremely small and heavy.[4] [5] In special relativity, the momentum of a particle is given by where "m" is the particle's rest mass, v its velocity, "v" is the modulus of v, and "c" is the speed of light. If "v" is very small compared to "c", "v"/"c" is approximately zero, and so Thus the Newtonian equation is an approximation of the relativistic equation for bodies moving with low speeds compared to the speed of light. For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage magnetron is given by where "f" is the classical frequency of an electron (or other charged particle) with kinetic energy "T" and (rest) mass "m" circling in a magnetic field. The (rest) mass of an electron is 511 keV. So the frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current accelerating voltage. The ray approximation of classical mechanics breaks down when the de Broglie wavelength is not much smaller than other dimensions of the system. For non-relativistic particles, this wavelength is where "h" is Planck's constant and "p" is the momentum. Again, this happens with electrons before it happens with heavier particles. For example, the electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 V, had a wavelength of 0.167 nm, which was long enough to exhibit a single diffraction side lobe when reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With a larger vacuum chamber, it would seem relatively easy to increase the angular resolution from around a radian to a milliradian and see quantum diffraction from the periodic patterns of integrated circuit computer memory. More practical examples of the failure of classical mechanics on an engineering scale are conduction by quantum tunneling in tunnel diodes and very narrow transistor gates in integrated circuits. Classical mechanics is the same extreme high frequency approximation as geometric optics. It is more often accurate because it describes particles and bodies with rest mass. These have more momentum and therefore shorter De Broglie wavelengths than massless particles, such as light, with the same kinetic energies. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology, Some Greek philosophers of antiquity, among them Aristotle, founder of Aristotelian physics, may have been the first to maintain the idea that "everything happens for a reason" and that theoretical principles can assist in the understanding of nature. While to a modern reader, many of these preserved ideas come forth as eminently reasonable, there is a conspicuous lack of both mathematical theory and controlled experiment, as we know it. These later became decisive factors in forming modern science, and their early application came to be known as classical mechanics. In his "Elementa super demonstrationem ponderum", medieval mathematician Jordanus de Nemore introduced the concept of "positional gravity" and the use of component forces. The first published causal explanation of the motions of planets was Johannes Kepler's "Astronomia nova," published in 1609. He concluded, based on Tycho Brahe's observations on the orbit of Mars, that the planet's orbits were ellipses. This break with ancient thought was happening around the same time that Galileo was proposing abstract mathematical laws for the motion of objects. He may (or may not) have performed the famous experiment of dropping two cannonballs of different weights from the tower of Pisa, showing that they both hit the ground at the same time. The reality of that particular experiment is disputed, but he did carry out quantitative experiments by rolling balls on an inclined plane. His theory of accelerated motion was derived from the results of such experiments and forms a cornerstone of classical mechanics. Newton founded his principles of natural philosophy on three proposed laws of motion: the law of inertia, his second law of acceleration (mentioned above), and the law of action and reaction; and hence laid the foundations for classical mechanics. Both Newton's second and third laws were given the proper scientific and mathematical treatment in Newton's "Philosophiæ Naturalis Principia Mathematica." Here they are distinguished from earlier attempts at explaining similar phenomena, which were either incomplete, incorrect, or given little accurate mathematical expression. Newton also enunciated the principles of conservation of momentum and angular momentum. In mechanics, Newton was also the first to provide the first correct scientific and mathematical formulation of gravity in Newton's law of universal gravitation. The combination of Newton's laws of motion and gravitation provide the fullest and most accurate description of classical mechanics. He demonstrated that these laws apply to everyday objects as well as to celestial objects. In particular, he obtained a theoretical explanation of Kepler's laws of motion of the planets. Newton had previously invented the calculus, of mathematics, and used it to perform the mathematical calculations. For acceptability, his book, the "Principia", was formulated entirely in terms of the long-established geometric methods, which were soon eclipsed by his calculus. However, it was Leibniz who developed the notation of the derivative and integral preferred today. Newton, and most of his contemporaries, with the notable exception of Huygens, worked on the assumption that classical mechanics would be able to explain all phenomena, including light, in the form of geometric optics. Even when discovering the so-called Newton's rings (a wave interference phenomenon) he maintained his own corpuscular theory of light. After Newton, classical mechanics became a principal field of study in mathematics as well as physics. Several re-formulations progressively allowed finding solutions to a far greater number of problems. The first notable re-formulation was in 1788 by Joseph Louis Lagrange. Lagrangian mechanics was in turn re-formulated in 1833 by William Rowan Hamilton. Some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. Some of these difficulties related to compatibility with electromagnetic theory, and the famous Michelson–Morley experiment. The resolution of these problems led to the special theory of relativity, often still considered a part of classical mechanics. A second set of difficulties were related to thermodynamics. When combined with thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical mechanics, in which entropy is not a well-defined quantity. Black-body radiation was not explained without the introduction of quanta. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the energy levels and sizes of atoms and the photo-electric effect. The effort at resolving these problems led to the development of quantum mechanics. Since the end of the 20th century, classical mechanics in physics has no longer been an independent theory. Instead, classical mechanics is now considered an approximate theory to the more general quantum mechanics. Emphasis has shifted to understanding the fundamental forces of nature as in the Standard model and its more modern extensions into a unified theory of everything. Classical mechanics is a theory useful for the study of the motion of non-quantum mechanical, low-energy particles in weak gravitational fields. Also, it has been extended into the complex domain where complex classical mechanics exhibits behaviors very similar to quantum mechanics. Classical mechanics was traditionally divided into three main branches: Another division is based on the choice of mathematical formalism: Alternatively, a division can be made by region of application:	Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.	en	en	30	[ 250004, 250054, 581, 25632, 65508, 7, 70, 62822, 23755, 7, 111, 54704, 289, 135969, 7, 5, 1326, 134381, 939, 4, 442, 27983, 115774, 2773, 9, 32554, 36746, 7, 237, 6275, 2878, 66695, 15, 187694, 7, 678, 22024, 735, 2661, 13267, 194, 581, 78112, 111, 10, 6275, 915, 26147, 83, 62816, 29367, 390, 10, 19336, 14012, 111, 171859, 7, 12, 6863, 19069, 4, 46889, 4, 136, 70, 84616, 190659, 47, 442, 5, 98423, 111, 6097, 171859, 7, 83, 45252, 297, 23, 15504, 5, 360, 50081, 4, 70, 8562, 111, 36746, 7, 450, 54704, 289, 135969, 7, 831, 98363, 11343, 765, 10, 351, 9, 80510, 13267, 5, 15, 3957, 6, 34053, 27744, 7, 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summarize: The Greeks, including Aristotle, Vitruvius, and Pliny the Elder, were interested in the cause and mitigation of friction. They were aware of differences between static and kinetic friction with Themistius stating in 350 that "it is easier to further the motion of a moving body than to move a body at rest". The classic laws of sliding friction were discovered by Leonardo da Vinci in 1493, a pioneer in tribology, but the laws documented in his notebooks, were not published and remained unknown. These laws were rediscovered by Guillaume Amontons in 1699 and became known as Amonton's three laws of dry friction "(below)". Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together. This view was further elaborated by Bernard Forest de Bélidor and Leonhard Euler (1750), who derived the angle of repose of a weight on an inclined plane and first distinguished between static and kinetic friction. John Theophilus Desaguliers (1734) first recognized the role of adhesion in friction. Microscopic forces cause surfaces to stick together; he proposed that friction was the force necessary to tear the adhering surfaces apart. The understanding of friction was further developed by Charles-Augustin de Coulomb (1785). Coulomb investigated the influence of four main factors on friction: the nature of the materials in contact and their surface coatings; the extent of the surface area; the normal pressure (or load); and the length of time that the surfaces remained in contact (time of repose). Coulomb further considered the influence of sliding velocity, temperature and humidity, in order to decide between the different explanations on the nature of friction that had been proposed. The distinction between static and dynamic friction is made in Coulomb's friction law (see below), although this distinction was already drawn by Johann Andreas von Segner in 1758. The effect of the time of repose was explained by Pieter van Musschenbroek (1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases. John Leslie (1766–1832) noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities, why then isn't it balanced through descending the opposite slope? Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion. In Leslie's view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before. Arthur Jules Morin (1833) developed the concept of sliding versus rolling friction. Osborne Reynolds (1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering. In 1877, Fleeming Jenkin and J. A. Ewing investigated the continuity between static and kinetic friction. The focus of research during the 20th century has been to understand the physical mechanisms behind friction. Frank Philip Bowden and David Tabor (1950) showed that, at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by asperities increases with pressure. The development of the atomic force microscope (ca. 1986) enabled scientists to study friction at the atomic scale, showing that, on that scale, dry friction is the product of the inter-surface shear stress and the contact area. These two discoveries explain Amonton's first law "(below)"; the macroscopic proportionality between normal force and static frictional force between dry surfaces. L.A. Sosnovskiy, S.S. Sherbakov and V.V. Komissarov showed that the friction force is proportional to both the contact and the volumetric (tensile-compression, bending, torsion, etc.) load, if the volumetric load causes cyclic stresses (±σ) in the contact area. The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws: Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are'static friction' ("stiction") between non-moving surfaces, and "kinetic friction" (sometimes called sliding friction or dynamic friction) between moving surfaces. Coulomb friction, named after Charles-Augustin de Coulomb, is an approximate model used to calculate the force of dry friction. It is governed by the model: where The Coulomb friction formula_2 may take any value from zero up to formula_6, and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction. The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road. The normal force is defined as the net force compressing two parallel surfaces together, and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where formula_7. In this case, the magnitude of the friction force is the product of the mass of the object, the acceleration due to gravity, and the coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends only on the material. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence on the mass of the block. If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal force formula_8 between the object and the surface is just its weight, which is equal to its mass multiplied by the acceleration due to earth's gravity, "g". If the object is on a tilted surface such as an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane. Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis, usually via a free body diagram. Depending on the situation, the calculation of the normal force may include forces other than gravity. The coefficient of friction (COF), often symbolized by the Greek letter μ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one. It is an axiom of the nature of friction between metal surfaces that it is greater between two surfaces of similar metals than between two surfaces of different metals— hence, brass will have a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum. For surfaces at rest relative to each other formula_9, where formula_10 is the "coefficient of static friction". This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and surface roughness, both of which have their origins in the chemical bonding between atoms in each of the bulk materials and between the material surfaces and any adsorbed material. The fractality of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction. For surfaces in relative motion formula_11, where formula_12 is the "coefficient of kinetic friction". The Coulomb friction is equal to formula_2, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface. Arthur Morin introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an empirical measurement – it has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is "usually" larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that μ is always < 1, but this is not true. While in most relevant applications μ < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, silicone rubber or acrylic rubber-coated surfaces have a coefficient of friction that can be substantially larger than 1. While it is often stated that the COF is a "material property," it is better categorized as a "system property." Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like temperature, velocity, atmosphere and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials, namely surface structure. For example, a copper pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test. Under certain conditions some materials have very low friction coefficients. An example is (highly ordered pyrolytic) graphite which can have a friction coefficient below 0.01. This ultralow-friction regime is called superlubricity. Static friction is friction between two or more solid objects that are not moving relative to each other. For example, static friction can prevent an object from sliding down a sloped surface. The coefficient of static friction, typically denoted as "μ", is usually higher than the coefficient of kinetic friction. Static friction is considered to arise as the result of surface roughness features across multiple length-scales at solid surfaces. These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area. The linearity between applied load and true contact area, arising from asperity deformation, gives rise to the linearity between static frictional force and normal force, found for typical Amonton-Coulomb type friction. The static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: formula_14. When there is no sliding occurring, the friction force can have any value from zero up to formula_15. Any force smaller than formula_15 attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than formula_15 overcomes the force of static friction and causes sliding to occur. The instant sliding occurs, static friction is no longer applicable—the friction between the two surfaces is then called kinetic friction. An example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction. The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction, although this term is not used universally. Kinetic friction, also known as dynamic friction or sliding friction, occurs when two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as "μ", and is usually less than the coefficient of static friction for the same materials. However, Richard Feynman comments that "with dry metals it is very hard to show any difference." The friction force between two surfaces after sliding begins is the product of the coefficient of kinetic friction and the normal force: formula_18. New models are beginning to show how kinetic friction can be greater than static friction. Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities; however, in many other cases roughness effects are dominant, for example in rubber to road friction. Surface roughness and contact area affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces. The origin of kinetic friction at nanoscale can be explained by thermodynamics. Upon sliding, new surface forms at the back of a sliding true contact, and existing surface disappears at the front of it. Since all surfaces involve the thermodynamic surface energy, work must be spent in creating the new surface, and energy is released as heat in removing the surface. Thus, a force is required to move the back of the contact, and frictional heat is released at the front. For certain applications, it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the "angle of friction" or "friction angle". It is defined as: where "θ" is the angle from horizontal and "μ" is the static coefficient of friction between the objects. This formula can also be used to calculate "μ" from empirical measurements of the friction angle. Determining the forces required to move atoms past each other is a challenge in designing nanomachines. In 2008 scientists for the first time were able to move a single atom across a surface, and measure the forces required. Using ultrahigh vacuum and nearly zero temperature (5o K), a modified atomic force microscope was used to drag a cobalt atom, and a carbon monoxide molecule, across surfaces of copper and platinum. The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area; that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact); and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. It is a rule-of-thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility. Though the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems. When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, adhesive tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications. , a single study has demonstrated the potential for an "effectively negative coefficient of friction in the low-load regime", meaning that a decrease in normal force leads to an increase in friction. This contradicts everyday experience in which an increase in normal force leads to an increase in friction. This was reported in the journal "Nature" in October 2012 and involved the friction encountered by an atomic force microscope stylus when dragged across a graphene sheet in the presence of graphene-adsorbed oxygen. Despite being a simplified model of friction, the Coulomb model is useful in many numerical simulation applications such as multibody systems and granular material. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite nonlinear effects, such as the so-called Painlevé paradoxes, may be encountered with Coulomb friction. Dry friction can induce several types of instabilities in mechanical systems which display a stable behaviour in the absence of friction. These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding, by material expansion due to heat generation during friction (the thermo-elastic instabilities), or by pure dynamic effects of sliding of two elastic materials (the Adams-Martins instabilities). The latter were originally discovered in 1995 by George G. Adams and João Arménio Correia Martins for smooth surfaces and were later found in periodic rough surfaces. In particular, friction-related dynamical instabilities are thought to be responsible for brake squeal and the'song' of a glass harp, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity. A practically important case is the self-oscillation of the strings of bowed instruments such as the violin, cello, hurdy-gurdy, erhu, etc. A connection between dry friction and flutter instability in a simple mechanical system has been discovered, watch the movie for more details. Frictional instabilities can lead to the formation of new self-organized patterns (or "secondary structures") at the sliding interface, such as in-situ formed tribofilms which are utilized for the reduction of friction and wear in so-called self-lubricating materials. Fluid friction occurs between fluid layers that are moving relative to each other. This internal resistance to flow is named "viscosity". In everyday terms, the viscosity of a fluid is described as its "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. The less viscous the fluid, the greater its ease of deformation or movement. All real fluids (except superfluids) offer some resistance to shearing and therefore are viscous. For teaching and explanatory purposes it is helpful to use the concept of an inviscid fluid or an ideal fluid which offers no resistance to shearing and so is not viscous. Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. Lubrication is a technique employed to reduce wear of one or both surfaces in close proximity moving relative to each another by interposing a substance called a lubricant between the surfaces. In most cases the applied load is carried by pressure generated within the fluid due to the frictional viscous resistance to motion of the lubricating fluid between the surfaces. Adequate lubrication allows smooth continuous operation of equipment, with only mild wear, and without excessive stresses or seizures at bearings. When lubrication breaks down, metal or other components can rub destructively over each other, causing heat and possibly damage or failure. Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the area of the surface of the body that is in contact with the fluid. Skin friction follows the drag equation and rises with the square of the velocity. Skin friction is caused by viscous drag in the boundary layer around the object. There are two ways to decrease skin friction: the first is to shape the moving body so that smooth flow is possible, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as is practicable. Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation. Plastic deformation in solids is an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) an applied force or a change in temperature. The change of an object's shape is called strain. The force causing it is called stress. Elastic deformation in solids is reversible change in the internal molecular structure of an object. Stress does not necessarily cause permanent change. As deformation occurs, internal forces oppose the applied force. If the applied stress is not too large these opposing forces may completely resist the applied force, allowing the object to assume a new equilibrium state and to return to its original shape when the force is removed. This is known as elastic deformation or elasticity. As a consequence of light pressure, Einstein in 1909 predicted the existence of "radiation friction" which would oppose the movement of matter. He wrote, “radiation will exert pressure on both sides of the plate. The forces of pressure exerted on the two sides are equal if the plate is at rest. However, if it is in motion, more radiation will be reflected on the surface that is ahead during the motion (front surface) than on the back surface. The backwardacting force of pressure exerted on the front surface is thus larger than the force of pressure acting on the back. Hence, as the resultant of the two forces, there remains a force that counteracts the motion of the plate and that increases with the velocity of the plate. We will call this resultant 'radiation friction' in brief.” Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. Typical values for the coefficient of rolling resistance are 0.001. One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products. Any wheel equipped with a brake is capable of generating a large retarding force, usually for the purpose of slowing and stopping a vehicle or piece of rotating machinery. Braking friction differs from rolling friction because the coefficient of friction for rolling friction is small whereas the coefficient of friction for braking friction is designed to be large by choice of materials for brake pads. Rubbing dissimilar materials against one another can cause a build-up of electrostatic charge, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges, explosions can be caused by ignition of the flammable mixture. Belt friction is a physical property observed from the forces acting on a belt wrapped around a pulley, when one end is being pulled. The resulting tension, which acts on both ends of the belt, can be modeled by the belt friction equation. In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks. Devices such as wheels, ball bearings, roller bearings, and air cushion or other types of fluid bearings can change sliding friction into a much smaller type of rolling friction. Many thermoplastic materials such as nylon, HDPE and PTFE are commonly used in low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load. For improved wear resistance, very high molecular weight grades are usually specified for heavy duty or critical bearings. A common way to reduce friction is by using a lubricant, such as oil, water, or grease, which is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called tribology. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives. Superlubricity, a recently discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated. Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and talc; acoustic lubrication actually uses sound as a lubricant. Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as dither. According to the law of conservation of energy, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into thermal energy. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat which raises the thermal energy of the puck and the ice surface. Since heat quickly dissipates, many early philosophers, including Aristotle, wrongly concluded that moving objects lose energy without a driving force. When an object is pushed along a surface along a path C, the energy converted to heat is given by a line integral, in accordance with the definition of work where Energy lost to a system as a result of friction is a classic example of thermodynamic irreversibility. In the reference frame of the interface between two surfaces, static friction does "no" work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does "negative" work. However, friction can do "positive" work in certain frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing "positive" work. The work done by friction can translate into deformation, wear, and heat that can affect the contact surface properties (even the coefficient of friction between the surfaces). This can be beneficial as in polishing. The work of friction is used to mix and join materials such as in the process of friction welding. Excessive erosion or wear of mating sliding surfaces occurs when work due to frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces in relative motion (fretting) exacerbates wear of frictional forces. As surfaces are worn by work due to friction, fit and surface finish of an object may degrade until it no longer functions properly. For example, bearing seizure or failure may result from excessive wear due to work of friction. Friction is an important factor in many engineering disciplines.	Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. 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summarize: Gastronomy involves discovering, tasting, experiencing, researching, understanding and writing about food preparation and the sensory qualities of human nutrition as a whole. It also studies how nutrition interfaces with the broader culture. The biological and chemical basis of cooking has become known as molecular gastronomy, while gastronomy covers a much broader, interdisciplinary ground. The culinary term appears for the first time in a title in a poem by Joseph Berchoux in 1801 entitled "Gastronomie" Pascal Ory, a French historian, defines gastronomy as the establishment of rules of eating and drinking, an "art of the table," and distinguishes it from good cooking (bonne cuisine) or fine cooking (haute cuisine). Ory traces the origins of gastronomy back to the French reign of Louis XIV when people took interest in developing rules to discriminate between good and bad style and extended their thinking to define good culinary taste. The lavish and sophisticated cuisine and practices of the French court became the culinary model for the French. Alexandre Grimod de La Reyniere wrote the first gastronomic work "Almanach des gourmands (1803)" elevating the status of food discourse to a disciplined level based on his views of French tradition and morals. Grimod aimed to reestablish order lost after the revolution and institute gastronomy as a serious subject in France. Grimod expanded gastronomic literature to the three forms of the genre: the guidebook, the gastronomic treatise, and the gourmet periodical. The invention of gastronomic literature coincided with important cultural transformations in France that increased the relevance of the subject. The end of nobility in France changed how people consumed food; fewer wealthy households employed cooks and the new bourgeoisie class wanted to assert their status by consuming elitist food. The emergence of the restaurant satisfied these social needs and provided good food available for popular consumption. The center of culinary excellence in France shifted from Versailles to Paris, a city with a competitive and innovative culinary culture. The culinary commentary of Grimod and other gastronomes influenced the tastes and expectations of consumers in an unprecedented manner as a third party to the consumer-chef interaction. The French origins of gastronomy explain the widespread use of French terminology in gastronomic literature. Gastronomic literature, Pascal Ory criticizes, is conceptually vague relying heavily on anecdotal evidence and using confusing, poorly defined terminology. Despite Ory’s criticism, gastronomy has grown from a marginalized subject in France to a serious and popular interest worldwide. The derivative "gourmet" has come into use since the publication of the book by Brillat-Savarin, "The Physiology of Taste". According to Brillat-Savarin, "Gastronomy is the knowledge and understanding of all that relates to man as he eats. Its purpose is to ensure the conservation of men, using the best food possible." Many writings on gastronomy throughout the world capture the thoughts and esthetics of a culture's cuisine during a period in their history. Some works continue to define or influence the contemporary gastronomic thought and cuisine of their respective cultures as listed below:	Gastronomy is the study of the relationship between food and culture, the art of preparing and serving rich or delicate and appetizing food, the cooking styles of particular regions, and the science of good eating. One who is well versed in gastronomy is called a gastronome, while a gastronomist is one who unites theory and practice in the study of gastronomy. Practical gastronomy is associated with the practice and study of the preparation, production, and service of the various foods and beverages, from countries around the world. Theoretical gastronomy supports practical gastronomy. It is related with a system and process approach, focused on recipes, techniques and cookery books. Food gastronomy is connected with food and beverages and their genesis. 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summarize: The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in "Cartesian frame of reference". Sometimes the state of motion is emphasized, as in "rotating frame of reference". Sometimes the way it transforms to frames considered as related is emphasized as in "Galilean frame of reference". Sometimes frames are distinguished by the scale of their observations, as in "macroscopic" and "microscopic frames of reference". In this article, the term "observational frame of reference" is used when emphasis is upon the "state of motion" rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a "coordinate system" may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs "generalized coordinates", "normal modes" or "eigenvectors", which are only indirectly related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below: Here is a quotation applicable to moving observational frames formula_1 and various associated Euclidean three-space coordinate systems ["R", "R′", "etc."]: and this on the utility of separating the notions of formula_1 and ["R", "R′", "etc."]: and this, also on the distinction between formula_1 and ["R", "R′", "etc."]: and from J. D. Norton: The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani. Extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, and quantum gravity. Although the term "coordinate system" is often used (particularly by physicists) in a nontechnical sense, the term "coordinate system" does have a precise meaning in mathematics, and sometimes that is what the physicist means as well. A coordinate system in mathematics is a facet of geometry or of algebra, in particular, a property of manifolds (for example, in physics, configuration spaces or phase spaces). The coordinates of a point r in an "n"-dimensional space are simply an ordered set of "n" numbers: In a general Banach space, these numbers could be (for example) coefficients in a functional expansion like a Fourier series. In a physical problem, they could be spacetime coordinates or normal mode amplitudes. In a robot design, they could be angles of relative rotations, linear displacements, or deformations of joints. Here we will suppose these coordinates can be related to a Cartesian coordinate system by a set of functions: where "x", "y", "z", "etc." are the "n" Cartesian coordinates of the point. Given these functions, coordinate surfaces are defined by the relations: The intersection of these surfaces define coordinate lines. At any selected point, tangents to the intersecting coordinate lines at that point define a set of basis vectors {e, e,..., e} at that point. That is: which can be normalized to be of unit length. For more detail see curvilinear coordinates. Coordinate surfaces, coordinate lines, and basis vectors are components of a coordinate system. If the basis vectors are orthogonal at every point, the coordinate system is an orthogonal coordinate system. An important aspect of a coordinate system is its metric tensor "g", which determines the arc length "ds" in the coordinate system in terms of its coordinates: where repeated indices are summed over. As is apparent from these remarks, a coordinate system is a mathematical construct, part of an axiomatic system. There is no necessary connection between coordinate systems and physical motion (or any other aspect of reality). However, coordinate systems can include time as a coordinate, and can be used to describe motion. Thus, Lorentz transformations and Galilean transformations may be viewed as coordinate transformations. General and specific topics of coordinate systems can be pursued following the See also links below. An observational frame of reference, often referred to as a "physical frame of reference", a "frame of reference", or simply a "frame", is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized "only by its state of motion". However, there is lack of unanimity on this point. In special relativity, the distinction is sometimes made between an "observer" and a "frame". According to this view, a "frame" is an "observer" plus a coordinate lattice constructed to be an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector. See Doran. This restricted view is not used here, and is not universally adopted even in discussions of relativity. In general relativity the use of general coordinate systems is common (see, for example, the Schwarzschild solution for the gravitational field outside an isolated sphere). There are two types of observational reference frame: inertial and non-inertial. An inertial frame of reference is defined as one in which all laws of physics take on their simplest form. In special relativity these frames are related by Lorentz transformations, which are parametrized by rapidity. In Newtonian mechanics, a more restricted definition requires only that Newton's first law holds true; that is, a Newtonian inertial frame is one in which a free particle travels in a straight line at constant speed, or is at rest. These frames are related by Galilean transformations. These relativistic and Newtonian transformations are expressed in spaces of general dimension in terms of representations of the Poincaré group and of the Galilean group. In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations. An example is an observational frame of reference centered at a point on the Earth's surface. This frame of reference orbits around the center of the Earth, which introduces the fictitious forces known as the Coriolis force, centrifugal force, and gravitational force. (All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall.) A further aspect of a frame of reference is the role of the measurement apparatus (for example, clocks and rods) attached to the frame (see Norton quote above). This question is not addressed in this article, and is of particular interest in quantum mechanics, where the relation between observer and measurement is still under discussion (see measurement problem). In physics experiments, the frame of reference in which the laboratory measurement devices are at rest is usually referred to as the laboratory frame or simply "lab frame." An example would be the frame in which the detectors for a particle accelerator are at rest. The lab frame in some experiments is an inertial frame, but it is not required to be (for example the laboratory on the surface of the Earth in many physics experiments is not inertial). In particle physics experiments, it is often useful to transform energies and momenta of particles from the lab frame where they are measured, to the center of momentum frame "COM frame" in which calculations are sometimes simplified, since potentially all kinetic energy still present in the COM frame may be used for making new particles. In this connection it may be noted that the clocks and rods often used to describe observers' measurement equipment in thought, in practice are replaced by a much more complicated and indirect metrology that is connected to the nature of the vacuum, and uses atomic clocks that operate according to the standard model and that must be corrected for gravitational time dilation. (See second, meter and kilogram). In fact, Einstein felt that clocks and rods were merely expedient measuring devices and they should be replaced by more fundamental entities based upon, for example, atoms and molecules. Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities. See Figure 1. At some particular moment, they are separated by 200 metres. The car in front is travelling at 22 metres per second and the car behind is travelling at 30 metres per second. If we want to find out how long it will take the second car to catch up with the first, there are three obvious "frames of reference" that we could choose. First, we could observe the two cars from the side of the road. We define our "frame of reference" "S" as follows. We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance apart. Since neither of the cars is accelerating, we can determine their positions by the following formulas, where formula_9 is the position in meters of car one after time "t" in seconds and formula_10 is the position of car two after time "t". Notice that these formulas predict at "t" = 0 s the first car is 200 m down the road and the second car is right beside us, as expected. We want to find the time at which formula_12. Therefore, we set formula_12 and solve for formula_14, that is: Alternatively, we could choose a frame of reference "S′" situated in the first car. In this case, the first car is stationary and the second car is approaching from behind at a speed of. In order to catch up to the first car, it will take a time of, that is, 25 seconds, as before. Note how much easier the problem becomes by choosing a suitable frame of reference. The third possible frame of reference would be attached to the second car. That example resembles the case just discussed, except the second car is stationary and the first car moves backward towards it at. It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily. It is also necessary to note that one is able to convert measurements made in one coordinate system to another. For example, suppose that your watch is running five minutes fast compared to the local standard time. If you know that this is the case, when somebody asks you what time it is, you are able to deduct five minutes from the time displayed on your watch in order to obtain the correct time. The measurements that an observer makes about a system depend therefore on the observer's frame of reference (you might say that the bus arrived at 5 past three, when in fact it arrived at three). For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving towards the right. However, for the person facing west, the car was moving toward the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system. For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the -axis and the direction in front of him as the positive -axis. To him, the car moves along the axis with some velocity in the positive -direction. Alfred's frame of reference is considered an inertial frame of reference because he is not accelerating (ignoring effects such as Earth's rotation and gravity). Now consider Betsy, the person driving the car. Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive -axis, and the direction in front of her as the positive -axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving – for instance, as she drives past Alfred, she observes him moving with velocity in the negative -direction. If she is driving north, then north is the positive -direction; if she turns east, east becomes the positive -direction. Finally, as an example of non-inertial observers, assume Candace is accelerating her car. As she passes by him, Alfred measures her acceleration and finds it to be in the negative -direction. Assuming Candace's acceleration is constant, what acceleration does Betsy measure? If Betsy's velocity is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same as Alfred in her frame of reference, in the negative -direction. However, if she is accelerating at rate in the negative -direction (in other words, slowing down), she will find Candace's acceleration to be in the negative -direction—a smaller value than Alfred has measured. Similarly, if she is accelerating at rate "A" in the positive -direction (speeding up), she will observe Candace's acceleration as in the negative -direction—a larger value than Alfred's measurement. Frames of reference are especially important in special relativity, because when a frame of reference is moving at some significant fraction of the speed of light, then the flow of time in that frame does not necessarily apply in another frame. The speed of light is considered to be the only true constant between moving frames of reference. It is important to note some assumptions made above about the various inertial frames of reference. Newton, for instance, employed universal time, as explained by the following example. Suppose that you own two clocks, which both tick at exactly the same rate. You synchronize them so that they both display exactly the same time. The two clocks are now separated and one clock is on a fast moving train, traveling at constant velocity towards the other. According to Newton, these two clocks will still tick at the same rate and will both show the same time. Newton says that the rate of time as measured in one frame of reference should be the same as the rate of time in another. That is, there exists a "universal" time and all other times in all other frames of reference will run at the same rate as this universal time irrespective of their position and velocity. This concept of time and simultaneity was later generalized by Einstein in his special theory of relativity (1905) where he developed transformations between inertial frames of reference based upon the universal nature of physical laws and their economy of expression (Lorentz transformations). The definition of inertial reference frame can also be extended beyond three-dimensional Euclidean space. Newton's assumed a Euclidean space, but general relativity uses a more general geometry. As an example of why this is important, consider the geometry of an ellipsoid. In this geometry, a "free" particle is defined as one at rest or traveling at constant speed on a geodesic path. Two free particles may begin at the same point on the surface, traveling with the same constant speed in different directions. After a length of time, the two particles collide at the opposite side of the ellipsoid. Both "free" particles traveled with a constant speed, satisfying the definition that no forces were acting. No acceleration occurred and so Newton's first law held true. This means that the particles were in inertial frames of reference. Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again. In a similar way, it is now common to describe that we exist in a four-dimensional geometry known as spacetime. In this picture, the curvature of this 4D space is responsible for the way in which two bodies with mass are drawn together even if no forces are acting. This curvature of spacetime replaces the force known as gravity in Newtonian mechanics and special relativity. Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below. An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g. "x′", "y′", "a′". The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R. Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called r, and the vector from the accelerated origin to the point is called r′. From the geometry of the situation, we get Taking the first and second derivatives of this with respect to time, we obtain where V and A are the velocity and acceleration of the accelerated system with respect to the inertial system and v and a are the velocity and acceleration of the point of interest with respect to the inertial frame. These equations allow transformations between the two coordinate systems; for example, we can now write Newton's second law as When there is accelerated motion due to a force being exerted there is manifestation of inertia. If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia. However, the manifestation of inertia does not prevent acceleration (or deceleration), for manifestation of inertia occurs in response to change in velocity due to a force. Seen from the perspective of a rotating frame of reference the manifestation of inertia appears to exert a force (either in centrifugal direction, or in a direction orthogonal to an object's motion, the Coriolis effect). A common sort of accelerated reference frame is a frame that is both rotating and translating (an example is a frame of reference attached to a CD which is playing while the player is carried). This arrangement leads to the equation (see Fictitious force for a derivation): or, to solve for the acceleration in the accelerated frame, Multiplying through by the mass "m" gives where	In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements within that frame.	en	en	43	[ 250004, 250054, 581, 3871, 47, 157167, 1495, 17721, 70, 67842, 91084, 7, 111, 44, 160328, 111, 91067, 58, 1556, 12441, 47, 10, 96551, 111, 69407, 5, 1326, 27781, 4, 68018, 70, 10644, 111, 176866, 13, 5426, 83, 220642, 237, 10, 158254, 4, 237, 23, 44, 21851, 67, 39209, 123789, 111, 91067, 740, 160193, 70, 11341, 111, 78112, 83, 20244, 10557, 29367, 4, 237, 23, 44, 109645, 1916, 123789, 111, 91067, 740, 160193, 70, 3917, 442, 27198, 7, 47, 2674, 90, 90698, 237, 62548, 83, 20244, 10557, 29367, 237, 23, 44, 70696, 1340, 66, 123789, 111, 91067, 740, 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summarize: The adjective "Cartesian" refers to the French mathematician and philosopher René Descartes, who published this idea in 1637. It was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. The French cleric Nicole Oresme used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat. Both Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes' "La Géométrie" was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes' work. The development of the Cartesian coordinate system would play a fundamental role in the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space. Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point "O" of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by "O" is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point "P" of the line can be specified by its distance from "O", taken with a + or − sign depending on which half-line contains "P". A line with a chosen Cartesian system is called a number line. Every real number has a unique location on the line. Conversely, every point on the line can be interpreted as a number in an ordered continuum such as the real numbers. A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For any point "P", a line is drawn through "P" perpendicular to each axis, and the position where it meets the axis is interpreted as a number. The two numbers, in that chosen order, are the "Cartesian coordinates" of "P". The reverse construction allows one to determine the point "P" given its coordinates. The first and second coordinates are called the "abscissa" and the "ordinate" of "P", respectively; and the point where the axes meet is called the "origin" of the coordinate system. The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in. Thus the origin has coordinates, and the points on the positive half-axes, one unit away from the origin, have coordinates and. In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards. (However, in some computer graphics contexts, the ordinate axis may be oriented downwards.) The origin is often labeled "O", and the two coordinates are often denoted by the letters "X" and "Y", or "x" and "y". The axes may then be referred to as the "X"-axis and "Y"-axis. The choices of letters come from the original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values. A Euclidean plane with a chosen Cartesian coordinate system is called a "Cartesian plane". In a Cartesian plane one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at and ), the unit hyperbola, and so on. The two axes divide the plane into four right angles, called "quadrants". The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the "first quadrant". If the coordinates of a point are, then its distances from the "X"-axis and from the "Y"-axis are \|"y"\| and \|"x"\|, respectively; where \|...\| denotes the absolute value of a number. A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines (the "axes") that go through a common point (the "origin"), and are pair-wise perpendicular; an orientation for each axis; and a single unit of length for all three axes. As in the two-dimensional case, each axis becomes a number line. For any point "P" of space, one considers a hyperplane through "P" perpendicular to each coordinate axis, and interprets the point where that hyperplane cuts the axis as a number. The Cartesian coordinates of "P" are those three numbers, in the chosen order. The reverse construction determines the point "P" given its three coordinates. Alternatively, each coordinate of a point "P" can be taken as the distance from "P" to the hyperplane defined by the other two axes, with the sign determined by the orientation of the corresponding axis. Each pair of axes defines a "coordinate hyperplane". These hyperplanes divide space into eight trihedra, called "octants". The octants are: \| (+x,+y,+z) \| (-x,+y,+z) \| (+x,+y,-z) \| (-x,+y,-z) \| (+x,-y,+z) \| (-x,-y,+z) \| (+x,-y,-z) \| (-x,-y,-z) \| The coordinates are usually written as three numbers (or algebraic formulas) surrounded by parentheses and separated by commas, as in or. Thus, the origin has coordinates, and the unit points on the three axes are,, and. There are no standard names for the coordinates in the three axes (however, the terms "abscissa", "ordinate" and "applicate" are sometimes used). The coordinates are often denoted by the letters "X", "Y", and "Z", or "x", "y", and "z". The axes may then be referred to as the "X"-axis, "Y"-axis, and "Z"-axis, respectively. Then the coordinate hyperplanes can be referred to as the "XY"-plane, "YZ"-plane, and "XZ"-plane. In mathematics, physics, and engineering contexts, the first two axes are often defined or depicted as horizontal, with the third axis pointing up. In that case the third coordinate may be called "height" or "altitude". The orientation is usually chosen so that the 90 degree angle from the first axis to the second axis looks counter-clockwise when seen from the point ; a convention that is commonly called "the right hand rule". Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product formula_1, where formula_2 is the set of all real numbers. In the same way, the points in any Euclidean space of dimension "n" be identified with the tuples (lists) of "n" real numbers, that is, with the Cartesian product formula_3. The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see affine plane). The Cartesian coordinates of a point are usually written in parentheses and separated by commas, as in or. The origin is often labelled with the capital letter "O". In analytic geometry, unknown or generic coordinates are often denoted by the letters ("x", "y") in the plane, and ("x", "y", "z") in three-dimensional space. This custom comes from a convention of algebra, which uses letters near the end of the alphabet for unknown values (such as the coordinates of points in many geometric problems), and letters near the beginning for given quantities. These conventional names are often used in other domains, such as physics and engineering, although other letters may be used. For example, in a graph showing how a pressure varies with time, the graph coordinates may be denoted "p" and "t". Each axis is usually named after the coordinate which is measured along it; so one says the "x-axis", the "y-axis", the "t-axis", etc. Another common convention for coordinate naming is to use subscripts, as ("x", "x",..., "x") for the "n" coordinates in an "n"-dimensional space, especially when "n" is greater than 3 or unspecified. Some authors prefer the numbering ("x", "x",..., "x"). These notations are especially advantageous in computer programming: by storing the coordinates of a point as an array, instead of a record, the subscript can serve to index the coordinates. In mathematical illustrations of two-dimensional Cartesian systems, the first coordinate (traditionally called the abscissa) is measured along a horizontal axis, oriented from left to right. The second coordinate (the ordinate) is then measured along a vertical axis, usually oriented from bottom to top. Young children learning the Cartesian system, commonly learn the order to read the values before cementing the "x"-, "y"-, and "z"-axis concepts, by starting with 2D mnemonics (e.g. 'Walk along the hall then up the stairs' akin to straight across the "x"-axis then up vertically along the "y"-axis). Computer graphics and image processing, however, often use a coordinate system with the "y"-axis oriented downwards on the computer display. This convention developed in the 1960s (or earlier) from the way that images were originally stored in display buffers. For three-dimensional systems, a convention is to portray the "xy"-plane horizontally, with the "z"-axis added to represent height (positive up). Furthermore, there is a convention to orient the "x"-axis toward the viewer, biased either to the right or left. If a diagram (3D projection or 2D perspective drawing) shows the "x"- and "y"-axis horizontally and vertically, respectively, then the "z"-axis should be shown pointing "out of the page" towards the viewer or camera. In such a 2D diagram of a 3D coordinate system, the "z"-axis would appear as a line or ray pointing down and to the left or down and to the right, depending on the presumed viewer or camera perspective. In any diagram or display, the orientation of the three axes, as a whole, is arbitrary. However, the orientation of the axes relative to each other should always comply with the right-hand rule, unless specifically stated otherwise. All laws of physics and math assume this right-handedness, which ensures consistency. For 3D diagrams, the names "abscissa" and "ordinate" are rarely used for "x" and "y", respectively. When they are, the "z"-coordinate is sometimes called the applicate. The words "abscissa", "ordinate" and "applicate" are sometimes used to refer to coordinate axes rather than the coordinate values. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are I (+,+), II (−,+), III (−,−), and IV (+,−). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("north-east") quadrant. Similarly, a three-dimensional Cartesian system defines a division of space into eight regions or octants, according to the signs of the coordinates of the points. The convention used for naming a specific octant is to list its signs, e.g. or. The generalization of the quadrant and octant to an arbitrary number of dimensions is the orthant, and a similar naming system applies. The Euclidean distance between two points of the plane with Cartesian coordinates formula_4 and formula_5 is This is the Cartesian version of Pythagoras's theorem. In three-dimensional space, the distance between points formula_7 and formula_8 is which can be obtained by two consecutive applications of Pythagoras' theorem. The Euclidean transformations or Euclidean motions are the (bijective) mappings of points of the Euclidean plane to themselves which preserve distances between points. There are four types of these mappings (also called isometries): translations, rotations, reflections and glide reflections. Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers to the Cartesian coordinates of every point in the set. That is, if the original coordinates of a point are, after the translation they will be To rotate a figure counterclockwise around the origin by some angle formula_11 is equivalent to replacing every point with coordinates ("x","y") by the point with coordinates ("x<nowiki>'</nowiki>","y<nowiki>'</nowiki>"), where Thus: formula_14 If are the Cartesian coordinates of a point, then are the coordinates of its reflection across the second coordinate axis (the y-axis), as if that line were a mirror. Likewise, are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle formula_11 with the x-axis, is equivalent to replacing every point with coordinates by the point with coordinates, where Thus: formula_18 A glide reflection is the composition of a reflection across a line followed by a translation in the direction of that line. It can be seen that the order of these operations does not matter (the translation can come first, followed by the reflection). These Euclidean transformations of the plane can all be described in a uniform way by using matrices. The result formula_19 of applying a Euclidean transformation to a point formula_20 is given by the formula where "A" is a 2×2 orthogonal matrix and is an arbitrary ordered pair of numbers; that is, where To be "orthogonal", the matrix "A" must have orthogonal rows with same Euclidean length of one, that is, and This is equivalent to saying that "A" times its transpose must be the identity matrix. If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of "A" is not zero. The formula defines a translation if and only if "A" is the identity matrix. The transformation is a rotation around some point if and only if "A" is a rotation matrix, meaning that A reflection or glide reflection is obtained when, Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices. Another way to represent coordinate transformations in Cartesian coordinates is through affine transformations. In affine transformations an extra dimension is added and all points are given a value of 1 for this extra dimension. The advantage of doing this is that point translations can be specified in the final column of matrix "A". In this way, all of the euclidean transformations become transactable as matrix point multiplications. The affine transformation is given by: Using affine transformations multiple different euclidean transformations including translation can be combined by simply multiplying the corresponding matrices. An example of an affine transformation which is not a Euclidean motion is given by scaling. To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number "m". If are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates If "m" is greater than 1, the figure becomes larger; if "m" is between 0 and 1, it becomes smaller. A shearing transformation will push the top of a square sideways to form a parallelogram. Horizontal shearing is defined by: Shearing can also be applied vertically: Fixing or choosing the "x"-axis determines the "y"-axis up to direction. Namely, the "y"-axis is necessarily the perpendicular to the "x"-axis through the point marked 0 on the "x"-axis. But there is a choice of which of the two half lines on the perpendicular to designate as positive and which as negative. Each of these two choices determines a different orientation (also called "handedness") of the Cartesian plane. The usual way of orienting the plane, with the positive "x"-axis pointing right and the positive "y"-axis pointing up (and the "x"-axis being the "first" and the "y"-axis the "second" axis), is considered the "positive" or "standard" orientation, also called the "right-handed" orientation. A commonly used mnemonic for defining the positive orientation is the "right-hand rule". Placing a somewhat closed right hand on the plane with the thumb pointing up, the fingers point from the "x"-axis to the "y"-axis, in a positively oriented coordinate system. The other way of orienting the plane is following the "left hand rule", placing the left hand on the plane with the thumb pointing up. When pointing the thumb away from the origin along an axis towards positive, the curvature of the fingers indicates a positive rotation along that axis. Regardless of the rule used to orient the plane, rotating the coordinate system will preserve the orientation. Switching any two axes will reverse the orientation, but switching both will leave the orientation unchanged. Once the "x"- and "y"-axes are specified, they determine the line along which the "z"-axis should lie, but there are two possible orientation for this line. The two possible coordinate systems which result are called 'right-handed' and 'left-handed'. The standard orientation, where the "xy"-plane is horizontal and the "z"-axis points up (and the "x"- and the "y"-axis form a positively oriented two-dimensional coordinate system in the "xy"-plane if observed from "above" the "xy"-plane) is called right-handed or positive. The name derives from the right-hand rule. If the index finger of the right hand is pointed forward, the middle finger bent inward at a right angle to it, and the thumb placed at a right angle to both, the three fingers indicate the relative orientation of the "x"-, "y"-, and "z"-axes in a "right-handed" system. The thumb indicates the "x"-axis, the index finger the "y"-axis and the middle finger the "z"-axis. Conversely, if the same is done with the left hand, a left-handed system results. Figure 7 depicts a left and a right-handed coordinate system. Because a three-dimensional object is represented on the two-dimensional screen, distortion and ambiguity result. The axis pointing downward (and to the right) is also meant to point "towards" the observer, whereas the "middle"-axis is meant to point "away" from the observer. The red circle is "parallel" to the horizontal "xy"-plane and indicates rotation from the "x"-axis to the "y"-axis (in both cases). Hence the red arrow passes "in front of" the "z"-axis. Figure 8 is another attempt at depicting a right-handed coordinate system. Again, there is an ambiguity caused by projecting the three-dimensional coordinate system into the plane. Many observers see Figure 8 as "flipping in and out" between a convex cube and a concave "corner". This corresponds to the two possible orientations of the space. Seeing the figure as convex gives a left-handed coordinate system. Thus the "correct" way to view Figure 8 is to imagine the "x"-axis as pointing "towards" the observer and thus seeing a concave corner. A point in space in a Cartesian coordinate system may also be represented by a position vector, which can be thought of as an arrow pointing from the origin of the coordinate system to the point. If the coordinates represent spatial positions (displacements), it is common to represent the vector from the origin to the point of interest as formula_33. In two dimensions, the vector from the origin to the point with Cartesian coordinates (x, y) can be written as: where formula_35, and formula_36 are unit vectors in the direction of the "x"-axis and "y"-axis respectively, generally referred to as the "standard basis" (in some application areas these may also be referred to as versors). Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates formula_37 can be written as: where formula_39 is the unit vector in the direction of the z-axis. There is no "natural" interpretation of multiplying vectors to obtain another vector that works in all dimensions, however there is a way to use complex numbers to provide such a multiplication. In a two dimensional cartesian plane, identify the point with coordinates with the complex number. Here, i is the imaginary unit and is identified with the point with coordinates, so it is not the unit vector in the direction of the "x"-axis. Since the complex numbers can be multiplied giving another complex number, this identification provides a means to "multiply" vectors. In a three dimensional cartesian space a similar identification can be made with a subset of the quaternions. Cartesian coordinates are an abstraction that have a multitude of possible applications in the real world. However, three constructive steps are involved in superimposing coordinates on a problem application. 1) Units of distance must be decided defining the spatial size represented by the numbers used as coordinates. 2) An origin must be assigned to a specific spatial location or landmark, and 3) the orientation of the axes must be defined using available directional cues for all but one axis. Consider as an example superimposing 3D Cartesian coordinates over all points on the Earth (i.e. geospatial 3D). What units make sense? Kilometers are a good choice, since the original definition of the kilometer was geospatial—10 000 km equaling the surface distance from the Equator to the North Pole. Where to place the origin? Based on symmetry, the gravitational center of the Earth suggests a natural landmark (which can be sensed via satellite orbits). Finally, how to orient X-, Y- and Z-axis? The axis of Earth's spin provides a natural orientation strongly associated with "up vs. down", so positive Z can adopt the direction from geocenter to North Pole. A location on the Equator is needed to define the X-axis, and the prime meridian stands out as a reference orientation, so the X-axis takes the orientation from geocenter out to 0 degrees longitude, 0 degrees latitude. Note that with three dimensions, and two perpendicular axes orientations pinned down for X and Z, the Y-axis is determined by the first two choices. In order to obey the right-hand rule, the Y-axis must point out from the geocenter to 90 degrees longitude, 0 degrees latitude. So what are the geocentric coordinates of the Empire State Building in New York City? From a longitude of −73.985656 degrees, a latitude 40.748433 degrees, and Earth radius of 40,000/2π km, and transforming from spherical to Cartesian coordinates, you can estimate the geocentric coordinates of the Empire State Building, ("x", "y", "z") = (1330.53 km, –4635.75 km, 4155.46 km). GPS navigation relies on such geocentric coordinates. In engineering projects, agreement on the definition of coordinates is a crucial foundation. One cannot assume that coordinates come predefined for a novel application, so knowledge of how to erect a coordinate system where there is none is essential to applying René Descartes' thinking. While spatial applications employ identical units along all axes, in business and scientific applications, each axis may have different units of measurement associated with it (such as kilograms, seconds, pounds, etc.). Although four- and higher-dimensional spaces are difficult to visualize, the algebra of Cartesian coordinates can be extended relatively easily to four or more variables, so that certain calculations involving many variables can be done. (This sort of algebraic extension is what is used to define the geometry of higher-dimensional spaces.) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables. The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, "f", the set of all points, where is the graph of the function "f". For a function "g" of two variables, the set of all points, where is the graph of the function "g". A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.	A Cartesian coordinate system (, ) is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a "coordinate axis" or just "axis" (plural "axes") of the system, and the point where they meet is its "origin", at ordered pair. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.	en	en	119	[ 250004, 250054, 581, 606, 170, 100034, 44, 21851, 67, 39209, 58, 15005, 7, 47, 70, 92265, 48909, 13, 47148, 3378, 136, 6, 119598, 56, 157370, 68320, 10845, 7, 4, 2750, 91376, 903, 6528, 23, 611, 10945, 5, 1650, 509, 41371, 538, 134053, 390, 58807, 8, 8002, 2227, 4, 2750, 2843, 79786, 23, 17262, 158208, 4, 102971, 8002, 2227, 6777, 959, 80299, 70, 103882, 53, 5, 581, 92265, 181186, 121220, 86380, 12746, 11814, 50961, 7, 21373, 47, 106274, 39209, 176866, 90, 5299, 8108, 70, 1733, 111, 68320, 10845, 7, 136, 8002, 2227, 5, 149766, 68320, 10845, 7, 136, 8002, 2227, 11814, 10, 11001, 10, 33102, 23, 2363, 39734, 7, 136, 765, 10, 77336, 140909, 72350, 71, 23, 91067, 47, 903, 10, 33102, 5, 581, 23755, 111, 17368, 10, 80836, 111, 10, 31195, 509, 65508, 71, 14432, 4, 7103, 68320, 10845, 7, 25, 44, 2729, 71774, 306, 2305, 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summarize: In the simplest case of circular motion at radius formula_2, with position given by the angular displacement formula_3 from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: formula_4. If formula_5 is measured in radians, the arc-length from the positive x-axis around the circle to the particle is formula_6, and the linear velocity is formula_7, so that formula_8. In the general case of a particle moving in the plane, the orbital angular velocity is the rate at which the position vector relative to a chosen origin "sweeps out" angle. The diagram shows the position vector formula_9 from the origin formula_10 to a particle formula_11, with its polar coordinates formula_12. (All variables are functions of time formula_13.) The particle has linear velocity splitting as formula_14, with the radial component formula_15 parallel to the radius, and the cross-radial (or tangential) component formula_16 perpendicular to the radius. When there is no radial component, the particle moves around the origin in a circle; but when there is no cross-radial component, it moves in a straight line from the origin. Since radial motion leaves the angle unchanged, only the cross-radial component of linear velocity contributes to angular velocity. The angular velocity "ω" is the rate of change of angular position with respect to time, which can be computed from the cross-radial velocity as: Here the cross-radial speed formula_18 is the signed magnitude of formula_16, positive for counter-clockwise motion, negative for clockwise. Taking polar coordinates for the linear velocity formula_20 gives magnitude formula_21 (linear speed) and angle formula_22 relative to the radius vector; in these terms, formula_23, so that These formulas may be derived from formula_25, formula_26 and formula_27, together with the projection formula formula_28, where formula_29. In two dimensions, angular velocity is a number with plus or minus sign indicating orientation, but not pointing in a direction. The sign is conventionally taken to be positive if the radius vector turns counter-clockwise, and negative if clockwise. Angular velocity then may be termed a pseudoscalar, a numerical quantity which changes sign under a parity inversion, such as inverting one axis or switching the two axes. In three-dimensional space, we again have the position vector r of a moving particle. Here, orbital angular velocity is a pseudovector whose magnitude is the rate at which r sweeps out angle, and whose direction is perpendicular to the instantaneous plane in which r sweeps out angle (i.e. the plane spanned by r and v). However, as there are "two" directions perpendicular to any plane, an additional condition is necessary to uniquely specify the direction of the angular velocity; conventionally, the right-hand rule is used. Let the pseudovector formula_30 be the unit vector perpendicular to the plane spanned by r and v, so that the right-hand rule is satisfied (i.e. the instantaneous direction of angular displacement is counter-clockwise looking from the top of formula_30). Taking polar coordinates formula_32 in this plane, as in the two-dimensional case above, one may define the orbital angular velocity vector as: where "θ" is the angle between r and v. In terms of the cross product, this is: From the above equation, one can recover the tangential velocity as: If a point rotates with orbital angular velocity formula_36 about its center of rotation in a coordinate frame formula_37 which itself rotates with a spin angular velocity formula_38 with respect to an external frame formula_39, we can define formula_40 to be the composite orbital angular velocity vector of the point about its center of rotation with respect to formula_39. This operation coincides with usual addition of vectors, and it gives angular velocity the algebraic structure of a true vector, rather than just a pseudo-vector. The only non-obvious property of the above addition is commutativity. This can be proven from the fact that the velocity tensor "W" (see below) is skew-symmetric, so that formula_42 is a rotation matrix which can be expanded as formula_43. The composition of rotations is not commutative, but formula_44 is commutative to first order, and therefore formula_45. Notice that this also defines the subtraction as the addition of a negative vector. Given a rotating frame of three unit coordinate vectors, all the three must have the same angular speed at each instant. In such a frame, each vector may be considered as a moving particle with constant scalar radius. The rotating frame appears in the context of rigid bodies, and special tools have been developed for it: the spin angular velocity may be described as a vector or equivalently as a tensor. Consistent with the general definition, the spin angular velocity of a frame is defined as the orbital angular velocity of any of the three vectors (same for all) with respect to its own centre of rotation. The addition of angular velocity vectors for frames is also defined by the usual vector addition (composition of linear movements), and can be useful to decompose the rotation as in a gimbal. All components of the vector can be calculated as derivatives of the parameters defining the moving frames (Euler angles or rotation matrices). As in the general case, addition is commutative: formula_45. By Euler's rotation theorem, any rotating frame possesses an instantaneous axis of rotation, which is the direction of the angular velocity vector, and the magnitude of the angular velocity is consistent with the two-dimensional case. Considering a coordinate vector of the frame as a particle, formula_47 with formula_48, we obtain the orbital angular velocity vector: Here formula_50 are the columns of the matrix of the frame, and formula_51 their time derivatives. The components of the spin angular velocity pseudovector were first calculated by Leonhard Euler using his Euler angles and the use of an intermediate frame: Euler proved that the projections of the angular velocity pseudovector on each of these three axes is the derivative of its associated angle (which is equivalent to decomposing the instantaneous rotation into three instantaneous Euler rotations). Therefore: This basis is not orthonormal and it is difficult to use, but now the velocity vector can be changed to the fixed frame or to the moving frame with just a change of bases. For example, changing to the mobile frame: where formula_54 are unit vectors for the frame fixed in the moving body. This example has been made using the Z-X-Z convention for Euler angles. The angular velocity vector formula_55 defined above may be equivalently expressed as an angular velocity tensor, the matrix (or linear mapping) "W" = "W"("t") defined by: This is an infinitesimal rotation matrix. The linear mapping "W" acts as formula_57: A vector formula_59 undergoing uniform circular motion around an axis satisfies: Given the orientation matrix "A"("t") of a frame, whose columns are the moving orthonormal coordinate vectors formula_61, we can obtain its angular velocity tensor "W"("t") as follows. Angular velocity must be the same for the three vectors formula_62, so arranging the three vector equations into columns of a matrix, we have: (This holds even if "A"("t") does not rotate uniformly.) Therefore the angular velocity tensor is: since the inverse of the orthogonal matrix formula_65 is its transpose formula_66. In general, the angular velocity in an "n"-dimensional space is the time derivative of the angular displacement tensor, which is a second rank skew-symmetric tensor. This tensor "W" will have independent components, which is the dimension of the Lie algebra of the Lie group of rotations of an "n"-dimensional inner product space. In three dimensions, angular velocity can be represented by a pseudovector because second rank tensors are dual to pseudovectors in three dimensions. Since the angular velocity tensor "W" = "W"("t") is a skew-symmetric matrix: its Hodge dual is a vector, which is precisely the previous angular velocity vector formula_68. If we know an initial frame "A"(0) and we are given a "constant" angular velocity tensor "W", we can obtain "A"("t") for any given "t". Recall the matrix differential equation: This equation can be integrated to give: which shows a connection with the Lie group of rotations. We prove that angular velocity tensor is skew symmetric, i.e. formula_71 satisfies formula_72. A rotation matrix "A" is orthogonal, inverse to its transpose, so we have formula_73. For formula_74 a frame matrix, taking the time derivative of the equation gives: Applying the formula formula_76, Thus, "W" is the negative of its transpose, which implies it is skew symmetric. At any instant formula_13, the angular velocity tensor represents a linear map between the position vector formula_79 and the velocity vectors formula_80 of a point on a rigid body rotating around the origin: The relation between this linear map and the angular velocity pseudovector formula_82 is the following. Because "W" is the derivative of an orthogonal transformation, the bilinear form is skew-symmetric. Thus we can apply the fact of exterior algebra that there is a unique linear form formula_84 on formula_85 that where formula_87 is the exterior product of formula_9 and formula_89. Taking the sharp "L" of "L" we get Introducing formula_91, as the Hodge dual of "L", and applying the definition of the Hodge dual twice supposing that the preferred unit 3-vector is formula_92 where by definition. Because formula_89 is an arbitrary vector, from nondegeneracy of scalar product follows Since the spin angular velocity tensor of a rigid body (in its rest frame) is a linear transformation that maps positions to velocities (within the rigid body), it can be regarded as a constant vector field. In particular, the spin angular velocity is a Killing vector field belonging to an element of the Lie algebra SO(3) of the 3-dimensional rotation group SO(3). Also, it can be shown that the spin angular velocity vector field is exactly half of the curl of the linear velocity vector field v(r) of the rigid body. In symbols, The same equations for the angular speed can be obtained reasoning over a rotating rigid body. Here is not assumed that the rigid body rotates around the origin. Instead, it can be supposed rotating around an arbitrary point that is moving with a linear velocity "V"("t") in each instant. To obtain the equations, it is convenient to imagine a rigid body attached to the frames and consider a coordinate system that is fixed with respect to the rigid body. Then we will study the coordinate transformations between this coordinate and the fixed "laboratory" system. As shown in the figure on the right, the lab system's origin is at point "O", the rigid body system origin is at and the vector from "O" to is R. A particle ("i") in the rigid body is located at point P and the vector position of this particle is R in the lab frame, and at position r in the body frame. It is seen that the position of the particle can be written: The defining characteristic of a rigid body is that the distance between any two points in a rigid body is unchanging in time. This means that the length of the vector formula_99 is unchanging. By Euler's rotation theorem, we may replace the vector formula_99 with formula_101 where formula_102 is a 3×3 rotation matrix and formula_103 is the position of the particle at some fixed point in time, say. This replacement is useful, because now it is only the rotation matrix formula_102 that is changing in time and not the reference vector formula_103, as the rigid body rotates about point. Also, since the three columns of the rotation matrix represent the three versors of a reference frame rotating together with the rigid body, any rotation about any axis becomes now visible, while the vector formula_99 would not rotate if the rotation axis were parallel to it, and hence it would only describe a rotation about an axis perpendicular to it (i.e., it would not see the component of the angular velocity pseudovector parallel to it, and would only allow the computation of the component perpendicular to it). The position of the particle is now written as: Taking the time derivative yields the velocity of the particle: where V is the velocity of the particle (in the lab frame) and V is the velocity of (the origin of the rigid body frame). Since formula_102 is a rotation matrix its inverse is its transpose. So we substitute formula_110: or where formula_115 is the previous angular velocity tensor. It can be proved that this is a skew symmetric matrix, so we can take its dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector formula_116: Substituting "ω" for "W" into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the orbital angular velocity of the particle with respect to the reference point. This angular velocity is what physicists call the "spin angular velocity" of the rigid body, as opposed to the "orbital" angular velocity of the reference point about the origin "O". We have supposed that the rigid body rotates around an arbitrary point. We should prove that the spin angular velocity previously defined is independent of the choice of origin, which means that the spin angular velocity is an intrinsic property of the spinning rigid body. (Note the marked contrast of this with the "orbital" angular velocity of a point particle, which certainly "does" depend on the choice of origin.) See the graph to the right: The origin of lab frame is "O", while "O" and "O" are two fixed points on the rigid body, whose velocity is formula_119 and formula_120 respectively. Suppose the angular velocity with respect to "O" and O is formula_121 and formula_122 respectively. Since point "P" and "O" have only one velocity, The above two yields that Since the point "P" (and thus formula_126) is arbitrary, it follows that If the reference point is the instantaneous axis of rotation the expression of the velocity of a point in the rigid body will have just the angular velocity term. This is because the velocity of the instantaneous axis of rotation is zero. An example of the instantaneous axis of rotation is the hinge of a door. Another example is the point of contact of a purely rolling spherical (or, more generally, convex) rigid body.	In physics, angular velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time. There are two types of angular velocity: orbital angular velocity and spin angular velocity. Spin angular velocity refers to how fast a rigid body rotates with respect to its centre of rotation. Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. 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summarize: The simplest example of a coordinate system is the identification of points on a line with real numbers using the "number line". In this system, an arbitrary point "O" (the "origin") is chosen on a given line. The coordinate of a point "P" is defined as the signed distance from "O" to "P", where the signed distance is the distance taken as positive or negative depending on which side of the line "P" lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point. The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes. This can be generalized to create "n" coordinates for any point in "n"-dimensional Euclidean space. Depending on the direction and order of the coordinate axes, the three-dimensional system may be a right-handed or a left-handed system. This is one of many coordinate systems. Another common coordinate system for the plane is the "polar coordinate system". A point is chosen as the "pole" and a ray from this point is taken as the "polar axis". For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line). Then there is a unique point on this line whose signed distance from the origin is "r" for given number "r". For a given pair of coordinates ("r", θ) there is a single point, but any point is represented by many pairs of coordinates. For example, ("r", θ), ("r", θ+2π) and (−"r", θ+π) are all polar coordinates for the same point. The pole is represented by (0, θ) for any value of θ. There are two common methods for extending the polar coordinate system to three dimensions. In the cylindrical coordinate system, a "z"-coordinate with the same meaning as in Cartesian coordinates is added to the "r" and "θ" polar coordinates giving a triple ("r", "θ", "z"). Spherical coordinates take this a step further by converting the pair of cylindrical coordinates ("r", "z") to polar coordinates ("ρ", "φ") giving a triple ("ρ", "θ", "φ"). A point in the plane may be represented in "homogeneous coordinates" by a triple ("x", "y", "z") where "x"/"z" and "y"/"z" are the Cartesian coordinates of the point. This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the use of infinity. In general, a homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values. Some other common coordinate systems are the following: There are ways of describing curves without coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length. These include: Coordinates systems are often used to specify the position of a point, but they may also be used to specify the position of more complex figures such as lines, planes, circles or spheres. For example, Plücker coordinates are used to determine the position of a line in space. When there is a need, the type of figure being described is used to distinguish the type of coordinate system, for example the term "line coordinates" is used for any coordinate system that specifies the position of a line. It may occur that systems of coordinates for two different sets of geometric figures are equivalent in terms of their analysis. An example of this is the systems of homogeneous coordinates for points and lines in the projective plane. The two systems in a case like this are said to be "dualistic". Dualistic systems have the property that results from one system can be carried over to the other since these results are only different interpretations of the same analytical result; this is known as the "principle of duality". Because there are often many different possible coordinate systems for describing geometrical figures, it is important to understand how they are related. Such relations are described by "coordinate transformations" which give formulas for the coordinates in one system in terms of the coordinates in another system. For example, in the plane, if Cartesian coordinates ("x", "y") and polar coordinates ("r", "θ") have the same origin, and the polar axis is the positive "x" axis, then the coordinate transformation from polar to Cartesian coordinates is given by "x" = "r" cos"θ" and "y" = "r" sin"θ". With every bijection from the space to itself two coordinate transformations can be associated: For example, in 1D, if the mapping is a translation of 3 to the right, the first moves the origin from 0 to 3, so that the coordinate of each point becomes 3 less, while the second moves the origin from 0 to −3, so that the coordinate of each point becomes 3 more. In two dimensions, if one of the coordinates in a point coordinate system is held constant and the other coordinate is allowed to vary, then the resulting curve is called a coordinate curve. In the Cartesian coordinate system the coordinate curves are, in fact, straight lines, thus coordinate lines. Specifically, they are the lines parallel to one of the coordinate axes. For other coordinate systems the coordinates curves may be general curves. For example, the coordinate curves in polar coordinates obtained by holding "r" constant are the circles with center at the origin. A coordinate system for which some coordinate curves are not lines is called a curvilinear coordinate system. This procedure does not always make sense, for example there are no coordinate curves in a homogeneous coordinate system. In three-dimensional space, if one coordinate is held constant and the other two are allowed to vary, then the resulting surface is called a coordinate surface. For example, the coordinate surfaces obtained by holding ρ constant in the spherical coordinate system are the spheres with center at the origin. In three-dimensional space the intersection of two coordinate surfaces is a coordinate curve. In the Cartesian coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the -dimensional spaces resulting from fixing a single coordinate of an "n"-dimensional coordinate system. The concept of a "coordinate map", or "coordinate chart" is central to the theory of manifolds. A coordinate map is essentially a coordinate system for a subset of a given space with the property that each point has exactly one set of coordinates. More precisely, a coordinate map is a homeomorphism from an open subset of a space "X" to an open subset of R. It is often not possible to provide one consistent coordinate system for an entire space. In this case, a collection of coordinate maps are put together to form an atlas covering the space. A space equipped with such an atlas is called a "manifold" and additional structure can be defined on a manifold if the structure is consistent where the coordinate maps overlap. For example, a differentiable manifold is a manifold where the change of coordinates from one coordinate map to another is always a differentiable function. In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as "global" or "world" coordinate system). For instance, the orientation of a rigid body can be represented by an orientation matrix, which includes, in its three columns, the Cartesian coordinates of three points. These points are used to define the orientation of the axes of the local system; they are the tips of three unit vectors aligned with those axes.	In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and "vice versa"; this is the basis of analytic geometry.	en	en	136	[ 250004, 250054, 581, 30362, 18, 27781, 111, 10, 176866, 13, 5426, 83, 70, 6, 221160, 111, 26847, 98, 10, 13315, 678, 2773, 101935, 17368, 70, 44, 2606, 1297, 13315, 740, 360, 903, 5426, 4, 142, 61799, 1294, 6275, 44, 670, 58, 15, 2347, 44, 3929, 6820, 18939, 83, 19667, 19, 98, 10, 34475, 13315, 5, 581, 176866, 13, 111, 10, 6275, 44, 683, 58, 83, 61924, 71, 237, 70, 181141, 62488, 1295, 44, 670, 58, 47, 44, 683, 830, 7440, 70, 181141, 62488, 83, 70, 62488, 39958, 237, 24491, 707, 40907, 8, 96819, 98, 3129, 5609, 111, 70, 13315, 44, 683, 58, 400, 90, 5, 98423, 6275, 83, 34475, 10, 36998, 176866, 13, 136, 12638, 2773, 14012, 83, 70, 176866, 13, 111, 10, 36998, 6275, 5, 581, 160469, 21533, 27781, 111, 10, 176866, 13, 5426, 83, 70, 106274, 39209, 176866, 13, 5426, 5, 360, 70, 47880, 4, 6626, 117, 40930, 25667, 124519, 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summarize: In its most simple and basic form, a moment is the product of the distance to some point, raised to some power, and some physical quantity such as the force, charge, etc. at that point: where formula_2 is the physical quantity such as a force applied at a point, or a point charge, or a point mass, etc. If the quantity is not concentrated solely at a single point, the moment is the integral of that quantity's density over space: where formula_4 is the distribution of the density of charge, mass, or whatever quantity is being considered. More complex forms take into account the angular relationships between the distance and the physical quantity, but the above equations capture the essential feature of a moment, namely the existence of an underlying formula_5 or equivalent term. This implies that there are multiple moments (one for each value of "n") and that the moment generally depends on the reference point from which the distance formula_6 is measured, although for certain moments (technically, the lowest non-zero moment) this dependence vanishes and the moment becomes independent of the reference point. Each value of "n" corresponds to a different moment: the 1st moment corresponds to "n" = 1; the 2nd moment to "n" = 2, etc. The 0th moment ("n" = 0) is sometimes called the "monopole moment"; the 1st moment ("n" = 1) is sometimes called the "dipole moment", and the 2nd moment ("n" = 2) is sometimes called the "quadrupole moment", especially in the context of electric charge distributions. Moments of mass: Assuming a density function that is finite and localized to a particular region, outside that region a 1/"r" potential may be expressed as a series of spherical harmonics: The coefficients formula_21 are known as "multipole moments", and take the form: where formula_23 expressed in spherical coordinates formula_24 is a variable of integration. A more complete treatment may be found in pages describing multipole expansion or spherical multipole moments. (Note: the convention in the above equations was taken from Jackson. The conventions used in the referenced pages may be slightly different.) When formula_4 represents an electric charge density, the formula_26 are, in a sense, projections of the moments of electric charge: formula_27 is the monopole moment; the formula_28 are projections of the dipole moment, the formula_29 are projections of the quadrupole moment, etc. The multipole expansion applies to 1/"r" scalar potentials, examples of which include the electric potential and the gravitational potential. For these potentials, the expression can be used to approximate the strength of a field produced by a localized distribution of charges (or mass) by calculating the first few moments. For sufficiently large "r", a reasonable approximation can be obtained from just the monopole and dipole moments. Higher fidelity can be achieved by calculating higher order moments. Extensions of the technique can be used to calculate interaction energies and intermolecular forces. The technique can also be used to determine the properties of an unknown distribution formula_4. Measurements pertaining to multipole moments may be taken and used to infer properties of the underlying distribution. This technique applies to small objects such as molecules, but has also been applied to the universe itself, being for example the technique employed by the WMAP and Planck experiments to analyze the cosmic microwave background radiation. The concept of moment in physics is derived from the mathematical concept of moments. The principle of moments is derived from Archimedes' discovery of the operating principle of the lever. In the lever one applies a force, in his day most often human muscle, to an arm, a beam of some sort. Archimedes noted that the amount of force applied to the object, the moment of force, is defined as M = rF, where F is the applied force, and r is the distance from the applied force to object. However, historical evolution of the term'moment' and its use in different branches of science, such as mathematics, physics and engineering, is unclear. Federico Commandino, in 1565, translated into Latin from Archimedes: This was apparently the first use of the word "moment" (Latin, "momentorum") in the sense which we now know it: a moment about a center of rotation.	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summarize: In physics, uniform circular motion describes the motion of a body traversing a circular path at constant speed. Since the body describes circular motion, its distance from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, produced by a centripetal force which is also constant in magnitude and directed towards the axis of rotation. In the case of rotation around a fixed axis of a rigid body that is not negligibly small compared to the radius of the path, each particle of the body describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varying with the position with respect to the axis. For motion in a circle of radius "r", the circumference of the circle is "C" = 2"r". If the period for one rotation is "T", the angular rate of rotation, also known as angular velocity, ω is: The speed of the object travelling the circle is: The angle θ swept out in a time "t" is: The angular acceleration, "α", of the particle is: In the case of uniform circular motion, α will be zero. The acceleration due to change in the direction is: The centripetal and centrifugal force can also be found out using acceleration: The vector relationships are shown in Figure 1. The axis of rotation is shown as a vector ω perpendicular to the plane of the orbit and with a magnitude ω = "d"θ / "dt". The direction of ω is chosen using the right-hand rule. With this convention for depicting rotation, the velocity is given by a vector cross product as which is a vector perpendicular to both ω and r("t"), tangential to the orbit, and of magnitude ω "r". Likewise, the acceleration is given by which is a vector perpendicular to both ω and v("t") of magnitude ω \|v\| = ω "r" and directed exactly opposite to r("t"). In the simplest case the speed, mass and radius are constant. Consider a body of one kilogram, moving in a circle of radius one metre, with an angular velocity of one radian per second. During circular motion the body moves on a curve that can be described in polar coordinate system as a fixed distance "R" from the center of the orbit taken as origin, oriented at an angle θ("t") from some reference direction. See Figure 4. The displacement "vector" formula_9 is the radial vector from the origin to the particle location: where formula_11 is the unit vector parallel to the radius vector at time "t" and pointing away from the origin. It is convenient to introduce the unit vector orthogonal to formula_11 as well, namely formula_13. It is customary to orient formula_13 to point in the direction of travel along the orbit. The velocity is the time derivative of the displacement: Because the radius of the circle is constant, the radial component of the velocity is zero. The unit vector formula_11 has a time-invariant magnitude of unity, so as time varies its tip always lies on a circle of unit radius, with an angle θ the same as the angle of formula_17. If the particle displacement rotates through an angle "d"θ in time "dt", so does formula_11, describing an arc on the unit circle of magnitude "d"θ. See the unit circle at the left of Figure 4. Hence: where the direction of the change must be perpendicular to formula_11 (or, in other words, along formula_13) because any change formula_22 in the direction of formula_11 would change the size of formula_11. The sign is positive, because an increase in "d"θ implies the object and formula_11 have moved in the direction of formula_13. Hence the velocity becomes: The acceleration of the body can also be broken into radial and tangential components. The acceleration is the time derivative of the velocity: The time derivative of formula_13 is found the same way as for formula_11. Again, formula_13 is a unit vector and its tip traces a unit circle with an angle that is /2 + θ. Hence, an increase in angle "d"θ by formula_17 implies formula_13 traces an arc of magnitude "d"θ, and as formula_13 is orthogonal to formula_11, we have: where a negative sign is necessary to keep formula_13 orthogonal to formula_11. (Otherwise, the angle between formula_13 and formula_11 would "decrease" with increase in "d"θ.) See the unit circle at the left of Figure 4. Consequently, the acceleration is: The centripetal acceleration is the radial component, which is directed radially inward: while the tangential component changes the magnitude of the velocity: Circular motion can be described using complex numbers. Let the axis be the real axis and the formula_44 axis be the imaginary axis. The position of the body can then be given as formula_45, a complex "vector": where is the imaginary unit, and formula_47 is the argument of the complex number as a function of time, "t". Since the radius is constant: where a "dot" indicates differentiation in respect of time. With this notation the velocity becomes: and the acceleration becomes: The first term is opposite in direction to the displacement vector and the second is perpendicular to it, just like the earlier results shown before. Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity v is tangent to the circular path, no two velocities point in the same direction. Although the object has a constant "speed", its "direction" is always changing. This change in velocity is caused by an acceleration a, whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The acceleration points radially inwards (centripetally) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration. For a path of radius "r", when an angle θ is swept out, the distance travelled on the periphery of the orbit is "s" = "r"θ. Therefore, the speed of travel around the orbit is where the angular rate of rotation is ω. (By rearrangement, ω = "v"/"r".) Thus, "v" is a constant, and the velocity vector v also rotates with constant magnitude "v", at the same angular rate ω. In this case the three-acceleration vector is perpendicular to the three-velocity vector, and the square of proper acceleration, expressed as a scalar invariant, the same in all reference frames, becomes the expression for circular motion, or, taking the positive square root and using the three-acceleration, we arrive at the proper acceleration for circular motion: The left-hand circle in Figure 2 is the orbit showing the velocity vectors at two adjacent times. On the right, these two velocities are moved so their tails coincide. Because speed is constant, the velocity vectors on the right sweep out a circle as time advances. For a swept angle "d"θ = ω "dt" the change in v is a vector at right angles to v and of magnitude "v" "d"θ, which in turn means that the magnitude of the acceleration is given by In non-uniform circular motion an object is moving in a circular path with a varying speed. Since the speed is changing, there is tangential acceleration in addition to normal acceleration. In non-uniform circular motion the net acceleration (a) is along direction of Δv which is directed inside circle but does not pass through its center (see figure). The net acceleration may be resolved into two components: tangential acceleration and normal acceleration also known as the centripetal or radial acceleration. Unlike tangential acceleration, centripetal acceleration is present in both uniform and non-uniform circular motion. In non-uniform circular motion, normal force does not always point in the opposite direction of weight. Here is an example with an object traveling in a straight path then loops a loop back into a straight path again. This diagram shows the normal force pointing in other directions rather than opposite to the weight force. The normal force is actually the sum of the radial and tangential forces. The component of weight force is responsible for the tangential force here (We have neglected frictional force). The radial force (centripetal force) is due the change in direction of velocity as discussed earlier. In non-uniform circular motion, normal force and weight may point in the same direction. Both forces can point down, yet the object will remain in a circular path without falling straight down. First let's see why normal force can point down in the first place. In the first diagram, let's say the object is a person sitting inside a plane, the two forces point down only when it reaches the top of the circle. The reason for this is that the normal force is the sum of the tangential force and centripetal force. The tangential force is zero at the top (as no work is performed when the motion is perpendicular to the direction of force applied. Here weight force is perpendicular to the direction of motion of the object at the top of the circle) and centripetal force points down, thus normal force will point down as well. From a logical standpoint, a person who is travelling in the plane will be upside down at the top of the circle. At that moment, the person's seat is actually pushing down on the person, which is the normal force. The reason why the object does not fall down when subjected to only downward forces is a simple one. Think about what keeps an object up after it is thrown. Once an object is thrown into the air, there is only the downward force of earth's gravity that acts on the object. That does not mean that once an object is thrown in the air, it will fall instantly. What keeps that object up in the air is its velocity. The first of Newton's laws of motion states that an object's inertia keeps it in motion, and since the object in the air has a velocity, it will tend to keep moving in that direction. A varying angular speed for an object moving in a circular path can also be achieved if the rotating body does not have an homogeneous mass distribution. For inhomogeneous objects, it is necessary to approach the problem as in. Solving applications dealing with non-uniform circular motion involves force analysis. With uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration. Although there are additional forces acting upon the object, the sum of all the forces acting on the object will have to equal to the centripetal force. Radial acceleration is used when calculating the total force. Tangential acceleration is not used in calculating total force because it is not responsible for keeping the object in a circular path. The only acceleration responsible for keeping an object moving in a circle is the radial acceleration. Since the sum of all forces is the centripetal force, drawing centripetal force into a free body diagram is not necessary and usually not recommended. Using formula_58, we can draw free body diagrams to list all the forces acting on an object then set it equal to formula_59. Afterwards, we can solve for what ever is unknown (this can be mass, velocity, radius of curvature, coefficient of friction, normal force, etc.). For example, the visual above showing an object at the top of a semicircle would be expressed as formula_60. In uniform circular motion, total acceleration of an object in a circular path is equal to the radial acceleration. Due to the presence of tangential acceleration in non uniform circular motion, that does not hold true any more. To find the total acceleration of an object in non uniform circular, find the vector sum of the tangential acceleration and the radial acceleration. Radial acceleration is still equal to formula_62. Tangential acceleration is simply the derivative of the velocity at any given point: formula_63. This root sum of squares of separate radial and tangential accelerations is only correct for circular motion; for general motion within a plane with polar coordinates formula_64, the Coriolis term formula_65 should be added to formula_66, whereas radial acceleration then becomes formula_67.	In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body.	en	en	81	[ 250004, 250054, 360, 6, 34053, 27744, 7, 4, 61514, 115339, 78112, 98363, 7, 70, 78112, 111, 10, 14361, 37317, 214, 10, 115339, 60875, 99, 53697, 38352, 5, 66016, 70, 14361, 98363, 7, 115339, 78112, 4, 6863, 62488, 1295, 70, 10, 33102, 111, 2062, 22062, 47143, 7, 53697, 99, 756, 20028, 5, 145733, 70, 14361, 25, 7, 38352, 83, 53697, 4, 6863, 191060, 939, 83, 959, 53697, 12, 191060, 939, 4, 10, 173, 18770, 102134, 939, 4, 56566, 7, 98, 15044, 70, 14361, 25, 7, 38352, 136, 6863, 48225, 111, 26983, 5, 3293, 151134, 191060, 939, 117414, 7, 70, 169424, 111, 142, 197108, 1830, 74, 903, 69514, 5408, 289, 197108, 1830, 83, 111, 53697, 101668, 13, 136, 8951, 297, 99, 756, 20028, 98186, 70, 10, 33102, 111, 2062, 22062, 5, 3293, 197108, 1830, 83, 4, 23, 15504, 4, 181653, 390, 10, 69514, 5408, 289, 37772, 3129, 83, 2843, 53697, 23, 101668, 13, 136, 8951, 297, 98186, 70, 10, 33102, 111, 2062, 22062, 5, 360, 70, 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summarize: The order is divided into three suborders, Tyranni (suboscines), Passeri (oscines), and the basal Acanthisitti. Oscines have the best control of their syrinx muscles among birds, producing a wide range of songs and other vocalizations (though some of them, such as the crows, do not sound musical to human beings); some such as the lyrebird are accomplished imitators. The acanthisittids or New Zealand wrens are tiny birds restricted to New Zealand, at least in modern times; they were long placed in Passeri. Most passerines are smaller than typical members of other avian orders. The heaviest and altogether largest passerines are the thick-billed raven and the larger races of common raven, each exceeding and. The superb lyrebird and some birds-of-paradise, due to very long tails or tail coverts, are longer overall. The smallest passerine is the short-tailed pygmy tyrant, at and. The foot of a passerine has three toes directed forward and one toe directed backward, called anisodactyl arrangement, and the hind toe (hallux) joins the leg at approximately the same level as the front toes. This arrangement enables passerine birds to easily perch upright on branches. The toes have no webbing or joining, but in some cotingas, the second and third toes are united at their basal third. The leg of passerine birds contains an additional special adaptation for perching. A tendon in the rear of the leg running from the underside of the toes to the muscle behind the tibiotarsus will automatically be pulled and tighten when the leg bends, causing the foot to curl and become stiff when the bird lands on a branch. This enables passerines to sleep while perching without falling off. Most passerine birds have 12 tail feathers but the superb lyrebird has 16, and several spinetails in the family Furnariidae have 10, 8, or even 6, as is the case of Des Murs's wiretail. Species adapted to tree trunk climbing such as woodcreeper and treecreepers have stiff tail feathers that are used as props during climbing. Extremely long tails used as sexual ornaments are shown by species in different families. A well-known example is the long-tailed widowbird. The chicks of passerines are altricial: blind, featherless, and helpless when hatched from their eggs. Hence, the chicks require extensive parental care. Most passerines lay coloured eggs, in contrast with nonpasserines, most of whose eggs are white except in some ground-nesting groups such as Charadriiformes and nightjars, where camouflage is necessary, and in some parasitic cuckoos, which match the passerine host's egg. Vinous-throated parrotbill has two egg colours, white and blue. This can prevent the brood parasitic Common cuckoo. Clutches vary considerably in size: some larger passerines of Australia such as lyrebirds and scrub-robins lay only a single egg, most smaller passerines in warmer climates lay between two and five, while in the higher latitudes of the Northern Hemisphere, hole-nesting species like tits can lay up to a dozen and other species around five or six. The family Viduidae do not build their own nests, instead, they lay eggs in other birds' nests. The evolutionary history of the passerine families and the relationships among them remained rather mysterious until the late 20th century. In many cases, passerine families were grouped together on the basis of morphological similarities that, it is now believed, are the result of convergent evolution, not a close genetic relationship. For example, the wrens of the Americas and Eurasia; those of Australia; and those of New Zealand look superficially similar and behave in similar ways, and yet belong to three far-flung branches of the passerine family tree; they are as unrelated as it is possible to be while remaining Passeriformes. Much research remains to be done, but advances in molecular biology and improved paleobiogeographical data gradually are revealing a clearer picture of passerine origins and evolution that reconciles molecular affinities, the constraints of morphology and the specifics of the fossil record. The first passerines are now thought to have evolved in the Southern Hemisphere in the late Paleocene or early Eocene, around 50 million years ago. The initial split was between the New Zealand wrens (Acanthisittidae) and all other passerines, and the second split involved the Tyranni (suboscines) and the Passeri (oscines or songbirds). The latter experienced a great radiation of forms out of the Australian continent. A major branch of the Passeri, parvorder Passerida, expanded deep into Eurasia and Africa, where a further explosive radiation of new lineages occurred. This eventually led to three major Passerida lineages comprising about 4,000 species, which in addition to the Corvida and numerous minor lineages make up songbird diversity today. Extensive biogeographical mixing happens, with northern forms returning to the south, southern forms moving north, and so on. Perching bird osteology, especially of the limb bones, is rather diagnostic. However, the early fossil record is poor because the first Passeriformes were apparently on the small side of the present size range, and their delicate bones did not preserve well. Queensland Museum specimens F20688 (carpometacarpus) and F24685 (tibiotarsus) from Murgon, Queensland, are fossil bone fragments initially assigned to Passeriformes. However, the material is too fragmentary and their affinities have been questioned. Several more recent fossils from the Oligocene of Europe, such as "Wieslochia", "Jamna", and "Resoviaornis", are more complete and definitely represent early passeriforms, although their exact position in the evolutionary tree is not known. From the Bathans Formation at the Manuherikia River in Otago, New Zealand, MNZ S42815 (a distal right tarsometatarsus of a tui-sized bird) and several bones of at least one species of saddleback-sized bird have recently been described. These date from the Early to Middle Miocene (Awamoan to Lillburnian, 19–16 mya). In Europe, perching birds are not too uncommon in the fossil record from the Oligocene onward, but most are too fragmentary for a more definite placement: That suboscines expanded much beyond their region of origin is proven by several fossil from Germany such as a broadbill (Eurylaimidae) humerus fragment from the Early Miocene (roughly 20 mya) of, Germany, the Late Oligocene carpometacarpus from France listed above, and "Wieslochia", among others. Extant Passeri super-families were quite distinct by that time and are known since about 12–13 mya when modern genera were present in the corvoidean and basal songbirds. The modern diversity of Passerida genera is known mostly from the Late Miocene onwards and into the Pliocene (about 10–2 mya). Pleistocene and early Holocene lagerstätten (<1.8 mya) yield numerous extant species, and many yield almost nothing but extant species or their chronospecies and paleosubspecies. In the Americas, the fossil record is more scant before the Pleistocene, from which several still-existing suboscine families are documented. Apart from the indeterminable MACN-SC-1411 (Pinturas Early/Middle Miocene of Santa Cruz Province, Argentina), an extinct lineage of perching birds has been described from the Late Miocene of California, United States: the Palaeoscinidae with the single genus "Palaeoscinis". ""Palaeostruthus" eurius" (Pliocene of Florida) probably belongs to an extant family, most likely passeroidean. The Passeriformes is currently divided into three suborders: Acanthisitti (New Zealand wrens), Tyranni (suboscines) and Passeri (oscines). The Passeri has been traditionally subdivided into two major groups recognized now as Corvida and Passerida respectively containing the large superfamilies Corvoidea and Meliphagoidea, as well as minor lineages, and the superfamilies Sylvioidea, Muscicapoidea, and Passeroidea but this arrangement has been found to be oversimplified. Since the mid-2000s, literally, dozens of studies have investigated the phylogeny of the Passeriformes and found that many families from Australasia traditionally included in the Corvoidea actually represent more basal lineages within oscines. Likewise, the traditional three-superfamily arrangement within the Passeri has turned out to be far more complex and will require changes in classification. Major "wastebin" families such as the Old World warblers and Old World babblers have turned out to be paraphyletic and are being rearranged. Several taxa turned out to represent highly distinct lineages, so new families had to be established, some of them – like the stitchbird of New Zealand and the Eurasian bearded reedling – monotypic with only one living species. In the Passeri alone, a number of minor lineages will eventually be recognized as distinct superfamilies. For example, the kinglets constitute a single genus with less than 10 species today but seem to have been among the first perching bird lineages to diverge as the group spread across Eurasia. No particularly close relatives of them have been found among comprehensive studies of the living Passeri, though they might be fairly close to some little-studied tropical Asian groups. Nuthatches, wrens, and their closest relatives as currently grouped in a distinct super-family Certhioidea. This list is in taxonomic order, placing related families next to one another. The families listed are those recognised by the International Ornithologists' Union (IOC). The order and the division into infraorders, parvorders and superfamilies follows the phylogenetic analysis published by Carl Oliveros and colleagues in 2019. The relationships between the families in the suborder Tyranni (suboscines) were all well determined but some of the nodes in Passeri (oscines) were unclear owing to the rapid splitting of the lineages. Living Passeriformes based on the "Taxonomy in Flux family phylogenetic tree" by John Boyd.	A passerine is any bird of the order Passeriformes, which includes more than half of all bird species. 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summarize: The word 'jaguar' is thought to derive from the Tupian word "yaguara", meaning "beast of prey". The word entered English presumably via the Amazonian trade language Tupinambá, via Portuguese "jaguar". The specific word for jaguar is "yaguareté", with the suffix -"eté" meaning "real" or "true". The word 'panther' derives from classical Latin "panthēra", itself from the ancient Greek "pánthēr" (πάνθηρ). In Mexican Spanish, its nickname is "el tigre": 16th century Spaniards had no native word in their language for the jaguar, which is smaller than a lion, but bigger than a leopard, nor had ever encountered it in the Old World, and so named it after the tiger, since its ferocity would have been known to them through Roman writings and popular literature during the Renaissance. "Onca" is the Portuguese "onça", with the cedilla dropped for typographical reasons, found in English as "ounce" for the snow leopard, "Panthera uncia". It derives from the Latin "lyncea" lynx, with the letter L confused with the definite article (Italian "lonza", Old French "l'once)". In 1758, Carl Linnaeus described the jaguar in his work "Systema Naturae" and gave it the scientific name "Felis onca". In the 19th and 20th centuries, several jaguar type specimens formed the basis for descriptions of subspecies. In 1939, Reginald Innes Pocock recognized eight subspecies based on geographic origins and skull morphology of these specimens. Pocock did not have access to sufficient zoological specimens to critically evaluate their subspecific status, but expressed doubt about the status of several. Later consideration of his work suggested only three subspecies should be recognized. The description of "P. o. palustris" was based on a fossil skull. The author of "Mammal Species of the World" listed nine subspecies and both "P. o. palustris" or "P. o. paraguensis" separately. Results of morphologic and genetic research indicate a clinal north–south variation between populations, but no evidence for subspecific differentiation. A subsequent, more detailed study confirmed the predicted population structure within jaguar populations in Colombia. IUCN Red List assessors for the species and members of the Cat Specialist Group do not recognize any jaguar subspecies as valid. The following table is based on the former classification of the species provided in "Mammal Species of the World". The genus "Panthera" probably evolved in Asia between six and ten million years ago. The jaguar is thought to have diverged from a common ancestor of the "Panthera" at least 1.5 million years ago and to have entered the American continent in the Early Pleistocene via Beringia, the land bridge that once spanned the Bering Strait. Results of jaguar mitochondrial DNA analysis indicate that the species' lineage evolved between 280,000 and 510,000 years ago. Its immediate ancestor was "Panthera onca augusta", which was larger than the contemporary jaguar. Phylogenetic studies generally have shown the clouded leopard ("Neofelis nebulosa") is basal to this group. Fossils of extinct "Panthera" species, such as the European jaguar ("P. gombaszoegensis") and the American lion ("P. atrox"), show characteristics of both the jaguar and the lion ("P. leo"). Based on morphological evidence, the British zoologist Reginald Innes Pocock concluded that the jaguar is most closely related to the leopard ("P. pardus"). However, DNA-based evidence is inconclusive, and the position of the jaguar relative to the other species varies between studies. The jaguar is a compact and well-muscled animal. It is the largest cat native to the Americas and the third largest in the world, exceeded in size by the tiger and the lion. Its coat is generally a tawny yellow, but ranges to reddish-brown, for most of the body. The ventral areas are white. The fur is covered with rosettes for camouflage in the dappled light of its forest habitat. The spots and their shapes vary between individual jaguars: rosettes may include one or several dots. The spots on the head and neck are generally solid, as are those on the tail, where they may merge to form a band. Forest jaguars are frequently darker and considerably smaller than those in open areas, possibly due to the smaller numbers of large, herbivorous prey in forest areas. While the jaguar closely resembles the leopard, it is generally more robust, with a stockier limbs and a squarer head. The rosettes on a jaguar's coat are larger, darker, fewer in number and have thicker lines with a small spot in the middle. Its size and weight vary considerably: weights are normally in the range of. Exceptionally big males have been recorded to weigh as much as. The smallest females weigh about. Females are typically 10–20 percent smaller than males. The length, from the nose to the base of the tail, varies from. The tail is the shortest of any big cat, at in length. Legs are also short, but thick and powerful, considerably shorter when compared to a small tiger or lion in a similar weight range. The jaguar stands tall at the shoulders. Further variations in size have been observed across regions and habitats, with size tending to increase from north to south. Jaguars in the Chamela-Cuixmala Biosphere Reserve on the Pacific coast weighed around, about the size of a female cougar. South American jaguars in Venezuela or Brazil are much larger with average weights of about in males and of about in females. A short and stocky limb structure makes the jaguar adept at climbing, crawling, and swimming. The head is robust and the jaw extremely powerful, it has the third highest bite force of all felids, after the tiger and the lion. A jaguar can bite with a force of with the canine teeth and at the carnassial notch. This allows it to pierce the shells of armored reptiles and turtles. A comparative study of bite force adjusted for body size ranked it as the top felid, alongside the clouded leopard and ahead of the tiger and lion. It has been reported that an individual jaguar can drag an bull in its jaws and pulverize the heaviest bones. Melanistic jaguars are informally known as black panthers, but as with all forms of polymorphism they do not form a separate species. The black morph is less common than the spotted morph, estimated at occurring in about 6% of the South American jaguar population. In Mexico's Sierra Madre Occidental, the first black jaguar was recorded in 2004. Some evidence indicates that the melanistic allele is dominant, and being supported by natural selection. The black form may be an example of heterozygote advantage; breeding in captivity is not yet conclusive on this. Melanistic jaguars (or "black" jaguars) occur primarily in parts of South America, and are virtually unknown in wild populations residing in the subtropical and temperate regions of North America; they have rarely been documented north of Mexico's Isthmus of Tehuantepec. Extremely rare albino individuals, sometimes called white panthers, also occur among jaguars, as with the other big cats. As usual with albinos in the wild, selection keeps the frequency close to the rate of mutation. At present, the jaguar's range extends from Mexico through Central America to South America, including much of Amazonian Brazil. The countries included in this range are Argentina, Belize, Bolivia, Colombia, Costa Rica (particularly on the Osa Peninsula), Ecuador, French Guiana, Guatemala, Guyana, Honduras, Nicaragua, Panama, Paraguay, Peru, Suriname, the United States and Venezuela. It is now locally extinct in El Salvador and Uruguay. The inclusion of the United States in the list is based on occasional sightings in the southwest, particularly in Arizona, New Mexico and Texas. There are rock drawings made by the Hopi, Anasazi, and Pueblo all over the desert and chaparral regions of the American Southwest of an explicitly spotted cat: the only other feline that could even come close to such a profile would be the ocelot, but the pictographs distinctly display a much larger beast more than twice as large as any known ocelot. There are records of the beast being sold for its pelt in the vicinity of San Antonio, Texas for $18 apiece in the mid 19th century and there are records from well before California was a state that fit the description of this cat perfectly, mostly written down in Spanish. The historic range of the species included much of the southern half of the United States, and in the south extended much farther to cover most of the South American continent. In total, its northern range has receded southward and its southern range northward. Ice age fossils of the jaguar, dated between 40,000 and 11,500 years ago, have been discovered in the United States, including some at an important site as far north as Missouri. Fossil evidence shows jaguars of up to, much larger than the contemporary average for the animal. The habitat of the cat typically includes the rain forests and cloud forests of South and Central America, open, seasonally flooded wetlands, and dry grassland terrain. Of these habitats, the jaguar much prefers dense forest; the cat has lost range most rapidly in regions of drier habitat, such as the Argentine pampas, the arid grasslands of Mexico, and the southwestern United States. The cat will range across tropical, subtropical, and dry deciduous forests (including, historically, oak forests in the United States). The jaguar prefers to live by rivers, swamps, and in dense rainforest with thick cover for stalking prey. Jaguars have been found at elevations as high as 3,800 m, but they typically avoid montane forest and are not found in the high plateau of central Mexico or in the Andes. The jaguars preferred habitats are usually swamps and wooded regions, but jaguars also live in scrublands and deserts. The adult jaguar is an apex predator, meaning it exists at the top of its food chain and is not preyed on in the wild. The jaguar has also been termed a keystone species, as it is assumed, through controlling the population levels of prey such as herbivorous and granivorous mammals, apex felids maintain the structural integrity of forest systems. However, accurately determining what effect species like the jaguar have on ecosystems is difficult, because data must be compared from regions where the species is absent as well as its current habitats, while controlling for the effects of human activity. It is accepted that mid-sized prey species undergo population increases in the absence of the keystone predators, and this has been hypothesized to have cascading negative effects. However, field work has shown this may be natural variability and the population increases may not be sustained. Thus, the keystone predator hypothesis is not accepted by all scientists. The jaguar also has an effect on other predators. The jaguar and the cougar, which is the next-largest feline of South America, but the biggest in Central or North America, are often sympatric (related species sharing overlapping territory) and have often been studied in conjunction. The jaguar tends to take larger prey, usually over and the cougar smaller, usually between, reducing the latter's size. This situation may be advantageous to the cougar. Its broader prey niche, including its ability to take smaller prey, may give it an advantage over the jaguar in human-altered landscapes; while both are classified as near-threatened species, the cougar has a significantly larger current distribution. Depending on the availability of prey, the cougar and jaguar may even share it. Jaguar females reach sexual maturity at about two years of age, and males at three or four. The cat probably mates throughout the year in the wild, with births increasing when prey is plentiful. Research on captive male jaguars supports the year-round mating hypothesis, with no seasonal variation in semen traits and ejaculatory quality; low reproductive success has also been observed in captivity. Generation length of the jaguar is 9.8 years. Female estrus is 6–17 days out of a full 37-day cycle, and females will advertise fertility with urinary scent marks and increased vocalization. Females range more widely than usual during courtship. Pairs separate after mating, and females provide all parenting. The gestation period lasts 93–105 days; females give birth to up to four cubs, and most commonly to two. The mother will not tolerate the presence of males after the birth of cubs, given a risk of infanticide; this behavior is also found in the tiger. The young are born blind, gaining sight after two weeks. Cubs are weaned at three months, but remain in the birth den for six months before leaving to accompany their mother on hunts. They will continue in their mother's company for one to two years before leaving to establish a territory for themselves. Young males are at first nomadic, jostling with their older counterparts until they succeed in claiming a territory. Typical lifespan in the wild is estimated at around 12–15 years; in captivity, the jaguar lives up to 23 years, placing it among the longest-lived cats. Like most cats, the jaguar is solitary outside mother–cub groups. Adults generally meet only to court and mate (though limited noncourting socialization has been observed anecdotally) and carve out large territories for themselves. Female territories, which range from 25 to 40 km in size, may overlap, but the animals generally avoid one another. Male ranges cover roughly twice as much area, varying in size with the availability of game and space, and do not overlap. The territory of a male can contain those of several females. The jaguar uses scrape marks, urine, and feces to mark its territory. Like the other big cats except the snow leopard, the jaguar is capable of roaring and does so to warn territorial and mating competitors away; intensive bouts of counter-calling between individuals have been observed in the wild. Their roar often resembles a repetitive cough, and they may also vocalize mews and grunts. Mating fights between males occur, but are rare, and aggression avoidance behavior has been observed in the wild. When it occurs, conflict is typically over territory: a male's range may encompass that of two or three females, and he will not tolerate intrusions by other adult males. The jaguar is often described as nocturnal, but is more specifically crepuscular (peak activity around dawn and dusk). Both sexes hunt, but males travel farther each day than females, befitting their larger territories. The jaguar may hunt during the day if game is available and is a relatively energetic feline, spending as much as 50–60 percent of its time active. The jaguar's elusive nature and the inaccessibility of much of its preferred habitat make it a difficult animal to sight, let alone study. Like all cats, the jaguar is an obligate carnivore, feeding only on meat. It is an opportunistic hunter and its diet encompasses at least 87 species. Range-wide, jaguars prefer prey weighing and the most significantly preferred species are capybara and giant anteater. Other commonly taken prey include wild boar, common caiman, collared peccary, deer in more northern parts of their range, frogs, fish, nine-banded armadillo and white-nosed coati. Other species like the agouti, other carnivorans, primates, common opossum and tapir are generally avoided. Jagaurs are unusual among large felids in that they do not have a special preference for even-toed ungulates. Some jaguars also prey on livestock and they will actively target horses, cattle, and llamas. The activity patterns of the jaguar have been found to coincide with the activity of their main prey species in their biomes. Camera trap studies have shown that jaguars primarily have a crepuscular–nocturnal activity pattern in all the biomes that they are found in; however jaguars have been recorded to have considerable diurnal activity in thickly forested regions of the Amazon Rainforest and the Pantanal, as well as purely nocturnal activity in other regions such as the Atlantic forest.. The jaguar is a stalk-and-ambush rather than a chase predator. The cat will walk slowly down forest paths, listening for and stalking prey before rushing or ambushing. The jaguar attacks from cover and usually from a target's blind spot with a quick pounce; the species' ambushing abilities are considered nearly peerless in the animal kingdom by both indigenous people and field researchers, and are probably a product of its role as an apex predator in several different environments. The ambush may include leaping into water after prey, as a jaguar is quite capable of carrying a large kill while swimming; its strength is such that carcasses as large as a heifer can be hauled up a tree to avoid flood levels. While the jaguar often employs the deep throat-bite and suffocation technique typical among "Panthera", it sometimes uses a killing method unique among cats: it pierces directly through the temporal bones of the skull between the ears of prey (especially the capybara) with its canine teeth, piercing the brain. This may be an adaptation to "cracking open" turtle shells; following the late Pleistocene extinctions, armored reptiles such as turtles would have formed an abundant prey base for the jaguar. After killing prey, the jaguar will drag the carcass to a thicket or other secluded spot. It begins eating at the neck and chest, rather than the midsection. The heart and lungs are consumed, followed by the shoulders. The daily food requirement of a animal, at the extreme low end of the species' weight range, has been estimated at. For captive animals in the range, more than of meat daily are recommended. In the wild, consumption is naturally more erratic; wild cats expend considerable energy in the capture and kill of prey, and they may consume up to of meat at one feeding, followed by periods of famine. Though carnivorous, there is evidence that wild jaguars consume the roots of "Banisteriopsis caapi". Jaguars very rarely attack humans. Upon catching the scent or sight of a human, overwhelmingly they run as fast as their legs can carry them or will climb a tree to hide rather than fight. They did not evolve eating large primates and do not normally see man as food. Experts have cited them as the least likely of all big cats to kill and eat man and the majority of attacks come when the feline has been cornered or wounded. However, such behavior appears to be more frequent where humans enter jaguar habitat and decrease prey. Captive jaguars sometimes attack zookeepers. When the conquistadors arrived in the Americas, they feared jaguars. Nevertheless, even in those times, the jaguar's chief prey was the capybara in South America and peccary further north. Charles Darwin reported a saying of Native Americans that people would not have to fear the jaguar as long as capybaras were abundant. Jaguar populations are rapidly declining. The species is listed as Near Threatened on the IUCN Red List. The loss of parts of its range, including its virtual elimination from its historic northern areas and the increasing fragmentation of the remaining range, have contributed to this status. Particularly significant declines occurred in the 1960s, when more than 15,000 jaguars were killed for their skins in the Brazilian Amazon yearly; the Convention on International Trade in Endangered Species of 1973 brought about a sharp decline in the pelt trade. Detailed work performed under the auspices of the Wildlife Conservation Society revealed the species has lost 37% of its historic range, with its status unknown in an additional 18% of the global range. More encouragingly, the probability of long-term survival was considered high in 70% of its remaining range, particularly in the Amazon basin and the adjoining Gran Chaco and Pantanal. The major risks to the jaguar include deforestation across its habitat, increasing competition for food with human beings, especially in dry and unproductive habitat, poaching, hurricanes in northern parts of its range, and the behavior of ranchers who will often kill the cat where it preys on livestock. When adapted to the prey, the jaguar has been shown to take cattle as a large portion of its diet; while land clearance for grazing is a problem for the species, the jaguar population may have increased when cattle were first introduced to South America, as the animals took advantage of the new prey base. This willingness to take livestock has induced ranch owners to hire full-time jaguar hunters. The skins of wild cats and other mammals have been highly valued by the fur trade for many decades. From the beginning of the 20th-century Jaguars were hunted in large numbers, but over-harvest and habitat destruction reduced the availability and induced hunters and traders to gradually shift to smaller species by the 1960s. The international trade of jaguar skins had its largest boom between the end of the Second World War and the early 1970, due to the growing economy and lack of regulations. From 1967 onwards, the regulations introduced by national laws and international agreements diminished the reported international trade from as high as 13000 skins in 1967, through 7000 skins in 1969, until it became negligible after 1976, although illegal trade and smuggling continue to be a problem. During this period, the biggest exporters were Brazil and Paraguay, and the biggest importers were the US and Germany. The jaguar is listed on CITES Appendix I, which means that all international trade in jaguars or their body parts is prohibited. Hunting jaguars is prohibited in Argentina, Brazil, Colombia, French Guiana, Honduras, Nicaragua, Panama, Paraguay, Suriname, the United States, and Venezuela. Hunting jaguars is restricted in Guatemala and Peru. Trophy hunting is still permitted in Bolivia, and it is not protected in Ecuador or Guyana. Jaguar conservation is complicated because of the species' large range spanning 18 countries with different policies and regulations. Specific areas of high importance for jaguar conservation, so-called "Jaguar Conservation Units" (JCU) were determined in 2000. These are large areas inhabited by at least 50 jaguars. Each unit was assessed and evaluated on the basis of size, connectivity, habitat quality for both jaguar and prey, and jaguar population status. That way, 51 Jaguar Conservation Units were determined in 36 geographic regions as priority areas for jaguar conservation including: Recent studies underlined that to maintain the robust exchange across the jaguar gene pool necessary for maintaining the species, it is important that jaguar habitats are interconnected. To facilitate this, a new project, the Paseo del Jaguar, has been established to connect several jaguar hotspots. In 1986, the Cockscomb Basin Wildlife Sanctuary was established in Belize as the world's first protected area for jaguar conservation. Given the inaccessibility of much of the species' range, particularly the central Amazon, estimating jaguar numbers is difficult. Researchers typically focus on particular bioregions, thus species-wide analysis is scant. In 1991, 600–1,000 (the highest total) were estimated to be living in Belize. A year earlier, 125–180 jaguars were estimated to be living in Mexico's 4,000-km (2400-mi) Calakmul Biosphere Reserve, with another 350 in the state of Chiapas. The adjoining Maya Biosphere Reserve in Guatemala, with an area measuring 15,000 km (9,000 mi), may have 465–550 animals. Work employing GPS telemetry in 2003 and 2004 found densities of only six to seven jaguars per 100 km in the critical Pantanal region, compared with 10 to 11 using traditional methods; this suggests the widely used sampling methods may inflate the actual numbers of cats. In setting up protected reserves, efforts generally also have to be focused on the surrounding areas, as jaguars are unlikely to confine themselves to the bounds of a reservation, especially if the population is increasing in size. Human attitudes in the areas surrounding reserves and laws and regulations to prevent poaching are essential to make conservation areas effective. To estimate population sizes within specific areas and to keep track of individual jaguars, camera trapping and wildlife tracking telemetry are widely used, and feces may be sought out with the help of detector dogs to study jaguar health and diet. Current conservation efforts often focus on educating ranch owners and promoting ecotourism. The jaguar is generally defined as an umbrella species – its home range and habitat requirements are sufficiently broad that, if protected, numerous other species of smaller range will also be protected. Umbrella species serve as "mobile links" at the landscape scale, in the jaguar's case through predation. Conservation organizations may thus focus on providing viable, connected habitat for the jaguar, with the knowledge other species will also benefit. Ecotourism setups are being used to generate public interest in charismatic animals such as the jaguar, while at the same time generating revenue that can be used in conservation efforts. Audits done in Africa have shown that ecotourism has helped in African cat conservation. As with large African cats, a key concern in jaguar ecotourism is the considerable habitat space the species requires, so if ecotourism is used to aid in jaguar conservation, some considerations need to be made as to how existing ecosystems will be kept intact, or how new ecosystems that are large enough to support a growing jaguar population will be put into place. The only extant cat native to North America that roars, the jaguar was recorded as an animal of the Americas by Thomas Jefferson in 1799. Jaguars are still occasionally sighted in Arizona and New Mexico, such as El Jefe, prompting actions for its conservation by authorities. For example, on 20 August 2012, the USFWS proposed setting aside 838,232 acres in Arizona and New Mexico – an area larger than Rhode Island – as critical jaguar habitat. In pre-Columbian Central and South America, the jaguar was a symbol of power and strength. Among the Andean cultures, a jaguar cult disseminated by the early Chavín culture became accepted over most of what is today Peru by 900 BC. The later Moche culture of northern Peru used the jaguar as a symbol of power in many of their ceramics. In the religion of the Muisca, who inhabited the cool Altiplano Cundiboyacense in the Colombian Andes, the jaguar was considered a sacred animal and during their religious rituals the people dressed in jaguar skins. The skins were traded with the lowland peoples of the tropical Llanos Orientales. The name of "zipa" Nemequene was derived from the Muysccubun words "nymy" and "quyne", meaning "force of the jaguar". In Mesoamerica, the Olmec—an early and influential culture of the Gulf Coast region roughly contemporaneous with the Chavín—developed a distinct "were-jaguar" motif of sculptures and figurines showing stylised jaguars or humans with jaguar characteristics. In the later Maya civilization, the jaguar was believed to facilitate communication between the living and the dead and to protect the royal household. The Maya saw these powerful felines as their companions in the spiritual world, and a number of Maya rulers bore names that incorporated the Mayan word for jaguar ("b'alam" in many of the Mayan languages). "Balam" ("Jaguar") remains a common Maya surname, and it is also the name of Chilam Balam, a legendary author to whom are attributed 17th and 18th-centuries Maya miscellanies preserving much important knowledge. The Aztec civilization shared this image of the jaguar as the representative of the ruler and as a warrior. The Aztecs formed an elite warrior class known as the Jaguar Knights. In Aztec mythology, the jaguar was considered to be the totem animal of the powerful deity Tezcatlipoca. Remains of jaguar bones were discovered in a burial site in Guatemala which indicates that Mayans kept jaguars as pets. The jaguar and its name are widely used as a symbol in contemporary culture. It is the national animal of Guyana, and is featured in its coat of arms. The flag of the Department of Amazonas, a Colombian department, features a black jaguar silhouette pouncing towards a hunter. The jaguar also appears in banknotes of Brazilian real. The jaguar is also a common fixture in the mythology of many contemporary native cultures in South America, usually being portrayed as the creature which gave humans the power over fire. Jaguar is widely used as a product name, most prominently for a British luxury car brand. The name has been adopted by sports franchises, including the NFL's Jacksonville Jaguars and the Mexican soccer club Chiapas F.C. The crest of Argentina's national federation in rugby union features a jaguar; however, because of a journalist error, the country's national team is nicknamed "Los Pumas". In the spirit of the ancient Mayan culture, the 1968 Olympics in Mexico City adopted a red jaguar as the first official Olympic mascot.	The jaguar ("Panthera onca") is a large felid species and the only extant member of the genus "Panthera" native to the Americas. The jaguar's present range extends from Southwestern United States and Mexico in North America, across much of Central America, and south to Paraguay and northern Argentina in South America. Though there are single cats now living within the Western United States, the species has largely been extirpated from the United States since the early 20th century. It is listed as Near Threatened on the IUCN Red List; and its numbers are declining. 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summarize: The ancient Greek philosopher Archimedes discovered the center of gravity of a triangle. He also postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity. The Roman architect and engineer Vitruvius in "De Architectura" postulated that gravity of an object did not depend on weight but its "nature". In ancient India, Aryabhata first identified the force to explain why objects are not thrown outward as the earth rotates. Brahmagupta described gravity as an attractive force and used the term "gurutvaakarshan" for gravity. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass fall more slowly in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity. In 1687, English mathematician Sir Isaac Newton published "Principia", which hypothesizes the inverse-square law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly." The equation is the following: formula_1 Where "F" is the force, "m" and "m" are the masses of the objects interacting, "r" is the distance between the centers of the masses and "G" is the gravitational constant. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune. A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century. Although Newton's theory has been superseded by Albert Einstein's general relativity, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies. The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the same rate when other forces (such as air resistance and electromagnetic effects) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space. Formulations of the equivalence principle include: In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground. In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force. Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. Like Newton's first law of motion, Einstein's theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, we are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us, and we are non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial. Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor. Notable solutions of the Einstein field equations include: The tests of general relativity included the following: An open question is whether it is possible to describe the small-scale interactions of gravity with the same framework as quantum mechanics. General relativity describes large-scale bulk properties whereas quantum mechanics is the framework to describe the smallest scale interactions of matter. Without modifications these frameworks are incompatible. One path is to describe gravity in the framework of quantum field theory, which has been successful to accurately describe the other fundamental interactions. The electromagnetic force arises from an exchange of virtual photons, where the QFT description of gravity is that there is an exchange of virtual gravitons. This description reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length, where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required. Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of the gravitational field is numerically equal to the acceleration of objects under its influence. The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities. For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures, under the International System of Units (SI). That value, denoted "g", is "g" = 9.80665 m/s (32.1740 ft/s). The standard value of 9.80665 m/s is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand. This value has persisted in meteorology and in some standard atmospheres as the value for 45° latitude even though it applies more precisely to latitude of 45°32'33". Assuming the standardized value for g and ignoring air resistance, this means that an object falling freely near the Earth's surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so on, adding 9.80665 m/s (32.1740 ft/s) to each resulting velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time. According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object does not bounce after it has collided with the Earth, each of them then exerts a repulsive contact force on the other which effectively balances the attractive force of gravity and prevents further acceleration. The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the centrifugal force caused by the Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s at the Equator to about 9.832 m/s at the poles. Under an assumption of constant gravitational attraction, Newton's law of universal gravitation simplifies to "F" = "mg", where "m" is the mass of the body and "g" is a constant vector with an average magnitude of 9.81 m/s on Earth. This resulting force is the object's weight. The acceleration due to gravity is equal to this "g". An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first of a second the ball drops one unit of distance (here, a unit is about 12 mm); by it has dropped at total of 4 units; by, 9 units and so on. Under the same constant gravity assumptions, the potential energy, "E", of a body at height "h" is given by "E" = "mgh" (or "E" = "Wh", with "W" meaning weight). This expression is valid only over small distances "h" from the surface of the Earth. Similarly, the expression formula_2 for the maximum height reached by a vertically projected body with initial velocity "v" is useful for small heights and small initial velocities only. The application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar System, the mass of the Sun, and details of quasars; even the existence of dark matter is inferred using Newton's law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects' masses and inversely proportional to the square of the distance between them. The earliest gravity (possibly in the form of quantum gravity, supergravity or a gravitational singularity), along with ordinary space and time, developed during the Planck epoch (up to 10 seconds after the birth of the Universe), possibly from a primeval state (such as a false vacuum, quantum vacuum or virtual particle), in a currently unknown manner. General relativity predicts that energy can be transported out of a system through gravitational radiation. Any accelerating matter can create curvatures in the space-time metric, which is how the gravitational radiation is transported away from the system. Co-orbiting objects can generate curvatures in space-time such as the Earth-Sun system, pairs of neutron stars, and pairs of black holes. Another astrophysical system predicted to lose energy in the form of gravitational radiation are exploding supernovae. The first indirect evidence for gravitational radiation was through measurements of the Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993. The first direct evidence for gravitational radiation was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion-light years from Earth were measured. This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang. Neutron star and black hole formation also create detectable amounts of gravitational radiation. This research was awarded the Nobel Prize in physics in 2017. , the gravitational radiation emitted by the Solar System is far too small to measure with current technology. In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light. This means that if the Sun suddenly disappeared, the Earth would keep orbiting it normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in the Chinese Science Bulletin in February 2013. In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from the same direction. This confirmed that the speed of gravitational waves was the same as the speed of light. There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.	Gravity (), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or "gravitate" toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing and forming stars and caused the stars to group together into galaxies, so gravity is responsible for many of the large-scale structures in the Universe. 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summarize: The "Belgae" were the inhabitants of the northernmost part of Gaul, which was significantly bigger than modern Belgium. Caesar used the word ""Belgium"" once, to refer to their region. "Gallia Belgica", as it was more commonly called, became a Roman province as a result of his conquests. Areas closer to the Rhine frontier, including the eastern part of modern Belgium, eventually became part of the province of "Germania Inferior", which interacted with Germanic tribes outside the empire. At the time when central government collapsed in the Western Roman Empire, the region of Belgium was inhabited by a mix of Frankish tribes and a more Romanized population. During the 5th century the area came under the rule of the Merovingian kings, who had already seized power in what is northern France. A gradual shift of power during the 8th century led the kingdom of the Franks to evolve into the Carolingian Empire. The Treaty of Verdun in 843 divided the Carolingian empire into three kingdoms, whose borders had a lasting impact on medieval political boundaries. Most of modern Belgium was in the Middle Kingdom, later known as Lotharingia. In 1830, the Belgian Revolution led to the separation of the Southern Provinces from the Netherlands and to the establishment of a Catholic and bourgeois, officially French-speaking and neutral, independent Belgium under a provisional government and a national congress. Since the installation of Leopold I as king on 1831, now celebrated as Belgium's National Day, Belgium has been a constitutional monarchy and parliamentary democracy, with a laicist constitution based on the Napoleonic code. Although the franchise was initially restricted, universal suffrage for men was introduced after the general strike of 1893 (with Belgium shares borders with France (), Germany (), Luxembourg () and the Netherlands (). Its total surface, including water area, is. Before 2018, its total area was believed to be. However, when the country's statistics were measured in 2018, a new calculation method was used. Unlike previous calculations, this one included the area from the coast to the low-water line, revealing the country to be larger in surface area than previously thought. Its land area alone is 30,278 km. It lies between latitudes 49°30' and 51°30' N, and longitudes 2°33' and 6°24' E. Belgium has three main geographical regions; the coastal plain in the northwest and the central plateau both belong to the Anglo-Belgian Basin, and the Ardennes uplands in the southeast to the Hercynian orogenic belt. The Paris Basin reaches a small fourth area at Belgium's southernmost tip, Belgian Lorraine. The coastal plain consists mainly of sand dunes and polders. Further inland lies a smooth, slowly rising landscape irrigated by numerous waterways, with fertile valleys and the northeastern sandy plain of the Campine ("Kempen"). The thickly forested hills and plateaus of the Ardennes are more rugged and rocky with caves and small gorges. Extending westward into France, this area is eastwardly connected to the Eifel in Germany by the High Fens plateau, on which the Signal de Botrange forms the country's highest point at. The climate is maritime temperate with significant precipitation in all seasons (Köppen climate classification: "Cfb"), like most of northwest Europe. The average temperature is lowest in January at and highest in July at. The average precipitation per month varies between for February and April, to for July. Averages for the years 2000 to 2006 show daily temperature minimums of and maximums of and monthly rainfall of ; these are about 1 °C and nearly 10 millimetres above last century's normal values, respectively. Phytogeographically, Belgium is shared between the Atlantic European and Central European provinces of the Circumboreal Region within the Boreal Kingdom. According to the World Wide Fund for Nature, the territory of Belgium belongs to the ecoregion of Atlantic mixed forests. Because of its high population density, industrialization and its location in the center of Western Europe, Belgium still faces some environmental problems. However, due to consistent efforts by the various levels of government in Belgium, the state of the environment in Belgium is gradually improving. This led to Belgium being ranked as one of the top 10 countries (9 out of 132) in terms of environmental protection trends, and to Belgium being ranked in 2012 as the 24th country out of 132 for environmental protection. Belgium moreover has one of Europe's highest waste recycling rates. In particular, the Flemish region of Belgium has the highest waste diversion rate in Europe. Almost 75 percent of the residential waste produced there is reused, recycled, or composted. Belgium is a constitutional, popular monarchy and a federal parliamentary democracy. The bicameral federal parliament is composed of a Senate and a Chamber of Representatives. The former is made up of 50 senators appointed by the parliaments of the communities and regions and 10 co-opted senators. Prior to 2014, most of the Senate's members were directly elected. The Chamber's 150 representatives are elected under a proportional voting system from 11 electoral districts. Belgium has compulsory voting and thus maintains one of the highest rates of voter turnout in the world. The King (currently Philippe) is the head of state, though with limited prerogatives. He appoints ministers, including a Prime Minister, that have the confidence of the Chamber of Representatives to form the federal government. The Council of Ministers is composed of no more than fifteen members. With the possible exception of the Prime Minister, the Council of Ministers is composed of an equal number of Dutch-speaking members and French-speaking members. The judicial system is based on civil law and originates from the Napoleonic code. The Court of Cassation is the court of last resort, with the courts of appeal one level below. Belgium's political institutions are complex; most political power is organized around the need to represent the main cultural communities. Since about 1970, the significant national Belgian political parties have split into distinct components that mainly represent the political and linguistic interests of these communities. The major parties in each community, though close to the political center, belong to three main groups: Christian Democrats, Liberals, and Social Democrats. Further notable parties came into being well after the middle of last century, mainly around linguistic, nationalist, or environmental themes and recently smaller ones of some specific liberal nature. A string of Christian Democrat coalition governments from 1958 was broken in 1999 after the Following a usage which can be traced back to the Burgundian and Habsburg courts, in the 19th century it was necessary to speak French to belong to the governing upper class, and those who could only speak Dutch were effectively second-class citizens. Late that century, and continuing into the 20th century, Flemish movements evolved to counter this situation. While the people in Southern Belgium spoke French or dialects of French, and most Brusselers adopted French as their first language, the Flemings refused to do so and succeeded progressively in making Dutch an equal language in the education system. Following World War II, Belgian politics became increasingly dominated by the autonomy of its two main linguistic communities. Intercommunal tensions rose and the constitution was amended to minimize the potential for conflict. The Federal State's authority includes justice, defense, federal police, social security, nuclear energy, monetary policy and public debt, and other aspects of public finances. State-owned companies include the Belgian Post Group and Belgian Railways. The Federal Government is responsible for the obligations of Belgium and its federalized institutions towards the European Union and NATO. It controls substantial parts of public health, home affairs and foreign affairs. The budget—without the debt—controlled by the federal government amounts to about 50% of the national fiscal income. The federal government employs around 12% of the civil servants. Communities exercise their authority only within linguistically determined geographical boundaries, originally oriented towards the individuals of a Community's language: culture (including audiovisual Because of its location at the crossroads of Western Europe, Belgium has historically been the route of invading armies from its larger neighbors. With virtually defenseless The Belgian Armed Forces have about 47,000 active troops. In 2010, Belgium's defense budget totaled €3.95 billion (representing 1.12% of its GDP). They are organized into one unified structure which consists of four main components: Land Component, or the Army; Air Component, or the Air Force; Naval Component, or the Navy; Medical Component. The operational commands of the four components are subordinate to the Staff Department for Operations and Training of the Ministry of Defense, which is headed by the Assistant Belgium's strongly globalized economy and its transport infrastructure are integrated with the rest of Europe. Its location at the heart of a highly industrialized region helped make it the world's 15th largest trading nation in 2007. The economy is characterized by a highly productive work force, high GNP and high exports per capita. Belgium's main imports are raw materials, machinery and equipment, chemicals, raw diamonds, pharmaceuticals, foodstuffs, transportation equipment, and oil products. Its main exports are machinery and equipment, chemicals, finished diamonds, metals and metal products, and foodstuffs. The Belgian economy is heavily service-oriented and shows a dual nature: a dynamic Flemish economy and a Walloon economy that lags behind. One of the founding members of the European Union, Belgium strongly supports an open economy and the extension of the powers of EU institutions to integrate member economies. Since 1922, through the Belgium-Luxembourg Economic Union, Belgium and Luxembourg have been a single trade market with customs and currency union. Belgium was the first continental European country to undergo the Industrial Revolution, in the early 19th century. Liège and Charleroi rapidly developed mining and steelmaking, which flourished until the mid-20th century in the Sambre and Meuse valley and made Belgium one of the three most industrialized nations in the world from 1830 to 1910. However, by the 1840s the textile industry of Flanders was in severe crisis, and the region experienced famine from 1846 to 1850. After World War II, Ghent and Antwerp experienced a rapid expansion of the chemical and petroleum industries. The 1973 and 1979 oil crises sent the economy into a recession; it was particularly prolonged in Wallonia, where the steel industry had become less competitive and experienced a serious decline. In the 1980s and 1990s, the economic center of the country continued to shift northwards and is now concentrated in the populous Flemish Diamond area. By the end of the 1980s, Belgian macroeconomic policies had resulted in a cumulative government debt of about 120% of GDP., the budget was balanced and public debt was equal to 90.30% of GDP. In 2005 and 2006, real GDP growth rates of 1.5% and 3.0%, respectively, were slightly above the average for the Euro area. Unemployment rates of 8.4% in 2005 and 8.2% in 2006 were close to the area average. By, this had grown to 8.5% compared to an average rate of 9.6% for the European Union as a whole (EU 27). From 1832 until 2002, Belgium's currency was the Belgian franc. Belgium switched to the euro in 2002, with the first sets of euro coins being minted in 1999. The standard Belgian euro coins designated for circulation show the portrait of the monarch (first King Albert II, since 2013 King Philippe). Despite an 18% decrease observed from 1970 to 1999, Belgium still had in 1999 the highest rail network density within the European Union with 113.8 km/1 000 km. On the other hand, the same period, 1970–1999, has seen a huge growth (+56%) of the motorway network. In 1999, the density of km motorways per 1000 km and 1000 inhabitants amounted to 55.1 and 16.5 respectively and were significantly superior to the EU's means of 13.7 and 15.9. From a biological resource perspective, Belgium has a low endowment: Belgium's biocapacity adds up to only 0.8 global hectares in 2016, just about half of the 1.6 global hectares of biocapacity available per person worldwide. In contrast, in 2016, Belgians used on average 6.3 global hectares of biocapacity - their ecological footprint of consumption. This means they required about eight times as much biocapacity as Belgium contains. As a result, Belgium was running a biocapacity deficit of 5.5 global hectares per person in 2016. Belgium experiences some of the most congested traffic in Europe. In 2010, commuters to the cities of Brussels and Antwerp spent respectively 65 and 64 hours a year in traffic jams. Like in most small European countries, more than 80% of the airways traffic is handled by a single airport, the Brussels Airport. The ports of Antwerp and Zeebrugge (Bruges) share more than 80% of Belgian maritime traffic, Antwerp being the second European harbor with a gross weight of goods handled of 115 988 000 t in 2000 after a growth of 10.9% over the preceding five years. In 2016, the port of Antwerp handled 214 million tons after a year-on-year growth of 2.7%. There is a large economic gap between Flanders and Wallonia. Wallonia was historically wealthy compared to Flanders, mostly due to its heavy industries, but the decline of the steel industry post-World War II led to the region's rapid decline, whereas Flanders rose swiftly. Since then, Flanders has been prosperous, among the wealthiest regions in Europe, whereas Wallonia has been languishing. As of 2007, the unemployment rate of Wallonia is over double that of Flanders. The divide has played a key part in the tensions between the Flemish and Walloons in addition to the already-existing language divide. Pro-independence movements have gained high popularity in Flanders as a consequence. The separatist New Flemish Alliance (N-VA) party, for instance, is the largest party in Belgium. As of 1 January 2020, the total population of Belgium according to its population register was 11,492,641. The population density of Belgium is as of January 2019, making it the 22nd most densely populated country in the world, and the 6th most densely populated country in Europe. The most densily populated province is Antwerp, the least densily populated province is Luxembourg. As of January 2019, the Flemish Region had a population of 6,589,069 (57.6% of Belgium), its most populous cities being Antwerp (523,248), Ghent (260,341) and Bruges (118,284). Wallonia had a population of 3,633,795 (31.8% of Belgium) with Charleroi (201,816), Liège (197,355) and Namur (110,939), its most populous cities. The Brussels Capital Region has 1,208,542 inhabitants (10.6% of Belgium) in the 19 municipalities, three of which have over 100,000 residents. In 2017 the average total fertility rate (TFR) across Belgium was 1.64 children per woman, below the replacement rate of 2.1, it remains considerably below the high of 4.87 children born per woman in 1873. Belgium subsequently has one of the oldest populations in the world, with the average age of 41.5 years. , nearly 92% of the population had Belgian citizenship, and other European Union member citizens account for around 6%. The prevalent foreign nationals were Italian (171,918), French (125,061), Dutch (116,970), Moroccan (80,579), Portuguese (43,509), Spanish (42,765), Turkish (39,419) and German (37,621). In 2007, there were 1.38 million foreign-born residents in Belgium, corresponding to 12.9% of the total population. Of these, 685,000 (6.4%) were born outside the EU and 695,000 (6.5%) were born in another EU Member Belgium has three official languages: Dutch, French and German. A number of non-official minority languages are spoken as well. As no census exists, there are no official statistical data regarding the distribution or usage of Belgium's three official languages or their dialects. However, various criteria, including the language(s) of parents, of education, or the second-language status of foreign born, may provide suggested figures. An estimated 60% of the Belgian population are native speakers of Dutch (often referred to as Flemish), and 40% of the population speaks French natively. French-speaking Belgians are often referred to as Walloons, although the French speakers in Brussels are not Walloons. The total number Since the country's independence, Roman Catholicism, counterbalanced by strong freethought movements, has had an important role in Belgium's politics. However Belgium is largely a secular country as the constitution provides for freedom of religion, and the government generally respects this right in practice. During the reigns of Albert I and Baudouin, the Belgian royal family had a reputation of deeply rooted Catholicism. Roman Catholicism has traditionally been Belgium's majority religion; being especially strong in Flanders. However, by 2009 Sunday church attendance was 5% for Belgium in total; The Belgians enjoy good health. According to 2012 estimates, the average life expectancy is 79.65 years. Since 1960, life expectancy has, in line with the European average, grown by two months per year. Death in Belgium is mainly due to heart and vascular disorders, neoplasms, disorders of the respiratory system and unnatural causes of death (accidents, suicide). Non-natural causes of death and cancer are the most common causes of death for females up to age 24 and males up to age 44. Healthcare in Belgium is financed through both social security contributions and taxation. Health insurance is compulsory. Health care is delivered by a mixed public and private system Education is compulsory from 6 to 18 years of age for Belgians. Among OECD countries in 2002, Belgium had the third highest proportion of 18- to 21-year-olds enrolled in postsecondary education, at 42%. Though an estimated 99% of the adult population is literate, concern is rising over functional illiteracy. The Programme for International Student Assessment (PISA), coordinated by the OECD, currently ranks Belgium's education Despite its political and linguistic divisions, the region corresponding to today's Belgium has seen the flourishing of major artistic movements that have had tremendous influence on European art and culture. Nowadays, to a certain extent, cultural life is concentrated within each language Community, and a variety of barriers have made a shared cultural sphere less pronounced. Since the 1970s, there are no bilingual universities or colleges in the country except the Royal Military Academy and the Antwerp Maritime Academy, no common media and no single large cultural or scientific organization in which both main communities are represented. Contributions to painting and architecture have been especially rich. The Mosan art, the Early Netherlandish, the Flemish Renaissance and Baroque painting and major examples of Romanesque, Gothic, Renaissance and Baroque architecture are milestones in the history of art. While the 15th century's art in the Low Countries is dominated by the religious paintings of Jan van Eyck and Rogier van der Weyden, the 16th century is characterized by a broader panel of styles such as Peter Breughel's landscape paintings and Lambert Lombard's representation of the antique. Though the Baroque style of Peter Paul Rubens and Anthony van Dyck flourished in the early 17th century in the Southern Netherlands, it gradually declined thereafter. During the 19th and 20th centuries many original romantic, expressionist and surrealist Belgian painters emerged, including James Ensor and other artists belonging to the Les XX group, Constant Permeke, Paul Delvaux and René Magritte. The avant-garde CoBrA movement appeared in the 1950s, while the sculptor Panamarenko remains a remarkable figure in contemporary art. Multidisciplinary artists Jan Fabre, Wim Delvoye and the painter Luc Tuymans are other internationally renowned figures on the contemporary art scene. Belgian contributions to architecture also continued into the 19th and 20th centuries, including the work of Victor Horta and Henry van de Velde, who were major initiators of Folklore plays a major role in Belgium's cultural life: the country has a comparatively high number of processions, cavalcades, parades, 'ommegangs' and 'ducasses', 'kermesse' and other local festivals, nearly always with an originally religious or mythological background. The Carnival of Binche with its famous Gilles and the 'Processional Giants and Dragons' of Ath, Brussels, Dendermonde, Mechelen and Mons are Many highly ranked Belgian restaurants can be found in the most influential restaurant guides, such as the Michelin Guide. Belgium is famous for beer, chocolate, waffles and french fries with mayonnaise. Contrary to their name, french fries are claimed to have originated in Belgium, although their exact place of origin is uncertain. The national Since the 1970s, sports clubs and federations are organized separately within each language community. Association football is the most popular sport in both parts of Belgium; also very popular are cycling, tennis, swimming, judo and basketball. Belgians hold the most Tour de France victories of any country except France. They have also the most victories on the UCI Road World Championships. Philippe Gilbert is the 2012 world champion. Another modern well-known Belgian cyclist is Tom Boonen. With five victories in the Tour de France and numerous other cycling records, Belgian cyclist Eddy Merckx is regarded as one of the greatest cyclists of all time. Jean-Marie Pfaff, a former Belgian goalkeeper, is considered one of the greatest in the history of association	Belgium, officially the Kingdom of Belgium, is a country in Western Europe. It is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to the southwest, and the North Sea to the northwest. It covers an area of and has a population of more than 11.5 million, making it the 22nd most densely populated country in the world and the 6th most densely populated country in Europe, with a density of. 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summarize: In three dimensions, any set of three-dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used. Commonly, one uses the familiar Cartesian coordinate system, or sometimes spherical polar coordinates, or cylindrical coordinates: where "t" is a parameter, owing to their rectangular or circular symmetry. These different coordinates and corresponding basis vectors represent the same position vector. More general curvilinear coordinates could be used instead and are in contexts like continuum mechanics and general relativity (in the latter case one needs an additional time coordinate). Linear algebra allows for the abstraction of an "n"-dimensional position vector. A position vector can be expressed as a linear combination of basis vectors: The set of all position vectors forms position space (a vector space whose elements are the position vectors), since positions can be added (vector addition) and scaled in length (scalar multiplication) to obtain another position vector in the space. The notion of "space" is intuitive, since each "x" ("i" = 1, 2,..., "n") can have any value, the collection of values defines a point in space. The "dimension" of the position space is "n" (also denoted dim("R") = "n"). The "coordinates" of the vector r with respect to the basis vectors e are "x". The vector of coordinates forms the coordinate vector or "n"-tuple ("x", "x",..., "x"). Each coordinate "x" may be parameterized a number of parameters "t". One parameter "x"("t") would describe a curved 1D path, two parameters "x"("t", "t") describes a curved 2D surface, three "x"("t", "t", "t") describes a curved 3D volume of space, and so on. The linear span of a basis set "B" = {e, e,..., e} equals the position space "R", denoted span("B") = "R". Position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter needs not be time, but can be (e.g.) arc length of the curve. In any equation of motion, the position vector r("t") is usually the most sought-after quantity because this function defines the motion of a particle (i.e. a point mass) – its location relative to a given coordinate system at some time "t". To define motion in terms of position, each coordinate may be parametrized by time; since each successive value of time corresponds to a sequence of successive spatial locations given by the coordinates, the continuum limit of many successive locations is a path the particle traces. In the case of one dimension, the position has only one component, so it effectively degenerates to a scalar coordinate. It could be, say, a vector in the "x" direction, or the radial "r" direction. Equivalent notations include For a position vector r that is a function of time "t", the time derivatives can be computed with respect to "t". These derivatives have common utility in the study of kinematics, control theory, engineering and other sciences. where dr is an infinitesimally small displacement (vector). These names for the first, second and third derivative of position are commonly used in basic kinematics. By extension, the higher-order derivatives can be computed in a similar fashion. Study of these higher-order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to accurately represent the displacement function as a sum of an infinite sequence, enabling several analytical techniques in engineering and physics.	In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point "P" in space in relation to an arbitrary reference origin "O". Usually denoted x, r, or s, it corresponds to the straight line segment from "O" to "P". 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summarize: The speed of light in a fluid is slower than the speed of light in vacuum, and it changes if the fluid is moving along with the light. In 1851, Fizeau measured the speed of light in a fluid moving parallel to the light using a interferometer. Fizeau's results were not in accord with the then-prevalent theories. Fizeau experimentally correctly determined the zeroth term of an expansion of the relativistically correct addition law in terms of as is described below. Fizeau's result led physicists to accept the empirical validity of the rather unsatisfactory theory by Fresnel that a fluid moving with respect to the stationary aether "partially" drags light with it, i.e. the speed is instead of, where is the speed of light in the aether, and is the speed of the fluid with respect to the aether. The aberration of light, of which the easiest explanation is the relativistic velocity addition formula, together with Fizeau's result, triggered the development of theories like Lorentz aether theory of electromagnetism in 1892. In 1905 Albert Einstein, with the advent of special relativity, derived the standard configuration formula ( in the ) for the addition of relativistic velocities. The issues involving aether were, gradually over the years, settled in favor of special relativity. It was observed by Galilei that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward. This observation is now regarded as the first clear statement of the principle of mechanical relativity. Galilei saw that from the point of view of a person standing on the shore, the motion of falling downwards on the ship would be combined with, or added to, the forward motion of the ship. In terms of velocities it can be said that the velocity of the falling body relative to the shore equals the velocity of that body relative to ship plus the velocity of the ship relative to the shore. In general for three objects A (e.g. Galilei on the shore), B (e.g. ship), C (e.g. falling body on ship) the velocity vector formula_1 of C relative to A (velocity of falling object as Galilei sees it) is the sum of the velocity formula_2 of C relative to B (velocity of falling object relative to ship) plus the velocity of B relative to A (ship's velocity away from the shore). The addition here is the vector addition of vector algebra and the resulting velocity is usually represented in the form The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of Galilean transformations. The relativity principle is called Galilean relativity. It is obeyed by Newtonian mechanics. According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change is not noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities. For collinear motions, the speed of the object (e.g. a cannonball fired horizontally out to sea) as measured from the ship would be measured by someone standing on the shore and watching the whole scene through a telescope as The composition formula can take an algebraically equivalent form, which can be easily derived by using only the principle of constancy of the speed of light, The cosmos of special relativity consists of Minkowski spacetime and the addition of velocities corresponds to composition of Lorentz transformations. In the special theory of relativity Newtonian mechanics is modified into relativistic mechanics. The formulas for boosts in the standard configuration follow most straightforwardly from taking differentials of the inverse Lorentz boost in standard configuration. If the primed frame is travelling with speed formula_6 with Lorentz factor formula_7 in the positive relative to the unprimed frame, then the differentials are Divide the first three equations by the fourth, or which is u_y'}{1 + \frac{v}{c^2}u_x'}, \quad u_y' = \frac{\sqrt{1-\frac{v^2}{c^2}}u_y}{1 - \frac{v}{c^2}u_x},</math> in which expressions for the primed velocities were obtained using the standard recipe by replacing by and swapping primed and unprimed coordinates. If coordinates are chosen so that all velocities lie in a (common) plane, then velocities may be expressed as (see polar coordinates) and one finds \tan \theta &= \frac{u_y}{u_x} = \frac{\sqrt{1-\frac{v^2}{c^2}}u_y'}{u_x' + v} = \frac{\sqrt{1-\frac{v^2}{c^2}}u'\sin \theta'}{u'\cos \theta' + v}.\end{align}</math> The proof as given is highly formal. There are other more involved proofs that may be more enlightening, such as the one below. Since a relativistic transformation rotates space and time into each other much as geometric rotations in the plane rotate the - and -axes, it is convenient to use the same units for space and time, otherwise a unit conversion factor appears throughout relativistic formulae, being the speed of light. In a system where lengths and times are measured in the same units, the speed of light is dimensionless and equal to. A velocity is then expressed as fraction of the speed of light. To find the relativistic transformation law, it is useful to introduce the four-velocities, which is the motion of the ship away from the shore, as measured from the shore, and which is the motion of the fly away from the ship, as measured from the ship. The four-velocity is defined to be a four-vector with relativistic length equal to, future-directed and tangent to the world line of the object in spacetime. Here, corresponds to the time component and to the component of the ship's velocity as seen from the shore. It is convenient to take the -axis to be the direction of motion of the ship away from the shore, and the -axis so that the plane is the plane spanned by the motion of the ship and the fly. This results in several components of the velocities being zero;. The ordinary velocity is the ratio of the rate at which the space coordinates are increasing to the rate at which the time coordinate is increasing, Since the relativistic length of is, so The Lorentz transformation matrix that converts velocities measured in the ship frame to the shore frame is the "inverse" of the transformation described on the Lorentz transformation page, so the minus signs that appear there must be inverted here: This matrix rotates the a pure time-axis vector to, and all its columns are relativistically orthogonal to one another, so it defines a Lorentz transformation. If a fly is moving with four-velocity in the ship frame, and it is boosted by multiplying by the matrix above, the new four-velocity in the shore frame is, Dividing by the time component and substituting for the components of the four-vectors and in terms of the components of the three-vectors and gives the relativistic composition law as The form of the relativistic composition law can be understood as an effect of the failure of simultaneity at a distance. For the parallel component, the time dilation decreases the speed, the length contraction increases it, and the two effects cancel out. The failure of simultaneity means that the fly is changing simultaneity slices as the projection of onto. Since this effect is entirely due to the time slicing, the same factor multiplies the perpendicular component, but for the perpendicular component there is no length contraction, so the time dilation multiplies by a factor of. Starting from the expression in coordinates for parallel to the, expressions for the perpendicular and parallel components can be cast in vector form as follows, a trick which also works for Lorentz transformations of other 3d physical quantities originally in set up standard configuration. Introduce the velocity vector in the unprimed frame and in the primed frame, and split them into components parallel (∥) and perpendicular (⊥) to the relative velocity vector (see hide box below) thus then with the usual Cartesian unit basis vectors, set the velocity in the unprimed frame to be which gives, using the results for the standard configuration, where · is the dot product. Since these are vector equations, they still have the same form for in "any" direction. The only difference from the coordinate expressions is that the above expressions refers to "vectors", not components. One obtains where is the reciprocal of the Lorentz factor. The ordering of operands in the definition is chosen to coincide with that of the standard configuration from which the formula is derived. Either the parallel or the perpendicular component for each vector needs to be found, since the other component will be eliminated by substitution of the full vectors. The parallel component of can be found by projecting the full vector into the direction of the relative motion and the perpendicular component of can be found by the geometric properties of the cross product (see figure above right), In each case, is a unit vector in the direction of relative motion. The expressions for and can be found in the same way. Substituting the parallel component into results in the above equation. Using an identity in formula_28 and formula_29, \left[\mathbf v + \frac{\mathbf u'}{\gamma_v} + \frac{1}{c^2}\frac{\gamma_v}{1+\gamma_v}(\mathbf u' \cdot \mathbf v)\mathbf v\right]\\ &= \frac{1}{1 + \frac{\mathbf u' \cdot \mathbf v}{c^2}}\left[\mathbf v + \mathbf u' + \frac{1}{c^2}\frac{\gamma_v}{1+\gamma_v} \mathbf v \times(\mathbf v \times \mathbf u')\right],\end{align}</math> where the last expression is by the standard vector analysis formula. The first expression extends to any number of spatial dimensions, but the cross product is defined in three dimensions only. The objects with having velocity relative to and having velocity relative to can be anything. In particular, they can be three frames, or they could be the laboratory, a decaying particle and one of the decay products of the decaying particle. The relativistic addition of 3-velocities is non-linear for any real numbers and, although it is true that Also, due to the last terms, is in general neither commutative nor associative It deserves special mention that if and refer to velocities of pairwise parallel frames (primed parallel to unprimed and doubly primed parallel to primed), then, according to Einstein's velocity reciprocity principle, the unprimed frame moves with velocity relative to the primed frame, and the primed frame moves with velocity relative to the doubly primed frame hence is the velocity of the unprimed frame relative to the doubly primed frame, and one might expect to have by naive application of the reciprocity principle. This does not hold, though the magnitudes are equal. The unprimed and doubly primed frames are "not" parallel, but related through a rotation. This is related to the phenomenon of Thomas precession, and is not dealt with further here. The norms are given by and Reverse formula found by using standard procedure of swapping for and for. It is clear that the non-commutativity manifests itself as an additional "rotation" of the coordinate frame when two boosts are involved, since the norm squared is the same for both orders of boosts. The gamma factors for the combined velocities are computed as Reverse formula found by using standard procedure of swapping for and for. Notations and conventions for the velocity addition vary from author to author. Different symbols may be used for the operation, or for the velocities involved, and the operands may be switched for the same expression, or the symbols may be switched for the same velocity. A completely separate symbol may also be used for the transformed velocity, rather than the prime used here. Since the velocity addition is non-commutative, one cannot switch the operands or symbols without changing the result. Examples of alternative notation include: Some classical applications of velocity-addition formulas, to the Doppler shift, to the aberration of light, and to the dragging of light in moving water, yielding relativistically valid expressions for these phenomena are detailed below. It is also possible to use the velocity addition formula, assuming conservation of momentum (by appeal to ordinary rotational invariance), the correct form of the -vector part of the momentum four-vector, without resort to electromagnetism, or a priori not known to be valid, relativistic versions of the Lagrangian formalism. This involves experimentalist bouncing off relativistic billiard balls from each other. This is not detailed here, but see for reference (primary source) and. When light propagates in a medium, its speed is reduced, in the rest frame of the medium, to, where is the index of refraction of the medium. The speed of light in a medium uniformly moving with speed in the positive -direction as measured in the lab frame is given directly by the velocity addition formulas. For the forward direction (standard configuration, drop index on ) one gets, Collecting the largest contributions explicitly, Fizeau found the first three terms. The classical result is the first two terms. Another basic application is to consider the deviation of light, i.e. change of its direction, when transforming to a new reference frame with parallel axes, called aberration of light. In this case,, and insertion in the formula for yields For this case one may also compute and from the standard formulae, the trigonometric manipulations essentially being identical in the case to the manipulations in the case. Consider the difference, correct to order. Employ in order to make small angle approximations a trigonometric formula, where were used. Thus the quantity the classical aberration angle, is obtained in the limit. Here "velocity components" will be used as opposed to "speed" for greater generality, and in order to avoid perhaps seemingly ad hoc introductions of minus signs. Minus signs occurring here will instead serve to illuminate features when speeds less than that of light are considered. For light waves in vacuum, time dilation together with a simple geometrical observation alone suffices to calculate the Doppler shift in standard configuration (collinear relative velocity of emitter and observer as well of observed light wave). All velocities in what follows are parallel to the common positive, so subscripts on velocity components are dropped. In the observers frame, introduce the geometrical observation as the spatial distance, or wavelength, between two pulses (wave crests), where is the time elapsed between the emission of two pulses. The time elapsed between the passage of two pulses "at the same point in space" is the "time period", and its inverse is the observed (temporal) frequency. The corresponding quantities in the emitters frame are endowed with primes. For light waves and the observed frequency is where is standard time dilation formula. Suppose instead that the wave is not composed of light waves with speed, but instead, for easy visualization, bullets fired from a relativistic machine gun, with velocity in the frame of the emitter. Then, in general, the geometrical observation is "precisely the same". But now,, and is given by velocity addition, The calculation is then essentially the same, except that here it is easier carried out upside down with instead of. One finds \right), \quad \nu = \gamma_{_V}\nu'\left(1+{V\over s'}\right)</math> Observe that in the typical case, the that enters is "negative". The formula has general validity though. When, the formula reduces to the formula calculated directly for light waves above, If the emitter is not firing bullets in empty space, but emitting waves in a medium, then the "formula still applies", but now, it may be necessary to first calculate from the velocity of the emitter relative to the medium. Returning to the case of a light emitter, in the case the observer and emitter are not collinear, the result has little modification, where is the angle between the light emitter and the observer. This reduces to the previous result for collinear motion when, but for transverse motion corresponding to, the frequency is shifted by the Lorentz factor. This does not happen in the classical optical Doppler effect. Associated to the relativistic velocity formula_60 of an object is a quantity formula_61 whose norm is called rapidity. These are related through where the vector formula_63 is thought of as being Cartesian coordinates on a 3-dimensional subspace of the Lie algebra formula_64 of the Lorentz group spanned by the boost generators formula_65. This space, call it "rapidity space", is isomorphic to as a vector space, and is mapped to the open unit ball, formula_66, "velocity space", via the above relation. The addition law on collinear form coincides with the law of addition of hyperbolic tangents with where the speed of light is set to unity so that formula_69 and formula_70 agree. It this expression, formula_71 and formula_72 are velocities of two objects in any one given frame. The quantity formula_73 is the speed of one or the other object "relative" to the other object as seen "in the given frame". The expression is Lorentz invariant, i.e. independent of which frame is the given frame, but the quantity it calculates is "not". For instance, if the given frame is the rest frame of object one, then formula_74. The line element is found by putting formula_75 or equivalently formula_76, with and the usual spherical angle coordinates for formula_60 taken in the -direction. Now introduce through and the line element on rapidity space formula_80 becomes In scattering experiments the primary objective is to measure the invariant scattering cross section. This enters the formula for scattering of two particle types into a final state formula_82 assumed to have two or more particles, where The objective is to find a correct expression for "relativistic relative speed" formula_95 and an invariant expression for the incident flux. Non-relativistically, one has for relative speed formula_96. If the system in which velocities are measured is the rest frame of particle type formula_97, it is required that formula_98 Setting the speed of light formula_99, the expression for formula_95 follows immediately from the formula for the norm (second formula) in the "general configuration" as The formula reduces in the classical limit to formula_102 as it should, and gives the correct result in the rest frames of the particles. The relative velocity is "incorrectly given" in most, perhaps "all" books on particle physics and quantum field theory. This is mostly harmless, since if either one particle type is stationary or the relative motion is collinear, then the right result is obtained from the incorrect formulas. The formula is invariant, but not manifestly so. It can be rewritten in terms of four-velocities as The correct expression for the flux, published by Christian Møller in 1945, is given by One notes that for collinear velocities, formula_105. In order to get a "manifestly" Lorentz invariant expression one writes formula_106 with formula_107, where formula_108is the density in the rest frame, for the individual particle fluxes and arrives at In the literature the quantity formula_110 as well as formula_73 are both referred to as the relative velocity. In some cases (statistical physics and dark matter literature), formula_110 is referred to as the "Møller velocity", in which case formula_73 means relative velocity. The true relative velocity is at any rate formula_95. The discrepancy between formula_95 and formula_73 is relevant though in most cases velocities are collinear. At LHC the crossing angle is small, around 300 rad, but at the old Intersecting Storage Ring at CERN, it was about 18.	In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. 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summarize: Prior to the Renaissance, the most generally accepted theory of motion in Western philosophy was based on Aristotle who around about 335 BC to 322 BC said that, in the absence of an external motive power, all objects (on Earth) would come to rest and that moving objects only continue to move so long as there is a power inducing them to do so. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, which continues to move the projectile in some way. Aristotle concluded that such violent motion in a void was impossible. Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly two millennia. For example, Lucretius (following, presumably, Epicurus) stated that the "default state" of matter was motion, not stasis. In the 6th century, John Philoponus criticized the inconsistency between Aristotle's discussion of projectiles, where the medium keeps projectiles going, and his discussion of the void, where the medium would hinder a body's motion. Philoponus proposed that motion was not maintained by the action of a surrounding medium, but by some property imparted to the object when it was set in motion. Although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was strongly opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, where Philoponus did have several supporters who further developed his ideas. In the 11th century, Persian polymath Ibn Sina (Avicenna) claimed that a projectile in a vacuum would not stop unless acted upon. In the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named "impetus", dissipated spontaneously. Buridan's position was that a moving object would be arrested by the resistance of the air and the weight of the body which would oppose its impetus. Buridan also maintained that impetus increased with speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Despite the obvious similarities to more modern ideas of inertia, Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other peripatetic views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also believed that impetus could be not only linear, but also circular in nature, causing objects (such as celestial bodies) to move in a circle. Buridan's thought was followed up by his pupil Albert of Saxony (1316–1390) and the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs. Shortly before Galileo's theory of inertia, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone: Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion. According to historian of science Charles Coulston Gillispie, inertia "entered science as a physical consequence of Descartes' geometrization of space-matter, combined with the immutability of God." The principle of inertia, which originated with Aristotle for "motions in a void", states that an object tends to resist a change in motion. According to Newton, an object will stay at rest or stay in motion (i.e. maintain its velocity) unless acted on by a net external force, whether it results from gravity, friction, contact, or some other force. The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of Nicolaus Copernicus in the 16th century, who argued that the Earth is never at rest, but is actually in constant motion around the Sun. Galileo, in his further development of the Copernican model, recognized these problems with the then-accepted nature of motion and, at least partially as a result, included a restatement of Aristotle's description of motion in a void as a basic physical principle: A body moving on a level surface will continue in the same direction at a constant speed unless disturbed. Galileo writes that "all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in movement towards the west (for example), it will maintain itself in that movement." This notion which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to, but distinct from, Newton's notion of rectilinear inertia. For Galileo, a motion is "horizontal" if it does not carry the moving body towards or away from the centre of the earth, and for him, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping." It is also worth noting that Galileo later (in 1632) concluded that based on this initial premise of inertia, it is impossible to tell the difference between a moving object and a stationary one without some outside reference to compare it against. This observation ultimately came to be the basis for Albert Einstein to develop the theory of special relativity. The first physicist to completely break away from the Aristotelian model of motion was Isaac Beeckman in 1614. Concepts of inertia in Galileo's writings would later come to be refined, modified and codified by Isaac Newton as the first of his Laws of Motion (first published in Newton's work, "Philosophiae Naturalis Principia Mathematica", in 1687): Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. Since initial publication, Newton's Laws of Motion (and by inclusion, this first law) have come to form the basis for the branch of physics known as classical mechanics. The term "inertia" was first introduced by Johannes Kepler in his "Epitome Astronomiae Copernicanae" (published in three parts from 1617–1621); however, the meaning of Kepler's term (which he derived from the Latin word for "idleness" or "laziness") was not quite the same as its modern interpretation. Kepler defined inertia only in terms of a resistance to movement, once again based on the presumption that rest was a natural state which did not need explanation. It was not until the later work of Galileo and Newton unified rest and motion in one principle that the term "inertia" could be applied to these concepts as it is today. Nevertheless, despite defining the concept so elegantly in his laws of motion, even Newton did not actually use the term "inertia" to refer to his First Law. In fact, Newton originally viewed the phenomenon he described in his First Law of Motion as being caused by "innate forces" inherent in matter, which resisted any acceleration. Given this perspective, and borrowing from Kepler, Newton attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; thus, Newton defined "inertia" to mean the cause of the phenomenon, rather than the phenomenon itself. However, Newton's original ideas of "innate resistive force" were ultimately problematic for a variety of reasons, and thus most physicists no longer think in these terms. As no alternate mechanism has been readily accepted, and it is now generally accepted that there may not be one which we can know, the term "inertia" has come to mean simply the phenomenon itself, rather than any inherent mechanism. Thus, ultimately, "inertia" in modern classical physics has come to be a name for the same phenomenon described by Newton's First Law of Motion, and the two concepts are now considered to be equivalent. Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies" was built on the understanding of inertial reference frames developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained unchanged from Newton's original meaning. However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to inertial reference frames. To address this limitation, Einstein developed his general theory of relativity ("The Foundation of the General Theory of Relativity", 1916), which provided a theory including "noninertial" (accelerated) reference frames. A quantity related to inertia is "rotational inertia" (→ moment of inertia), the property that a rotating rigid body maintains its state of uniform rotational motion. Its angular momentum remains unchanged, unless an external torque is applied; this is also called conservation of angular momentum. Rotational inertia is often considered in relation to the a rigid body. For example, a gyroscope uses the property that it resists any change in the axis of rotation.	Inertia is the resistance of any physical object to any change in its velocity. This includes changes to the object's speed, or direction of motion. 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summarize: Momentum is a vector quantity: it has both magnitude and direction. Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see multiple dimensions). The momentum of a particle is conventionally represented by the letter. It is the product of two quantities, the particle's mass (represented by the letter ) and its velocity (): The unit of momentum is the product of the units of mass and velocity. In SI units, if the mass is in kilograms and The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses and, and velocities and, the total momentum is The momenta of more than two particles can be added more generally with the following: A system of particles has a If the net force applied to a particle is constant, and is applied for a time interval, the momentum of the particle changes by an amount In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force acting on it, If the net force experienced by a particle changes as a function of time,, the change in momentum (or impulse ) between In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum is constant. This fact, known as the "law of conservation of momentum", is implied by Newton's laws of motion. Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second Momentum is a measurable quantity, and the measurement depends on the motion of the observer. For example: if an apple is sitting in a glass elevator that is descending, an outside observer, looking into the elevator, sees the apple moving, so, to that observer, the apple has a non-zero momentum. To someone inside the elevator, the apple does not move, so, it has zero momentum. The two observers each have a frame of reference, in which, they observe motions, and, if the elevator is descending steadily, they will see behavior that is consistent with those same physical laws. Suppose a particle has position in a stationary frame of reference. From the point of view of By itself, the law of conservation of momentum is not enough to determine the motion of particles after a collision. Another property of the motion, kinetic energy, must be known. This is not necessarily conserved. If it is conserved, the collision is called an "elastic collision"; if not, it is an "inelastic collision". An elastic collision is one in which no kinetic energy is absorbed in the collision. Perfectly elastic "collisions" can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps them apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls is a good example of an "almost" totally elastic collision, due to their high rigidity, but when bodies come in contact there is always some dissipation. A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision and and after, the equations In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound). Examples include traffic collisions, in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in the Franck–Hertz experiment); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles. In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision then in a perfectly inelastic collision both bodies will be travelling with velocity after the Real motion has both direction and velocity and must be represented by a vector. In a coordinate system with axes, velocity has components in the -direction, in the -direction, in the -direction. The vector is represented by a boldface symbol: Similarly, the momentum is a vector quantity and is represented by a boldface symbol: The equations in the previous sections, work in vector form if the scalars and are replaced by vectors and. Each vector equation The concept of momentum plays a fundamental role in explaining the behavior of variable-mass objects such as a rocket ejecting fuel or a star accreting gas. In analyzing such an object, one treats the object's mass as a function that varies with time:. The momentum of the object at time is therefore. One might then try to invoke Newton's second law of motion by saying that the external force on the object is related to Newtonian physics assumes that absolute time and space exist outside of any observer; this gives rise to Galilean invariance. It also results in a prediction that the speed of light can vary from one reference frame to another. This is contrary to observation. In the special theory of relativity, Einstein keeps the postulate that the equations of motion do not depend on the reference frame, but assumes that the speed of light is invariant. As a result, position and In the theory of special relativity, physical quantities are expressed in terms of four-vectors that include time as a fourth coordinate along with the three space coordinates. These vectors are generally represented by capital letters, for example for position. The expression for the "four-momentum" depends on how the coordinates are expressed. Time may be given in its normal units or multiplied by the speed of light so that all the components of the four-vector have dimensions of length. If the latter scaling is used, an interval of proper time,, defined by is invariant under Lorentz transformations (in this expression and in what follows the metric signature has been used, different authors use different conventions). Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time Newton's laws can be difficult to apply to many kinds of motion because the motion is limited by "constraints". For example, a bead on an abacus is constrained to move along its wire and a pendulum bob is constrained to swing at a fixed distance from the pivot. Many such constraints can be incorporated by changing the normal Cartesian coordinates to a set of "generalized coordinates" that may be fewer in number. Refined mathematical methods have been developed for solving mechanics problems in generalized coordinates. They introduce a "generalized momentum", also known as the "canonical" or "conjugate momentum", that extends the concepts of both linear momentum and angular momentum. To distinguish it from generalized momentum, the product of mass and velocity is also referred to as "mechanical", "kinetic" or "kinematic momentum". The two main methods are described below. In Lagrangian mechanics, a Lagrangian is defined as the difference between the kinetic energy and the potential energy : If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion (known as the Lagrange or Euler–Lagrange equations) are a set of equations: If a coordinate is not a Cartesian coordinate, the associated generalized momentum component does not necessarily have the dimensions of linear momentum. Even In Hamiltonian mechanics, the Lagrangian (a function of generalized coordinates and their derivatives) is replaced by a Hamiltonian that is a function of generalized coordinates and momentum. The Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields. The electromagnetic force ("Lorentz force") on a particle with charge due to a combination of electric field and magnetic field is (in SI units). It has an electric potential and magnetic vector potential. In the non-relativistic regime, its generalized momentum is In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction, which states that every force has a reciprocating equal and opposite force. Under some circumstances, moving charged particles can exert forces on each other in non-opposite directions. Nevertheless, the combined momentum of the particles and the electromagnetic field is conserved. The Lorentz force imparts a momentum to the particle, so by Newton's second law the particle must impart a momentum to the electromagnetic fields. In a vacuum, the momentum per unit volume is where is the vacuum permeability and is the speed of light. The momentum density is proportional to the Poynting vector which gives the directional rate of energy transfer per unit area: If momentum is to be conserved over the volume The above results are for the "microscopic" Maxwell equations, applicable to electromagnetic forces in a vacuum (or on a very small scale in media). It is more difficult to define momentum density in media because the division into electromagnetic and mechanical is arbitrary. The definition of electromagnetic momentum density is modified to where the H-field is related to the B-field and the magnetization by The electromagnetic stress tensor depends on the properties of the media. In quantum mechanics, momentum is defined as a self-adjoint operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables. For a single particle described in the position basis the momentum operator can be written as where is the gradient operator, is the reduced Planck constant, and is the imaginary unit. This is a commonly encountered form of the momentum operator, though In fields such as fluid dynamics and solid mechanics, it is not feasible to follow the motion of individual atoms or molecules. Instead, the materials must be approximated by a continuum in which there is a particle or fluid parcel at each point that is assigned the average of the properties of atoms in a small region nearby. In particular, it has a density and velocity that depend on time and position. The momentum per unit volume is. Consider a column of water A disturbance in a medium gives rise to oscillations, or waves, that propagate away from their source. In a fluid, small changes in pressure can often be described by the acoustic wave equation: where is the speed of sound. In a solid, similar equations can be obtained for propagation In about 530 AD, working in Alexandria, Byzantine philosopher John Philoponus developed a concept of momentum in his commentary to Aristotle's "Physics". Aristotle claimed that everything that is moving must be kept moving by something. For example, a thrown ball must be kept moving by motions of the air. Most writers continued to accept Aristotle's theory until the time of Galileo, but a few were skeptical. Philoponus pointed out the absurdity in Aristotle's claim that motion of an object is promoted by the same air that is resisting its passage. He proposed instead that an impetus was imparted to the object in the act of throwing it. Ibn Sīnā (also known by his Latinized name Avicenna) read Philoponus and published his own theory of motion in "The Book of Healing" in 1020. He agreed that an impetus is imparted to a projectile by the thrower; but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as a persistent, requiring external forces such as air resistance to dissipate it. The work of Philoponus, and possibly that of Ibn Sīnā, was read and refined by the European philosophers Peter Olivi and Jean Buridan. Buridan, who in about 1350 was made rector of the University of Paris, referred to impetus being proportional to the weight times the speed. Moreover, Buridan's theory was different from his predecessor's in that he did not consider impetus to be self-dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus. René Descartes believed that the total "quantity of motion" () in the universe is conserved, where the quantity of motion is understood as the product of size and speed. This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more important, he believed that it is speed rather than velocity that is conserved. So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion. Galileo, in his "Two New Sciences", used the Italian word "impeto" to similarly describe Descartes' quantity of motion. Leibniz, in his "Discourse on Metaphysics", gave an argument against Descartes' construction of the conservation of the "quantity of motion" using an example of dropping blocks of different sizes different distances. He points out that force is conserved but quantity of motion, construed as the product of size and speed of an object, is not conserved. Christiaan Huygens concluded quite early that Descartes's laws for the elastic collision of two bodies must be wrong, and he formulated the correct laws. An important step was his recognition of the Galilean invariance of the problems. His views then took many years to be circulated. He passed them on in person to William Brouncker and Christopher Wren in London, in 1661. What Spinoza wrote to Henry Oldenburg about them, in 1666 which was during the Second Anglo-Dutch War, was guarded. Huygens had actually worked them out in a manuscript "De motu corporum ex percussione" in the period 1652–6. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He published them in the "Journal des sçavans" in 1669. The first correct statement of the law of conservation of momentum was by English mathematician John Wallis in his 1670 work, "Mechanica sive De Motu, Tractatus Geometricus": "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result". Wallis used "momentum" for quantity of motion, and "vis" for force. Newton's "Philosophiæ Naturalis Principia Mathematica", when it was first published in 1687, showed a similar casting around for words to use for the mathematical momentum. His Definition II defines "quantitas motus", "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum. Thus when in Law II he refers to "mutatio motus", "change of motion", being proportional to the force impressed, he is generally taken to mean momentum and not motion. It remained only to assign a standard term to the quantity of motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jennings's "Miscellanea" in 1721, five years before the final edition of Newton's "Principia Mathematica", momentum or "quantity of motion" was being defined for students as "a rectangle", the product of and, where is "quantity of material" and is "velocity",.	In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. 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summarize: Impulse J produced from time "t" to "t" is defined to be where F is the resultant force applied from "t" to "t". From Newton's second law, force is related to momentum p by Therefore, where Δp is the change in linear momentum from time "t" to "t". This is often called the impulse-momentum theorem (analogous to the work-energy theorem). As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant: where Impulse has the same units and dimensions as momentum. In the International System of Units, these are. In English engineering units, they are. The term "impulse" is also used to refer to a fast-acting force or impact. This type of impulse is often "idealized" so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in game physics engines). Additionally, in rocketry, the term "total impulse" is commonly used and is considered synonymous with the term "impulse". The application of Newton's second law for variable mass allows impulse and momentum to be used as analysis tools for jet- or rocket-propelled vehicles. In the case of rockets, the impulse imparted can be normalized by unit of propellant expended, to create a performance parameter, specific impulse. This fact can be used to derive the Tsiolkovsky rocket equation, which relates the vehicle's propulsive change in velocity to the engine's specific impulse (or nozzle exhaust velocity) and the vehicle's propellant-mass ratio.	In classical mechanics, impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction. The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg⋅m/s). 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summarize: The role of fictitious forces in Newtonian mechanics is described by Tonnelat: Fictitious forces arise in classical mechanics and special relativity in all non-inertial frames. Inertial frames are privileged over non-inertial frames because they do not have physics whose causes are outside of the system, while non-inertial frames do. Fictitious forces, or physics whose cause is outside of the system, are no longer necessary in general relativity, since these physics are explained with the geodesics of spacetime. The surface of the Earth is a rotating reference frame. To solve classical mechanics problems exactly in an Earth-bound reference frame, three fictitious forces must be introduced: the Coriolis force, the centrifugal force (described below) and the Euler force. The Euler force is typically ignored because the variations in the angular velocity of the rotating Earth surface are usually insignificant. Both of the other fictitious forces are weak compared to most typical forces in everyday life, but they can be detected under careful conditions. For example, Léon Foucault used his Foucault pendulum to show that a Coriolis force results from the Earth's rotation. If the Earth were to rotate twenty times faster (making each day only ~72 minutes long), people could easily get the impression that such fictitious forces were pulling on them, as on a spinning carousel; people in temperate and tropical latitudes would, in fact, need to hold on in order to avoid being launched into orbit by the centrifugal force. Observers inside a closed box that is moving with a constant velocity cannot detect their own motion; however, observers within an accelerating reference frame can detect that they are in a non-inertial reference frame from the fictitious forces that arise. For example, for straight-line acceleration Vladimir Arnold presents the following theorem: Other accelerations also give rise to fictitious forces, as described mathematically below. The physical explanation of motions in an inertial frame is the simplest possible, requiring no fictitious forces: fictitious forces are zero, providing a means to distinguish inertial frames from others. An example of the detection of a non-inertial, rotating reference frame is the precession of a Foucault pendulum. In the non-inertial frame of the Earth, the fictitious Coriolis force is necessary to explain observations. In an inertial frame outside the Earth, no such fictitious force is necessary. Figure 1 (top) shows an accelerating car. When a car accelerates, a passenger feels like they're being pushed back into the seat. In an inertial frame of reference attached to the road, there is no physical force moving the rider backward. However, in the rider's non-inertial reference frame attached to the accelerating car, there "is" a backward fictitious force. We mention two possible reasons for the force to clarify its (the force's) existence: How can the accelerating frame be discovered to be non-inertial? In the accelerating frame, everything appears to be subject to zero net force, and nothing moves. Nonetheless, compression of the seat is observed and is explained in the accelerating frame (and in an inertial frame) by the force of acceleration on the seat from the car on one side, and the opposing force of reaction to acceleration by the passenger on the other. Identification of the accelerating frame as non-inertial cannot be based simply on the compression of the seat, which all observers can explain; rather it is based on the "simplicity" of the physical explanation for this compression. The explanation of the seat compression in the accelerating frame requires not only the thrust from the axle of the car, but additional (fictitious) forces. In an inertial frame, only the thrust from the axle is necessary. Therefore, the inertial frame has a "simpler" physical explanation (not necessarily a simpler mathematical formulation, however), indicating the accelerating frame is a non-inertial frame of reference. In other words, in the inertial frame, fictitious forces are zero. See inertial frame for more detail. This example illustrates how fictitious forces arise from switching from an inertial to a non-inertial reference frame. Calculations of physical quantities (compression of the seat, required force from the axle) made in any frame give the same answers, but in some cases calculations are easier to make in a non-inertial frame. (In this simple example, the calculations are equally complex for the two frames described.) A similar effect occurs in circular motion, circular from the standpoint of an inertial frame of reference attached to the road. When seen from a non-inertial frame of reference attached to the car, the fictitious force called the centrifugal force appears. If the car is moving at constant speed around a circular section of road, the occupants will feel pushed outside by this centrifugal force, away from the center of the turn. Again the situation can be viewed from inertial or non-inertial frames: A classic example of fictitious force in circular motion is the experiment of rotating spheres tied by a cord and spinning around their center of mass. In this case, as with the linearly accelerating car example, the identification of a rotating, non-inertial frame of reference can be based upon the vanishing of fictitious forces. In an inertial frame, fictitious forces are not necessary to explain the tension in the string joining the spheres. In a rotating frame, Coriolis and centrifugal forces must be introduced to predict the observed tension. In the rotating reference frame perceived on the surface of the Earth, centrifugal force reduces the apparent force of gravity by about one part in a thousand, depending on latitude. This reduction is zero at the poles, maximum at the equator. The fictitious Coriolis force, which is observed in rotational frames, is ordinarily visible only in very large-scale motion like the projectile motion of long-range guns or the circulation of the Earth's atmosphere (see Rossby number). Neglecting air resistance, an object dropped from a 50-meter-high tower at the equator will fall 7.7 millimeters eastward of the spot below where it is dropped because of the Coriolis force. In the case of distant objects and a rotating reference frame, what must be taken into account is the resultant force of centrifugal and Coriolis force. Consider a distant star observed from a rotating spacecraft. In the reference frame co-rotating with the spacecraft, the distant star appears to move along a circular trajectory around the spacecraft. The apparent motion of the star is an apparent centripetal acceleration. Just like in the example above of the car in circular motion, the centrifugal force has the same magnitude as the fictitious centripetal force, but is directed in the opposite, centrifugal direction. In this case the Coriolis force is twice the magnitude of the centrifugal force, and it points in centripetal direction. The vector sum of the centrifugal force and the Coriolis force is the total fictitious force, which in this case points in centripetal direction. Fictitious forces can be considered to do work, provided that they move an object on a trajectory that changes its energy from potential to kinetic. For example, consider a person in a rotating chair holding a weight in their outstretched hand. If they pull their hand inward toward their body, from the perspective of the rotating reference frame, they have done work against the centrifugal force. When the weight is let go, it spontaneously flies outward relative to the rotating reference frame, because the centrifugal force does work on the object, converting its potential energy into kinetic. From an inertial viewpoint, of course, the object flies away from them because it is suddenly allowed to move in a straight line. This illustrates that the work done, like the total potential and kinetic energy of an object, can be different in a non-inertial frame than an inertial one. The notion of "fictitious force" comes up in Einstein's general theory of relativity. All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity. This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, freefalling reference frames are equivalent to an inertial reference frame (the equivalence principle). Following up on this insight, Einstein was able to formulate a theory with gravity as a fictitious force and attributing the apparent acceleration of gravity to the curvature of spacetime. This idea underlies Einstein's theory of general relativity. See Eötvös experiment. Many problems require use of noninertial reference frames, for example, those involving satellites and particle accelerators. Figure 2 shows a particle with mass "m" and position vector x("t") in a particular inertial frame A. Consider a non-inertial frame B whose origin relative to the inertial one is given by X("t"). Let the position of the particle in frame B be x("t"). What is the force on the particle as expressed in the coordinate system of frame B? To answer this question, let the coordinate axis in B be represented by unit vectors u with "j" any of { 1, 2, 3 } for the three coordinate axes. Then The interpretation of this equation is that x is the vector displacement of the particle as expressed in terms of the coordinates in frame B at time "t". From frame A the particle is located at: As an aside, the unit vectors { u } cannot change magnitude, so derivatives of these vectors express only rotation of the coordinate system B. On the other hand, vector X simply locates the origin of frame B relative to frame A, and so cannot include rotation of frame B. Taking a time derivative, the velocity of the particle is: The second term summation is the velocity of the particle, say v as measured in frame B. That is: The interpretation of this equation is that the velocity of the particle seen by observers in frame A consists of what observers in frame B call the velocity, namely v, plus two extra terms related to the rate of change of the frame-B coordinate axes. One of these is simply the velocity of the moving origin v. The other is a contribution to velocity due to the fact that different locations in the non-inertial frame have different apparent velocities due to rotation of the frame; a point seen from a rotating frame has a rotational component of velocity that is greater the further the point is from the origin. To find the acceleration, another time differentiation provides: Using the same formula already used for the time derivative of x, the velocity derivative on the right is: Consequently, The interpretation of this equation is as follows: the acceleration of the particle in frame A consists of what observers in frame B call the particle acceleration a, but in addition there are three acceleration terms related to the movement of the frame-B coordinate axes: one term related to the acceleration of the origin of frame B, namely a, and two terms related to rotation of frame B. Consequently, observers in B will see the particle motion as possessing "extra" acceleration, which they will attribute to "forces" acting on the particle, but which observers in A say are "fictitious" forces arising simply because observers in B do not recognize the non-inertial nature of frame B. The factor of two in the Coriolis force arises from two equal contributions: (i) the apparent change of an inertially constant velocity with time because rotation makes the direction of the velocity seem to change (a "d"v/d"t" term) and (ii) an apparent change in the velocity of an object when its position changes, putting it nearer to or further from the axis of rotation (the change in formula_7 due to change in "x " ). To put matters in terms of forces, the accelerations are multiplied by the particle mass: The force observed in frame B, F = "m"a is related to the actual force on the particle, F, by where: Thus, we can solve problems in frame B by assuming that Newton's second law holds (with respect to quantities in that frame) and treating F as an additional force. Below are a number of examples applying this result for fictitious forces. More examples can be found in the article on centrifugal force. A common situation in which noninertial reference frames are useful is when the reference frame is rotating. Because such rotational motion is non-inertial, due to the acceleration present in any rotational motion, a fictitious force can always be invoked by using a rotational frame of reference. Despite this complication, the use of fictitious forces often simplifies the calculations involved. To derive expressions for the fictitious forces, derivatives are needed for the apparent time rate of change of vectors that take into account time-variation of the coordinate axes. If the rotation of frame 'B' is represented by a vector Ω pointed along the axis of rotation with orientation given by the right-hand rule, and with magnitude given by then the time derivative of any of the three unit vectors describing frame B is and as is verified using the properties of the vector cross product. These derivative formulas now are applied to the relationship between acceleration in an inertial frame, and that in a coordinate frame rotating with time-varying angular velocity ω("t"). From the previous section, where subscript A refers to the inertial frame and B to the rotating frame, setting a = 0 to remove any translational acceleration, and focusing on only rotational properties (see Eq. 1): Collecting terms, the result is the so-called "acceleration transformation formula": The physical acceleration a due to what observers in the inertial frame A call "real external forces" on the object is, therefore, not simply the acceleration a seen by observers in the rotational frame B, but has several additional geometric acceleration terms associated with the rotation of B. As seen in the rotational frame, the acceleration a of the particle is given by rearrangement of the above equation as: The net force upon the object according to observers in the rotating frame is F = "m"a. If their observations are to result in the correct force on the object when using Newton's laws, they must consider that the additional force F is present, so the end result is F = F + F. Thus, the fictitious force used by observers in B to get the correct behavior of the object from Newton's laws equals: Here, the first term is the "Coriolis force", the second term is the "centrifugal force", and the third term is the "Euler force". As a related example, suppose the moving coordinate system "B" rotates with a constant angular speed ω in a circle of radius "R" about the fixed origin of inertial frame "A", but maintains its coordinate axes fixed in orientation, as in Figure 3. The acceleration of an observed body is now (see Eq. 1): where the summations are zero inasmuch as the unit vectors have no time dependence. The origin of system "B" is located according to frame "A" at: leading to a velocity of the origin of frame "B" as: leading to an acceleration of the origin of "B" given by: Because the first term, which is is of the same form as the normal centrifugal force expression: it is a natural extension of standard terminology (although there is no standard terminology for this case) to call this term a "centrifugal force". Whatever terminology is adopted, the observers in frame "B" must introduce a fictitious force, this time due to the acceleration from the orbital motion of their entire coordinate frame, that is radially outward away from the center of rotation of the origin of their coordinate system: and of magnitude: Notice that this "centrifugal force" has differences from the case of a rotating frame. In the rotating frame the centrifugal force is related to the distance of the object from the origin of frame "B", while in the case of an orbiting frame, the centrifugal force is independent of the distance of the object from the origin of frame "B", but instead depends upon the distance of the origin of frame "B" from "its" center of rotation, resulting in the "same" centrifugal fictitious force for "all" objects observed in frame "B". As a combination example, Figure 4 shows a coordinate system "B" that orbits inertial frame "A" as in Figure 3, but the coordinate axes in frame "B" turn so unit vector u always points toward the center of rotation. This example might apply to a test tube in a centrifuge, where vector u points along the axis of the tube toward its opening at its top. It also resembles the Earth-Moon system, where the Moon always presents the same face to the Earth. In this example, unit vector u retains a fixed orientation, while vectors u, u rotate at the same rate as the origin of coordinates. That is, Hence, the acceleration of a moving object is expressed as (see Eq. 1): where the angular acceleration term is zero for constant rate of rotation. Because the first term, which is is of the same form as the normal centrifugal force expression: it is a natural extension of standard terminology (although there is no standard terminology for this case) to call this term the "centrifugal force". Applying this terminology to the example of a tube in a centrifuge, if the tube is far enough from the center of rotation, \|X\| = "R" ≫ \|x\|, all the matter in the test tube sees the same acceleration (the same centrifugal force). Thus, in this case, the fictitious force is primarily a uniform centrifugal force along the axis of the tube, away from the center of rotation, with a value \|F\| = ω "R", where "R" is the distance of the matter in the tube from the center of the centrifuge. It is standard specification of a centrifuge to use the "effective" radius of the centrifuge to estimate its ability to provide centrifugal force. Thus, a first estimate of centrifugal force in a centrifuge can be based upon the distance of the tubes from the center of rotation, and corrections applied if needed. Also, the test tube confines motion to the direction down the length of the tube, so v is opposite to u and the Coriolis force is opposite to u, that is, against the wall of the tube. If the tube is spun for a long enough time, the velocity v drops to zero as the matter comes to an equilibrium distribution. For more details, see the articles on sedimentation and the Lamm equation. A related problem is that of centrifugal forces for the Earth-Moon-Sun system, where three rotations appear: the daily rotation of the Earth about its axis, the lunar-month rotation of the Earth-Moon system about their center of mass, and the annual revolution of the Earth-Moon system about the Sun. These three motions influence the tides. Figure 5 shows another example comparing the observations of an inertial observer with those of an observer on a rotating carousel. The carousel rotates at a constant angular velocity represented by the vector Ω with magnitude ω, pointing upward according to the right-hand rule. A rider on the carousel walks radially across it at constant speed, in what appears to the walker to be the straight line path inclined at 45° in Figure 5. To the stationary observer, however, the walker travels a spiral path. The points identified on both paths in Figure 5 correspond to the same times spaced at equal time intervals. We ask how two observers, one on the carousel and one in an inertial frame, formulate what they see using Newton's laws. The observer at rest describes the path followed by the walker as a spiral. Adopting the coordinate system shown in Figure 5, the trajectory is described by r("t"): where the added π/4 sets the path angle at 45° to start with (just an arbitrary choice of direction), u is a unit vector in the radial direction pointing from the center of the carousel to the walker at time "t". The radial distance "R"("t") increases steadily with time according to: with "s" the speed of walking. According to simple kinematics, the velocity is then the first derivative of the trajectory: with u a unit vector perpendicular to u at time "t" (as can be verified by noticing that the vector dot product with the radial vector is zero) and pointing in the direction of travel. The acceleration is the first derivative of the velocity: The last term in the acceleration is radially inward of magnitude ω "R", which is therefore the instantaneous centripetal acceleration of circular motion. The first term is perpendicular to the radial direction, and pointing in the direction of travel. Its magnitude is 2"s"ω, and it represents the acceleration of the walker as the edge of the carousel is neared, and the arc of circle traveled in a fixed time increases, as can be seen by the increased spacing between points for equal time steps on the spiral in Figure 5 as the outer edge of the carousel is approached. Applying Newton's laws, multiplying the acceleration by the mass of the walker, the inertial observer concludes that the walker is subject to two forces: the inward, radially directed centripetal force, and another force perpendicular to the radial direction that is proportional to the speed of the walker. The rotating observer sees the walker travel a straight line from the center of the carousel to the periphery, as shown in Figure 5. Moreover, the rotating observer sees that the walker moves at a constant speed in the same direction, so applying Newton's law of inertia, there is "zero" force upon the walker. These conclusions do not agree with the inertial observer. To obtain agreement, the rotating observer has to introduce fictitious forces that appear to exist in the rotating world, even though there is no apparent reason for them, no apparent gravitational mass, electric charge or what have you, that could account for these fictitious forces. To agree with the inertial observer, the forces applied to the walker must be exactly those found above. They can be related to the general formulas already derived, namely: In this example, the velocity seen in the rotating frame is: with u a unit vector in the radial direction. The position of the walker as seen on the carousel is: and the time derivative of Ω is zero for uniform angular rotation. Noticing that and we find: To obtain a straight-line motion in the rotating world, a force exactly opposite in sign to the fictitious force must be applied to reduce the net force on the walker to zero, so Newton's law of inertia will predict a straight line motion, in agreement with what the rotating observer sees. The fictitious forces that must be combated are the Coriolis force (first term) and the centrifugal force (second term). (These terms are approximate.) By applying forces to counter these two fictitious forces, the rotating observer ends up applying exactly the same forces upon the walker that the inertial observer predicted were needed. Because they differ only by the constant walking velocity, the walker and the rotational observer see the same accelerations. From the walker's perspective, the fictitious force is experienced as real, and combating this force is necessary to stay on a straight line radial path holding constant speed. It's like battling a crosswind while being thrown to the edge of the carousel. Notice that this kinematical discussion does not delve into the mechanism by which the required forces are generated. That is the subject of kinetics. In the case of the carousel, the kinetic discussion would involve perhaps a study of the walker's shoes and the friction they need to generate against the floor of the carousel, or perhaps the dynamics of skateboarding, if the walker switched to travel by skateboard. Whatever the means of travel across the carousel, the forces calculated above must be realized. A very rough analogy is heating your house: you must have a certain temperature to be comfortable, but whether you heat by burning gas or by burning coal is another problem. Kinematics sets the thermostat, kinetics fires the furnace.	A fictitious force (also called a pseudo force, d'Alembert force, or inertial force) is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as an accelerating or rotating reference frame. An example is seen in a passenger vehicle that is accelerating in the forward direction - passengers perceive that they are acted upon by a force in the rearward direction pushing them back into their seats. An example in a rotating reference frame is the force that appears to push objects outwards towards the rim of a centrifuge. 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2363, 14361, 4, 1295, 70, 80280, 111, 70, 47014, 1916, 91067, 123789, 4, 1836, 765, 16940, 4488, 26548, 70, 69514, 3125, 2870, 37772, 5, 14847, 70, 57888, 83, 2633, 738, 4, 442, 150189, 79850, 33977, 90, 1810, 19364, 35845, 47, 70, 47014, 1916, 91067, 123789, 4, 6637, 70, 69514, 3125, 2870, 37772, 14602, 4488, 98, 70, 36746, 4, 96760, 214, 6863, 38516, 48302, 3934, 200, 86, 9523, 5, 28090, 142, 23, 2529, 15403, 21455, 38496, 4, 111, 15411, 4, 70, 36746, 33977, 90, 16065, 1295, 2856, 6637, 442, 83, 186683, 107003, 47, 25813, 23, 10, 80560, 13315, 5, 3293, 58755, 1636, 450, 70, 4488, 16940, 4, 1884, 70, 3622, 38516, 136, 200, 86, 9523, 48302, 111, 142, 36746, 4, 831, 186, 12921, 23, 10, 351, 9, 20037, 118, 289, 123789, 3501, 142, 23, 2529, 15403, 1632, 5, 581, 110, 1363, 111, 44, 20941, 31821, 10821, 37772, 58, 32497, 1257, 23, 119225, 25, 7, 4537, 154453, 111, 90816, 939, 5, 3164, 6, 20941, 31821, 10821, 84616, 621, 123875, 289, 47, 70, 46889, 111, 70, 36746, 54799, 3129, 1836, 27992, 4, 3129, 83, 2843, 29568, 100, 64002, 939, 5, 3293, 12441, 24748, 119225, 47, 32195, 36766, 64002, 939, 509, 10, 6, 20941, 31821, 10821, 37772, 237, 5299, 5, 1529, 959, 297, 450, 10, 4092, 9146, 214, 160073, 23, 10, 155738, 16530, 2806, 959, 186, 19048, 47, 96391, 70, 37772, 111, 64002, 939, 74, 8311, 329, 4, 4092, 9146, 214, 91067, 2674, 90, 621, 183234, 47, 142, 23, 2529, 15403, 91067, 123789, 15, 2347, 224743, 3956, 24702, 133, 194, 77168, 214, 1257, 98, 903, 149201, 4, 119225, 509, 19048, 47, 26168, 67, 10, 154453, 678, 64002, 939, 237, 10, 6, 20941, 31821, 10821, 37772, 136, 150380, 214, 70, 173676, 197108, 1830, 111, 64002, 939, 47, 70, 130661, 6644, 111, 32628, 6032, 5, 3293, 6528, 1379, 25720, 119225, 25, 7, 154453, 111, 4537, 90816, 939, 5, 6872, 241, 16463, 68709, 7, 28007, 5, 52455, 44402, 64209, 4527, 111, 351, 20037, 118, 289, 91067, 2674, 90, 4, 100, 27781, 4, 8382, 23, 3784, 6496, 99675, 90, 136, 915, 26147, 197108, 25251, 5, 55412, 13, 116, 45831, 10, 915, 26147, 678, 46889, 44, 39, 58, 136, 19069, 173, 18770, 1022, 132, 58, 18, 18939, 23, 10, 17311, 23, 2529, 15403, 123789, 62, 5, 137399, 10, 351, 9, 20037, 118, 289, 123789, 335, 124901, 59665, 35845, 47, 70, 23, 2529, 15403, 1632, 83, 34475, 390, 1193, 132, 58, 18, 51029, 10842, 70, 19069, 111, 70, 915, 26147, 23, 123789, 335, 186, 1022, 132, 58, 18, 51029, 4865, 83, 70, 37772, 98, 70, 915, 26147, 237, 36510, 297, 23, 70, 176866, 13, 5426, 111, 123789, 335, 32, 717, 35166, 903, 9655, 4, 2633, 70, 176866, 13, 10, 33102, 23, 335, 186, 33636, 297, 390, 25072, 22834, 22230, 75, 678, 44, 170, 58, 2499, 111, 10666, 106, 4, 116, 4, 138, 51912, 100, 70, 17262, 176866, 13, 10, 31195, 5, 47009, 581, 206019, 111, 903, 28, 5490, 2320, 83, 450, 1022, 83, 70, 173, 18770, 2837, 23935, 674, 111, 70, 915, 26147, 237, 36510, 297, 23, 69407, 111, 70, 176866, 90, 23, 123789, 335, 99, 1733, 44, 18, 740, 28090, 123789, 62, 70, 915, 26147, 83, 105866, 99, 12, 1301, 142, 10, 8752, 4, 70, 25072, 22834, 22230, 10666, 75, 51912, 53418, 15549, 101668, 13, 4, 221, 30057, 42991, 111, 6097, 22834, 22230, 36510, 4734, 2062, 22062, 111, 70, 176866, 13, 5426, 335, 5, 2161, 70, 3789, 3535, 4, 173, 18770, 1193, 42856, 64040, 1636, 70, 59665, 111, 123789, 335, 35845, 47, 123789, 62, 4, 136, 221, 53418, 26698, 2062, 22062, 111, 123789, 335, 5, 2561, 214, 10, 1733, 30057, 4935, 4, 70, 191060, 939, 111, 70, 915, 26147, 83, 12, 581, 17932, 13579, 29334, 1363, 83, 70, 191060, 939, 111, 70, 915, 26147, 4, 5154, 81, 237, 72350, 71, 23, 123789, 335, 5, 9925, 83, 12, 581, 206019, 111, 903, 28, 5490, 2320, 83, 450, 70, 191060, 939, 111, 70, 915, 26147, 51592, 390, 160073, 7, 23, 123789, 62, 58055, 7, 111, 2367, 160073, 7, 23, 123789, 335, 11782, 70, 191060, 939, 4, 24, 110987, 81, 4, 1001, 6626, 4173, 69407, 62548, 47, 70, 34515, 111, 15549, 111, 70, 123789, 9, 571, 176866, 13, 10, 31195, 5, 6561, 111, 6097, 83, 42856, 70, 191060, 939, 111, 70, 98567, 59665, 81, 5, 581, 3789, 83, 10, 127752, 47, 191060, 939, 4743, 47, 70, 15824, 450, 12921, 31913, 7, 23, 70, 351, 9, 20037, 118, 289, 123789, 765, 12921, 173676, 191060, 2449, 4743, 47, 2062, 22062, 111, 70, 123789, 74, 10, 6275, 51592, 1295, 10, 47014, 1916, 123789, 1556, 10, 47014, 43315, 82761, 111, 191060, 939, 450, 83, 117396, 70, 53333, 70, 6275, 83, 1295, 70, 59665, 5, 717, 7413, 70, 197108, 1830, 4, 15700, 1733, 99710, 2320, 87344, 12, 345, 6953, 70, 5701, 26168, 21771, 11814, 100, 70, 1733, 30057, 4935, 111, 1022, 4, 70, 191060, 939, 30057, 4935, 98, 70, 7108, 83, 12, 1657, 184, 26513, 18, 538, 4, 581, 206019, 111, 903, 28, 5490, 2320, 83, 237, 28960, 7, 12, 70, 197108, 1830, 111, 70, 915, 26147, 23, 123789, 62, 58055, 7, 111, 2367, 160073, 7, 23, 123789, 335, 11782, 70, 915, 26147, 197108, 1830, 10, 4, 1284, 23, 66044, 2685, 621, 17262, 197108, 1830, 69407, 62548, 47, 70, 112664, 111, 70, 123789, 9, 571, 176866, 13, 10, 31195, 12, 1632, 13579, 62548, 47, 70, 197108, 1830, 111, 70, 59665, 111, 123789, 335, 4, 24, 110987, 10, 4, 136, 6626, 69407, 62548, 47, 2062, 22062, 111, 123789, 335, 5, 1657, 184, 26513, 18, 538, 4, 160073, 7, 23, 335, 1221, 1957, 70, 915, 26147, 78112, 237, 158566, 214, 44, 112779, 58, 197108, 1830, 4, 3129, 1836, 1221, 150380, 13, 47, 44, 50930, 7, 58, 1030, 1916, 98, 70, 915, 26147, 4, 1284, 3129, 160073, 7, 23, 62, 5154, 621, 44, 20941, 31821, 10821, 58, 84616, 187, 72219, 42856, 6637, 160073, 7, 23, 335, 54, 959, 125296, 70, 351, 9, 20037, 118, 289, 31425, 111, 123789, 335, 5, 581, 31461, 111, 6626, 23, 70, 5631, 846, 4086, 37772, 187, 62093, 1295, 6626, 105950, 127752, 7, 12, 15, 14, 16, 70, 173676, 15549, 111, 142, 23, 56, 118, 25958, 53697, 191060, 939, 678, 1733, 6637, 2062, 22062, 30482, 70, 48225, 111, 70, 191060, 939, 48903, 47, 15549, 15, 11, 44, 71, 58, 334, 64, 71, 58, 18, 58, 13579, 16, 136, 15, 1573, 16, 142, 173676, 15549, 23, 70, 191060, 939, 111, 142, 36746, 3229, 6863, 19069, 65572, 4, 118620, 442, 43573, 56, 47, 707, 53333, 1295, 70, 10, 33102, 111, 2062, 22062, 15, 2347, 15549, 23, 26168, 454, 966, 4743, 47, 15549, 23, 44, 425, 44, 6, 194, 717, 3884, 26866, 7, 23, 69407, 111, 84616, 4, 70, 197108, 17514, 621, 118126, 297, 390, 70, 915, 26147, 46889, 12, 581, 37772, 139999, 71, 23, 123789, 335, 4, 563, 2203, 44, 39, 58, 11, 83, 62548, 47, 70, 8561, 37772, 98, 70, 915, 26147, 4, 563, 4, 390, 7440, 12, 12613, 7, 4, 642, 831, 86869, 44402, 23, 123789, 335, 390, 10, 66596, 214, 450, 145076, 25, 7, 17932, 27165, 16401, 7, 15, 76228, 15072, 47, 102134, 2449, 23, 450, 123789, 16, 136, 85689, 214, 563, 237, 142, 78301, 37772, 5, 873, 17336, 621, 10, 14012, 111, 27781, 7, 59911, 214, 903, 16750, 100, 6, 20941, 31821, 10821, 84616, 5, 5455, 27781, 7, 831, 186, 14037, 23, 70, 5582, 98, 69514, 3125, 2870, 37772, 5, 62, 39210, 16648, 23, 3129, 351, 20037, 118, 289, 91067, 2674, 90, 621, 80234, 83, 3229, 70, 91067, 123789, 83, 47014, 1916, 5, 88949, 6044, 47014, 43315, 78112, 83, 351, 9, 20037, 118, 289, 4, 4743, 47, 70, 197108, 1830, 13379, 23, 2499, 47014, 43315, 78112, 4, 10, 6, 20941, 31821, 10821, 37772, 831, 11343, 186, 23, 23253, 297, 390, 17368, 10, 47014, 43315, 123789, 111, 91067, 5, 262, 61518, 903, 51455, 1363, 4, 70, 4527, 111, 6, 20941, 31821, 10821, 84616, 27983, 112892, 1029, 90, 70, 74481, 5256, 75412, 5, 717, 122, 5844, 125195, 7, 100, 70, 6, 20941, 31821, 10821, 84616, 4, 30057, 42991, 621, 44841, 100, 70, 173676, 1733, 34515, 111, 15549, 111, 22834, 22230, 450, 5646, 3934, 15426, 1733, 9, 21690, 2320, 111, 70, 176866, 13, 10, 31195, 5, 4263, 70, 2062, 22062, 111, 123789, 242, 571, 25, 83, 33636, 297, 390, 10, 173, 18770, 6, 20723, 6275, 297, 33233, 70, 10, 33102, 111, 2062, 22062, 678, 6, 180324, 34475, 390, 70, 7108, 9, 12336, 79986, 4, 136, 678, 101668, 13, 34475, 390, 7068, 70, 1733, 30057, 4935, 111, 2499, 111, 70, 17262, 25072, 22834, 22230, 28852, 23709, 123789, 335, 83, 136, 237, 83, 493, 47314, 17368, 70, 183871, 111, 70, 173, 18770, 41421, 12996, 5, 32255, 30057, 4935, 26168, 7, 5036, 621, 190659, 47, 70, 76755, 17721, 197108, 1830, 23, 142, 23, 2529, 15403, 123789, 4, 136, 450, 23, 10, 176866, 13, 123789, 47014, 1916, 678, 1733, 9, 1961, 38543, 348, 35975, 191060, 939, 6, 2778, 132, 58, 18, 51029, 28090, 70, 96362, 40059, 4, 7440, 1614, 32032, 62, 15005, 7, 47, 70, 23, 2529, 15403, 123789, 136, 335, 47, 70, 47014, 1916, 123789, 4, 53550, 10, 2203, 757, 47, 87388, 2499, 153648, 289, 197108, 1830, 4, 136, 32153, 214, 98, 4734, 47014, 43315, 183871, 15, 21231, 241, 864, 5, 4879, 12, 138521, 214, 69407, 4, 70, 16750, 83, 70, 221, 9, 85763, 297, 44, 151932, 1363, 167201, 26168, 58, 12, 581, 72761, 197108, 1830, 10, 4743, 47, 2367, 160073, 7, 23, 70, 23, 2529, 15403, 123789, 62, 11782, 44, 30544, 173591, 84616, 58, 98, 70, 36746, 83, 4, 127298, 4, 959, 42856, 70, 197108, 1830, 10, 51592, 390, 160073, 7, 23, 70, 47014, 43315, 123789, 335, 4, 1284, 1556, 40368, 78301, 84183, 238, 197108, 1830, 69407, 137272, 678, 70, 2062, 22062, 111, 335, 5, 1301, 51592, 23, 70, 47014, 43315, 123789, 4, 70, 197108, 1830, 10, 111, 70, 915, 26147, 83, 34475, 390, 456, 225628, 111, 70, 36917, 28, 5490, 2320, 237, 12, 581, 2043, 37772, 54799, 70, 36746, 59499, 47, 160073, 7, 23, 70, 47014, 1916, 123789, 83, 563, 2203, 44, 39, 58, 11, 5, 4263, 2363, 150556, 7, 621, 47, 16750, 23, 70, 26785, 37772, 98, 70, 36746, 3229, 17368, 145076, 25, 7, 131703, 4, 1836, 8110, 16916, 450, 70, 78301, 37772, 563, 83, 13379, 4, 221, 70, 3564, 16750, 83, 563, 2203, 563, 997, 563, 5, 12613, 7, 4, 70, 6, 20941, 31821, 10821, 37772, 11814, 390, 160073, 7, 23, 335, 47, 2046, 70, 26785, 123166, 111, 70, 36746, 1295, 145076, 25, 7, 131703, 105950, 7, 12, 11853, 4, 70, 5117, 13579, 83, 70, 44, 50886, 846, 4086, 37772, 830, 70, 17932, 13579, 83, 70, 44, 46899, 45862, 2870, 37772, 830, 136, 70, 50960, 13579, 83, 70, 44, 52283, 603, 37772, 740, 1301, 10, 62548, 27781, 4, 139124, 70, 98567, 176866, 13, 5426, 44, 571, 58, 47014, 1636, 678, 10, 53697, 348, 35975, 38352, 6, 2778, 23, 10, 42154, 133, 111, 4567, 223, 44, 1052, 58, 1672, 70, 188347, 59665, 111, 23, 2529, 15403, 123789, 44, 284, 830, 1284, 76104, 7, 6863, 176866, 13, 10, 31195, 188347, 23, 6, 180324, 4, 237, 23, 55412, 13, 1031, 581, 197108, 1830, 111, 142, 139999, 71, 14361, 83, 5036, 15, 21231, 241, 864, 5, 4879, 12, 7440, 70, 29334, 5256, 621, 45234, 23, 162, 561, 206, 237, 70, 25072, 22834, 22230, 765, 110, 1733, 6, 215131, 5, 581, 59665, 111, 5426, 44, 571, 58, 83, 105866, 59499, 47, 123789, 44, 284, 58, 99, 12, 105207, 47, 10, 191060, 939, 111, 70, 59665, 111, 123789, 44, 571, 58, 237, 12, 105207, 47, 142, 197108, 1830, 111, 70, 59665, 111, 44, 571, 58, 34475, 390, 12, 88949, 70, 5117, 13579, 4, 3129, 83, 83, 111, 70, 5701, 3173, 237, 70, 3638, 69514, 3125, 2870, 37772, 125195, 12, 442, 83, 10, 6083, 111938, 111, 5570, 18614, 25443, 15, 289, 197271, 2685, 83, 110, 5570, 18614, 25443, 100, 903, 7225, 16, 47, 11782, 903, 13579, 10, 44, 46899, 45862, 2870, 37772, 740, 4865, 30441, 18614, 25443, 83, 30666, 297, 4, 70, 160073, 7, 23, 123789, 44, 571, 58, 8110, 65508, 10, 6, 20941, 31821, 10821, 37772, 4, 903, 1733, 4743, 47, 70, 197108, 1830, 1295, 70, 103173, 289, 78112, 111, 2363, 64194, 176866, 13, 123789, 4, 450, 83, 4567, 25958, 1810, 19364, 16065, 1295, 70, 27585, 111, 2062, 22062, 111, 70, 59665, 111, 2363, 176866, 13, 5426, 12, 136, 111, 101668, 13, 12, 438, 24494, 450, 903, 44, 46899, 45862, 2870, 37772, 58, 1556, 60212, 7, 1295, 70, 7225, 111, 10, 47014, 1916, 123789, 5, 360, 70, 47014, 1916, 123789, 70, 69514, 3125, 2870, 37772, 83, 62548, 47, 70, 62488, 111, 70, 36746, 1295, 70, 59665, 111, 123789, 44, 571, 830, 12960, 23, 70, 7225, 111, 142, 103173, 214, 123789, 4, 70, 69514, 3125, 2870, 37772, 83, 41371, 111, 70, 62488, 111, 70, 36746, 1295, 70, 59665, 111, 123789, 44, 571, 830, 1284, 64457, 56566, 7, 54799, 70, 62488, 111, 70, 59665, 111, 123789, 44, 571, 58, 1295, 44, 14481, 58, 27585, 111, 2062, 22062, 4, 16750, 214, 23, 70, 44, 40175, 58, 69514, 3125, 2870, 6, 20941, 31821, 10821, 37772, 100, 44, 5584, 58, 36746, 7, 139999, 71, 23, 123789, 44, 571, 740, 1301, 10, 162515, 27781, 4, 55412, 13, 201, 45831, 10, 176866, 13, 5426, 44, 571, 58, 450, 103173, 7, 23, 2529, 15403, 123789, 44, 284, 58, 237, 23, 55412, 13, 138, 4, 1284, 70, 176866, 13, 10, 31195, 23, 123789, 44, 571, 58, 15504, 221, 25072, 173, 18770, 75, 11343, 26847, 154732, 70, 27585, 111, 2062, 22062, 5, 3293, 27781, 13648, 59911, 47, 10, 3034, 43333, 23, 10, 69514, 54957, 13, 4, 7440, 173, 18770, 75, 26847, 33233, 70, 10, 33102, 111, 70, 43333, 154732, 6863, 73432, 99, 6863, 2663, 5, 1650, 2843, 3332, 195, 13566, 70, 64883, 9, 9083, 191, 5426, 4, 7440, 70, 55583, 11343, 13379, 7, 70, 5701, 2577, 47, 70, 64883, 5, 360, 903, 27781, 4, 25072, 173, 18770, 75, 112033, 5425, 10, 188347, 6, 180324, 4, 12960, 22834, 22230, 75, 4, 75, 47014, 67, 99, 70, 5701, 34515, 237, 70, 59665, 111, 176866, 90, 5, 9925, 83, 4, 572, 6620, 4, 70, 197108, 1830, 111, 10, 98567, 36746, 83, 36510, 297, 237, 15, 21231, 241, 864, 5, 4879, 12, 7440, 70, 348, 35975, 197108, 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summarize: Specifically, the term "Galilean invariance" today usually refers to this principle as applied to Newtonian mechanics, that is, Newton’s laws hold in all frames related to one another by a Galilean transformation. In other words, all frames related to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called "Newtonian relativity". Among the axioms from Newton's theory are: Galilean relativity can be shown as follows. Consider two inertial frames "S" and "S' ". A physical event in "S" will have position coordinates "r" = ("x", "y", "z") and time "t" in "S", and "r' " = ("x' ", "y' ", "z' ") and time "t' " in "S' ". By the second axiom above, one can synchronize the clock in the two frames and assume "t" = "t' ". Suppose "S' " is in relative uniform motion to "S" with velocity "v". Consider a point object whose position is given by functions "r' "("t") " in "S' " and r"("t") in "S". We see that The velocity of the particle is given by the time derivative of the position: Another differentiation gives the acceleration in the two frames: It is this simple but crucial result that implies Galilean relativity. Assuming that mass is invariant in all inertial frames, the above equation shows Newton's laws of mechanics, if valid in one frame, must hold for all frames. But it is assumed to hold in absolute space, therefore Galilean relativity holds. A comparison can be made between Newtonian relativity and special relativity. Some of the assumptions and properties of Newton's theory are: In comparison, the corresponding statements from special relativity are as follows: Notice both theories assume the existence of inertial frames. In practice, the size of the frames in which they remain valid differ greatly, depending on gravitational tidal forces. In the appropriate context, a "local Newtonian inertial frame", where Newton's theory remains a good model, extends to, roughly, 10 light years. In special relativity, one considers "Einstein's cabins", cabins that fall freely in a gravitational field. According to Einstein's thought experiment, a man in such a cabin experiences (to a good approximation) no gravity and therefore the cabin is an approximate inertial frame. However, one has to assume that the size of the cabin is sufficiently small so that the gravitational field is approximately parallel in its interior. This can greatly reduce the sizes of such approximate frames, in comparison to Newtonian frames. For example, an artificial satellite orbiting around earth can be viewed as a cabin. However, reasonably sensitive instruments would detect "microgravity" in such a situation because the "lines of force" of the Earth's gravitational field converge. In general, the convergence of gravitational fields in the universe dictates the scale at which one might consider such (local) inertial frames. For example, a spaceship falling into a black hole or neutron star would (at a certain distance) be subjected to tidal forces so strong that it would be crushed in width and torn apart in length. In comparison, however, such forces might only be uncomfortable for the astronauts inside (compressing their joints, making it difficult to extend their limbs in any direction perpendicular to the gravity field of the star). Reducing the scale further, the forces at that distance might have almost no effects at all on a mouse. This illustrates the idea that all freely falling frames are locally inertial (acceleration and gravity-free) if the scale is chosen correctly. Maxwell's equations governing electromagnetism possess a different symmetry, Lorentz invariance, under which lengths and times "are" affected by a change in velocity, which is then described mathematically by a Lorentz transformation. Albert Einstein's central insight in formulating special relativity was that, for full consistency with electromagnetism, mechanics must also be revised such that Lorentz invariance replaces Galilean invariance. At the low relative velocities characteristic of everyday life, Lorentz invariance and Galilean invariance are nearly the same, but for relative velocities close to that of light they are very different. Because the distance covered while applying a force to an object depends on the inertial frame of reference, so does the work done. Due to Newton's law of reciprocal actions there is a reaction force; it does work depending on the inertial frame of reference in an opposite way. The total work done is independent of the inertial frame of reference. Correspondingly the kinetic energy of an object, and even the change in this energy due to a change in velocity, depends on the inertial frame of reference. The total kinetic energy of an isolated system also depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass. Due to the conservation of momentum the latter does not change with time, so changes with time of the total kinetic energy do not depend on the inertial frame of reference. By contrast, while the momentum of an object also depends on the inertial frame of reference, its change due to a change in velocity does not.	Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 in his "Dialogue Concerning the Two Chief World Systems" using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary.	en	en	76	[ 250004, 250054, 209052, 25958, 4, 70, 13579, 44, 70696, 1340, 66, 23, 21690, 7154, 58, 18925, 56104, 15005, 7, 47, 903, 24702, 133, 237, 190659, 47, 145076, 3378, 135969, 7, 4, 450, 83, 4, 145076, 26, 7, 131703, 16401, 23, 756, 2674, 90, 62548, 47, 1632, 15700, 390, 10, 30888, 34677, 167201, 5, 360, 3789, 34153, 4, 756, 2674, 90, 62548, 47, 1632, 15700, 390, 6044, 10, 167201, 621, 23, 2529, 15403, 15, 37440, 592, 4, 145076, 25, 7, 28, 5490, 2320, 111, 78112, 83, 35604, 23, 6097, 2674, 90, 194, 360, 903, 43701, 442, 83, 68018, 35839, 44, 46568, 27706, 66, 90816, 939, 740, 2022, 4021, 70, 10, 5134, 28016, 1295, 145076, 25, 7, 154453, 621, 12, 30888, 34677, 90816, 939, 831, 186, 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summarize: The motion of a body can only be described relative to something else—other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body that has no external forces acting on it is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, a coordinate system could describe the simple flight of a free body in space as a complicated zig-zag in its coordinate system. Indeed, an intuitive summary of inertial frames can be given: in an inertial reference frame, the laws of mechanics take their simplest form. In an inertial frame, Newton's first law, the "law of inertia", is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form: with F the net force (a vector), "m" the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate "Ω" about an axis, takes the form: which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics): where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation "Ω", symbol × denotes the vector cross product, vector x locates the body and vector v is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer). The extra terms in the force F′ are the "fictitious" forces for this frame, whose causes are external to the system in the frame. The first extra term is the Coriolis force, the second the centrifugal force, and the third the Euler force. These terms all have these properties: they vanish when "Ω" = 0; that is, they are zero for an inertial frame (which, of course, does not rotate); they take on a different magnitude and direction in every rotating frame, depending upon its particular value of Ω; they are ubiquitous in the rotating frame (affect every particle, regardless of circumstance); and they have no apparent source in identifiable physical sources, in particular, matter. Also, fictitious forces do not drop off with distance (unlike, for example, nuclear forces or electrical forces). For example, the centrifugal force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis. All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present. In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force. Two experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking two spheres rotating about their center of gravity, and the example of the curvature of the surface of water in a rotating bucket. In both cases, application of Newton's second law would not work for the rotating observer without invoking centrifugal and Coriolis forces to account for their observations (tension in the case of the spheres; parabolic water surface in the case of the rotating bucket). As we now know, the fixed stars are not fixed. Those that reside in the Milky Way turn with the galaxy, exhibiting proper motions. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to expansion of the universe, and partly due to peculiar velocities. The Andromeda Galaxy is on collision course with the Milky Way at a speed of 117 km/s. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property. In practice, although not a requirement, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces very little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun about the galactic center. To illustrate further, consider the question: "Does our Universe rotate?" To answer, we might attempt to explain the shape of the Milky Way galaxy using the laws of physics, although other observations might be more definitive, that is, provide larger discrepancies or less measurement uncertainty, like the anisotropy of the microwave background radiation or Big Bang nucleosynthesis. The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If we attribute its apparent rate of rotation entirely to rotation in an inertial frame, a different "flatness" is predicted than if we suppose part of this rotation actually is due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example, dark matter is invoked to explain the galactic rotation curve. So far, observations show any rotation of the universe is very slow, no faster than once every 60·10 years (10 rad/yr), and debate persists over whether there is "any" rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter along the geodesics in general relativity. When quantum effects are important, there are additional conceptual complications that arise in quantum reference frames. According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation: This simplicity manifests in that inertial frames have self-contained physics without the need for external causes, while physics in non-inertial frames have external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity; see Nagel and also Blagojević. In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame. According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup. In Newtonian mechanics, which can be viewed as a limiting case of special relativity in which the speed of light is infinite, inertial frames of reference are related by the Galilean group of symmetries. Newton posited an absolute space considered well approximated by a frame of reference stationary relative to the fixed stars. An inertial frame was then one in uniform translation relative to absolute space. However, some scientists (called "relativists" by Mach), even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced. Indeed, the expression "inertial frame of reference" () was coined by Ludwig Lange in 1885, to replace Newton's definitions of "absolute space and time" by a more operational definition. As translated by Iro, Lange proposed the following definition: A discussion of Lange's proposal can be found in Mach. The inadequacy of the notion of "absolute space" in Newtonian mechanics is spelled out by Blagojević: The utility of operational definitions was carried much further in the special theory of relativity. Some historical background including Lange's definition is provided by DiSalle, who says in summary: Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame, is one in which Newton's first law of motion is valid. However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton's first law. Newton viewed the first law as valid in any reference frame that is in uniform motion relative to the fixed stars; that is, neither rotating nor accelerating relative to the stars. Today the notion of "absolute space" is abandoned, and an inertial frame in the field of classical mechanics is defined as: Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed. Newtonian inertial frames transform among each other according to the Galilean group of symmetries. If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then we have to be able to determine when zero net force is applied. The problem was summarized by Einstein: There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that a body is far enough away from all sources to ensure that no force is present. A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is that we might miss something, or account inappropriately for their influence, perhaps, again, due to Mach's principle and an incomplete understanding of the universe. A third approach is to look at the way the forces transform when we shift reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames, and have complicated rules of transformation in general cases. On the basis of universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces. Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion: This principle differs from the special principle in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares with the special principle the invariance of the form of the description among mutually translating reference frames. The role of fictitious forces in classifying reference frames is pursued further below. Inertial and non-inertial reference frames can be distinguished by the absence or presence of fictitious forces, as explained shortly. The presence of fictitious forces indicates the physical laws are not the simplest laws available so, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame: Bodies in non-inertial reference frames are subject to so-called "fictitious" forces (pseudo-forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames. How then, are "fictitious" forces to be separated from "real" forces? It is hard to apply the Newtonian definition of an inertial frame without this separation. For example, consider a stationary object in an inertial frame. Being at rest, no net force is applied. But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force (which is made up of the Coriolis force and the centrifugal force). How can we decide that the rotating frame is a non-inertial frame? There are two approaches to this resolution: one approach is to look for the origin of the fictitious forces (the Coriolis force and the centrifugal force). We will find there are no sources for these forces, no associated force carriers, no originating bodies. A second approach is to look at a variety of frames of reference. For any inertial frame, the Coriolis force and the centrifugal force disappear, so application of the principle of special relativity would identify these frames where the forces disappear as sharing the same and the simplest physical laws, and hence rule that the rotating frame is not an inertial frame. Newton examined this problem himself using rotating spheres, as shown in Figure 2 and Figure 3. He pointed out that if the spheres are not rotating, the tension in the tying string is measured as zero in every frame of reference. If the spheres only appear to rotate (that is, we are watching stationary spheres from a rotating frame), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed. If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion. Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value. That is, the inertial frame is the one where the fictitious forces vanish. So much for fictitious forces due to rotation. However, for linear acceleration, Newton expressed the idea of undetectability of straight-line accelerations held in common: This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, we can define inertial frames collectively as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set. For these ideas to apply, everything observed in the frame has to be subject to a base-line, common acceleration shared by the frame itself. That situation would apply, for example, to the elevator example, where all objects are subject to the same gravitational acceleration, and the elevator itself accelerates at the same rate. Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it. Three orthogonal gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position. Thus, inertial navigation is a form of dead reckoning that requires no external input, and therefore cannot be jammed by any external or internal signal source. A gyrocompass, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour. Classical theories that use the Galilean transformation postulate the equivalence of all inertial reference frames. Some theories may even postulate the existence of a privileged frame which provides absolute space and absolute time. The Galilean transformation transforms coordinates from one inertial reference frame, formula_4, to another, formula_5, by simple addition or subtraction of coordinates: where r and "t" represent shifts in the origin of space and time, and v is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time "t" − "t" between two events is the same for all reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, \|r − r\|) is also the same. Einstein's theory of special relativity, like Newtonian mechanics, postulates the equivalence of all inertial reference frames. However, because special relativity postulates that the speed of light in free space is invariant, the transformation between inertial frames is the Lorentz transformation, not the Galilean transformation which is used in Newtonian mechanics. The invariance of the speed of light leads to counter-intuitive phenomena, such as time dilation and length contraction, and the relativity of simultaneity, which have been extensively verified experimentally. The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero. General relativity is based upon the principle of equivalence: This idea was introduced in Einstein's 1907 article "Principle of Relativity and Gravitation" and later developed in 1911. Support for this principle is found in the Eötvös experiment, which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 10. For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin. Einstein's general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature. In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity. However, the general theory reduces to the special theory over sufficiently small regions of spacetime, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a "local theory". "Local" can encompass, for example, the entire Milky Way galaxy: The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the solar system. Schwarzschild pointed out that that was invariably seen: the direction of the angular momentum of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is approximately Galilean or Minkowskian.	An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant velocity. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. 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summarize: The position of a rigid body is the position of all the particles of which it is composed. To simplify the description of this position, we exploit the property that the body is rigid, namely that all its particles maintain the same distance relative to each other. If the body is rigid, it is sufficient to describe the position of at least three non-collinear particles. This makes it possible to reconstruct the position of all the other particles, provided that their time-invariant position relative to the three selected particles is known. However, typically a different, mathematically more convenient, but equivalent approach is used. The position of the whole body is represented by: Thus, the position of a rigid body has two components: linear and angular, respectively. The same is true for other kinematic and kinetic quantities describing the motion of a rigid body, such as linear and angular velocity, acceleration, momentum, impulse, and kinetic energy. The linear position can be represented by a vector with its tail at an arbitrary reference point in space (the origin of a chosen coordinate system) and its tip at an arbitrary point of interest on the rigid body, typically coinciding with its center of mass or centroid. This reference point may define the origin of a coordinate system fixed to the body. There are several ways to numerically describe the orientation of a rigid body, including a set of three Euler angles, a quaternion, or a direction cosine matrix (also referred to as a rotation matrix). All these methods actually define the orientation of a basis set (or coordinate system) which has a fixed orientation relative to the body (i.e. rotates together with the body), relative to another basis set (or coordinate system), from which the motion of the rigid body is observed. For instance, a basis set with fixed orientation relative to an airplane can be defined as a set of three orthogonal unit vectors "b", "b", "b", such that "b" is parallel to the chord line of the wing and directed forward, "b" is normal to the plane of symmetry and directed rightward, and "b" is given by the cross product formula_1. In general, when a rigid body moves, both its position and orientation vary with time. In the kinematic sense, these changes are referred to as "translation" and "rotation", respectively. Indeed, the position of a rigid body can be viewed as a hypothetic translation and rotation (roto-translation) of the body starting from a hypothetic reference position (not necessarily coinciding with a position actually taken by the body during its motion). Velocity (also called linear velocity) and angular velocity are measured with respect to a frame of reference. The linear velocity of a rigid body is a vector quantity, equal to the time rate of change of its linear position. Thus, it is the velocity of a reference point fixed to the body. During purely translational motion (motion with no rotation), all points on a rigid body move with the same velocity. However, when motion involves rotation, the instantaneous velocity of any two points on the body will generally not be the same. Two points of a rotating body will have the same instantaneous velocity only if they happen to lie on an axis parallel to the instantaneous axis of rotation. Angular velocity is a vector quantity that describes the angular speed at which the orientation of the rigid body is changing and the instantaneous axis about which it is rotating (the existence of this instantaneous axis is guaranteed by the Euler's rotation theorem). All points on a rigid body experience the same angular velocity at all times. During purely rotational motion, all points on the body change position except for those lying on the instantaneous axis of rotation. The relationship between orientation and angular velocity is not directly analogous to the relationship between position and velocity. Angular velocity is not the time rate of change of orientation, because there is no such concept as an orientation vector that can be differentiated to obtain the angular velocity. The angular velocity of a rigid body B in a reference frame N is equal to the sum of the angular velocity of a rigid body D in N and the angular velocity of B with respect to D: In this case, rigid bodies and reference frames are indistinguishable and completely interchangeable. For any set of three points P, Q, and R, the position vector from P to R is the sum of the position vector from P to Q and the position vector from Q to R: The velocity of point P in reference frame N is defined as the time derivative in N of the position vector from O to P: where O is any arbitrary point fixed in reference frame N, and the N to the left of the d/d"t" operator indicates that the derivative is taken in reference frame N. The result is independent of the selection of O so long as O is fixed in N. The acceleration of point P in reference frame N is defined as the time derivative in N of its velocity: For two points P and Q that are fixed on a rigid body B, where B has an angular velocity formula_6 in the reference frame N, the velocity of Q in N can be expressed as a function of the velocity of P in N: where formula_8 is the position vector from Q to P. By differentiating the equation for the Velocity of two points fixed on a rigid body in N with respect to time, the acceleration in reference frame N of a point Q fixed on a rigid body B can be expressed as where formula_10 is the angular acceleration of B in the reference frame N. As mentioned above, all points on a rigid body B have the same angular velocity formula_11 in a fixed reference frame N, and thus the same angular acceleration formula_12 If the point R is moving in rigid body B while B moves in reference frame N, then the velocity of R in N is where Q is the point fixed in B that is instantaneously coincident with R at the instant of interest. This relation is often combined with the relation for the Velocity of two points fixed on a rigid body. The acceleration in reference frame N of the point R moving in body B while B is moving in frame N is given by where Q is the point fixed in B that instantaneously coincident with R at the instant of interest. This equation is often combined with Acceleration of two points fixed on a rigid body. If "C" is the origin of a local coordinate system "L", attached to the body, where In 2D, the angular velocity is a scalar, and matrix A(t) simply represents a rotation in the "xy"-plane by an angle which is the integral of the angular velocity over time. Vehicles, walking people, etc., usually rotate according to changes in the direction of the velocity: they move forward with respect to their own orientation. Then, if the body follows a closed orbit in a plane, the angular velocity integrated over a time interval in which the orbit is completed once, is an integer times 360°. This integer is the winding number with respect to the origin of the velocity. Compare the amount of rotation associated with the vertices of a polygon. Any point that is rigidly connected to the body can be used as reference point (origin of coordinate system "L") to describe the linear motion of the body (the linear position, velocity and acceleration vectors depend on the choice). However, depending on the application, a convenient choice may be: When the center of mass is used as reference point: Two rigid bodies are said to be different (not copies) if there is no proper rotation from one to the other. A rigid body is called chiral if its mirror image is different in that sense, i.e., if it has either no symmetry or its symmetry group contains only proper rotations. In the opposite case an object is called achiral: the mirror image is a copy, not a different object. Such an object may have a symmetry plane, but not necessarily: there may also be a plane of reflection with respect to which the image of the object is a rotated version. The latter applies for "S, of which the case "n" = 1 is inversion symmetry. For a (rigid) rectangular transparent sheet, inversion symmetry corresponds to having on one side an image without rotational symmetry and on the other side an image such that what shines through is the image at the top side, upside down. We can distinguish two cases: A sheet with a through and through image is achiral. We can distinguish again two cases: The configuration space of a rigid body with one point fixed (i.e., a body with zero translational motion) is given by the underlying manifold of the rotation group SO(3). The configuration space of a nonfixed (with non-zero translational motion) rigid body is "E"(3), the subgroup of direct isometries of the Euclidean group in three dimensions (combinations of translations and rotations).	In physics, a rigid body (also known as a rigid object ) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces exerted on it. 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summarize: A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance or moment. The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. This is called a "simple couple". The forces have a turning effect or moment called a torque about an axis which is normal (perpendicular) to the plane of the forces. The SI unit for the torque of the couple is newton metre. If the two forces are F and −F, then the magnitude of the torque is given by the following formula: where The magnitude of the torque is equal to "F d", with the direction of the torque given by the unit vector formula_3, which is perpendicular to the plane containing the two forces and positive being a counter-clockwise couple. When d is taken as a vector between the points of action of the forces, then the torque is the cross product of d and F, i.e. The moment of a force is only defined with respect to a certain point "P" (it is said to be the "moment about "P"") and, in general, when "P" is changed, the moment changes. However, the moment (torque) of a "couple" is "independent" of the reference point "P": Any point will give the same moment. In other words, a torque vector, unlike any other moment vector, is a "free vector". The proof of this claim is as follows: Suppose there are a set of force vectors F, F, etc. that form a couple, with position vectors (about some origin "P") r, r, etc., respectively. The moment about "P" is Now we pick a new reference point "P that differs from "P" by the vector r"'. The new moment is Now the distributive property of the cross product implies However, the definition of a force couple means that Therefore, This proves that the moment is independent of reference point, which is proof that a couple is a free vector. A force "F" applied to a rigid body at a distance "d" from the center of mass has the same effect as the same force applied directly to the center of mass and a couple "Cl = Fd". The couple produces an angular acceleration of the rigid body at right angles to the plane of the couple. The force at the center of mass accelerates the body in the direction of the force without change in orientation. The general theorems are: Couples are very important in mechanical engineering and the physical sciences. A few examples are: In a liquid crystal it is the rotation of an optic axis called the "director" that produces the functionality of these compounds. As Jerald Ericksen explained	In mechanics, a couple refers to two parallel forces that are equal in magnitude, opposite in direction and do not share a line of action.	en	en	28	[ 250004, 250054, 62, 24941, 83, 10, 80836, 111, 84616, 4, 105950, 23, 101668, 13, 4, 198274, 538, 8951, 297, 4, 136, 2837, 23935, 71, 390, 117, 40930, 25667, 62488, 707, 3095, 5, 581, 30362, 18, 8562, 111, 24941, 58055, 7, 111, 6626, 105950, 136, 198274, 84616, 124901, 124519, 111, 22631, 54, 959, 60754, 13, 5, 3293, 83, 35839, 10, 44, 191560, 24941, 740, 581, 84616, 765, 10, 174548, 21543, 707, 3095, 35839, 10, 9983, 944, 1672, 142, 10, 33102, 3129, 83, 3638, 15, 1264, 40930, 25667, 16, 47, 70, 47880, 111, 70, 84616, 5, 581, 10000, 25072, 100, 70, 9983, 944, 111, 70, 24941, 83, 3525, 1507, 106810, 5, 4263, 70, 6626, 84616, 621, 563, 136, 48768, 919, 4, 7068, 70, 101668, 13, 111, 70, 9983, 944, 83, 34475, 390, 70, 25632, 26168, 12, 7440, 581, 101668, 13, 111, 70, 9983, 944, 83, 105950, 47, 44, 919, 104, 830, 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summarize: An important property of systems at mechanical equilibrium is their stability. If we have a function which describes the system's potential energy, we can determine the system's equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable, we apply the second derivative test: When considering more than one dimension, it is possible to get different results in different directions, for example stability with respect to displacements in the "x"-direction but instability in the "y"-direction, a case known as a saddle point. Generally an equilibrium is only referred to as stable if it is stable in all directions. Sometimes there is not enough information about the forces acting on a body to determine if it is in equilibrium or not. This makes it a statically indeterminate system. A stationary object (or set of objects) is in "static equilibrium," which is a special case of mechanical equilibrium. A paperweight on a desk is an example of static equilibrium. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing. Objects in motion can also be in equilibrium. A child sliding down a slide at constant speed would be in mechanical equilibrium, but not in static equilibrium (in the reference frame of the earth or slide). Another example of mechanical equilibrium is a person pressing a spring to a defined point. He or she can push it to an arbitrary point and hold it there, at which point the compressive load and the spring reaction are equal. In this state the system is in mechanical equilibrium. When the compressive force is removed the spring returns to its original state. The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest. In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point. Such an object is called a gömböc.	In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.	en	en	48	[ 250004, 250054, 893, 5526, 57266, 111, 76519, 99, 135969, 289, 6, 155159, 316, 83, 2363, 40780, 53, 5, 4263, 642, 765, 10, 32354, 3129, 98363, 7, 70, 5426, 25, 7, 38516, 48302, 4, 642, 831, 83324, 70, 5426, 25, 7, 6, 155159, 11, 17368, 44805, 223, 5, 62, 5426, 83, 23, 135969, 289, 6, 155159, 316, 99, 70, 130306, 26847, 111, 70, 32354, 28852, 23709, 70, 5426, 25, 7, 38516, 48302, 5, 1401, 831, 64040, 67, 6097, 26847, 17368, 70, 15824, 450, 70, 30057, 4935, 111, 70, 32354, 83, 45234, 99, 6097, 26847, 5, 717, 83324, 36766, 707, 959, 70, 5426, 83, 144142, 707, 2234, 22819, 4, 642, 59911, 70, 17932, 30057, 4935, 3034, 12, 14847, 179635, 1286, 3501, 1632, 6, 91403, 4, 442, 83, 7722, 47, 2046, 12921, 50339, 23, 12921, 48225, 7, 4, 100, 27781, 40780, 53, 678, 15072, 47, 2837, 23935, 9035, 23, 70, 44, 425, 58, 9, 936, 58994, 1284, 23, 271, 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summarize: Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. Thus the object would balance on the intersection point of the medians. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from. Each median divides the area of the triangle in half; hence the name, and hence a triangular object of uniform density would balance on any median. (Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.) The three medians divide the triangle into six smaller triangles of equal area. Consider a triangle "ABC". Let "D" be the midpoint of formula_1, "E" be the midpoint of formula_2, "F" be the midpoint of formula_3, and "O" be the centroid (most commonly denoted "G"). By definition, formula_4. Thus formula_5 and formula_6, where formula_7 represents the area of triangle formula_8 ; these hold because in each case the two triangles have bases of equal length and share a common altitude from the (extended) base, and a triangle's area equals one-half its base times its height. We have: Thus, formula_11 and formula_12 Since formula_13, therefore, formula_14. Using the same method, one can show that formula_15. The lengths of the medians can be obtained from Apollonius' theorem as: where "a", "b" and "c" are the sides of the triangle with respective medians "m", "m", and "m" from their midpoints. Thus we have the relationships: Let "ABC" be a triangle, let "G" be its centroid, and let "D", "E", and "F" be the midpoints of "BC", "CA", and "AB", respectively. For any point "P" in the plane of "ABC" then The centroid divides each median into parts in the ratio 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. For any triangle with sides formula_23 and medians formula_24 and The medians from sides of lengths "a" and "b" are perpendicular if and only if formula_27 The medians of a right triangle with hypotenuse "c" satisfy formula_28 Any triangle's area "T" can be expressed in terms of its medians formula_29, and formula_30 as follows. Denoting their semi-sum as σ, we have A tetrahedron is a three-dimensional object having four triangular faces. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a "median" of the tetrahedron. There are four medians, and they are all concurrent at the "centroid" of the tetrahedron. As in the two-dimensional case, the centroid of the tetrahedron is the center of mass. However contrary to the two-dimensional case the centroid divides the medians not in a 2:1 ratio but in a 3:1 ratio (Commandino's theorem).	In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. 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summarize: Fluids display properties such as: These properties are typically a function of their inability to support a shear stress in static equilibrium. In contrast, solids respond to shear either with a spring-like restoring force, which means that deformations are reversible, or they require a certain initial stress before they deform (see plasticity). Solids respond with restoring forces to both shear stresses and to normal stresses—both compressive and tensile. In contrast, ideal fluids only respond with restoring forces to normal stresses, called pressure: fluids can be subjected to both compressive stress, corresponding to positive pressure, and to tensile stress, corresponding to negative pressure. Both solids and liquids also have tensile strengths, which when exceeded in solids makes irreversible deformation and fracture, and in liquids causes the onset of cavitation. Both solids and liquids have free surfaces, which cost some amount of free energy to form. In the case of solids, the amount of free energy to form a given unit of surface area is called surface energy, whereas for liquids the same quantity is called surface tension. The ability of liquids to flow results in different behaviour in response to surface tension than in solids, although in equilibrium both will try to minimise their surface energy: liquids tend to form rounded droplets, whereas pure solids tend to form crystals. Gases do not have free surfaces, and freely diffuse. In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state. Depending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as one of the following: The behavior of fluids can be described by the Navier–Stokes equations—a set of partial differential equations which are based on: The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.	In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases and plasmas. 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summarize: In 1954, Zamecnik and Hoagland discovered tRNA. In 1955, George E. Palade discovered ribosomes. The basic process of translation is the addition of one amino acid at a time to the end of the polypeptide being formed. This process takes place inside the ribosome. A ribosome is made up of a subunit, a small 40S subunit or a large 60S subunit. These subunits come together before translation of mRNA into a protein to provide a location for translation to be carried out and a polypeptide to be produced. The choice of amino acid type to be added is determined by the genetic code on the mRNA molecule. Each amino acid added is matched to a three nucleotide subsequence of the mRNA. For each such triplet possible, the corresponding amino acid is accepted. The successive amino acids added to the chain are matched to successive nucleotide triplets in the mRNA. In this way, the sequence of nucleotides in the template mRNA chain determines the sequence of amino acids in the generated polypeptide. Addition of an amino acid occurs at the C-terminus of the peptide and thus translation is said to be amino-to-carboxyl directed. The mRNA carries genetic information encoded as a DNA sequence from the chromosomes to the nucleolus. The ribonucleotides are "read" by translational machinery in a sequence of nucleotide triplets called codons. Each of those triplets codes for a specific amino acid. The ribosome translates this code to a specific sequence of amino acids. The ribosome is a multi-subunit structure containing rRNA and proteins. It is the "factory" where amino acids are assembled into proteins. tRNAs are small noncoding RNA chains (75-90 nucleotides) that transport amino acids to the ribosome. tRNAs have a site for amino acid attachment, and a site called an anticodon. The anticodon is an RNA triplet complementary to the mRNA triplet that codes for their cargo amino acid. Aminoacyl tRNA synthetases (enzymes) catalyze the bonding between specific tRNAs and the amino acids that their anticodon sequences call for. The product of this reaction is an aminoacyl-tRNA. In prokaryotes, this aminoacyl-tRNA is carried to the ribosome by EF-Tu, where mRNA codons are matched through complementary base pairing to specific tRNA anticodons. Aminoacyl-tRNA synthetases that mispair tRNAs with the wrong amino acids can produce mischarged aminoacyl-tRNAs, which can result in inappropriate amino acids at the respective position in protein. This "mistranslation" of the genetic code naturally occurs at low levels in most organisms, but certain cellular environments cause an increase in permissive mRNA decoding, sometimes to the benefit of the cell. The ribosome has three sites for tRNA to bind. They are the aminoacyl site (abbreviated A), the peptidyl site (abbreviated P) and the exit site (abbreviated E). With respect to the mRNA, the three sites are oriented 5’ to 3’ E-P-A, because ribosomes move toward the 3' end of mRNA. The A-site binds the incoming tRNA with the complementary codon on the mRNA. The P-site holds the tRNA with the growing polypeptide chain. The E-site holds the tRNA without its amino acid, and the tRNA is then released. When an aminoacyl-tRNA initially binds to its corresponding codon on the mRNA, it is in the A site. Then, a peptide bond forms between the amino acid of the tRNA in the A site and the amino acid of the charged tRNA in the P site. The growing polypeptide chain is transferred to the tRNA in the A site. Translocation occurs, moving the tRNA in the P site, now without an amino acid, to the E site; the tRNA that was in the A site, now charged with the polypeptide chain, is moved to the P site. The tRNA in the E site leaves and another aminoacyl-tRNA enters the A site to repeat the process. After the new amino acid is added to the chain, and after the mRNA is released out of the nucleus and into the ribosome's core, the energy provided by the hydrolysis of an ATP bound to the translocase EF-G (in prokaryotes) and eEF-2 (in eukaryotes) moves the ribosome down one codon towards the 3' end. The energy required for translation of proteins is significant. For a protein containing "n" amino acids, the number of high-energy phosphate bonds required to translate it is 4"n"+1. The rate of translation varies; it is significantly higher in prokaryotic cells (up to 17-21 amino acid residues per second) than in eukaryotic cells (up to 6-9 amino acid residues per second). Even though the ribosomes are usually considered accurate, processive machines, the translation process is subject to errors that can lead either to the synthesis of erroneous proteins or to the premature abandonment of translation. The rate of error in synthesizing proteins has been estimated to be between 1/10 and 1/10 misincorporated amino acids, depending on the experimental conditions. The rate of premature translation abandonment, instead, has been estimated to be of the order of magnitude of 10 events per translated codon. The correct amino acid is covalently bonded to the correct transfer RNA (tRNA) by amino acyl transferases. The amino acid is joined by its carboxyl group to the 3' OH of the tRNA by an ester bond. When the tRNA has an amino acid linked to it, the tRNA is termed "charged". Initiation involves the small subunit of the ribosome binding to the 5' end of mRNA with the help of initiation factors (IF). In prokaryotes, initiation of protein synthesis involves the recognition of a purine-rich initiation sequence on the mRNA called the Shine-Dalgarno sequence. The Shine-Dalgarno sequence binds to a complementary pyrimidine-rich sequence on the 3' end of the 16S rRNA part of the 30S ribosomal subunit. The binding of these complementary sequences ensures that the 30S ribosomal subunit is bound to the mRNA and is aligned such that the initiation codon is placed in the 30S portion of the P-site. Once the mRNA and 30S subunit are properly bound, an initiation factor brings the initiator tRNA-amino acid complex, f-Met-tRNA, to the 30S P site. The initiation phase is completed once a 50S subunit joins the 30 subunit, forming an active 70S ribosome. Termination of the polypeptide occurs when the A site of the ribosome is occupied by a stop codon (UAA, UAG, or UGA) on the mRNA. tRNA usually cannot recognize or bind to stop codons. Instead, the stop codon induces the binding of a release factor protein (RF1 & RF2) that prompts the disassembly of the entire ribosome/mRNA complex by the hydrolysis of the polypeptide chain from the peptidyl transferase center of the ribosome. Drugs or special sequence motifs on the mRNA can change the ribosomal structure so that near-cognate tRNAs are bound to the stop codon instead of the release factors. In such cases of 'translational readthrough', translation continues until the ribosome encounters the next stop codon. The process of translation is highly regulated in prokaryotic and eukaryotic organisms. Regulation of translation can impact the global rate of protein synthesis which is closely coupled to the metabolic and proliferative state of a cell. In addition, recent work has revealed that genetic differences and their subsequent expression as mRNAs can also impact translation rate in an RNA-specific manner. The transcription-translation process description, mentioning only the most basic ”elementary” processes, consists of: The process of protein synthesis and translation is a subject of mathematical modeling for a long time starting from the first detailed kinetic models such as or others taking into account stochastic aspects of translation and using computer simulations. Many chemical kinetics-based models of protein synthesis have been developed and analyzed in the last four decades. Beyond chemical kinetics, various modeling formalisms such as Totally Asymmetric Simple Exclusion Process (TASEP) Probabilistic Boolean Networks (PBN), Petri Nets and max-plus algebra have been applied to model the detailed kinetics of protein synthesis or some of its stages. A basic model of protein synthesis that took into account all eight 'elementary' processes has been developed, following the paradigm that "useful models are simple and extendable". The simplest model "M0" is represented by the reaction kinetic mechanism (Figure M0). It was generalised to include 40S, 60S and initiation factors (IF) binding (Figure M1'). It was extended further to include effect of microRNA on protein synthesis. Most of models in this hierarchy can be solved analytically. These solutions were used to extract 'kinetic signatures' of different specific mechanisms of synthesis regulation. Whereas other aspects such as the 3D structure, called tertiary structure, of protein can only be predicted using sophisticated algorithms, the amino acid sequence, called primary structure, can be determined solely from the nucleic acid sequence with the aid of a translation table. This approach may not give the correct amino acid composition of the protein, in particular if unconventional amino acids such as selenocysteine are incorporated into the protein, which is coded for by a conventional stop codon in combination with a downstream hairpin (SElenoCysteine Insertion Sequence, or SECIS). There are many computer programs capable of translating a DNA/RNA sequence into a protein sequence. Normally this is performed using the Standard Genetic Code, however, few programs can handle all the "special" cases, such as the use of the alternative initiation codons. For instance, the rare alternative start codon CTG codes for methionine when used as a start codon, and for leucine in all other positions. Example: Condensed translation table for the Standard Genetic Code (from the NCBI Taxonomy webpage). The "Starts" row indicate three start codons, UUG, CUG, and the very common AUG. It also indicates the first amino acid residue when interpreted as a start: in this case it is all methionine. Even when working with ordinary eukaryotic sequences such as the yeast genome, it is often desired to be able to use alternative translation tables—namely for translation of the mitochondrial genes. Currently the following translation tables are defined by the NCBI Taxonomy Group for the translation of the sequences in GenBank:	In molecular biology and genetics, translation is the process in which ribosomes in the cytoplasm or ER synthesize proteins after the process of transcription of DNA to RNA in the cell's nucleus. 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summarize: There are three basic classes of ideal gas: The classical ideal gas can be separated into two types: The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. Both are essentially the same, except that the classical thermodynamic ideal gas is based on classical statistical mechanics, and certain thermodynamic parameters such as the entropy are only specified to within an undetermined additive constant. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas and quantum Fermi gas in the limit of high temperature to specify these additive constants. The behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur–Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma. The classical thermodynamic properties of an ideal gas can be described by two equations of state: The ideal gas law is the equation of state for an ideal gas, given by: where The ideal gas law is an extension of experimentally discovered gas laws. It can also be derived from microscopic considerations. Real fluids at low density and high temperature approximate the behavior of a classical ideal gas. However, at lower temperatures or a higher density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or as it deposits from a gas into a solid. This deviation is expressed as a compressibility factor. This equation is derived from After combining three laws we get That is: The other equation of state of an ideal gas must express Joule's law, that the internal energy of a fixed mass of ideal gas is a function only of its temperature. For the present purposes it is convenient to postulate an exemplary version of this law by writing: where That for an ideal gas depends only on temperature is a consequence of the ideal gas law, although in the general case depends on temperature and an integral is needed to compute. In order to switch from macroscopic quantities (left hand side of the following equation) to microscopic ones (right hand side), we use where The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution. The ideal gas model depends on the following assumptions: The assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas. The following three assumptions are very related: molecules are hard, collisions are elastic, and there are no inter-molecular forces. The assumption that the space between particles is much larger than the particles themselves is of paramount importance, and explains why the ideal gas approximation fails at high pressures. The dimensionless heat capacity at constant volume is generally defined by where is the entropy. This quantity is generally a function of temperature due to intermolecular and intramolecular forces, but for moderate temperatures it is approximately constant. Specifically, the Equipartition Theorem predicts that the constant for a monatomic gas is = while for a diatomic gas it is = if vibrations are neglected (which is often an excellent approximation). Since the heat capacity depends on the atomic or molecular nature of the gas, macroscopic measurements on heat capacity provide useful information on the microscopic structure of the molecules. The dimensionless heat capacity at constant pressure of an ideal gas is: where is the enthalpy of the gas. Sometimes, a distinction is made between an ideal gas, where and could vary with temperature, and a perfect gas, for which this is not the case. The ratio of the constant volume and constant pressure heat capacity is the adiabatic index For air, which is a mixture of gases, this ratio is 1.4. Using the results of thermodynamics only, we can go a long way in determining the expression for the entropy of an ideal gas. This is an important step since, according to the theory of thermodynamic potentials, if we can express the entropy as a function of ( is a thermodynamic potential), volume and the number of particles, then we will have a complete statement of the thermodynamic behavior of the ideal gas. We will be able to derive both the ideal gas law and the expression for internal energy from it. Since the entropy is an exact differential, using the chain rule, the change in entropy when going from a reference state 0 to some other state with entropy may be written as where: where the reference variables may be functions of the number of particles. Using the definition of the heat capacity at constant volume for the first differential and the appropriate Maxwell relation for the second we have: Expressing in terms of as developed in the above section, differentiating the ideal gas equation of state, and integrating yields: which implies that the entropy may be expressed as: where all constants have been incorporated into the logarithm as which is some function of the particle number having the same dimensions as in order that the argument of the logarithm be dimensionless. We now impose the constraint that the entropy be extensive. This will mean that when the extensive parameters ( and ) are multiplied by a constant, the entropy will be multiplied by the same constant. Mathematically: From this we find an equation for the function Differentiating this with respect to, setting equal to 1, and then solving the differential equation yields : where may vary for different gases, but will be independent of the thermodynamic state of the gas. It will have the dimensions of. Substituting into the equation for the entropy: and using the expression for the internal energy of an ideal gas, the entropy may be written: Since this is an expression for entropy in terms of,, and, it is a fundamental equation from which all other properties of the ideal gas may be derived. This is about as far as we can go using thermodynamics alone. Note that the above equation is flawed – as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics. In the above "ideal" development, there is a critical point, not at absolute zero, at which the argument of the logarithm becomes unity, and the entropy becomes zero. This is unphysical. The above equation is a good approximation only when the argument of the logarithm is much larger than unity – the concept of an ideal gas breaks down at low values of. Nevertheless, there will be a "best" value of the constant in the sense that the predicted entropy is as close as possible to the actual entropy, given the flawed assumption of ideality. A quantum-mechanical derivation of this constant is developed in the derivation of the Sackur–Tetrode equation which expresses the entropy of a monatomic ( = ) ideal gas. In the Sackur–Tetrode theory the constant depends only upon the mass of the gas particle. The Sackur–Tetrode equation also suffers from a divergent entropy at absolute zero, but is a good approximation for the entropy of a monatomic ideal gas for high enough temperatures. An alternative way of expressing the change in entropy: formula_22 Expressing the entropy as a function of,, and : The chemical potential of the ideal gas is calculated from the corresponding equation of state (see thermodynamic potential): where is the Gibbs free energy and is equal to so that: The chemical potential is usually referenced to the potential at some standard pressure "P" so that, with formula_26: For a mixture ("j"=1,2...) of ideal gases, each at partial pressure "P", it can be shown that the chemical potential "μ" will be given by the above expression with the pressure "P" replaced by "P". The thermodynamic potentials for an ideal gas can now be written as functions of,, and as: where, as before, The most informative way of writing the potentials is in terms of their natural variables, since each of these equations can be used to derive all of the other thermodynamic variables of the system. In terms of their natural variables, the thermodynamic potentials of a single-species ideal gas are: In statistical mechanics, the relationship between the Helmholtz free energy and the partition function is fundamental, and is used to calculate the thermodynamic properties of matter; see configuration integral for more details. The speed of sound in an ideal gas is given by the Newton-Laplace formula: where the isentropic Bulk modulus formula_34. For an isentropic process of an ideal gas, formula_35, therefore Here, In the above-mentioned Sackur–Tetrode equation, the best choice of the entropy constant was found to be proportional to the quantum thermal wavelength of a particle, and the point at which the argument of the logarithm becomes zero is roughly equal to the point at which the average distance between particles becomes equal to the thermal wavelength. In fact, quantum theory itself predicts the same thing. Any gas behaves as an ideal gas at high enough temperature and low enough density, but at the point where the Sackur–Tetrode equation begins to break down, the gas will begin to behave as a quantum gas, composed of either bosons or fermions. (See the gas in a box article for a derivation of the ideal quantum gases, including the ideal Boltzmann gas.) Gases tend to behave as an ideal gas over a wider range of pressures when the temperature reaches the Boyle temperature. The ideal Boltzmann gas yields the same results as the classical thermodynamic gas, but makes the following identification for the undetermined constant : where is the thermal de Broglie wavelength of the gas and is the degeneracy of states. An ideal gas of bosons (e.g. a photon gas) will be governed by Bose–Einstein statistics and the distribution of energy will be in the form of a Bose–Einstein distribution. An ideal gas of fermions will be governed by Fermi–Dirac statistics and the distribution of energy will be in the form of a Fermi–Dirac distribution.	An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions. 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summarize: Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, cisterns, aqueducts and fountains. Archimedes is credited with the discovery of Archimedes' Principle, which relates the buoyancy force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The Roman engineer Vitruvius warned readers about lead pipes bursting under hydrostatic pressure. The concept of pressure and the way it is transmitted by fluids was formulated by the French mathematician and philosopher Blaise Pascal in 1647. The "fair cup" or Pythagorean cup, which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool. The cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied. Heron's fountain is a device invented by Heron of Alexandria that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several cannula (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir. Pascal made contributions to developments in both hydrostatics and hydrodynamics. Pascal's Law is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed. Due to the fundamental nature of fluids, a fluid cannot remain at rest under the presence of a shear stress. However, fluids can exert pressure normal to any contacting surface. If a point in the fluid is thought of as an infinitesimally small cube, then it follows from the principles of equilibrium that the pressure on every side of this unit of fluid must be equal. If this were not the case, the fluid would move in the direction of the resulting force. Thus, the pressure on a fluid at rest is isotropic; i.e., it acts with equal magnitude in all directions. This characteristic allows fluids to transmit force through the length of pipes or tubes; i.e., a force applied to a fluid in a pipe is transmitted, via the fluid, to the other end of the pipe. This principle was first formulated, in a slightly extended form, by Blaise Pascal, and is now called Pascal's law. In a fluid at rest, all frictional and inertial stresses vanish and the state of stress of the system is called "hydrostatic". When this condition of is applied to the Navier–Stokes equations, the gradient of pressure becomes a function of body forces only. For a barotropic fluid in a conservative force field like a gravitational force field, the pressure exerted by a fluid at equilibrium becomes a function of force exerted by gravity. The hydrostatic pressure can be determined from a control volume analysis of an infinitesimally small cube of fluid. Since pressure is defined as the force exerted on a test area (, with : pressure, : force normal to area, : area), and the only force acting on any such small cube of fluid is the weight of the fluid column above it, hydrostatic pressure can be calculated according to the following formula: where: For water and other liquids, this integral can be simplified significantly for many practical applications, based on the following two assumptions: Since many liquids can be considered incompressible, a reasonable good estimation can be made from assuming a constant density throughout the liquid. (The same assumption cannot be made within a gaseous environment.) Also, since the height of the fluid column between and is often reasonably small compared to the radius of the Earth, one can neglect the variation of. Under these circumstances, the integral is simplified into the formula: where is the height of the liquid column between the test volume and the zero reference point of the pressure. This formula is often called Stevin's law. Note that this reference point should lie at or below the surface of the liquid. Otherwise, one has to split the integral into two (or more) terms with the constant and. For example, the absolute pressure compared to vacuum is: where is the total height of the liquid column above the test area to the surface, and is the atmospheric pressure, i.e., the pressure calculated from the remaining integral over the air column from the liquid surface to infinity. This can easily be visualized using a pressure prism. Hydrostatic pressure has been used in the preservation of foods in a process called pascalization. In medicine, hydrostatic pressure in blood vessels is the pressure of the blood against the wall. It is the opposing force to oncotic pressure. Statistical mechanics shows that, for a gas of constant temperature, "T", its pressure, "p" will vary with height, "h", as: where: This is known as the barometric formula, and maybe derived from assuming the pressure is hydrostatic. If there are multiple types of molecules in the gas, the partial pressure of each type will be given by this equation. Under most conditions, the distribution of each species of gas is independent of the other species. Anybody of arbitrary shape which is immersed, partly or fully, in a fluid will experience the action of a net force in the opposite direction of the local pressure gradient. If this pressure gradient arises from gravity, the net force is in the vertical direction opposite that of the gravitational force. This vertical force is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Mathematically, where is the density of the fluid, is the acceleration due to gravity, and is the volume of fluid directly above the curved surface. In the case of a ship, for instance, its weight is balanced by pressure forces from the surrounding water, allowing it to float. If more cargo is loaded onto the ship, it would sink more into the water – displacing more water and thus receive a higher buoyant force to balance the increased weight. Discovery of the principle of buoyancy is attributed to Archimedes. The horizontal and vertical components of the hydrostatic force acting on a submerged surface are given by the following: where: Liquids can have free surfaces at which they interface with gases, or with a vacuum. In general, the lack of the ability to sustain a shear stress entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from surface tension. When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, surface tension effects become important leading to the formation of a meniscus through capillary action. This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in plant xylem, the transpirational pull. Without surface tension, drops would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid.	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summarize: Newton's laws are applied to objects which are idealised as single point masses, in the sense that the size and shape of the object's body are neglected to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newton's laws of motion for rigid bodies called Euler's laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton's laws of motion, then Euler's laws can be derived from Newton's laws. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law holds only when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light. One translation of Newton's laws reads: Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed. Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. The first law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant. The first law can be stated mathematically when the mass is a non-zero constant, as, Consequently, This is known as "uniform motion". An object "continues" to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest (demonstrated when a tablecloth is skilfully whipped from under dishes on a tabletop and the dishes remain in their initial state of rest). If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continuously move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely. Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. However, Newton implicitly referred to the absolute co-ordinate of cosmos for this frame. Since we cannot precisely measure our velocity relative to a far star, Newton's frame is based on a pure imagination, not based on measurable physics. In current physics, an observer defines himself as in inertial frame by preparing one stone hooked by a spring, and rotating the spring to any direction, and observing the stone static and the length of that spring unchanged. By Einstein's equivalence principle, if there was one such observer A and another observer B moving in a constant velocity related to A, then A and B will both observe the same physics phenomena. if A verified the first law, then B will verify it too. In this way, the definition of inertial can get rid of absolute space or far star, and only refer to the objects locally reachable and measurable. A particle not subject to forces moves (related to inertial frame) in a straight line at a constant speed. Newton's first law is often referred to as the "law of inertia". Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as: Newton's first and second laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity. The second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force. The second law can also be stated in terms of an object's acceleration. Since Newton's second law is valid only for constant-mass systems, can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus, where F is the net force applied, is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it. The above statements hint that the second law is merely a definition of formula_4, not a precious observation of nature. However, current physics restate the second law in measurable steps: (1)defining the term 'one unit of mass' by a specified stone, (2)defining the term 'one unit of force' by a specified spring with specified length, (3)measuring by experiment or proving by theory (with a principle that every direction of space are equivalent), that force can be added as a mathematical vector, (4)finally conclude that formula_5. These steps hint the second law is a precious feature of nature. The second law also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum. Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below). Newton's second law is an approximation that is increasingly worse at high speeds because of relativistic effects. According to modern ideas of how Newton was using his terminology, the law is understood, in modern terms, as an equivalent of: This may be expressed by the formula formula_6, where formula_7 is the time derivative of the momentum formula_8. This equation can be seen clearly in the Wren Library of Trinity College, Cambridge, in a glass case in which Newton's manuscript is open to the relevant page. Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading: The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations. An impulse J occurs when a force F acts over an interval of time Δ"t", and it is given by Since force is the time derivative of momentum, it follows that This relation between impulse and momentum is closer to Newton's wording of the second law. Impulse is a concept frequently used in the analysis of collisions and impacts. Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law; that is, the following formula is wrong: The falsehood of this formula can be seen by noting that it does not respect Galilean invariance: a variable-mass object with F = 0 in one frame will be seen to have F ≠ 0 in another frame. The correct equation of motion for a body whose mass "m" varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected/accreted mass; the result is where u is the velocity of the escaping or incoming mass relative to the body. From this equation one can derive the equation of motion for a varying mass system, for example, the Tsiolkovsky rocket equation. Under some conventions, the quantity u d"m"/d"t" on the left-hand side, which represents the advection of momentum, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity F. Then, by substituting the definition of acceleration, the equation becomes F = "m"a. The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object "A" exerts a force F on a second object "B", then "B" simultaneously exerts a force F on "A", and the two forces are equal in magnitude and opposite in direction: F = −F. The third law means that all forces are "interactions" between different bodies, or different regions within one body, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude and direction of the forces are determined entirely by one of the two bodies, say Body "A"; the force exerted by Body "A" on Body "B" is called the "action", and the force exerted by Body "B" on Body "A" is called the "reaction". This law is sometimes referred to as the "action-reaction law", with F called the "action" and F the "reaction". In other situations the magnitude and directions of the forces are determined jointly by both bodies and it isn't necessary to identify one force as the "action" and the other as the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the "action" and which is called "reaction"; both forces are part of a single interaction, and neither force exists without the other. The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road). From a conceptual standpoint, Newton's third law is seen when a person walks: they push against the floor, and the floor pushes against the person. Similarly, the tires of a car push against the road while the road pushes back on the tires—the tires and road simultaneously push against each other. In swimming, a person interacts with the water, pushing the water backward, while the water simultaneously pushes the person forward—both the person and the water push against each other. The reaction forces account for the motion in these examples. These forces depend on friction; a person or car on ice, for example, may be unable to exert the action force to produce the needed reaction force. Newton used the third law to derive the law of conservation of momentum; from a deeper perspective, however, conservation of momentum is the more fundamental idea (derived via Noether's theorem from Galilean invariance), and holds in cases where Newton's third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics. The ancient Greek philosopher Aristotle had the view that all objects have a natural place in the universe: that heavy objects (such as rocks) wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed continually to propel it, otherwise it would stop moving. Galileo Galilei, however, realised that a force is necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its velocity. In other words, Galileo stated that, in the "absence" of a force, a moving object will continue moving. (The tendency of objects to resist changes in motion was what Johannes Kepler had called "inertia".) This insight was refined by Newton, who made it into his first law, also known as the "law of inertia"—no force means no acceleration, and hence the body will maintain its velocity. As Newton's first law is a restatement of the law of inertia which Galileo had already described, Newton appropriately gave credit to Galileo. Leonardo da Vinci understood that "An object offers as much resistance to the air as the air does to the object". The law of inertia apparently occurred to several different natural philosophers and scientists independently, including Thomas Hobbes in his "Leviathan" (1651). The 17th-century philosopher and mathematician René Descartes also formulated the law, although he did not perform any experiments to confirm it. Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena. These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton's laws (combined with universal gravitation and classical electrodynamics) are inappropriate for use in certain circumstances, most notably at very small scales, at very high speeds, or in very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a semiconductor, optical properties of substances, errors in non-relativistically corrected GPS systems and superconductivity. Explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory. In quantum mechanics, concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form F = dp/d"t", where F and p are four-vectors. In modern physics, the laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics. This can be stated simply, "Momentum, energy and angular momentum cannot be created or destroyed." Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g., quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forces originate out of exchange by virtual particles. Other forces, such as gravity and fermionic degeneracy pressure, also arise from the momentum conservation. Indeed, the conservation of 4-momentum in inertial motion via curved space-time results in what we call gravitational force in general relativity theory. The application of the space derivative (which is a momentum operator in quantum mechanics) to the overlapping wave functions of a pair of fermions (particles with half-integer spin) results in shifts of maxima of compound wavefunction away from each other, which is observable as the "repulsion" of the fermions. Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. However, he was prepared for philosophical criticism of this action at a distance, and it was in this context that he stated the famous phrase "I feign no hypotheses". In modern physics, action at a distance has been completely eliminated, except for subtle effects involving quantum entanglement. (In particular, this refers to Bell's theorem—that no local model can reproduce the predictions of quantum theory.) Despite only being an approximation, in modern engineering and all practical applications involving the motion of vehicles and satellites, the concept of action at a distance is used extensively. The discovery of the second law of thermodynamics by Carnot in the 19th century showed that not every physical quantity is conserved over time, thus disproving the validity of inducing the opposite metaphysical view from Newton's laws. Hence, a "steady-state" worldview based solely on Newton's laws and the conservation laws does not take entropy into account.	Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:	en	en	100	[ 250004, 250054, 145076, 25, 7, 131703, 621, 190659, 47, 36746, 7, 3129, 621, 6528, 48353, 237, 11001, 6275, 23860, 7, 4, 23, 70, 10422, 450, 70, 13267, 136, 115700, 111, 70, 36746, 25, 7, 14361, 621, 124789, 89829, 47, 32153, 98, 6863, 78112, 1286, 72546, 5, 3293, 831, 186, 16940, 3229, 70, 36746, 83, 19336, 154186, 47, 70, 62488, 7, 75412, 23, 6863, 114137, 4, 707, 70, 8, 5037, 2320, 136, 2062, 22062, 111, 70, 14361, 621, 111, 110, 131011, 5, 360, 903, 3917, 4, 3853, 10, 23208, 831, 186, 6528, 48353, 237, 10, 915, 26147, 100, 114137, 111, 6863, 103173, 289, 78112, 10932, 10, 6057, 5, 360, 2363, 7311, 3173, 4, 145076, 25, 7, 131703, 111, 78112, 621, 959, 160370, 13, 47, 62816, 3075, 70, 78112, 111, 128652, 337, 34204, 136, 8, 5037, 2886, 337, 34204, 5, 31746, 25612, 5177, 603, 23, 729, 2525, 65508, 71, 10, 4537, 15032, 111, 145076, 25, 7, 131703, 111, 78112, 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summarize: Alexander Cumming, a watchmaker and mechanic, has a claim to having made the first effective recording barograph in the 1760s using an aneroid cell. Cumming created a series of barometrical clocks, including one for King George III. However, this type of design fell out of favour. Since the amount of movement that can be generated by a single aneroid is minuscule, up to seven aneroids (so called Vidie-cans) are often stacked "in series" to amplify their motion. This type of barograph was invented in 1844 by the Frenchman Lucien Vidi (1805–1866). In such barographs one or more aneroid cells act through a gear or lever train to drive a recording arm that has at its extreme end either a scribe or a pen. A scribe records on smoked foil while a pen records on paper using ink, held in a nib. The recording material is mounted on a cylindrical drum which is rotated slowly by clockwork. Commonly, the drum makes one revolution per day, per week, or per month and the rotation rate can often be selected by the user. Various other types of barograph have also been invented. Karl Kreil described a machine in 1843 based on a syphon barometer, where a pencil marked a chart at uniform intervals. Francis Ronalds, the Honorary Director of the Kew Observatory, created the first successful barograph utilising photography in 1845. The changing height of the mercury in the barometer was recorded on a continuously moving photosensitive surface. By 1847, a sophisticated temperature-compensation mechanism was also employed. Ronalds’ barograph was utilised by the UK Meteorological Office for many years to assist in weather forecasting and the machines were supplied to numerous observatories around the world. Today, traditional recording barographs for meteorological use have commonly been superseded (though not all) by electronic weather instruments that use computer methods to record the barometric pressure. These are not only less expensive than earlier barographs but they may also offer both greater recording length and the ability to perform further data analysis on the captured data including automated use of the data to forecast the weather. Older mechanical barographs are highly prized by collectors as they make good display items, often being made of high quality woods and brass. The most common weather Barograph found in homes and public buildings these days are the 8-day type. Some important manufacturers of Barographs are Negretti and Zambra, Short and Mason, and Richard Ferris among others. The late Victorian to early 20th century is generally considered to be the heyday of Barograph manufacture, many important refinements were made at this time, including improved temperature compensation and modification of the pen arm, to allow less weight to be applied to the paper, allowing better registration of small pressure changes (i.e. less friction on the nib). Marine barographs (used on ships) often include damping, this evens out the motion of the ship so that a more stable reading can be obtained, this can be either oil damping of the mechanism or simple coiled spring feet on the base. But, newer solid state, digital barographs eliminate this issue altogether, since they use no moving parts. As atmospheric pressure responds in a predictable manner to changes in altitude, barographs may be used to record elevation changes during an aircraft flight. Barographs were required by the FAI to record certain tasks and record attempts associated with sailplanes. A continuously varying trace indicated that the sailplane had not landed during a task, while measurements from a calibrated trace could be used to establish the completion of altitude tasks or the setting of records. Examples of FAI approved sailplane barographs included the Replogle mechanical drum barograph and the EW electronic barograph (which may be used in conjunction with GPS). Mechanical barographs are not commonly used for flight documentation now, having been displaced by GNSS Flight Recorders. On the top right of the picture of the three-day barograph can be seen a silver knurled knob. This is to adjust the barograph so that it correctly reflects the station pressure. Barely visible below the knob is a small silver plunger. This is pressed every three hours to leave a time mark on the paper. The line between two of these marks is called the 'characteristic of barometric tendency' and is used by weather forecasters. The observer would first note if the pressure was lower or higher than three hours prior. Next, a code number would be chosen that best represents the three-hour trace. There are nine possible choices (0 to 8) and no single code has preference over another. In the case of the graph on the barograph, one of two codes could be picked. An 8 (steady then decreasing) or 6 (decreasing then steady). The observer should pick the 6 because it represents the last part of the trace and is thus most representative of the pressure change. In the bottom centre is the aneroid (large circular silver object). As the pressure increases, the aneroid is pushed down causing the arm to move up and leave a trace on the paper. As the pressure decreases, the spring lifts the aneroid and the arm moves down. After three days the drum to which the graph is attached is removed. At this point the clockwork motor is wound and if necessary corrections can be made to increase or decrease the speed and new chart is attached.	A barograph is a barometer that records the barometric pressure over time in graphical form. This instrument is also used to make a continuous recording of atmospheric pressure. The pressure-sensitive element, a partially evacuated metal cylinder, is linked to a pen arm in such a way that the vertical displacement of the pen is proportional to the changes in the atmospheric pressure.	en	en	67	[ 250004, 250054, 42814, 7140, 14578, 4, 10, 39544, 55474, 136, 135969, 4, 1556, 10, 63043, 47, 19441, 7228, 70, 5117, 60266, 182304, 59140, 41382, 23, 70, 729, 4598, 7, 17368, 142, 10, 86, 63964, 38750, 5, 7140, 14578, 75935, 10, 36549, 111, 1909, 58174, 6827, 20450, 22824, 4, 26719, 1632, 100, 18813, 14787, 4830, 5, 33306, 4, 903, 10644, 111, 4331, 77736, 1810, 111, 1238, 141775, 5, 66016, 70, 41170, 111, 112664, 450, 831, 186, 139392, 71, 390, 10, 11001, 10, 86, 63964, 83, 26948, 75449, 4, 1257, 47, 59671, 142, 4036, 30185, 15, 991, 35839, 582, 7814, 9, 4398, 7, 16, 621, 27983, 177261, 297, 44, 73, 36549, 58, 47, 70827, 18929, 2363, 78112, 5, 3293, 10644, 111, 59140, 41382, 509, 26868, 297, 23, 543, 12465, 390, 70, 92265, 669, 51181, 33, 13888, 14, 7435, 8194, 132869, 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summarize: The word "barometer" is derived from the, and "meter" from Ancient Greek meaning "measure". Although Evangelista Torricelli is universally credited with inventing the barometer in 1643,<ref name="http://www.islandnet.com/~see/weather/history/barometerhistory1.htm"></ref><ref name="http://www.barometerfair.com/history_of_the_barometer.htm"></ref><ref name="http://www.juliantrubin.com/bigten/torricellibarometer.html"></ref> historical documentation also suggests Gasparo Berti, an Italian mathematician and astronomer, unintentionally built a water barometer sometime between 1640 and 1643. French scientist and philosopher René Descartes described the design of an experiment to determine atmospheric pressure as early as 1631, but there is no evidence that he built a working barometer at that time. On July 27, 1630, Giovanni Battista Baliani wrote a letter to Galileo Galilei explaining an experiment he had made in which a siphon, led over a hill about twenty-one meters high, failed to work. Galileo responded with an explanation of the phenomenon: he proposed that it was the power of a vacuum that held the water up, and at a certain height the amount of water simply became too much and the force could not hold any more, like a cord that can support only so much weight. This was a restatement of the theory of "horror vacui" ("nature abhors a vacuum"), which dates to Aristotle, and which Galileo restated as "resistenza del vacuo". Galileo's ideas reached Rome in December 1638 in his "Discorsi". Raffaele Magiotti and Gasparo Berti were excited by these ideas, and decided to seek a better way to attempt to produce a vacuum other than with a siphon. Magiotti devised such an experiment, and sometime between 1639 and 1641, Berti (with Magiotti, Athanasius Kircher and Niccolò Zucchi present) carried it out. Four accounts of Berti's experiment exist, but a simple model of his experiment consisted of filling with water a long tube that had both ends plugged, then standing the tube in a basin already full of water. The bottom end of the tube was opened, and water that had been inside of it poured out into the basin. However, only part of the water in the tube flowed out, and the level of the water inside the tube stayed at an exact level, which happened to be, the same height Baliani and Galileo had observed that was limited by the siphon. What was most important about this experiment was that the lowering water had left a space above it in the tube which had no intermediate contact with air to fill it up. This seemed to suggest the possibility of a vacuum existing in the space above the water. Torricelli, a friend and student of Galileo, interpreted the results of the experiments in a novel way. He proposed that the weight of the atmosphere, not an attracting force of the vacuum, held the water in the tube. In a letter to Michelangelo Ricci in 1644 concerning the experiments, he wrote: Many have said that a vacuum does not exist, others that it does exist in spite of the repugnance of nature and with difficulty; I know of no one who has said that it exists without difficulty and without a resistance from nature. I argued thus: If there can be found a manifest cause from which the resistance can be derived which is felt if we try to make a vacuum, it seems to me foolish to try to attribute to vacuum those operations which follow evidently from some other cause; and so by making some very easy calculations, I found that the cause assigned by me (that is, the weight of the atmosphere) ought by itself alone to offer a greater resistance than it does when we try to produce a vacuum. It was traditionally thought (especially by the Aristotelians) that the air did not have weight: that is, that the kilometers of air above the surface did not exert any weight on the bodies below it. Even Galileo had accepted the weightlessness of air as a simple truth. Torricelli questioned that assumption, and instead proposed that air had weight and that it was the latter (not the attracting force of the vacuum) which held (or rather, pushed) up the column of water. He thought that the level the water stayed at (c. 10.3 m) was reflective of the force of the air's weight pushing on it (specifically, pushing on the water in the basin and thus limiting how much water can fall from the tube into it). In other words, he viewed the barometer as a balance, an instrument for measurement (as opposed to merely being an instrument to create a vacuum), and because he was the first to view it this way, he is traditionally considered the inventor of the barometer (in the sense in which we now use the term). Because of rumors circulating in Torricelli's gossipy Italian neighborhood, which included that he was engaged in some form of sorcery or witchcraft, Torricelli realized he had to keep his experiment secret to avoid the risk of being arrested. He needed to use a liquid that was heavier than water, and from his previous association and suggestions by Galileo, he deduced by using mercury, a shorter tube could be used. With mercury, which is about 14 times denser than water, a tube only 80 cm was now needed, not 10.5 m. In 1646, Blaise Pascal along with Pierre Petit, had repeated and perfected Torricelli's experiment after hearing about it from Marin Mersenne, who himself had been shown the experiment by Torricelli toward the end of 1644. Pascal further devised an experiment to test the Aristotelian proposition that it was vapours from the liquid that filled the space in a barometer. His experiment compared water with wine, and since the latter was considered more "spiritous", the Aristotelians expected the wine to stand lower (since more vapours would mean more pushing down on the liquid column). Pascal performed the experiment publicly, inviting the Aristotelians to predict the outcome beforehand. The Aristotelians predicted the wine would stand lower. It did not. However, Pascal went even further to test the mechanical theory. If, as suspected by mechanical philosophers like Torricelli and Pascal, air had weight, the pressure would be less at higher altitudes. Therefore, Pascal wrote to his brother-in-law, Florin Perier, who lived near a mountain called the Puy de Dome, asking him to perform a crucial experiment. Perier was to take a barometer up the Puy de Dome and make measurements along the way of the height of the column of mercury. He was then to compare it to measurements taken at the foot of the mountain to see if those measurements taken higher up were in fact smaller. In September 1648, Perier carefully and meticulously carried out the experiment, and found that Pascal's predictions had been correct. The mercury barometer stood lower the higher one went. The concept that decreasing atmospheric pressure predicts stormy weather, postulated by Lucien Vidi, provides the theoretical basis for a weather prediction device called a "weather glass" or a "Goethe barometer" (named for Johann Wolfgang Von Goethe, the renowned German writer and polymath who developed a simple but effective weather ball barometer using the principles developed by Torricelli). The French name, "le baromètre Liègeois", is used by some English speakers. This name reflects the origins of many early weather glasses – the glass blowers of Liège, Belgium. The weather ball barometer consists of a glass container with a sealed body, half filled with water. A narrow spout connects to the body below the water level and rises above the water level. The narrow spout is open to the atmosphere. When the air pressure is lower than it was at the time the body was sealed, the water level in the spout will rise above the water level in the body; when the air pressure is higher, the water level in the spout will drop below the water level in the body. A variation of this type of barometer can be easily made at home. A mercury barometer has a vertical glass tube closed at the top sitting in an open mercury-filled basin at the bottom. Mercury in the tube adjusts until the weight of the mercury column balances the atmospheric force exerted on the reservoir. High atmospheric pressure places more force on the reservoir, forcing mercury higher in the column. Low pressure allows the mercury to drop to a lower level in the column by lowering the force placed on the reservoir. Since higher temperature levels around the instrument will reduce the density of the mercury, the scale for reading the height of the mercury is adjusted to compensate for this effect. The tube has to be at least as long as the amount dipping in the mercury + head space + the maximum length of the column. Torricelli documented that the height of the mercury in a barometer changed slightly each day and concluded that this was due to the changing pressure in the atmosphere. He wrote: "We live submerged at the bottom of an ocean of elementary air, which is known by incontestable experiments to have weight". Inspired by Torricelli, Otto von Guericke on 5 December 1660 found that air pressure was unusually low and predicted a storm, which occurred the next day. The mercury barometer's design gives rise to the expression of atmospheric pressure in inches or millimeters of mercury (mmHg). A torr was originally defined as 1 mmHg. The pressure is quoted as the level of the mercury's height in the vertical column. Typically, atmospheric pressure is measured between and of Hg. One atmosphere (1 atm) is equivalent to of mercury. Design changes to make the instrument more sensitive, simpler to read, and easier to transport resulted in variations such as the basin, siphon, wheel, cistern, Fortin, multiple folded, stereometric, and balance barometers. "Fitzroy" barometers combine the standard mercury barometer with a thermometer, as well as a guide of how to interpret pressure changes. Fortin barometers use a variable displacement mercury cistern, usually constructed with a thumbscrew pressing on a leather diaphragm bottom (V in the diagram). This compensates for displacement of mercury in the column with varying pressure. To use a Fortin barometer, the level of mercury is set to zero by using the thumbscrew to make an ivory pointer (O in the diagram) just touch the surface of the mercury. The pressure is then read on the column by adjusting the vernier scale so that the mercury just touches the sightline at Z.. Some models also employ a valve for closing the cistern, enabling the mercury column to be forced to the top of the column for transport. This prevents water-hammer damage to the column in transit. On June 5, 2007, a European Union directive was enacted to restrict the sale of mercury, thus effectively ending the production of new mercury barometers in Europe. Around 1810 the wheel barometer, which could be read from a great distance, became the first practical and commercial instrument favoured by farmers and the educated classes in the UK. The face of the barometer was circular with a simple dial pointing to an easily readable scale: "Rain - Change - Dry" with the "Change" at the top centre of the dial. Later models added a barometric scale with finer graduations "Stormy (28 inches of mercury), Much Rain (28.5), Rain (29), Change (29.5), Fair (30), Set fair (30.5), very dry(31)". Using vacuum pump oil as the working fluid in a barometer has led to the creation of the new "World's Tallest Barometer" in February 2013. The barometer at Portland State University (PSU) uses doubly distilled vacuum pump oil and has a nominal height of about 12.4 m for the oil column height; expected excursions are in the range of ±0.4 m over the course of a year. Vacuum pump oil has very low vapour pressure and it is available in a range of densities; the lowest density vacuum oil was chosen for the PSU barometer to maximize the oil column height. An aneroid barometer is an instrument used for measuring pressure as a method that does not involve liquid. Invented in 1844 by French scientist Lucien Vidi, the aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule), which is made from an alloy of beryllium and copper. The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. Many models include a manually set needle which is used to mark the current measurement so a change can be seen. This type of barometer is common in homes and in recreational boats. It is also used in meteorology, mostly in barographs and as a pressure instrument in radiosondes. A barograph is a recording aneroid barometer where the changes in atmospheric pressure are recorded on a paper chart. Principle & Working: The principle of the barograph is same as that of the aneroid barometer. A metal box partially exhausted of air will undergo changes of shape as the outside pressure varies. These small movements of the box are transmitted by a system of levers to a recording arm that has at its extreme end either a scribe or a pen. A scribe records on smoked foil while a pen records on paper using ink, held in a nib. The recording material is mounted on a cylindrical drum which is rotated slowly by a clock. Commonly, the drum makes one revolution per day, per week, or per month and the rotation rate can often be selected by the user. Micro Electro Mechanical Systems (or MEMS) barometers are extremely small devices between 1 and 100 micrometres in size (0.001 to 0.1 mm). They are created via photolithography or photochemical machining. Typical applications include miniaturized weather stations, electronic barometers and altimeters. A barometer can also be found in smartphones such as the Samsung Galaxy Nexus, Samsung Galaxy S3-S6, Motorola Xoom, Apple iPhone 6 smartphones, and Timex Expedition WS4 smartwatch, based on MEMS and piezoresistive pressure-sensing technologies. Inclusion of barometers on smartphones was originally intended to provide a faster GPS lock. However, third party researchers were unable to confirm additional GPS accuracy or lock speed due to barometric readings. The researchers suggest that the inclusion of barometers in smartphones may provide a solution for determining a user's elevation, but also suggest that several pitfalls must first be overcome. There are many other more unusual types of barometer. From variations on the storm barometer, such as the Collins Patent Table Barometer, to more traditional-looking designs such as Hooke's Otheometer and the Ross Sympiesometer. Some, such as the Shark Oil barometer, work only in a certain temperature range, achieved in warmer climates. Barometric pressure and the pressure tendency (the change of pressure over time) have been used in weather forecasting since the late 19th century. When used in combination with wind observations, reasonably accurate short-term forecasts can be made. Simultaneous barometric readings from across a network of weather stations allow maps of air pressure to be produced, which were the first form of the modern weather map when created in the 19th century. Isobars, lines of equal pressure, when drawn on such a map, give a contour map showing areas of high and low pressure. Localized high atmospheric pressure acts as a barrier to approaching weather systems, diverting their course. Atmospheric lift caused by low-level wind convergence into the surface brings clouds and sometimes precipitation. The larger the change in pressure, especially if more than 3.5 hPa (0.1 inHg), the greater the change in weather that can be expected. If the pressure drop is rapid, a low pressure system is approaching, and there is a greater chance of rain. Rapid pressure rises, such as in the wake of a cold front, are associated with improving weather conditions, such as clearing skies. With falling air pressure, gases trapped within the coal in deep mines can escape more freely. Thus low pressure increases the risk of firedamp accumulating. Collieries therefore keep track of the pressure. In the case of the Trimdon Grange colliery disaster of 1882 the mines inspector drew attention to the records and in the report stated "the conditions of atmosphere and temperature may be taken to have reached a dangerous point". Aneroid barometers are used in scuba diving. A submersible pressure gauge is used to keep track of the contents of the diver's air tank. Another gauge is used to measure the hydrostatic pressure, usually expressed as a depth of sea water. Either or both gauges may be replaced with electronic variants or a dive computer. The density of mercury will change with increase or decrease in temperature, so a reading must be adjusted for the temperature of the instrument. For this purpose a mercury thermometer is usually mounted on the instrument. Temperature compensation of an aneroid barometer is accomplished by including a bi-metal element in the mechanical linkages. Aneroid barometers sold for domestic use typically have no compensation under the assumption that they will be used within a controlled room temperature range. As the air pressure decreases at altitudes above sea level (and increases below sea level) the uncorrected reading of the barometer will depend on its location. The reading is then adjusted to an equivalent sea-level pressure for purposes of reporting. For example, if a barometer located at sea level and under fair weather conditions is moved to an altitude of 1,000 feet (305 m), about 1 inch of mercury (~35 hPa) must be added on to the reading. The barometer readings at the two locations should be the same if there are negligible changes in time, horizontal distance, and temperature. If this were not done, there would be a false indication of an approaching storm at the higher elevation. Aneroid barometers have a mechanical adjustment that allows the equivalent sea level pressure to be read directly and without further adjustment if the instrument is not moved to a different altitude. Setting an aneroid barometer is similar to resetting an analog clock that is not at the correct time. Its dial is rotated so that the current atmospheric pressure from a known accurate and nearby barometer (such as the local weather station) is displayed. No calculation is needed, as the source barometer reading has already been converted to equivalent sea-level pressure, and this is transferred to the barometer being set—regardless of its altitude. Though somewhat rare, a few aneroid barometers intended for monitoring the weather are calibrated to manually adjust for altitude. In this case, knowing "either" the altitude or the current atmospheric pressure would be sufficient for future accurate readings. The table below shows examples for three locations in the city of San Francisco, California. Note the corrected barometer readings are identical, and based on equivalent sea-level pressure. (Assume a temperature of 15 °C.) In 1787, during a scientific expedition on Mont Blanc, De Saussure undertook research and executed physical experiments on the boiling point of water at different heights. He calculated the height at each of his experiments by measuring how long it took an alcohol burner to boil an amount of water, and by these means he determined the height of the mountain to be 4775 metres. (This later turned out to be 32 metres less than the actual height of 4807 metres). For these experiments De Saussure brought specific scientific equipment, such as a barometer and thermometer. His calculated boiling temperature of water at the top of the mountain was fairly accurate, only off by 0.1 kelvin. Based on his findings, the altimeter could be developed as a specific application of the barometer. In the mid-19th century, this method was used by explorers. When atmospheric pressure is measured by a barometer, the pressure is also referred to as the "barometric pressure". Assume a barometer with a cross-sectional area "A", a height "h", filled with mercury from the bottom at Point B to the top at Point C. The pressure at the bottom of the barometer, Point B, is equal to the atmospheric pressure. The pressure at the very top, Point C, can be taken as zero because there is only mercury vapour above this point and its pressure is very low relative to the atmospheric pressure. Therefore, one can find the atmospheric pressure using the barometer and this equation: where ρ is the density of mercury, g is the gravitational acceleration, and h is the height of the mercury column above the free surface area. The physical dimensions (length of tube and cross-sectional area of the tube) of the barometer itself have no effect on the height of the fluid column in the tube. In thermodynamic calculations, a commonly used pressure unit is the "standard atmosphere". This is the pressure resulting from a column of mercury of 760 mm in height at 0 °C. For the density of mercury, use ρ = 13,595 kg/m and for gravitational acceleration use g = 9.807 m/s. If water were used (instead of mercury) to meet the standard atmospheric pressure, a water column of roughly 10.3 m (33.8 ft) would be needed. Standard atmospheric pressure as a function of elevation: Note: 1 torr = 133.3 Pa = 0.03937 inHg	A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis to help find surface troughs, pressure systems and frontal boundaries.	en	en	52	[ 250004, 250054, 581, 2565, 44, 1299, 102220, 58, 83, 16406, 4126, 1295, 70, 4, 136, 44, 29089, 58, 1295, 893, 45964, 160600, 91084, 44, 37440, 56851, 740, 106073, 53938, 1035, 6653, 416, 144002, 83, 32813, 538, 22299, 297, 678, 26868, 214, 70, 1909, 102220, 23, 611, 11548, 4, 16093, 29087, 9351, 22422, 5475, 696, 1574, 5, 164, 1760, 1179, 5, 277, 64, 2306, 21231, 64, 1177, 11, 9319, 64, 979, 86385, 64, 1299, 102220, 979, 86385, 418, 5, 79983, 58, 172132, 29087, 74047, 29087, 9351, 22422, 5475, 696, 1574, 5, 1299, 102220, 93771, 5, 277, 64, 979, 86385, 454, 4390, 454, 2347, 454, 1299, 102220, 5, 79983, 58, 172132, 29087, 74047, 29087, 9351, 22422, 5475, 696, 1574, 5, 461, 38820, 9774, 7568, 5, 277, 64, 32976, 510, 64, 1290, 416, 144002, 1299, 102220, 5, 7693, 58, 172132, 29087, 2740, 186768, 209806, 2843, 42459, 7, 27967, 88777, 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summarize: Volumetric flow rate is defined by the limit: That is, the flow of volume of fluid through a surface per unit time. Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. The change in volume is the amount that flows "after" crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow. Volumetric flow rate can also be defined by: where: The above equation is only true for flat, plane cross-sections. In general, including curved surfaces, the equation becomes a surface integral: This is the definition used in practice. The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The vector area is a combination of the magnitude of the area through which the volume passes through,, and a unit vector normal to the area,. The relation is. The reason for the dot product is as follows. The only volume flowing "through" the cross-section is the amount normal to the area, that is, parallel to the unit normal. This amount is: where is the angle between the unit normal and the velocity vector of the substance elements. The amount passing through the cross-section is reduced by the factor. As increases less volume passes through. Substance which passes tangential to the area, that is perpendicular to the unit normal, does not pass through the area. This occurs when and so this amount of the volumetric flow rate is zero: These results are equivalent to the dot product between velocity and the normal direction to the area. When the mass flow rate is known, and the density can be assumed constant, this is an easy way to get formula_6. Where: In internal combustion engines, the time area integral is considered over the range of valve opening. The time lift integral is given by: where is the time per revolution, is the distance from the camshaft centreline to the cam tip, is the radius of the camshaft (that is, is the maximum lift), is the angle where opening begins, and is where the valve closes (seconds, mm, radians). This has to be factored by the width (circumference) of the valve throat. The answer is usually related to the cylinder's swept volume.	In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes per unit time; usually represented by the symbol (sometimes ). The SI unit is cubic metres per second (m/s). 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summarize: Turbulence is characterized by the following features: "Turbulent diffusion" is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle. In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula. Via this energy cascade, turbulent flow can be realized as a superposition of a spectrum of flow velocity fluctuations and eddies upon a mean flow. The eddies are loosely defined as coherent patterns of flow velocity, vorticity and pressure. Turbulent flows may be viewed as made of an entire hierarchy of eddies over a wide range of length scales and the hierarchy can be described by the energy spectrum that measures the energy in flow velocity fluctuations for each length scale (wavenumber). The scales in the energy cascade are generally uncontrollable and highly non-symmetric. Nevertheless, based on these length scales these eddies can be divided into three categories. The integral time scale for a Lagrangian flow can be defined as: where "u"′ is the velocity fluctuation, and formula_2 is the time lag between measurements. Although it is possible to find some particular solutions of the Navier–Stokes equations governing fluid motion, all such solutions are unstable to finite perturbations at large Reynolds numbers. Sensitive dependence on the initial and boundary conditions makes fluid flow irregular both in time and in space so that a statistical description is needed. The Russian mathematician Andrey Kolmogorov proposed the first statistical theory of turbulence, based on the aforementioned notion of the energy cascade (an idea originally introduced by Richardson) and the concept of self-similarity. As a result, the Kolmogorov microscales were named after him. It is now known that the self-similarity is broken so the statistical description is presently modified. A complete description of turbulence is one of the unsolved problems in physics. According to an apocryphal story, Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." A similar witticism has been attributed to Horace Lamb in a speech to the British Association for the Advancement of Science: "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic." The onset of turbulence can be, to some extent, predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe. A similar effect is created by the introduction of a stream of higher velocity fluid, such as the hot gases from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, as more kinetic energy is absorbed by a more viscous fluid. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation. This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full size version. Such scaling is not always linear and the application of Reynolds numbers to both situations allows scaling factors to be developed. A flow situation in which the kinetic energy is significantly absorbed due to the action of fluid molecular viscosity gives rise to a laminar flow regime. For this the dimensionless quantity the Reynolds number () is used as a guide. With respect to laminar and turbulent flow regimes: The Reynolds number is defined as where: While there is no theorem directly relating the non-dimensional Reynolds number to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In Poiseuille flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040; moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 4000. The transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased. When flow is turbulent, particles exhibit additional transverse motion which enhances the rate of energy and momentum exchange between them thus increasing the heat transfer and the friction coefficient. Assume for a two-dimensional turbulent flow that one was able to locate a specific point in the fluid and measure the actual flow velocity of every particle that passed through that point at any given time. Then one would find the actual flow velocity fluctuating about a mean value: and similarly for temperature () and pressure (), where the primed quantities denote fluctuations superposed to the mean. This decomposition of a flow variable into a mean value and a turbulent fluctuation was originally proposed by Osborne Reynolds in 1895, and is considered to be the beginning of the systematic mathematical analysis of turbulent flow, as a sub-field of fluid dynamics. While the mean values are taken as predictable variables determined by dynamics laws, the turbulent fluctuations are regarded as stochastic variables. The heat flux and momentum transfer (represented by the shear stress ) in the direction normal to the flow for a given time are where is the heat capacity at constant pressure, is the density of the fluid, is the coefficient of turbulent viscosity and is the turbulent thermal conductivity. Richardson's notion of turbulence was that a turbulent flow is composed by "eddies" of different sizes. The sizes define a characteristic length scale for the eddies, which are also characterized by flow velocity scales and time scales (turnover time) dependent on the length scale. The large eddies are unstable and eventually break up originating smaller eddies, and the kinetic energy of the initial large eddy is divided into the smaller eddies that stemmed from it. These smaller eddies undergo the same process, giving rise to even smaller eddies which inherit the energy of their predecessor eddy, and so on. In this way, the energy is passed down from the large scales of the motion to smaller scales until reaching a sufficiently small length scale such that the viscosity of the fluid can effectively dissipate the kinetic energy into internal energy. In his original theory of 1941, Kolmogorov postulated that for very high Reynolds numbers, the small-scale turbulent motions are statistically isotropic (i.e. no preferential spatial direction could be discerned). In general, the large scales of a flow are not isotropic, since they are determined by the particular geometrical features of the boundaries (the size characterizing the large scales will be denoted as ). Kolmogorov's idea was that in the Richardson's energy cascade this geometrical and directional information is lost, while the scale is reduced, so that the statistics of the small scales has a universal character: they are the same for all turbulent flows when the Reynolds number is sufficiently high. Thus, Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the kinematic viscosity and the rate of energy dissipation. With only these two parameters, the unique length that can be formed by dimensional analysis is This is today known as the Kolmogorov length scale (see Kolmogorov microscales). A turbulent flow is characterized by a hierarchy of scales through which the energy cascade takes place. Dissipation of kinetic energy takes place at scales of the order of Kolmogorov length, while the input of energy into the cascade comes from the decay of the large scales, of order. These two scales at the extremes of the cascade can differ by several orders of magnitude at high Reynolds numbers. In between there is a range of scales (each one with its own characteristic length ) that has formed at the expense of the energy of the large ones. These scales are very large compared with the Kolmogorov length, but still very small compared with the large scale of the flow (i.e. ). Since eddies in this range are much larger than the dissipative eddies that exist at Kolmogorov scales, kinetic energy is essentially not dissipated in this range, and it is merely transferred to smaller scales until viscous effects become important as the order of the Kolmogorov scale is approached. Within this range inertial effects are still much larger than viscous effects, and it is possible to assume that viscosity does not play a role in their internal dynamics (for this reason this range is called "inertial range"). Hence, a third hypothesis of Kolmogorov was that at very high Reynolds number the statistics of scales in the range are universally and uniquely determined by the scale and the rate of energy dissipation. The way in which the kinetic energy is distributed over the multiplicity of scales is a fundamental characterization of a turbulent flow. For homogeneous turbulence (i.e., statistically invariant under translations of the reference frame) this is usually done by means of the "energy spectrum function", where is the modulus of the wavevector corresponding to some harmonics in a Fourier representation of the flow velocity field : where is the Fourier transform of the flow velocity field. Thus, represents the contribution to the kinetic energy from all the Fourier modes with, and therefore, where is the mean turbulent kinetic energy of the flow. The wavenumber corresponding to length scale is. Therefore, by dimensional analysis, the only possible form for the energy spectrum function according with the third Kolmogorov's hypothesis is where would be a universal constant. This is one of the most famous results of Kolmogorov 1941 theory, and considerable experimental evidence has accumulated that supports it. In spite of this success, Kolmogorov theory is at present under revision. This theory implicitly assumes that the turbulence is statistically self-similar at different scales. This essentially means that the statistics are scale-invariant in the inertial range. A usual way of studying turbulent flow velocity fields is by means of flow velocity increments: that is, the difference in flow velocity between points separated by a vector (since the turbulence is assumed isotropic, the flow velocity increment depends only on the modulus of ). Flow velocity increments are useful because they emphasize the effects of scales of the order of the separation when statistics are computed. The statistical scale-invariance implies that the scaling of flow velocity increments should occur with a unique scaling exponent, so that when is scaled by a factor, should have the same statistical distribution as with independent of the scale. From this fact, and other results of Kolmogorov 1941 theory, it follows that the statistical moments of the flow velocity increments (known as "structure functions" in turbulence) should scale as where the brackets denote the statistical average, and the would be universal constants. There is considerable evidence that turbulent flows deviate from this behavior. The scaling exponents deviate from the value predicted by the theory, becoming a non-linear function of the order of the structure function. The universality of the constants have also been questioned. For low orders the discrepancy with the Kolmogorov value is very small, which explain the success of Kolmogorov theory in regards to low order statistical moments. In particular, it can be shown that when the energy spectrum follows a power law with, the second order structure function has also a power law, with the form Since the experimental values obtained for the second order structure function only deviate slightly from the value predicted by Kolmogorov theory, the value for is very near to (differences are about 2%). Thus the "Kolmogorov − spectrum" is generally observed in turbulence. However, for high order structure functions the difference with the Kolmogorov scaling is significant, and the breakdown of the statistical self-similarity is clear. This behavior, and the lack of universality of the constants, are related with the phenomenon of intermittency in turbulence. This is an important area of research in this field, and a major goal of the modern theory of turbulence is to understand what is really universal in the inertial range.	In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. 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summarize: When a body is free to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram metre squared (kg·m) in SI units and pound-foot-second squared (lbf·ft·s) in imperial or US units. Moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like mass, the moment of inertia about some axis is given by formula_1, where formula_2 is the distance of the point from the axis, and formula_3 is the mass. For an extended rigid body, the moment of inertia is just the sum of all the small pieces of mass multiplied by the square of their distances from the axis in rotation. For an extended body of a regular shape Moment of inertia formula_4 is defined as the ratio of the net angular momentum formula_5 of a system to its angular velocity formula_6 around a principal axis, that is If the angular momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase. This occurs when spinning figure skaters pull in their outstretched arms or divers curl their bodies into a tuck position during a dive, to spin faster. If the shape of the body does not change, then its moment of inertia appears in Newton's law of motion as the ratio of an applied torque formula_8 on a body to the angular acceleration formula_9 around Moment of inertia can be measured using a simple pendulum, because it is the resistance to the rotation caused by gravity. Mathematically, the moment of inertia of the pendulum is the ratio of the torque due to gravity about the pivot of a pendulum to its angular acceleration about that pivot point. For a simple pendulum this is found to be the product of the mass of the particle formula_3 with the square of its distance formula_2 to the pivot, that is This can be shown as follows: The force of gravity on the mass of a simple pendulum generates a torque formula_27 around the axis perpendicular to the plane of the pendulum movement. Here formula_28 is the distance vector perpendicular to and from the force to the torque axis, and formula_29 is the net force on the mass. Associated A compound pendulum is a body formed from an assembly of particles of continuous shape that rotates rigidly around a pivot. Its moment of inertia is the sum of the moments of inertia of each of the particles that it is composed of. The natural frequency (formula_45) of a compound pendulum depends on its moment of inertia, formula_46, where formula_3 is the mass of the object, formula_49 is local acceleration of gravity, and formula_2 is the distance from the pivot point to the center of mass of the object. Measuring this frequency of oscillation over small angular displacements provides an effective way of measuring moment of inertia of a body. Thus, to determine the moment of inertia of the body, simply suspend it from a convenient pivot point formula_51 so that it swings freely in a plane perpendicular to the direction of the desired moment of inertia, then measure its natural frequency or period of oscillation (formula_52), to obtain where formula_52 is the period (duration) of oscillation (usually averaged over multiple periods). A simple pendulum that has the same natural frequency as a compound pendulum defines the length formula_5 from the pivot to a point called the center of oscillation of the compound pendulum. This point also corresponds to the center of percussion. The length formula_5 is determined from the formula, or The seconds pendulum, which provides the "tick" and "tock" of a grandfather clock, takes one second to swing from side-to-side. This is a period of two seconds, or a natural frequency of formula_59 for the pendulum. In this case, the distance to the center of oscillation, formula_5, can be computed to be Notice that the distance to the center of oscillation of the seconds pendulum must be adjusted to accommodate different values for the local acceleration of gravity. Kater's pendulum is a compound pendulum that uses this property to measure the local acceleration of gravity, and is called a gravimeter. The moment of inertia of a complex system such as a vehicle or airplane around its vertical axis can be measured by suspending the system from three points The moment of inertia about an axis of a body is calculated by summing formula_1 for every particle in the body, where formula_2 is the perpendicular distance to the specified axis. To see how moment of inertia arises in the study of the movement of an extended body, it is convenient to consider a rigid assembly of point masses. (This equation can be used for axes that are not principal axes provided that it is understood that this does not fully describe the moment of inertia.) Consider the kinetic energy of an assembly of formula_64 masses formula_65 that lie at the distances formula_66 from the pivot point formula_51, which is the nearest point on the axis of rotation. It is the sum of the kinetic energy of the individual masses, This shows that the moment of inertia of the body is the sum of each of the formula_1 terms, that is Thus, moment of inertia is a physical property that combines the mass and distribution of the particles around If a mechanical system is constrained to move parallel to a fixed plane, then the rotation of a body in the system occurs around an axis formula_34 perpendicular to this plane. In this case, the moment of inertia of the mass in this system is a scalar known as the "polar moment of inertia". The definition of the polar moment of inertia can be obtained by considering momentum, kinetic energy and Newton's laws for the planar movement of a rigid system of particles. If a system of formula_104 particles, formula_105, are assembled into a rigid body, then the momentum of the system can be written in terms of positions relative to a reference point formula_106, and absolute velocities formula_107: where formula_40 is the angular velocity of the system and formula_110 is the velocity of formula_106. For planar movement the angular velocity vector is directed along the unit The angular momentum vector for the planar movement of a rigid system of particles is given by Use the center of mass formula_119 as the reference point so and define the moment of inertia relative to the center of mass formula_121 as then the equation for angular momentum simplifies to The moment of inertia formula_121 about an axis perpendicular to the movement of the rigid system and The kinetic energy of a rigid system of particles moving in the plane is given by Let the reference point be the center of mass Newton's laws for a rigid system of formula_104 particles, formula_105, can be written in terms of a resultant force and torque at a reference point formula_106, to yield where formula_115 denotes the trajectory of each particle. The kinematics of a rigid body yields the formula for the acceleration of the particle formula_135 in terms of the position formula_106 and acceleration formula_137 of the reference particle as well as the angular velocity vector formula_40 and angular acceleration vector formula_30 of the rigid system The scalar moments of inertia appear as elements in a matrix when a system of particles is assembled into a rigid body that moves in three-dimensional space. This inertia matrix appears in the calculation of the angular momentum, kinetic energy and resultant torque of the rigid system of particles. Let the system of formula_104 particles, formula_105 be located at the coordinates formula_115 with velocities formula_107 relative to a fixed reference frame. For a (possibly moving) reference point formula_106, the relative positions are and the (absolute) velocities are where formula_40 is the angular velocity of the system, and formula_162 is the velocity of formula_106. Note that the cross product can be equivalently written as matrix multiplication by combining the first operand and the operator into a skew-symmetric matrix, formula_164, constructed from the components of formula_165: The inertia matrix is constructed by considering the angular momentum, with the reference point formula_106 The kinetic energy of a rigid system of particles can be formulated in terms of the center of mass and a matrix of mass moments of inertia of the system. Let the system of formula_104 particles formula_105 be located at the coordinates formula_115 with velocities formula_107, then the kinetic energy is where formula_173 The inertia matrix appears in the application of Newton's second law to a rigid assembly of particles. The resultant torque on this system is, where formula_192 is the acceleration of the particle formula_135. The kinematics of a rigid body yields the formula for the acceleration of the particle formula_135 in terms of the position formula_106 and acceleration formula_196 of the reference The inertia matrix of a body depends on the choice of the reference point. There is a useful relationship between the inertia matrix relative to the center of mass formula_119 and the inertia matrix relative to another point formula_106. This relationship is called the parallel axis theorem. Consider the inertia matrix formula_209 obtained for a rigid system of particles measured relative to a reference point formula_106, given by Let formula_119 be the center of mass of the rigid system, then where formula_214 is the vector from the center of mass formula_119 to the reference point formula_106. Use this equation to compute the inertia The scalar moment of inertia, formula_231, of a body about a specified axis whose direction is specified by the unit vector formula_34 and passes through the body at a point formula_106 is as follows: where formula_209 is the moment of inertia matrix of the system relative to the reference point formula_106, and formula_172 is the skew symmetric matrix obtained from the vector formula_159. This is derived as follows. Let a rigid assembly of formula_104 particles, formula_105, have coordinates formula_115. Choose formula_106 as a reference point and compute the moment of inertia around a line L defined by the unit vector formula_34 through the reference point formula_106, formula_245. The perpendicular vector from this line to the particle formula_135 is obtained from formula_247 by For the same object, different axes of rotation will have different moments of inertia about those axes. In general, the moments of inertia are not equal unless the object is symmetric about all axes. The moment of inertia tensor is a convenient way to summarize all moments of inertia of an object with one quantity. It may be calculated with respect to any point in space, although for practical purposes the center of mass is most commonly used. For a rigid object of formula_64 point masses formula_270, the moment of inertia tensor is given by Its components are defined as where Note that, by the definition, formula_281 is a symmetric tensor. The diagonal elements are more succinctly written as while the off-diagonal elements, also called the products of inertia, are Here formula_288 denotes the moment of inertia around the formula_80-axis when the objects are rotated around the x-axis, formula_290 denotes the moment of inertia around the formula_81-axis when the objects are rotated around the formula_80-axis, and so on. These quantities can be generalized to an object with distributed mass, described by a mass density function, in a similar fashion to the The distance formula_2 of a particle at formula_310 from the axis of rotation passing through the origin in the formula_311 direction is formula_312. By using the formula formula_313 (and some simple vector algebra) it can be seen that the moment of inertia of The use of the inertia matrix in Newton's second law assumes its components are computed relative to axes parallel to the inertial frame and not relative to a body-fixed reference frame. This means that as the body moves the components of the inertia matrix change with time. In contrast, the components of the inertia matrix measured in a body-fixed frame are constant. Let the body frame inertia matrix relative to the center of mass be denoted formula_318, and define the orientation of the body frame relative to the inertial frame by the rotation matrix Measured in the body frame the inertia matrix is a constant real symmetric matrix. A real symmetric matrix has the eigendecomposition into the product of a rotation matrix formula_326 and a diagonal matrix formula_327, given by where The columns of the rotation matrix formula_326 define the directions of the principal axes of the body, and the constants formula_331, formula_332, and formula_333 are called the principal moments of inertia. This result was first shown by J. J. Sylvester (1852), and is a form of Sylvester's law of inertia. The principal axis with the highest moment of inertia is sometimes called the figure axis or axis of figure. When all principal moments of inertia are distinct, the principal axes through center of mass are uniquely specified. If two principal moments are the same, the rigid body is called a symmetrical top and there is no unique choice for the The moment of inertia matrix in body-frame coordinates is a quadratic form that defines a surface in the body called Poinsot's ellipsoid. Let formula_327 be the inertia matrix relative to the center of mass aligned with the principal axes, then the surface or defines an ellipsoid in the body frame. Write this equation	The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. 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summarize: The drag coefficient formula_4 is defined as where: The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere formula_10 (note this is not the surface area = formula_11). For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed. Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume (volume to the two-thirds power). Submerged streamlined bodies use the wetted surface area. Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less. It has been demonstrated that drag coefficient formula_12 is a function of Bejan number (formula_13), Reynolds number (formula_14) and the ratio between wet area formula_15and front area formula_16: formula_17 where formula_18is the Reynold Number related to fluid path length L. The drag equation is essentially a statement that the drag force on any object is proportional to the density of the fluid and proportional to the square of the relative flow speed between the object and the fluid. "C" is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number formula_20. formula_1 is thus a function of formula_20. In a compressible flow, the speed of sound is relevant, and formula_1 is also a function of Mach number formula_24. For certain body shapes, the drag coefficient formula_1 only depends on the Reynolds number formula_20, Mach number formula_24 and the direction of the flow. For low Mach number formula_24, the drag coefficient is independent of Mach number. Also, the variation with Reynolds number formula_20 within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed, the incoming flow direction is also more-or-less the same. Therefore, the drag coefficient formula_1 can often be treated as a constant. For a streamlined body to achieve a low drag coefficient, the boundary layer around the body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high "form drag" results in a broad wake. The boundary layer will transition from laminar to turbulent if Reynolds number of the flow around the body is sufficiently great. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers. For other objects, such as small particles, one can no longer consider that the drag coefficient formula_1 is constant, but certainly is a function of Reynolds number. At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers, without flow separation, the drag force formula_32 is proportional to formula_33 instead of formula_34; for a sphere this is known as Stokes law. The Reynolds number will be low for small objects, low velocities, and high viscosity fluids. A formula_1 equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate, the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph. Only considering the front side, the formula_1 of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall formula_1 of a real square flat plate perpendicular to the flow is often given as 1.17. Flow patterns and therefore formula_1 for some shapes can change with the Reynolds number and the roughness of the surfaces. In general, formula_4 is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number formula_14). A smooth sphere, for example, has a formula_4 that varies from high values for laminar flow to 0.47 for turbulent flow. Although the drag coefficient decreases with increasing formula_14, the drag force increases. As noted above, aircraft use their wing area as the reference area when computing formula_4, while automobiles (and many other objects) use frontal cross sectional area; thus, coefficients are not directly comparable between these classes of vehicles. In the aerospace industry, the drag coefficient is sometimes expressed in drag counts where 1 drag count = 0.0001 of a formula_44. Drag, in the context of fluid dynamics, refers to forces that act on a solid object in the direction of the relative flow velocity (note that the diagram below shows the drag in the opposite direction to the flow). The aerodynamic forces on a body come primarily from differences in pressure and viscous shearing stresses. Thereby, the drag force on a body could be divided into two components, namely frictional drag (viscous drag) and pressure drag (form drag). The net drag force could be decomposed as follows: where: Therefore, when the drag is dominated by a frictional component, the body is called a streamlined body; whereas in the case of dominant pressure drag, the body is called a blunt body. Thus, the shape of the body and the angle of attack determine the type of drag. For example, an airfoil is considered as a body with a small angle of attack by the fluid flowing across it. This means that it has attached boundary layers, which produce much less pressure drag. The wake produced is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as streamlined, whereas for bodies with fluid flow at high angles of attack, boundary layer separation takes place. This mainly occurs due to adverse pressure gradients at the top and rear parts of an airfoil. Due to this, wake formation takes place, which consequently leads to eddy formation and pressure loss due to pressure drag. In such situations, the airfoil is stalled and has higher pressure drag than friction drag. In this case, the body is described as a blunt body. A streamlined body looks like a fish (Tuna), Oropesa, etc. or an airfoil with small angle of attack, whereas a blunt body looks like a brick, a cylinder or an airfoil with high angle of attack. For a given frontal area and velocity, a streamlined body will have lower resistance than a blunt body. Cylinders and spheres are taken as blunt bodies because the drag is dominated by the pressure component in the wake region at high Reynolds number. To reduce this drag, either the flow separation could be reduced or the surface area in contact with the fluid could be reduced (to reduce friction drag). This reduction is necessary in devices like cars, bicycle, etc. to avoid vibration and noise production. The aerodynamic design of cars has evolved from the 1920s to the end of the 20th century. This change in design from a blunt body to a more streamlined body reduced the drag coefficient from about 0.95 to 0.30. "Time history of cars' aerodynamic drag in comparison to change in geometry of streamlined bodies (blunt to streamline)."	In fluid dynamics, the drag coefficient (commonly denoted as: formula_1, formula_2 or formula_3) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. 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summarize: In most flows of liquids, and of gases at low Mach number, the density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. Therefore, the fluid can be considered to be incompressible and these flows are called incompressible flows. Bernoulli performed his experiments on liquids, so his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline, is: where: The constant on the right-hand side of the equation depends only on the streamline chosen, whereas, and depend on the particular point on that streamline. The following assumptions must be met for this Bernoulli equation to apply: For conservative force fields (not limited to the gravitational field), Bernoulli's equation can be generalized as: where is the force potential at the point considered on the streamline. E.g. for the Earth's gravity. By multiplying with the fluid density, equation () can be rewritten as: or: where The constant in the Bernoulli equation can be normalised. A common approach is in terms of total head or energy head : The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached. In liquids – when the pressure becomes too low – cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid. In many applications of Bernoulli's equation, the change in the term along the streamline is so small compared with the other terms that it can be ignored. For example, in the case of aircraft in flight, the change in height along a streamline is so small the term can be omitted. This allows the above equation to be presented in the following simplified form: where is called "total pressure", and is "dynamic pressure". Many authors refer to the pressure as static pressure to distinguish it from total pressure and dynamic pressure. In "Aerodynamics", L.J. Clancy writes: "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure." The simplified form of Bernoulli's equation can be summarized in the following memorable word equation: Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure and dynamic pressure. Their sum is defined to be the total pressure. The significance of Bernoulli's principle can now be summarized as "total pressure is constant along a streamline". If the fluid flow is irrotational, the total pressure on every streamline is the same and Bernoulli's principle can be summarized as "total pressure is constant everywhere in the fluid flow". It is reasonable to assume that irrotational flow exists in any situation where a large body of fluid is flowing past a solid body. Examples are aircraft in flight, and ships moving in open bodies of water. However, it is important to remember that Bernoulli's principle does not apply in the boundary layer or in fluid flow through long pipes. If the fluid flow at some point along a streamline is brought to rest, this point is called a stagnation point, and at this point the total pressure is equal to the stagnation pressure. Bernoulli's equation is sometimes valid for the flow of gases: provided that there is no transfer of kinetic or potential energy from the gas flow to the compression or expansion of the gas. If both the gas pressure and volume change simultaneously, then work will be done on or by the gas. In this case, Bernoulli's equation – in its incompressible flow form – cannot be assumed to be valid. However, if the gas process is entirely isobaric, or isochoric, then no work is done on or by the gas, (so the simple energy balance is not upset). According to the gas law, an isobaric or isochoric process is ordinarily the only way to ensure constant density in a gas. Also the gas density will be proportional to the ratio of pressure and absolute temperature, however this ratio will vary upon compression or expansion, no matter what non-zero quantity of heat is added or removed. The only exception is if the net heat transfer is zero, as in a complete thermodynamic cycle, or in an individual isentropic (frictionless adiabatic) process, and even then this reversible process must be reversed, to restore the gas to the original pressure and specific volume, and thus density. Only then is the original, unmodified Bernoulli equation applicable. In this case the equation can be used if the flow speed of the gas is sufficiently below the speed of sound, such that the variation in density of the gas (due to this effect) along each streamline can be ignored. Adiabatic flow at less than Mach 0.3 is generally considered to be slow enough. The Bernoulli equation for unsteady potential flow is used in the theory of ocean surface waves and acoustics. For an irrotational flow, the flow velocity can be described as the gradient of a velocity potential. In that case, and for a constant density, the momentum equations of the Euler equations can be integrated to: which is a Bernoulli equation valid also for unsteady—or time dependent—flows. Here denotes the partial derivative of the velocity potential with respect to time, and is the flow speed. The function depends only on time and not on position in the fluid. As a result, the Bernoulli equation at some moment does not only apply along a certain streamline, but in the whole fluid domain. This is also true for the special case of a steady irrotational flow, in which case and are constants so equation () can be applied in every point of the fluid domain. Further can be made equal to zero by incorporating it into the velocity potential using the transformation resulting in Note that the relation of the potential to the flow velocity is unaffected by this transformation:. The Bernoulli equation for unsteady potential flow also appears to play a central role in Luke's variational principle, a variational description of free-surface flows using the Lagrangian (not to be confused with Lagrangian coordinates). Bernoulli developed his principle from his observations on liquids, and his equation is applicable only to incompressible fluids, and steady compressible fluids up to approximately Mach number 0.3. It is possible to use the fundamental principles of physics to develop similar equations applicable to compressible fluids. There are numerous equations, each tailored for a particular application, but all are analogous to Bernoulli's equation and all rely on nothing more than the fundamental principles of physics such as Newton's laws of motion or the first law of thermodynamics. For a compressible fluid, with a barotropic equation of state, and under the action of conservative forces, where: In engineering situations, elevations are generally small compared to the size of the Earth, and the time scales of fluid flow are small enough to consider the equation of state as adiabatic. In this case, the above equation for an ideal gas becomes: where, in addition to the terms listed above: In many applications of compressible flow, changes in elevation are negligible compared to the other terms, so the term can be omitted. A very useful form of the equation is then: where: The most general form of the equation, suitable for use in thermodynamics in case of (quasi) steady flow, is: Here is the enthalpy per unit mass (also known as specific enthalpy), which is also often written as (not to be confused with "head" or "height"). Note that formula_15 where formula_16 is the thermodynamic energy per unit mass, also known as the specific internal energy. So, for constant internal energy formula_16 the equation reduces to the incompressible-flow form. The constant on the right-hand side is often called the Bernoulli constant, and denoted. For steady inviscid adiabatic flow with no additional sources or sinks of energy, is constant along any given streamline. More generally, when may vary along streamlines, it still proves a useful parameter, related to the "head" of the fluid (see below). When the change in can be ignored, a very useful form of this equation is: where is total enthalpy. For a calorically perfect gas such as an ideal gas, the enthalpy is directly proportional to the temperature, and this leads to the concept of the total (or stagnation) temperature. When shock waves are present, in a reference frame in which the shock is stationary and the flow is steady, many of the parameters in the Bernoulli equation suffer abrupt changes in passing through the shock. The Bernoulli parameter itself, however, remains unaffected. An exception to this rule is radiative shocks, which violate the assumptions leading to the Bernoulli equation, namely the lack of additional sinks or sources of energy. For a compressible fluid, with a barotropic equation of state, the unsteady momentum conservation equation formula_19 With the irrotational assumption, namely, the flow velocity can be described as the gradient ∇"φ" of a velocity potential φ. The unsteady momentum conservation equation becomes formula_20 which leads to formula_21 In this case, the above equation for isentropic flow becomes: formula_22 In modern everyday life there are many observations that can be successfully explained by application of Bernoulli's principle, even though no real fluid is entirely inviscid and a small viscosity often has a large effect on the flow. Many explanations for the generation of lift (on airfoils, propeller blades, etc.) can be found; some of these explanations can be misleading, and some are false. There has been debate about whether lift is best introduced to students using Bernoulli's principle or Newton's laws of motion. Modern writings agree that both Bernoulli's principle and Newton's laws are relevant, and either can be used to correctly describe lift. Several of these explanations use the Bernoulli principle to connect the flow kinematics to the flow-induced pressures. In cases of incorrect (or partially correct) explanations relying on the Bernoulli principle, the errors generally occur in the assumptions on the flow kinematics and how these are produced. It is not the Bernoulli principle itself that is questioned, because this principle is well established (the airflow above the wing "is" faster, the question is "why" it is faster). There are several common classroom demonstrations that are sometimes incorrectly explained using Bernoulli's principle. One involves holding a piece of paper horizontally so that it droops downward and then blowing over the top of it. As the demonstrator blows over the paper, the paper rises. It is then asserted that this is because "faster moving air has lower pressure". One problem with this explanation can be seen by blowing along the bottom of the paper: were the deflection due simply to faster moving air one would expect the paper to deflect downward, but the paper deflects upward regardless of whether the faster moving air is on the top or the bottom. Another problem is that when the air leaves the demonstrator's mouth it has the "same" pressure as the surrounding air; the air does not have lower pressure just because it is moving; in the demonstration, the static pressure of the air leaving the demonstrator's mouth is "equal" to the pressure of the surrounding air. A third problem is that it is false to make a connection between the flow on the two sides of the paper using Bernoulli's equation since the air above and below are "different" flow fields and Bernoulli's principle only applies within a flow field. As the wording of the principle can change its implications, stating the principle correctly is important. What Bernoulli's principle actually says is that within a flow of constant energy, when fluid flows through a region of lower pressure it speeds up and vice versa. Thus, Bernoulli's principle concerns itself with "changes" in speed and "changes" in pressure "within" a flow field. It cannot be used to compare different flow fields. A correct explanation of why the paper rises would observe that the plume follows the curve of the paper and that a curved streamline will develop a pressure gradient perpendicular to the direction of flow, with the lower pressure on the inside of the curve. Bernoulli's principle predicts that the decrease in pressure is associated with an increase in speed, i.e. that as the air passes over the paper it speeds up and moves faster than it was moving when it left the demonstrator's mouth. But this is not apparent from the demonstration. Other common classroom demonstrations, such as blowing between two suspended spheres, inflating a large bag, or suspending a ball in an airstream are sometimes explained in a similarly misleading manner by saying "faster moving air has lower pressure".	In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book "Hydrodynamica" in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's equation in its usual form in 1752. 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summarize: "For a table of sovereign states and dependent territories in Africa with geographical data such as area, population, and population density, see Africa: territories and regions." Geologically, Africa is connected to Eurasia by the Isthmus of Suez and forms part of Afro-Eurasia. "For a table of sovereign states and dependent territories in Asia with geographical data such as area, population, and population density, see Asia: territories and regions." Geologically, Asia is part of Eurasia and due to the Isthmus of Suez forms part of Afro-Eurasia. "For a table of sovereign states and dependent territories in Europe with geographical data such as area, population, and population density, see Europe: political geography." Geologically, Europe is part of Eurasia and due to the Isthmus of Suez forms part of Afro-Eurasia. "For a table of sovereign states and dependent territories in North America with geographical data such as area, population, and population density, see North America: countries and territories." Geologically, North America is joined with South America by the Isthmus of Panama to form the Americas. "For a table of sovereign states and dependent territories in Oceania with geographical data such as area, population, and population density, see Oceania: territories and regions." "For a table of sovereign states and dependent territories in South America with geographical data such as area, population, and population density, see South America: demographics." Geologically, South America is joined with North America by the Isthmus of Panama to form the Americas. Antarctica is regulated by the Antarctic Treaty System, which defines it as all land and ice shelves south of 60°S, and has no government and belongs to no country. However, the following territorial claims in Antarctica have been made: The United States and Russia have reserved the right to claim territory on Antarctica. Unlike Antarctica itself, other nearby subantarctic island territories most commonly associated with the Antarctic continent, but lying north of 60°S, have had full sovereignty established over them by a governing state. The following dependent territories are situated within in the wider Antarctic Region, but are not directly part of the Antarctic Treaty System: In addition to the dependent territories listed above, the following islands are governed as a direct part of a controlling state. Thus they are fully and legally integrated within the governance structure of the respective state. They are similarly also not part of the Antarctic Treaty System.	This is a list of sovereign states and dependent territories of the world by continent, displayed with their respective national flags, including the following entities:	en	en	28	[ 250004, 250054, 44, 18537, 10, 23180, 111, 95934, 38529, 117249, 136, 108750, 43396, 90, 23, 36941, 678, 20787, 48461, 289, 2053, 6044, 237, 16128, 4, 43904, 4, 136, 43904, 168, 7, 2481, 4, 1957, 36941, 12, 43396, 90, 136, 10776, 7, 1242, 2206, 109622, 538, 4, 36941, 83, 162711, 47, 50005, 19920, 390, 70, 2071, 927, 2647, 111, 1832, 1255, 136, 3173, 7, 2831, 111, 167766, 9, 647, 474, 19920, 5, 44, 18537, 10, 23180, 111, 95934, 38529, 117249, 136, 108750, 43396, 90, 23, 14237, 678, 20787, 48461, 289, 2053, 6044, 237, 16128, 4, 43904, 4, 136, 43904, 168, 7, 2481, 4, 1957, 14237, 12, 43396, 90, 136, 10776, 7, 1242, 2206, 109622, 538, 4, 14237, 83, 2831, 111, 50005, 19920, 136, 4743, 47, 70, 2071, 927, 2647, 111, 1832, 1255, 3173, 7, 2831, 111, 167766, 9, 647, 474, 19920, 5, 44, 18537, 10, 23180, 111, 95934, 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summarize: The German name for Austria,, derives from the Old High German, which meant "eastern realm" and which first appeared in the "Ostarrîchi document" of 996. This word is probably a translation of Medieval Latin into a local (Bavarian) dialect. Another theory says that this The Central European land that is now Austria was settled in pre-Roman times by various Celtic tribes. The Celtic kingdom of Noricum was later claimed by the Roman Empire and made a province. Present-day Petronell-Carnuntum in eastern Austria was an important army camp turned capital city in what became known as the Upper Pannonia province. Carnuntum was home for 50,000 people for nearly 400 years. After the fall of the Roman Empire, the area was invaded by Bavarians, Slavs, and Avars. Charlemagne, King of the Franks, conquered the area in AD 788, encouraged colonization, and introduced Christianity. As part of Eastern Francia, the core areas that now encompass Austria were bequeathed to the house of Babenberg. The area was known as the "marchia Orientalis" and was given to Leopold of Babenberg in 976. The first record showing the name Austria is from 996, where it is written as "Ostarrîchi", referring to the territory of the Babenberg March. In 1156, the Privilegium Minus elevated Austria to the status of a duchy. In 1192, the Babenbergs also acquired the Duchy of Styria. With the death of Frederick II in 1246, the line of the Babenbergs was extinguished. As a result, Ottokar II of Bohemia effectively assumed control of the duchies of Austria, Styria, and Carinthia. His reign came to an end with his defeat at Dürnkrut at the hands of Rudolph I of Germany in 1278. Thereafter, until World War I, Austria's history was largely that of its ruling dynasty, the Habsburgs. In the 14th and 15th centuries, the Habsburgs began to accumulate other provinces in the vicinity of the Duchy of Austria. In 1438, Duke Albert V of Austria was chosen as the successor to his father-in-law, Emperor Sigismund. Although Albert himself only reigned for a year, henceforth every emperor of the Holy Roman Empire was a Habsburg, with only one exception. The Habsburgs began also to accumulate territory far from the hereditary lands. In 1477, Archduke Maximilian, only son of Emperor Frederick III, married the heiress Maria of Burgundy, During the long reign of Leopold I (1657–1705) and following the successful defence of Vienna against the Turks in 1683 (under the command of the King of Poland, John III Sobieski), a series of campaigns resulted in bringing most of Hungary to Austrian control by the Treaty of Karlowitz in 1699. Emperor Charles VI relinquished many Austria later became engaged in a war with Revolutionary France, at the beginning highly unsuccessfully, with successive defeats at the hands of Napoleon, meaning the end of the old Holy Roman Empire in 1806. Two years earlier, the Empire of Austria was founded. From 1792 to 1801, the Austrians had suffered 754,700 casualties. In 1814, Austria was part of the Allied forces that invaded France and brought to an end the Napoleonic Wars. It emerged from the Congress of Vienna in 1815 as one of the continent's four dominant powers and a recognised great power. The same year, the German Confederation () was founded under the presidency of Austria. As the Second Constitutional Era began in the Ottoman Empire, Austria-Hungary took the opportunity to annex Bosnia and Herzegovina in 1908. The assassination of Archduke Franz Ferdinand in Sarajevo in 1914 by Bosnian Serb Gavrilo Princip was used by leading Austrian politicians and generals to persuade the emperor to declare war on Serbia, thereby risking and prompting the outbreak of World War I, which eventually led to the dissolution of the Austro-Hungarian Empire. Over one million Austro-Hungarian soldiers died in World War I. On 21 October 1918, the elected German members of the "Reichsrat" (parliament of Imperial Austria) met After the war, inflation began to devalue the Krone, which was still Austria's currency. In autumn 1922, Austria was granted an international loan supervised by the League of Nations. The purpose of the loan was to avert bankruptcy, stabilise the currency, and improve Austria's general economic condition. The loan meant that Austria passed from an independent state to the control exercised by the League of Nations. In 1925, the "Schilling" was introduced, replacing the Krone at a rate of 10,000:1. Later, it was nicknamed the "Alpine dollar" due to its stability. From 1925 to 1929, the economy enjoyed a short high before nearly crashing after Black Tuesday. The First Austrian Republic lasted until 1933, when Chancellor Engelbert Dollfuss, using what he called "self-switch-off of Parliament", established an autocratic regime tending towards Italian fascism. The two big parties at this time, the Social Much like Germany, Austria was divided into American, British, French, and Soviet zones and governed by the Allied Commission for Austria. As forecast in the Moscow Declaration in 1943, a subtle difference was seen in the treatment of Austria by the Allies. The Austrian government, consisting of Social Democrats, Conservatives, and Communists (until 1947), and residing in Vienna, which was surrounded by the Soviet zone, was recognised by the Western Allies in October 1945 after some doubts that Renner could be Stalin's puppet. Thus, the creation of a separate Western Austrian government and the division of the country was avoided. Austria, in general, was treated as though it had been originally invaded by Germany and liberated by the Allies. On 15 May 1955, after talks which lasted for years and were influenced by the Cold War, Austria regained full independence by concluding the Austrian State Treaty with the Four Occupying Powers. On 26 October 1955, after all occupation troops had left, Austria declared its "permanent neutrality" by an act of parliament. This day is now Austria's National Day, a public holiday. The political system of the Second Republic is based on The Parliament of Austria is located in Vienna, the country's capital and most populous city. Austria became a federal, representative democratic republic through the Federal Constitution of 1920. The political system of the Second Republic with its nine states is based on the constitution of 1920, amended in 1929, which was reenacted on 1 May 1945. The head of state is the Federal President ("Bundespräsident"), who is directly elected by popular majority vote, with a run-off between the top-scoring candidates, if necessary. The head of the Federal Government is the Federal Chancellor ("Bundeskanzler"), who is selected by the President and tasked with forming a government based on the partisan composition of the lower house of parliament. The government can be removed from office by either a presidential decree or by vote of no confidence in the lower chamber of parliament, the Nationalrat. Voting for the Federal President and for the Parliament used to be compulsory in Austria, but this was abolished in steps from 1982 to 2004. Austria's parliament consists of two chambers. The composition of the Nationalrat (183 seats) is determined every five years (or whenever the Nationalrat has been dissolved by the federal president on a motion by the federal chancellor, or by Nationalrat itself) by a general election in which every citizen over the age of 16 has the right to vote. The voting age was lowered from 18 in 2007. While there is a general threshold of 4% of the vote for all parties in federal elections (Nationalratswahlen) to participate in the proportional allocation of seats, there remains the possibility of being elected to a seat directly in one of the 43 regional electoral districts (). The Nationalrat is the dominant chamber in the legislative process in Austria. However, the upper house of parliament, the Bundesrat, has a limited right of veto (the Nationalrat can—in almost all cases—ultimately pass the respective bill by voting a second time. This is referred to as "Beharrungsbeschluss", lit. "vote of persistence"). A constitutional convention, called the was convened on 30 June 2003 to consider reforms to the constitution, but failed to produce a proposal that would command a two-third majority in the Nationalrat, the margin necessary for constitutional amendments and/or reform. While the bicameral Parliament and the Government constitute the legislative and executive branches, respectively, the courts are the third branch of Austrian state powers. The Constitutional Court ("Verfassungsgerichtshof") exerts considerable influence on the political system because of its power to invalidate legislation and ordinances that are not in compliance with the constitution. Since 1995, the European Court of Justice may overrule Austrian decisions in all matters defined in laws of the European Union. Austria also implements the decisions of the European Court of Human Rights, since the European Convention on Human Rights is part of the Austrian constitution. Austria is a largely mountainous country because of its location in the Alps. The Central Eastern Alps, Northern Limestone Alps and Southern Limestone Alps are all partly in Austria. Of the total area of Austria (), only about a quarter can be considered low lying, and only 32% of the country is below. The Alps of western Austria give way somewhat into low lands and plains in the eastern part of the country. Austria lies between latitudes 46° and 49° N, and longitudes 9° and 18° E. It can be divided into five areas, the biggest being the Eastern Alps, which constitute 62% of the nation's total area. The Austrian foothills at the base of the Alps and the Carpathians account for around 12% and the foothills in the east and areas surrounding the periphery of the Pannoni low country amount to about 12% of the total landmass. The second greater mountain area (much lower than the Alps) is situated in the north. Known as the Austrian granite plateau, it is located in the central area of the Bohemian Mass and accounts for 10% of Austria. The Austrian portion of the Vienna basin makes up the remaining 4%. Phytogeographically, Austria belongs to the Central European province of the Circumboreal Region within the Boreal Kingdom. According to the WWF, the territory of Austria can be subdivided into four ecoregions: the Central European mixed forests, Pannonian mixed forests, Alps conifer and mixed forests and Western European broadleaf forests. The greater part of Austria lies in the cool/temperate climate zone, where humid westerly winds predominate. With nearly three-quarters of the country dominated by the Alps, the alpine climate is predominant. In the east—in the Pannonian Plain and along the Danube valley—the climate shows continental features with less rain than the alpine areas. Although Austria is cold in the winter (−10 to 0 °C), summer temperatures can be relatively high, with average temperatures in the mid-20s and a Austria consistently ranks high in terms of GDP per capita, due to its highly industrialized economy, and well-developed social market economy. Until the 1980s, many of Austria's largest industry firms were nationalised; in recent years, however, privatisation has reduced state holdings to a level comparable to other European economies. Labour movements are particularly influential, exercising large influence on labour politics and decisions related to the expansion of the economy. Next to a highly developed industry, international tourism is the most important part of the economy of Austria. Germany has historically been the main trading partner of Austria, making it vulnerable to rapid changes in the German economy. Since Austria became a member state of the European Union, it has gained closer ties to other EU economies, reducing its economic dependence on Germany. In addition, membership of the EU has drawn an influx of foreign investors attracted by Austria's access to the single European market and proximity to the aspiring economies of the European Union. Growth in GDP reached 3.3% in 2006. At least 67% of Austria's imports come from other European Union member states. Austria indicated on 16 November 2010 that it would withhold the December installment of its contribution to the EU bailout of Greece, citing the material worsening of the Greek debt situation and the apparent inability of Greece to collect the level of tax receipts it had previously promised. The Financial crisis of 2007–2008 dented the economy of Austria in other ways as well. It caused, for example, the Hypo Alpe-Adria-Bank International to be purchased in December 2009 by the government for 1 euro owing to credit difficulties, thus wiping out the €1.63bn of BayernLB., the HGAA situation was unresolved, causing Chancellor Werner Faymann to warn that its failure would be comparable to the 1931 Creditanstalt event. Since the fall of communism, Austrian companies have been quite active players and consolidators in Eastern Europe. Between 1995 and 2010, 4,868 mergers and acquisitions with a total known value of 163 bil. EUR with the involvement of Austrian firms have been announced. The largest transactions with involvement of Austrian companies have been: the acquisition of Bank Austria by Bayerische Hypo- und Vereinsbank for 7.8 billion EUR in 2000, the acquisition of Porsche Holding Salzburg by Volkswagen Group for 3.6 billion EUR in 2009, and the acquisition of Banca Comercială Română by Erste Group for 3.7 bil. EUR in 2005. Tourism in Austria accounts for almost 9% of its gross domestic product. In 2007, Austria ranked 9th worldwide in international tourism receipts, with 18.9 billion US$. In international tourist arrivals, Austria ranked 12th with 20.8 million tourists. Austria's population was estimated to be nearly 9 million (8.9) in 2020 by the Statistik Austria. The population of the capital, Vienna, exceeds 1.9 million (2.6 million, including the suburbs), representing about a quarter of the country's population. It is known for its cultural offerings and high standard of living. Vienna is by far the country's largest city. Graz is second in size, with 291,007 inhabitants, followed by Linz (206,604), Salzburg (155,031), Innsbruck (131,989), and Klagenfurt (101,303). All other cities have fewer than 100,000 inhabitants. According to Eurostat, in 2018 there were 1.69 million foreign-born residents in Austria, corresponding to 19.2% of the total population. Of these, 928,700 (10.5%) were born outside the EU and 762,000 (8.6%) were born in another EU Member State. There are more than 483,100 descendants of foreign-born immigrants. Turks form one of the largest ethnic groups in Austria, numbering around 350,000. 13,000 Turks were naturalised in 2003 and an unknown number have arrived in Austria at the same time. While 2,000 Turks left Austria in the same year, 10,000 immigrated to the country, confirming a strong trend of growth. Together, Serbs, Croats, Bosniaks and Slovenes make up about 5.1% of Austria's total population. The total fertility rate (TFR) in 2017 was estimated at 1.52 children born per woman, below the replacement rate of 2.1, it remains considerably below the high of 4.83 children born per woman in 1873. In 2015, 42.1% of births were to unmarried women. Austria subsequently has the 12th oldest population in the world, with the average age of 44.2 years. The life expectancy in 2016 was estimated at 81.5 years (78.9 years male, 84.3 years female). Statistics Austria estimates that nearly 10 million people will live in the country by 2080. Standard Austrian German is spoken in Austria, though used primarily just in education, publications, announcements and websites. It is mostly identical to the Standard German of Germany but with some vocabulary differences. This Standard German language is used in formal contexts across Germany, Austria, Switzerland and Liechtenstein, as well as among those with significant German-speaking minorities: Italy, Belgium and Denmark. However, the common spoken language of Austria is not the Standard German taught in schools but Austro-Bavarian: a group of Upper German local dialects with varying degrees of difficulty being understood by each other as well as by speakers of non-Austrian German dialects. Taken as a collective whole, German languages or dialects are thus spoken natively by 88.6% of the population, which includes the 2.5% German-born citizens who reside in Austria, followed by Turkish (2.28%), Serbian (2.21%), Croatian (1.63%), English (0.73%), Hungarian (0.51%), Bosnian (0.43%), Polish (0.35%), Albanian (0.35%), Slovenian (0.31%), Czech (0.22%), Arabic (0.22%), and Romanian (0.21%). The Austrian federal states of Carinthia and Styria are home to a significant indigenous Slovene-speaking minority while in the easternmost state, Burgenland (formerly part of the Hungarian portion of Austria–Hungary), there are Historically Austrians were regarded as ethnic Germans and viewed themselves as such, although this national identity was challenged by Austrian nationalism in the decades after the end of World War I and even more so after World War II. Austria was part of the Holy Roman Empire of the German Nation until its ending in 1806 and had been part of the German Confederation, a loose association of 39 separate German-speaking countries, until the Austro-Prussian war in 1866, which resulted in the exclusion of Austria from the German Confederation and the creation of the North German Confederation led by Prussia. In 1871, Germany was founded as a nation-state, Austria was not a part of it. After World In 2001, about 74% of Austria's population were registered as Roman Catholic, while about 5% considered themselves Protestants. Austrian Christians, both Catholic and Protestant, are obliged to pay a mandatory membership fee (calculated by income—about 1%) to their church; this payment is called "Kirchenbeitrag" ("Ecclesiastical/Church contribution"). Since the second half of the 20th century, the number of adherents and churchgoers has declined. Data for 2018 from the Austrian Roman Catholic Church list 5,050,000 members, or 56.9% of the total Austrian population. Sunday church Education in Austria is entrusted partly to the Austrian states (Bundesländer) and partly to the federal government. School attendance is compulsory for nine years, i.e. usually to the age of fifteen. Pre-school education (called "Kindergarten" in German), free in most states, is provided for all children between the ages of three and six years and, whilst optional, is considered a normal part of a child's education due to its high takeup rate. Maximum class size is around 30, each class normally being cared for by one qualified teacher and one assistant. Primary education, or Volksschule, lasts for four years, starting at age six. The maximum class size is 30, but may be as low as 15. It is generally expected Austria's past as a European power and its cultural environment generated a broad contribution to various forms of art, most notably among them music. Austria was the birthplace of many famous composers such as Joseph Haydn, Michael Haydn, Franz Liszt, Franz Schubert, Anton Bruckner, Johann Strauss, Sr. and Johann Strauss, Jr. as well as members of the Second Viennese School such as Arnold Schoenberg, Anton Webern and Alban Berg. Wolfgang Amadeus Mozart was born in Salzburg, then an independent Church Principality of the Holy Roman Empire, which later became part of Austria, and much of Mozart's career was spent in Vienna. Vienna was for a long time an important centre of musical innovation. 18th- Among Austrian Artists and architects one can find the painters Ferdinand Georg Waldmüller, Rudolf von Alt, Hans Makart, Gustav Klimt, Oskar Kokoschka, Egon Schiele, Carl Sascha Kolowrat was an Austrian pioneer of filmmaking. Billy Wilder, Fritz Lang, Josef von Sternberg, and Fred Zinnemann originally came from the Austrian Empire before establishing themselves as internationally relevant filmmakers. Willi Forst, Ernst Marischka, and Franz Antel enriched the popular cinema in German-speaking countries. Michael Haneke became internationally known for his disturbing cinematic studies, receiving a Golden Globe for his critically acclaimed film "The White Ribbon" (2010). Austria was the cradle of numerous scientists with international reputation. Among them are Ludwig Boltzmann, Ernst Mach, Victor Franz Hess and Christian Doppler, prominent scientists in the 19th century. In the 20th century, contributions by Lise Meitner, Erwin Schrödinger and Wolfgang Pauli to nuclear research and quantum mechanics were key to these areas' development during the 1920s and 1930s. A present-day quantum physicist is Anton Zeilinger, noted as the first scientist to demonstrate quantum teleportation. In addition to physicists, Austria was the birthplace of two of the most noteworthy philosophers of the 20th century, Ludwig Wittgenstein and Karl Popper. Complementing its status as a land of artists and scientists, Austria has always been a country of poets, writers, and novelists. It was the home of novelists Arthur Schnitzler, Austria's cuisine is derived from that of the Austro-Hungarian Empire. Austrian cuisine is mainly the tradition of Royal-Cuisine ("Hofküche") delivered over centuries. It is famous for its well-balanced variations of beef and pork and countless variations of vegetables. There is also the "Mehlspeisen" Bakery, which created particular delicacies such as Sachertorte, "Krapfen" which are doughnuts usually filled with apricot jam or custard, and "Strudel" such as "Apfelstrudel" filled with apple, "Topfenstrudel" filled with a type of cheese curd called "topfen", and "Millirahmstrudel" (milk-cream strudel). In addition to native regional traditions, the cuisine has been influenced by Hungarian, Czech, Polish, Jewish, Italian, Balkan and French cuisines, from which both dishes and methods of food preparation have often been borrowed. The Austrian cuisine is therefore one of the most multicultural and transcultural in Europe. Typical Austrian dishes include Wiener Schnitzel, Schweinsbraten, Kaiserschmarren, Knödel, Sachertorte and Tafelspitz. There are also Kärntner Kasnudeln, which are pockets of dough filled with Topfen, potatoes, herbs and peppermint which are boiled and served with a butter sauce. Kasnudeln are traditionally served with a salad. Eierschwammerl dishes are also popular. The sugar Due to the mountainous terrain, alpine skiing is a prominent sport in Austria and is extremely valuable in the promotion and economic growth of the country. Similar sports such as snowboarding or ski-jumping are also widely popular. Austrian athletes such as Annemarie Moser-Pröll, Franz Klammer, Hermann Maier, Toni Sailer, Benjamin Raich, Marlies Schild & Marcel Hirscher are widely regarded as some of the greatest alpine skiers of all time, Armin Kogler, Andreas Felder, Ernst Vettori, Andreas Goldberger, Andreas Widhölzl, Thomas Morgenstern & Gregor Schlierenzauer as some of the greatest ski jumpers of all time. Bobsleigh, luge, and skeleton are also popular events with a permanent track located in Igls, which hosted bobsleigh and luge competitions for the 1964 and 1976 Winter Olympics held in Innsbruck. The first Winter Youth Olympics in 2012 were held in Innsbruck as well. A popular team sport in Austria is football, which is governed by the Austrian Football Association. Austria was among the most successful football playing nations on the European continent placing 4th at the 1934 FIFA World Cup, 3rd at the 1954 FIFA World Cup and 7th at the 1978 FIFA World Cup. However, recently	Austria (, ; ), officially the Republic of Austria (, ), is a landlocked East Alpine country in the southern part of Central Europe. It is composed of nine federated states ("Bundeslände"r), one of which is Vienna, Austria's capital and its largest city. It is bordered by Germany to the northwest, Czech Republic to the north, Slovakia to the northeast, Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the west. Austria occupies an area of and has a population of nearly 9 million people. 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summarize: A fluid flowing around the surface of an object applies a force against it. It makes no difference whether the fluid is flowing past a stationary body or the body is moving through a stationary volume of fluid. Lift is the component of this force that is perpendicular to the oncoming flow direction. Lift is always accompanied by a drag force, which is the component of the surface force parallel to the flow direction. Lift is mostly associated with the wings of fixed-wing aircraft, although it is more widely generated by many other streamlined bodies such as propellers, kites, helicopter rotors, racing car wings, maritime sails, and wind turbines in air, and by sailboat keels, ship's rudders, and hydrofoils An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. A flat plate can generate lift, but not as much as a streamlined airfoil, and with somewhat higher drag. There are several ways to explain how an airfoil generates lift. Some are more complicated or more physically rigorous than others; some have been shown to be incorrect. For example, there are explanations based directly on Newton's laws of motion and explanations based on Bernoulli's principle. Either can be used to explain lift. An airfoil generates lift by exerting a downward force on the air as it flows past. According to Newton's third law, the air must exert an equal and opposite (upward) force on the airfoil, which is lift. The airflow changes direction as it passes the airfoil and follows a path that is curved downward. According to Newton's second law, this change in flow Bernoulli's principle states that there is a direct mathematical relationship between the pressure of a fluid and the speed of that fluid, so if one knows the speed at all points within the airflow one can calculate the pressure, and vice versa. For any airfoil generating lift, there must be a pressure imbalance, i.e. lower average air pressure on the top than on the bottom. Bernoulli's principle states that this pressure difference must be accompanied by a speed difference. Starting with the flow pattern observed in both theory and experiments, the increased flow speed over the upper surface can be explained in terms of streamtube pinching and conservation of mass. For incompressible flow, the rate of volume flow (e.g. volume units per minute) must be constant within each streamtube since matter is not created or destroyed. If a streamtube becomes narrower, the flow speed must increase in the narrower region to maintain the constant flow rate, to satisfy the principle of conservation of mass. The upper streamtubes constrict as they flow up and around the airfoil. Conservation of mass says that the flow speed must increase as the stream tube area decreases. Similarly, the lower streamtubes expand and their flowrate slows. From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower. This pressure difference creates a net aerodynamic force, pointing upward. As explained below under a more comprehensive physical explanation, producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions, and thus requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. The simplified explanations given above are therefore incomplete because they define lift in terms of only one or the other. And depending on the details, they have other shortcomings as well. The explanation based on flow deflection and Newton's laws is correct but is incomplete. It does not explain how the airfoil can impart downward Many alternative explanations for the generation of lift by an airfoil have been put forward, most intended to explain the phenomenon of lift to a general audience. Although the explanations may share features in common with the explanations above, additional assumptions and simplifications may be introduced. Some explanations introduce assumptions which proved to be wrong, such as "equal transit-time", and some used controversial terminology, such as "Coandă effect". Basic or popular sources often describe the "equal transit-time" theory of lift, which incorrectly assumes that the parcels of air that divide at the leading edge of an airfoil must rejoin at the trailing edge, forcing the air traveling along the longer upper surface to go faster. Bernoulli's principle is then cited to conclude that since the air moves slower along the bottom of the In its original sense, the "Coandă effect" refers to the tendency of a fluid jet to stay attached to an adjacent surface that curves away from the flow, and the resultant entrainment of ambient air into the flow. The effect is named for Henri Coandă, the Romanian aerodynamicist who exploited it in many of his patents. More broadly, some consider the effect to include the tendency of any fluid boundary layer to adhere to a curved surface, not just the boundary layer accompanying a fluid jet. It is in this broader sense that the Coandă effect is used by some to explain why airflow remains attached to the top Lift is a result of pressure differences and depends on angle of attack, airfoil shape, air density, and airspeed. Pressure is the normal force per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. Thus, the net force manifests itself as pressure differences. The direction of the net force implies that the average pressure on the upper surface of the airfoil is lower than the average pressure on the underside. These pressure differences arise in conjunction with the The angle of attack is the angle between the chord line of an airfoil and the oncoming airflow. A symmetrical airfoil will generate zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream The lift force depends on the shape of the airfoil, especially the amount of camber (curvature such that the upper surface is more convex than the lower surface, as illustrated at right). Increasing the camber generally increases lift. Cambered airfoils will The ambient flow conditions which affect lift include the fluid density, viscosity and Lift is proportional to the density of the air and approximately proportional to the square of the flow speed. Lift also depends on No matter how smooth the surface of an airfoil seems, any surface is rough on the scale of air molecules. Air molecules flying into the surface bounce off the rough surface in random directions relative to their original velocities. The result is that when the air is viewed as a continuous material, it is seen to be unable to slide along the surface, and the air's velocity relative to the airfoil decreases to nearly zero at the surface (i.e., the air molecules "stick" to the surface instead of sliding along it), something known as the no-slip condition. Because the air at the surface has near-zero velocity but the air An airfoil's maximum lift at a given airspeed is limited by boundary-layer separation. As the angle of attack is increased, a point is reached where the boundary layer can no longer remain attached to the upper surface. When the boundary layer separates, it leaves a region of recirculating flow above The flow around bluff bodies – i.e. without a streamlined shape, or stalling airfoils – may also generate lift, in addition to a strong drag force. This lift may be steady, or it may oscillate due to vortex shedding. Interaction of the object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause vortex-induced vibrations. For instance, the flow around a circular cylinder generates a Kármán vortex street: vortices being shed in an alternating fashion from the cylinder's sides. The oscillatory nature of the flow produces a fluctuating lift force on the cylinder, even though the net (mean) As described above under "Simplified physical explanations of lift on an airfoil", there are two main popular explanations: one based on downward deflection of the flow (Newton's laws), and one based on pressure differences accompanied by changes in flow speed (Bernoulli's principle). Either of these, by itself, correctly identifies some aspects of the lifting flow but leaves other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both downward deflection and pressure differences (including changes in flow speed associated with the pressure differences), and requires looking at the flow in more detail. The airfoil shape and angle of attack work together so that the airfoil exerts a downward force on the air as it flows past. According to Newton's third law, the air must then exert an equal and opposite (upward) force on the airfoil, which is the lift. The net force exerted by the air occurs as a pressure difference over the airfoil's surfaces. Pressure in a fluid is always positive in an absolute sense, so An airfoil affects the speed and direction of the flow over a wide area, producing a pattern called a "velocity field". When an airfoil produces lift, the flow ahead of the airfoil is deflected upward, the flow above and below the airfoil is deflected downward, and the flow behind the airfoil is deflected upward again, leaving the air far behind the airfoil in the same state as the oncoming flow far ahead. The flow above the upper surface is sped up, while the flow below the airfoil is slowed down. Together with the upward deflection of air in front and the downward The non-uniform pressure exerts forces on the air in the direction from higher pressure to lower pressure. The direction of the force is different at different locations around the airfoil, as indicated by the block arrows in the "pressure distribution with isobars" figure. Air above the airfoil is pushed toward the center of the low-pressure region, and air below the airfoil is pushed outward from the center of the high-pressure region. According to "Newton's second law", a force causes air to accelerate in the direction of the force. Thus the vertical arrows in the "pressure distribution with isobars" figure Producing a lift force requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. Each of the simplified explanations When the pressure distribution on the airfoil surface is known, determining the total lift requires adding up the contributions to the pressure force from local elements of the surface, each with its own local value of pressure. The total lift is thus the integral of the pressure, in the direction perpendicular to the farfield flow, over the airfoil surface. formula_2 where: Lift depends on the size of the wing, being approximately proportional to the wing area. It is often convenient to quantify the lift of a given airfoil by its "lift Mathematical theories of lift are based on continuum fluid mechanics, assuming that air flows as a continuous fluid. Lift is generated in accordance with the fundamental principles of physics, the most relevant being the following three principles: Because an airfoil affects the flow in a wide area around it, the conservation laws of mechanics are embodied in the form of partial differential equations combined with a set of boundary condition requirements which the flow has to satisfy at the airfoil surface and far away from the airfoil. To predict lift requires solving the equations for a particular airfoil shape and flow condition, which generally requires calculations that are so voluminous that they are practical only on a computer, through the methods of computational fluid dynamics (CFD). Determining the net aerodynamic force from a CFD solution requires "adding up" (integrating) the forces due to pressure and shear determined by the CFD over every surface element of the airfoil as described under "pressure integration". The Navier–Stokes equations (NS) provide the potentially most accurate theory of lift, but in practice, capturing the effects of turbulence in the boundary layer on the airfoil surface requires sacrificing some accuracy, and requires use of the Reynolds-averaged Navier–Stokes equations (RANS). Simpler but less accurate theories have also been developed. These equations represent conservation of mass, Newton's second law (conservation of momentum), conservation of energy, the Newtonian law for the action of viscosity, the Fourier heat conduction law, an equation of state relating density, temperature, and pressure, and formulas for the viscosity and thermal conductivity of the fluid. In principle, the NS equations, combined with boundary conditions of no through-flow and no slip at the airfoil surface, could be used to predict lift These are the NS equations with the turbulence motions averaged over time, and the effects of the turbulence on the time-averaged flow represented by turbulence modeling (an additional set of equations based on a combination of dimensional analysis and empirical information on how turbulence affects a boundary layer in a time-averaged average sense). A RANS solution consists of the time-averaged velocity vector, pressure, density, The Euler equations are the NS equations without the viscosity, heat conduction, and turbulence effects. As with a RANS solution, an Euler solution consists of the velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil. While the Euler equations are simpler than the NS equations, they do not lend themselves to exact analytic solutions. Further simplification is available through potential flow theory, which reduces the number of unknowns to be determined, and makes analytic solutions possible in some cases, as described below. Either Euler or potential-flow calculations predict This is potential-flow theory with the further assumptions that the airfoil is very thin and the angle of attack is small. The linearized theory predicts the general character of the When an airfoil generates lift, several components of the overall velocity field contribute to a net circulation of air around it: the upward flow ahead of the airfoil, the accelerated flow above, the decelerated flow below, and the downward flow behind. The circulation can be understood as the total amount of "spinning" (or vorticity) of an inviscid fluid around the airfoil. The Kutta–Joukowski theorem relates the lift per unit width of span of a two-dimensional airfoil to this circulation component of the flow. It is a key element in an explanation of lift that follows the development of the flow around an airfoil as the airfoil starts its motion from rest and a starting vortex is The flow around a three-dimensional wing involves significant additional issues, especially relating to the wing tips. For a wing of low aspect ratio, such as a typical delta wing, two-dimensional theories may provide a poor model and three-dimensional flow effects can dominate. Even for wings of high aspect ratio, the three-dimensional effects associated with finite span can affect the whole span, not just close to the tips. The vertical pressure gradient at the wing tips causes air to flow sideways, out from under the wing then up and back over the upper surface. This reduces the pressure gradient at the wing tip, therefore also reducing lift. The lift tends to decrease in the spanwise direction from root to tip, and the pressure distributions around the airfoil sections change accordingly in the spanwise direction. Pressure distributions in planes perpendicular to the flight direction tend to look like the illustration at right. This spanwise-varying pressure distribution is sustained by a mutual interaction with the velocity field. Flow below the wing is accelerated outboard, flow outboard of the tips is accelerated upward, and flow above The wingtip flow leaving the wing creates a tip vortex. As the main vortex sheet passes downstream from the trailing edge, it rolls up at its outer edges, merging with the tip vortices. The combination of the wingtip vortices and the vortex sheets feeding them is called the vortex wake. In addition to the vorticity in the trailing vortex wake there is vorticity in the wing's boundary layer, called 'bound vorticity', which connects the trailing sheets from the two sides of the wing into a vortex system in the general form of a horseshoe. The horseshoe form of the vortex system was recognized by the British aeronautical The flow around a lifting airfoil must satisfy Newton's second law regarding conservation of momentum, both locally at every point in the flow field, and in an integrated sense over any extended region of the flow. For an extended region, Newton's second law takes the form of the "momentum theorem for a control volume", where a control volume can be any region of the flow chosen for analysis. The momentum theorem states that the integrated force exerted at the boundaries of the control volume (a surface integral), is equal to the integrated time rate of change (material derivative) of the momentum of fluid parcels passing through the interior of the control volume. For a steady flow, this can be expressed in the form of the net surface integral of the flux of momentum through the boundary. The lifting flow around a 2D airfoil is usually analyzed in a control volume that completely surrounds the airfoil, so that the inner boundary of the control volume is the airfoil surface, where the downward force per unit span formula_12 is exerted on the fluid by the airfoil. The outer boundary is usually either a large circle An airfoil produces a pressure field in the surrounding air, as explained under "The wider flow around the airfoil" above. The pressure differences associated with this field die off gradually, becoming very small at large distances, but never disappearing altogether. Below the airplane, the pressure field persists as a positive pressure disturbance that reaches the ground, forming a pattern of slightly-higher-than-ambient pressure on the ground, as shown on the right. Although the pressure differences are very small far below the airplane, they	A fluid flowing around the surface of an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. 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summarize: The word "viscosity" is derived from the Latin In materials science and engineering, one is often interested in understanding the forces, or stresses, involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law, which says that the force experienced by a spring is proportional to the distance displaced from equilibrium. Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses. In other materials, stresses are present which can be attributed to the rate of change In very general terms, the viscous stresses in a fluid are defined as those resulting from the relative velocity of different fluid particles. As such, the viscous stresses must depend on spatial gradients of the flow velocity. If the velocity gradients are small, then to a first approximation the viscous stresses depend only on the first derivatives of the velocity. (For Newtonian fluids, this is also a linear dependence.) In Cartesian coordinates, the general relationship can then be written as where formula_23 is a viscosity tensor that maps the velocity gradient tensor formula_24 onto the viscous stress tensor formula_25. Since the indices in this expression can vary from 1 to 3, there are 81 "viscosity coefficients" formula_26 in total. However, assuming that the viscosity rank-4 tensor is isotropic reduces these 81 coefficients to three independent parameters formula_27, formula_28, formula_29: and furthermore, it is assumed that no viscous In fluid dynamics, it is common to work in terms of the "kinematic viscosity" (also called "momentum diffusivity"), defined as the ratio of the viscosity to the density Transport theory provides an alternative interpretation of viscosity in terms of momentum transport: viscosity is the material property which characterizes momentum transport within a fluid, just as thermal conductivity characterizes heat transport, and (mass) diffusivity characterizes mass transport. To see this, note that in Newton's law of viscosity, formula_48, the shear stress formula_49 has units equivalent to a momentum flux, i.e. momentum per unit time per unit area. Thus, formula_49 can be interpreted as specifying the flow of momentum in the formula_8 direction from one fluid layer to the next. Per Newton's law of viscosity, this momentum flow occurs across a velocity gradient, and the magnitude of Newton's law of viscosity is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law, Fick's law, and Ohm's law) which serves to define the viscosity formula_10. Its form is motivated by experiments which show that for a wide range of fluids, formula_10 is independent of strain rate. Such fluids are called Newtonian. Gases, water, and many common liquids can be considered Newtonian in ordinary conditions and contexts. The viscous forces that arise during fluid flow must not be confused with the elastic forces that arise in a solid in response to shear, compression or extension stresses. While in the latter the stress is proportional to the "amount" of shear deformation, in a fluid it is proportional to the "rate" of deformation over time. (For this reason, Maxwell used the term "fugitive elasticity" for fluid viscosity.) However, many liquids (including water) will briefly react Viscosity is measured with various types of viscometers and rheometers. A rheometer is used for those fluids that cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. Close temperature control of the fluid is essential to acquire accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. For some fluids, the viscosity is constant over a wide range of shear rates (Newtonian fluids). The fluids without a constant viscosity (non-Newtonian fluids) cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate. One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer. In coating industries, viscosity may be measured with a cup in which the The SI unit of dynamic viscosity is the pascal-second (Pa·s), or equivalently kilogram per meter per second (kg·m·s). The CGS unit is the poise (P, or g·cm·s = 0.1 Pa·s), named after Jean Léonard Marie Poiseuille. It is commonly expressed, particularly in ASTM standards, as "centipoise" (cP) since the latter is equal to the SI multiple millipascal seconds (mPa·s). The SI unit of kinematic viscosity is square meter per second (m/s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm·s = 0.0001 m·s), named after Sir George Gabriel Stokes. In U.S. usage, "stoke" is sometimes used In general, the viscosity of a system depends in detail on how the molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the "transient time correlation function" expressions derived by Evans and Morriss in 1988. Although these expressions are each exact, calculating the viscosity of a dense fluid using these relations currently requires the use of molecular dynamics computer simulations. On the other hand, much more progress can be made for a dilute gas. Even elementary assumptions about how gas molecules move and interact lead to a basic understanding of the molecular origins of viscosity. More sophisticated treatments can be constructed by systematically coarse-graining the equations of motion of the gas molecules. An example of such a treatment is Chapman–Enskog theory, which derives expressions for the viscosity of a dilute gas from the Boltzmann equation. Momentum transport in gases is generally mediated by discrete molecular collisions, and in liquids by attractive forces which bind molecules close together. Because of this, the dynamic viscosities of liquids are typically much larger than those of gases. Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. An elementary calculation for a dilute gas at temperature formula_62 and density formula_53 gives where formula_65 is the Boltzmann constant, formula_66 the molecular mass, and formula_27 a numerical constant on the order of formula_68. The quantity formula_69, the mean free path, measures the average distance a molecule travels between collisions. Even without "a priori" knowledge of formula_27, this expression has interesting implications. In particular, since formula_69 is typically inversely proportional A technique developed by Sydney Chapman and David Enskog in the early 1900s allows a more refined calculation of formula_10. It is based on the Boltzmann equation, which provides a systematic statistical description of a dilute gas in terms of intermolecular interactions. As such, their technique allows accurate calculation of formula_10 for more realistic molecular models, such as those incorporating intermolecular attraction rather than just hard-core repulsion. It turns out that a more realistic modeling of interactions is essential for accurate prediction of the temperature dependence of formula_10, which experiments show increases more rapidly than the formula_82 trend predicted for rigid elastic spheres. Indeed, the Chapman–Enskog analysis shows that the predicted temperature dependence can be tuned by varying the parameters in various molecular models. A simple example is the Sutherland model, which describes rigid elastic spheres with "weak" mutual In the kinetic-molecular picture, a non-zero bulk viscosity arises in gases whenever there are non-negligible relaxational timescales governing the exchange of energy between the translational energy of molecules and their internal energy, e.g. rotational and vibrational. As such, the bulk viscosity is formula_2 for a monatomic ideal gas, in which the internal energy of molecules in negligible, but is nonzero for a gas like carbon dioxide, whose molecules possess both rotational and vibrational energy. In contrast with gases, there is no simple yet accurate picture for the molecular origins of viscosity in liquids. At the simplest level of description, the relative motion of adjacent layers in a liquid is opposed primarily by attractive molecular forces acting across the layer boundary. In this picture, one (correctly) expects viscosity to decrease with increasing temperature. This is because increasing temperature increases the random thermal motion of the molecules, which makes it easier for them to overcome their attractive interactions. Building on this visualization, a simple theory can be constructed in analogy with the discrete structure of a solid: groups of molecules in a liquid are visualized as forming "cages" which surround and enclose single molecules. These cages can be occupied or unoccupied, and stronger molecular attraction corresponds to stronger cages. Due to random thermal motion, a molecule "hops" between cages at a rate which varies inversely with the strength of molecular attractions. In equilibrium these "hops" are not biased in any direction. On the other hand, in The same molecular-kinetic picture of a single component gas can also be applied to a gaseous mixture. For instance, in the Chapman–Enskog approach the viscosity formula_101 of a binary mixture of gases can be written in terms of the individual component viscosities formula_102, their respective volume fractions, and the intermolecular As for pure liquids, the viscosity of a blend of liquids is difficult to predict from molecular principles. One method is to extend the molecular "cage" theory presented above for a pure liquid. This can be done with varying levels of sophistication. One useful expression resulting from such an analysis is the Lederer–Roegiers equation for a binary mixture: where formula_27 is an empirical parameter, and formula_107 and formula_102 are the respective mole fractions and viscosities of the component liquids. Since blending is an important process in the lubricating and oil industries, a variety of empirical and propriety equations exist for predicting the viscosity of a blend, besides those stemming directly from molecular theory. Depending on the solute and range of concentration, an aqueous electrolyte solution can have either a larger or smaller viscosity compared with pure water at the same temperature and pressure. For instance, a 20% saline (sodium chloride) solution has viscosity over 1.5 times that of pure water, whereas a 20% potassium iodide solution has viscosity about 0.91 times that of pure water. An idealized model of dilute electrolytic solutions leads to the following prediction for In a suspension of solid particles (e.g. micron-size spheres suspended in oil), an effective viscosity formula_119 can be defined in terms of stress and strain components which are averaged over a volume large compared with the distance between the suspended particles, but small with respect to macroscopic dimensions. Such suspensions generally exhibit non-Newtonian behavior. However, for dilute systems in steady flows, the behavior is Newtonian and expressions for formula_119 can be derived directly from the particle dynamics. In a very dilute system, with volume fraction formula_121, interactions between the suspended particles can be ignored. In such a case one can explicitly calculate the flow field around each particle independently, and combine the results to obtain formula_122. For spheres, this results in the Einstein equation: where formula_87 is the viscosity of the suspending liquid. The linear dependence on formula_125 In the high and low temperature limits, viscous flow in amorphous materials (e.g. in glasses and melts) has the Arrhenius form: where is a relevant activation energy, given in terms of molecular parameters; is temperature; is the molar gas constant; and is approximately a constant. The activation energy takes a different value depending on whether the high or low temperature limit is being considered: it changes from a high value at low temperatures (in the glassy state) to a low value at high temperatures (in the liquid state). For intermediate temperatures, formula_139 varies nontrivially with temperature and the simple Arrhenius form fails. On the other hand, the two-exponential equation where formula_7, formula_100, formula_117, formula_56 are all constants, provides a good fit to experimental data over the entire range of temperatures, while at the same time reducing to the correct Arrhenius form in the low and high temperature limits. Besides being a convenient fit to data, the expression can also be derived In the study of turbulence in fluids, a common practical strategy is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an "effective" Observed values of viscosity vary over several orders of magnitude, even for common substances (see the order of magnitude table below). For instance, a 70% sucrose (sugar) solution has a viscosity over 400 times that of water, and 26000 times that of air. More dramatically, pitch has been estimated to have a viscosity 230 billion times that of water. The dynamic viscosity formula_10 of water is about 0.89 mPa·s at room temperature (25 °C). As a function of temperature in kelvins, the viscosity Under standard atmospheric conditions (25 °C and pressure of 1 bar), the dynamic viscosity of air is 18.5 μPa·s, roughly 50 times smaller than the viscosity of water at the same temperature. Except at very high pressure, the The following table illustrates the range of viscosity values observed in common substances. Unless otherwise noted, a temperature of 25 °C and	The viscosity of a fluid is a measure of its resistance to deformation at a given rate. 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summarize: Electric energy is most often measured either in joules (J), or in watt hours (W·h) representing a constant power over a period of time. Electric and electronic devices consume electric energy to generate desired output (i.e., light, heat, motion, etc.). During operation, some part of the energy—depending on the electrical efficiency—is consumed in unintended output, such as waste heat. Electricity has been generated in power stations since 1882. The invention of the steam turbine in 1883 to drive the electric generator started a strong increase of world electricity consumption. In 2008, the world total of electricity production was 20.279 petawatt-hours (PWh). This number corresponds to an average power of 2.31 TW continuously during the year. The total primary energy used in a thermal power station to produce this power is roughly a factor 2 to 3 higher because the efficiency of electricity generation is roughly 30–50% (see also energy conversion efficiency). The primary energy consumption to generate electric power is thus in the order of 5 TW. This is approximately a third of the total energy consumption of 15 TW ("see world energy consumption"). In 2005, the primary energy used to generate electricity was. This was compounded of Coal, Natural (fossil) gas, Petroleum, Nuclear electric power, Renewable energy respectively. The gross generation of electricity in that year was ; the difference of was conversion losses. Among all electricity, was used in residential area, used in commercial, used in industrial and used in transportation. 1 Quad = 1 Quadrillion BTU = 1 x 10 BTU = 293 TWh During the year 16,816 TWh (83%) of electric energy was consumed by final users. The difference of 3,464 TWh (17%) was consumed in the process of generating power and lost in transmission to end users. A sensitivity analysis on an adaptive neuro-fuzzy network model for electric demand estimation shows that employment is the most critical factor influencing electrical consumption. The study used six parameters as input data, employment, GDP, dwelling, population, heating degree day and cooling degree day, with electricity demand as output variable. At the world level, energy consumption was cut down by 1.5% during 2009, for the first time since World War II. Except in Asia and Middle East, consumptions were reduced in all the world regions. In OECD countries, accounting for 53% of the total, electricity demand scaled down by more than 4.5% in both Europe and North America while it shrank by above 7% in Japan. Electricity demand also dropped by more than 4.5% in CIS countries, driven by a large cut in Russian consumption. Conversely, in China and India (22% of the world's consumption), electricity consumption continued to rise at a strong pace (+6-7%) to meet energy demand related to high economic growth. In Middle East, growth rate was softened but remained high, just below 4%. The table lists the top 37 electricity consuming countries, which use 19,000 TWh/a. i.e. 90% of the consumption of all more than 190 countries. The total consumption (including the amount consumed by the power plants) and the energy sources to generate this electricity is given per country. The data is from 2012. Total consumption (2nd column) divided by number of inhabitants (last column) gives a country's consumption per head. In W-Europe this is between 5 and 8 MWh/a. (1 MWh equals 1000 kWh.) In Scandinavia, USA, Canada, Taiwan and South Korea it is much more, in developing countries much less. The worlds average is 3 MWh/a. A very low consumption per head, as in Indonesia, means that many inhabitants are not connected to the electricity grid, and this is the reason that the world's 7th and 8th most populous countries—Nigeria (177M) and Bangladesh (156M)—do not appear in the table. From 2012 to 2014 worldwide electricity consumption increased 5%. Nuclear and fossil generated electricity rose 3%, renewable electricity 12%. A small part of the renewables, solar and wind electricity, increased much more, 46% in line with the strong growth since 1990. In Brazil, wind power increased 140%, in China not only solar and wind increased fast, 81%, but also nuclear, 36%. Listed countries are top 20 populous countries and/or top 20 GDP (PPP) countries and Saudi Arabia as of CIA World Factbook 2009. <br> 30 countries (exclude EU/IEA) in this table represent 77% of world population, 84% of world GDP, 83% of world electricity generation.<br> Productivity per Electricity generation (concept similar to Energy intensity) can be measured by dividing GDP amount by the electricity generated. World average was $3.5 production/kWh.<br> Electricity generation include Final consumption, in process consumption, and losses. About 17% of total electricity production is consumed by in-processes, such as self-consumption of power plants, grid losses and storage losses. In 2008, total electricity generation accounted for 20,261 TWh (20.26 PWh), while 3,464 TWh (3.46 PWh) were self-consumption and losses and 16,816 TWh (16.82 PWh) went to final consumption. In the consumption rate in Industry, China is highest with 67.8%, South Korea is 51.0% (7th), Germany 46.1% (11th), Japan 31.5% (26th), USA 24.0% (28th) In the Commercial and Public Service, Japan is highest with 36.4%, USA 35.6% (3rd), China 5.4% (29th). For Domestic usage, Saudi Arabia is highest with 56.9%, USA 36.2% (8th), Japan 29.8% (16th), China 15.5% (29th), Korea 13.8% (30th). Definition Electric energy consumption per inhabitant by primary energy source in some countries and areas in 2008 is in the table. For the OECD with 8 991 kWh/yr/person: 1.026 watt/person. In a recent report, the IEA reported a total worlds electric energy consumption in 2017 of 21,372 TWh, which is an increase of 2.6% in comparison to 2016. The electric energy consumption of the OECD countries in 2017 was 9,518 TWh and thus about 0.2% higher than in 2016. This compares to a power production in the OECD countries of 11,051 TWh in 2017, and to 11,173 TWh in 2018. The electric power consumption of the non-OECD countries in 2017 amounts to 11,854 TWh. An increase of 4.6% over the year 2016. The share of the gross electric production by source is summarized in the following table for the available assessment in the years 2017 or 2018. In all scenarios, increasing efficiency will result in less electricity needed for a given demand of power and light. But demand will increase strongly on account of As transport and heating become more climate-friendly, the environmental effect of energy consumption will be more determined by electricity. This is mainly supplied by burning fossil fuel which disturbs the natural carbon cycle. The scenarios arrive at very different results for the environment. The International Energy Agency expects revision of subsidy for fossil fuel which amounted to 550 billion dollar in 2013, more than four times renewable energy subsidy. In this scenario almost half of the increase in 2040 of electricity consumption is covered by more than 80% growth of renewable energy. Many new nuclear plants will be constructed, mainly to replace old ones. The nuclear part of electricity generation will increase from 11 to 12%. The renewable part goes up much, from 21 to 33%. The IEA warns that in order to restrict global warming to 2 °C, the carbon dioxide emission must not exceed 1000 gigaton (Gt) from 2014. This limit is reached in 2040 and emissions will not drop to zero ever. The World Energy Council sees world electricity consumption increasing to more than 40,000 TWh/a in 2040. The fossil part of generation depends on energy policy. It can stay around 70% in the so-called Jazz scenario where countries rather independently "improvise" but it can also decrease to around 40% in the Symphony scenario if countries work "orchestrated" for more climate friendly policy. Carbon dioxide emission, 32 Gt/a in 2012, will increase to 46 Gt/a in Jazz but decrease to 26 Gt/a in Symphony. Accordingly, until 2040 the renewable part of generation will stay at about 20% in Jazz but increase to about 45% in Symphony.	Electric energy consumption is the form of energy consumption that uses electric energy. Electric energy consumption is the actual energy demand made on existing electricity supply.	en	en	28	[ 250004, 250054, 89917, 48302, 83, 2684, 27983, 72350, 71, 40101, 23, 2219, 1577, 15, 1375, 247, 707, 23, 793, 18, 21974, 15, 1456, 1280, 127, 16, 33636, 214, 10, 53697, 14537, 645, 10, 14922, 111, 1733, 5, 89917, 136, 65133, 128779, 18588, 13, 39108, 48302, 47, 139392, 104851, 71, 140992, 15, 14, 5, 13, 5, 4, 22729, 4, 80097, 4, 78112, 4, 3021, 5, 194, 133698, 41018, 4, 3060, 2831, 111, 70, 48302, 2451, 112, 96819, 98, 70, 39108, 289, 227066, 2451, 164, 18588, 297, 23, 51, 29272, 48141, 140992, 4, 6044, 237, 509, 67, 80097, 5, 89917, 2481, 1556, 2809, 139392, 71, 23, 14537, 29398, 7, 16792, 156999, 5, 581, 23, 57241, 111, 70, 2288, 302, 164552, 13, 23, 163055, 47, 22648, 70, 39108, 145823, 26859, 10, 37515, 51312, 111, 8999, 39108, 2481, 18588, 254, 1363, 5, 360, 43304, 70, 8999, 3622, 111, 39108, 2481, 36049, 509, 7085, 116518, 111534, 10686, 18, 9, 497, 12824, 15, 683, 1456, 127, 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summarize: There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of configurations of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from a potential are also called conservative forces. The work done by a conservative force is where formula_2 is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy. Common notations for potential energy are "PE", "U", "V", and "E". Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as a spring or the force of gravity. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. This work is stored in the force field, which is said to be stored as potential energy. If the external force is removed the force field acts on the body to perform the work as it moves the body back to the initial position, reducing the stretch of the spring or causing a body to fall. Consider a ball whose mass is m and whose height is h. The acceleration g of free fall is approximately constant, so the weight force of the ball mg is constant. Force × displacement gives the work done, which is equal to the gravitational potential energy, thus The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position. Potential energy is closely linked with forces. If the work done by a force on a body that moves from "A" to "B" does not depend on the path between these points (if the work is done by a conservative force), then the work of this force measured from "A" assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for an applied force is independent of the path, then the work done by the force is evaluated at the start and end of the trajectory of the point of application. This means that there is a function "U"(x), called a "potential," that can be evaluated at the two points x and x to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is where "C" is the trajectory taken from A to B. Because the work done is independent of the path taken, then this expression is true for any trajectory, "C", from A to B. The function "U"(x) is called the potential energy associated with the applied force. Examples of forces that have potential energies are gravity and spring forces. In this section the relationship between work and potential energy is presented in more detail. The line integral that defines work along curve "C" takes a special form if the force F is related to a scalar field φ(x) so that In this case, work along the curve is given by which can be evaluated using the gradient theorem to obtain This shows that when forces are derivable from a scalar field, the work of those forces along a curve "C" is computed by evaluating the scalar field at the start point "A" and the end point "B" of the curve. This means the work integral does not depend on the path between "A" and "B" and is said to be independent of the path. Potential energy "U"=-φ(x) is traditionally defined as the negative of this scalar field so that work by the force field decreases potential energy, that is In this case, the application of the del operator to the work function yields, and the force F is said to be "derivable from a potential." This also necessarily implies that F must be a conservative vector field. The potential "U" defines a force F at every point x in space, so the set of forces is called a force field. Given a force field F(x), evaluation of the work integral using the gradient theorem can be used to find the scalar function associated with potential energy. This is done by introducing a parameterized curve γ(t)=r(t) from γ(a)=A to γ(b)=B, and computing, For the force field F, let v= dr/dt, then the gradient theorem yields, The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity v of the point of application, that is Examples of work that can be computed from potential functions are gravity and spring forces. For small height changes, gravitational potential energy can be computed using where m is the mass in kg, g is the local gravitational field (9.8 metres per second squared on earth), h is the height above a reference level in metres, and U is the energy in joules. In classical physics, gravity exerts a constant downward force F=(0, 0, "F") on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r(t) = ("x"(t), "y"(t), "z"(t)), such as the track of a roller coaster is calculated using its velocity, v=("v", "v", "v"), to obtain where the integral of the vertical component of velocity is the vertical distance. The work of gravity depends only on the vertical movement of the curve r(t). A horizontal spring exerts a force F = (−"kx", 0, 0) that is proportional to its deformation in the axial or "x" direction. The work of this spring on a body moving along the space curve s("t") = ("x"("t"), "y"("t"), "z"("t")), is calculated using its velocity, v = ("v", "v", "v"), to obtain For convenience, consider contact with the spring occurs at "t" = 0, then the integral of the product of the distance "x" and the "x"-velocity, "xv", is "x"/2. The function is called the potential energy of a linear spring. Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology). It arises as a consequence of a force that tries to restore the object to its original shape, which is most often the electromagnetic force between the atoms and molecules that constitute the object. If the stretch is released, the energy is transformed into kinetic energy. The gravitational potential function, also known as gravitational potential energy, is: The negative sign follows the convention that work is gained from a loss of potential energy. The gravitational force between two bodies of mass "M" and "m" separated by a distance "r" is given by Newton's law where formula_19 is a vector of length 1 pointing from "M" to "m" and "G" is the gravitational constant. Let the mass "m" move at the velocity v then the work of gravity on this mass as it moves from position r(t) to r(t) is given by The position and velocity of the mass "m" are given by where e and e are the radial and tangential unit vectors directed relative to the vector from "M" to "m". Use this to simplify the formula for work of gravity to, This calculation uses the fact that The electrostatic force exerted by a charge "Q" on another charge "q" separated by a distance "r" is given by Coulomb's Law where formula_19 is a vector of length 1 pointing from "Q" to "q" and "ε" is the vacuum permittivity. This may also be written using Coulomb constant. The work "W" required to move "q" from "A" to any point "B" in the electrostatic force field is given by the potential function The potential energy is a function of the state a system is in, and is defined relative to that for a particular state. This reference state is not always a real state; it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces. Any arbitrary reference state could be used; therefore it can be chosen based on convenience. Typically the potential energy of a system depends on the "relative" positions of its components only, so the reference state can also be expressed in terms of relative positions. Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth's gravity. The potential energy due to elevated positions is called gravitational potential energy, and is evidenced by water in an elevated reservoir or kept behind a dam. If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. Consider a book placed on top of a table. As the book is raised from the floor to the table, some external force works against the gravitational force. If the book falls back to the floor, the "falling" energy the book receives is provided by the gravitational force. Thus, if the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy. When the book hits the floor this kinetic energy is converted into heat, deformation, and sound by the impact. The factors that affect an object's gravitational potential energy are its height relative to some reference point, its mass, and the strength of the gravitational field it is in. Thus, a book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard and less gravitational potential energy than a heavier book lying on the same table. An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height above the Earth's surface because the Moon's gravity is weaker. "Height" in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. The following sections provide more detail. The strength of a gravitational field varies with location. However, when the change of distance is small in relation to the distances from the center of the source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is constant. Near the surface of the Earth, for example, we assume that the acceleration due to gravity is a constant ("standard gravity"). In this case, a simple expression for gravitational potential energy can be derived using the "W" = "Fd" equation for work, and the equation The amount of gravitational potential energy held by an elevated object is equal to the work done against gravity in lifting it. The work done equals the force required to move it upward multiplied with the vertical distance it is moved (remember "W = Fd"). The upward force required while moving at a constant velocity is equal to the weight, "mg", of an object, so the work done in lifting it through a height "h" is the product "mgh". Thus, when accounting only for mass, gravity, and altitude, the equation is: where "U" is the potential energy of the object relative to its being on the Earth's surface, "m" is the mass of the object, "g" is the acceleration due to gravity, and "h" is the altitude of the object. If "m" is expressed in kilograms, "g" in m/s and "h" in metres then "U" will be calculated in joules. Hence, the potential difference is However, over large variations in distance, the approximation that "g" is constant is no longer valid, and we have to use calculus and the general mathematical definition of work to determine gravitational potential energy. For the computation of the potential energy, we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation, with respect to the distance "r" between the two bodies. Using that definition, the gravitational potential energy of a system of masses "m" and "M" at a distance "r" using gravitational constant "G" is where "K" is an arbitrary constant dependent on the choice of datum from which potential is measured. Choosing the convention that "K"=0 (i.e. in relation to a point at infinity) makes calculations simpler, albeit at the cost of making "U" negative; for why this is physically reasonable, see below. Given this formula for "U", the total potential energy of a system of "n" bodies is found by summing, for all formula_31 pairs of two bodies, the potential energy of the system of those two bodies. Considering the system of bodies as the combined set of small particles the bodies consist of, and applying the previous on the particle level we get the negative gravitational binding energy. This potential energy is more strongly negative than the total potential energy of the system of bodies as such since it also includes the negative gravitational binding energy of each body. The potential energy of the system of bodies as such is the negative of the energy needed to separate the bodies from each other to infinity, while the gravitational binding energy is the energy needed to separate all particles from each other to infinity. therefore, As with all potential energies, only differences in gravitational potential energy matter for most physical purposes, and the choice of zero point is arbitrary. Given that there is no reasonable criterion for preferring one particular finite "r" over another, there seem to be only two reasonable choices for the distance at which "U" becomes zero: formula_34 and formula_35. The choice of formula_36 at infinity may seem peculiar, and the consequence that gravitational energy is always negative may seem counterintuitive, but this choice allows gravitational potential energy values to be finite, albeit negative. The singularity at formula_34 in the formula for gravitational potential energy means that the only other apparently reasonable alternative choice of convention, with formula_36 for formula_34, would result in potential energy being positive, but infinitely large for all nonzero values of "r", and would make calculations involving sums or differences of potential energies beyond what is possible with the real number system. Since physicists abhor infinities in their calculations, and "r" is always non-zero in practice, the choice of formula_36 at infinity is by far the more preferable choice, even if the idea of negative energy in a gravity well appears to be peculiar at first. The negative value for gravitational energy also has deeper implications that make it seem more reasonable in cosmological calculations where the total energy of the universe can meaningfully be considered; see inflation theory for more on this. Gravitational potential energy has a number of practical uses, notably the generation of pumped-storage hydroelectricity. For example, in Dinorwig, Wales, there are two lakes, one at a higher elevation than the other. At times when surplus electricity is not required (and so is comparatively cheap), water is pumped up to the higher lake, thus converting the electrical energy (running the pump) to gravitational potential energy. At times of peak demand for electricity, the water flows back down through electrical generator turbines, converting the potential energy into kinetic energy and then back into electricity. The process is not completely efficient and some of the original energy from the surplus electricity is in fact lost to friction. Gravitational potential energy is also used to power clocks in which falling weights operate the mechanism. It's also used by counterweights for lifting up an elevator, crane, or sash window. Roller coasters are an entertaining way to utilize potential energy – chains are used to move a car up an incline (building up gravitational potential energy), to then have that energy converted into kinetic energy as it falls. Another practical use is utilizing gravitational potential energy to descend (perhaps coast) downhill in transportation such as the descent of an automobile, truck, railroad train, bicycle, airplane, or fluid in a pipeline. In some cases the kinetic energy obtained from the potential energy of descent may be used to start ascending the next grade such as what happens when a road is undulating and has frequent dips. The commercialization of stored energy (in the form of rail cars raised to higher elevations) that is then converted to electrical energy when needed by an electrical grid, is being undertaken in the United States in a system called Advanced Rail Energy Storage (ARES). Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. As an example, when a fuel is burned the chemical energy is converted to heat, same is the case with digestion of food metabolized in a biological organism. Green plants transform solar energy to chemical energy through the process known as photosynthesis, and electrical energy can be converted to chemical energy through electrochemical reactions. The similar term chemical potential is used to indicate the potential of a substance to undergo a change of configuration, be it in the form of a chemical reaction, spatial transport, particle exchange with a reservoir, etc. An object can have potential energy by virtue of its electric charge and several forces related to their presence. There are two main types of this kind of potential energy: electrostatic potential energy, electrodynamic potential energy (also sometimes called magnetic potential energy). Electrostatic potential energy between two bodies in space is obtained from the force exerted by a charge "Q" on another charge "q" which is given by where formula_19 is a vector of length 1 pointing from "Q" to "q" and "ε" is the vacuum permittivity. This may also be written using Coulomb's constant. If the electric charge of an object can be assumed to be at rest, then it has potential energy due to its position relative to other charged objects. The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the work that must be done to move it from an infinite distance away to its present location, adjusted for non-electrical forces on the object. This energy will generally be non-zero if there is another electrically charged object nearby. The work "W" required to move "q" from "A" to any point "B" in the electrostatic force field is given by typically given in "J" for Joules. A related quantity called "electric potential" (commonly denoted with a "V" for voltage) is equal to the electric potential energy per unit charge. The energy of a magnetic moment formula_44 in an externally produced magnetic B-field has potential energy The magnetization in a field is where the integral can be over all space or, equivalently, where is nonzero. Magnetic potential energy is the form of energy related not only to the distance between magnetic materials, but also to the orientation, or alignment, of those materials within the field. For example, the needle of a compass has the lowest magnetic potential energy when it is aligned with the north and south poles of the Earth's magnetic field. If the needle is moved by an outside force, torque is exerted on the magnetic dipole of the needle by the Earth's magnetic field, causing it to move back into alignment. The magnetic potential energy of the needle is highest when its field is in the same direction as the Earth's magnetic field. Two magnets will have potential energy in relation to each other and the distance between them, but this also depends on their orientation. If the opposite poles are held apart, the potential energy will be higher the further they are apart and lower the closer they are. Conversely, like poles will have the highest potential energy when forced together, and the lowest when they spring apart. Nuclear potential energy is the potential energy of the particles inside an atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay, such as beta decay. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them can have less mass than if they were individually free, in which case this mass difference can be liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured). The energy from the Sun is an example of this form of energy conversion. In the Sun, the process of hydrogen fusion converts about 4 million tonnes of solar matter per second into electromagnetic energy, which is radiated into space. Potential energy is closely linked with forces. If the work done by a force on a body that moves from "A" to "B" does not depend on the path between these points, then the work of this force measured from "A" assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. For example, gravity is a conservative force. The associated potential is the gravitational potential, often denoted by formula_47 or formula_48, corresponding to the energy per unit mass as a function of position. The gravitational potential energy of two particles of mass "M" and "m" separated by a distance "r" is The gravitational potential (specific energy) of the two bodies is where formula_51 is the reduced mass. The work done against gravity by moving an infinitesimal mass from point A with formula_52 to point B with formula_53 is formula_54 and the work done going back the other way is formula_55 so that the total work done in moving from A to B and returning to A is If the potential is redefined at A to be formula_57 and the potential at B to be formula_58, where formula_59 is a constant (i.e. formula_59 can be any number, positive or negative, but it must be the same at A as it is at B) then the work done going from A to B is as before. In practical terms, this means that one can set the zero of formula_62 and formula_47 anywhere one likes. One may set it to be zero at the surface of the Earth, or may find it more convenient to set zero at infinity (as in the expressions given earlier in this section). A conservative force can be expressed in the language of differential geometry as a closed form. As Euclidean space is contractible, its de Rham cohomology vanishes, so every closed form is also an exact form, and can be expressed as the gradient of a scalar field. This gives a mathematical justification of the fact that all conservative forces are gradients of a potential field.	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summarize: The adjective "kinetic" has its roots in the Greek word κίνησις "kinesis", meaning "motion". The dichotomy between kinetic energy and potential energy can be traced back to Aristotle's concepts of actuality and potentiality. The principle in classical mechanics that "E ∝ mv" was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the "living force", "vis viva". Willem's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Willem's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms "kinetic energy" and "work" in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled "Du Calcul de l'Effet des Machines" outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term "kinetic energy" c. 1849–51. Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two main classes: potential energy and kinetic energy. Kinetic energy is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction. The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat. Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space. However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolic, then throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Without loss or gain, however, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another. In the game of billiards, the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisions, in which kinetic energy is preserved. In inelastic collisions, kinetic energy is dissipated in various forms of energy, such as heat, sound, binding energy (breaking bound structures). Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is also stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation. For objects and processes in common human experience, the formula 1⁄2mv2 given by Newtonian (classical) mechanics is suitable. However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale, quantum mechanical effects are significant, and a quantum mechanical model must be employed. In classical mechanics, the kinetic energy of a "point object" (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body depends on the mass of the body as well as its speed. The kinetic energy is equal to 1/2 the product of the mass and the square of the speed. In formula form: where formula_2 is the mass and formula_3 is the speed (or the velocity) of the body. In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as When a person throws a ball, the person does work on it to give it speed as it leaves the hand. The moving ball can then hit something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work required to bring it from rest to that speed, or the work the object can do while being brought to rest: net force × displacement = kinetic energy, i.e., Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force. As a consequence of this quadrupling, it takes four times the work to double the speed. The kinetic energy of an object is related to its momentum by the equation: where: For the "translational kinetic energy," that is the kinetic energy associated with rectilinear motion, of a rigid body with constant mass formula_8, whose center of mass is moving in a straight line with speed formula_10, as seen above is equal to where: The kinetic energy of any entity depends on the reference frame in which it is measured. However the total energy of an isolated system, i.e. one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the Oberth effect. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames would however disagree on the value of this conserved energy. The kinetic energy of such systems depends on the choice of reference frame: the reference frame that gives the minimum value of that energy is the center of momentum frame, i.e. the reference frame in which the total momentum of the system is zero. This minimum kinetic energy contributes to the invariant mass of the system as a whole. The work done in accelerating a particle with mass "m" during the infinitesimal time interval "dt" is given by the dot product of "force" F and the infinitesimal "displacement "dx" where we have assumed the relationship p = "m" v and the validity of Newton's Second Law. (However, also see the special relativistic derivation below.) Applying the product rule we see that: Therefore, (assuming constant mass so that "dm" = 0), we have, Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call the result kinetic energy. Assuming the object was at rest at time 0, we integrate from time 0 to time t because the work done by the force to bring the object from rest to velocity "v" is equal to the work necessary to do the reverse: This equation states that the kinetic energy ("E") is equal to the integral of the dot product of the velocity (v) of a body and the infinitesimal change of the body's momentum (p). It is assumed that the body starts with no kinetic energy when it is at rest (motionless). If a rigid body Q is rotating about any line through the center of mass then it has "rotational kinetic energy" (formula_18) which is simply the sum of the kinetic energies of its moving parts, and is thus given by: where: (In this equation the moment of inertia must be taken about an axis through the center of mass and the rotation measured by ω must be around that axis; more general equations exist for systems where the object is subject to wobble due to its eccentric shape). A system of bodies may have internal kinetic energy due to the relative motion of the bodies in the system. For example, in the Solar System the planets and planetoids are orbiting the Sun. In a tank of gas, the molecules are moving in all directions. The kinetic energy of the system is the sum of the kinetic energies of the bodies it contains. A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However all internal energies of all types contribute to body's mass, inertia, and total energy. In fluid dynamics, the kinetic energy per unit volume at each point in an incompressible fluid flow field is called the dynamic pressure at that point. Dividing by V, the unit of volume: where formula_24 is the dynamic pressure, and ρ is the density of the incompressible fluid. The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference. For example, a bullet passing an observer has kinetic energy in the reference frame of this observer. The same bullet is stationary to an observer moving with the same velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's invariant mass, which is independent of the reference frame. The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass. This may be simply shown: let formula_25 be the relative velocity of the center of mass frame "i" in the frame "k". Since Then, However, let formula_28 the kinetic energy in the center of mass frame, formula_29 would be simply the total momentum that is by definition zero in the center of mass frame, and let the total mass: formula_30. Substituting, we get: Thus the kinetic energy of a system is lowest to center of momentum reference frames, i.e., frames of reference in which the center of mass is stationary (either the center of mass frame or any other center of momentum frame). In any different frame of reference, there is additional kinetic energy corresponding to the total mass moving at the speed of the center of mass. The kinetic energy of the system in the center of momentum frame is a quantity that is invariant (all observers see it to be the same). It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass (rotational energy): where: Thus the kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation. If a body's speed is a significant fraction of the speed of light, it is necessary to use relativistic mechanics to calculate its kinetic energy. In special relativity theory, the expression for linear momentum is modified. With "m" being an object's rest mass, v and "v" its velocity and speed, and "c" the speed of light in vacuum, we use the expression for linear momentum formula_33, where formula_34. Integrating by parts yields Since formula_36, formula_38 is a constant of integration for the indefinite integral. Simplifying the expression we obtain formula_38 is found by observing that when formula_41 and formula_42, giving resulting in the formula This formula shows that the work expended accelerating an object from rest approaches infinity as the velocity approaches the speed of light. Thus it is impossible to accelerate an object across this boundary. The mathematical by-product of this calculation is the mass-energy equivalence formula—the body at rest must have energy content At a low speed ("v" ≪ "c"), the relativistic kinetic energy is approximated well by the classical kinetic energy. This is done by binomial approximation or by taking the first two terms of the Taylor expansion for the reciprocal square root: So, the total energy formula_47 can be partitioned into the rest mass energy plus the Newtonian kinetic energy at low speeds. When objects move at a speed much slower than light (e.g. in everyday phenomena on Earth), the first two terms of the series predominate. The next term in the Taylor series approximation is small for low speeds. For example, for a speed of the correction to the Newtonian kinetic energy is 0.0417 J/kg (on a Newtonian kinetic energy of 50 MJ/kg) and for a speed of 100 km/s it is 417 J/kg (on a Newtonian kinetic energy of 5 GJ/kg). The relativistic relation between kinetic energy and momentum is given by This can also be expanded as a Taylor series, the first term of which is the simple expression from Newtonian mechanics: This suggests that the formulae for energy and momentum are not special and axiomatic, but concepts emerging from the equivalence of mass and energy and the principles of relativity. Using the convention that where the four-velocity of a particle is and formula_53 is the proper time of the particle, there is also an expression for the kinetic energy of the particle in general relativity. If the particle has momentum as it passes by an observer with four-velocity "u", then the expression for total energy of the particle as observed (measured in a local inertial frame) is and the kinetic energy can be expressed as the total energy minus the rest energy: Consider the case of a metric that is diagonal and spatially isotropic ("g", "g", "g", "g"). Since where "v" is the ordinary velocity measured w.r.t. the coordinate system, we get Solving for "u" gives Thus for a stationary observer ("v" = 0) and thus the kinetic energy takes the form Factoring out the rest energy gives: This expression reduces to the special relativistic case for the flat-space metric where In the Newtonian approximation to general relativity where Φ is the Newtonian gravitational potential. This means clocks run slower and measuring rods are shorter near massive bodies. In quantum mechanics, observables like kinetic energy are represented as operators. For one particle of mass "m", the kinetic energy operator appears as a term in the Hamiltonian and is defined in terms of the more fundamental momentum operator formula_65. The kinetic energy operator in the non-relativistic case can be written as Notice that this can be obtained by replacing formula_67 by formula_65 in the classical expression for kinetic energy in terms of momentum, In the Schrödinger picture, formula_65 takes the form formula_71 where the derivative is taken with respect to position coordinates and hence The expectation value of the electron kinetic energy, formula_73, for a system of "N" electrons described by the wavefunction formula_74 is a sum of 1-electron operator expectation values: where formula_76 is the mass of the electron and formula_77 is the Laplacian operator acting upon the coordinates of the "i" electron and the summation runs over all electrons. The density functional formalism of quantum mechanics requires knowledge of the electron density "only", i.e., it formally does not require knowledge of the wavefunction. Given an electron density formula_78, the exact N-electron kinetic energy functional is unknown; however, for the specific case of a 1-electron system, the kinetic energy can be written as where formula_80 is known as the von Weizsäcker kinetic energy functional.	In physics, the kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. 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summarize: A continuity equation is useful when a "flux" can be defined. To define flux, first there must be a quantity which can flow or move, such as mass, energy, electric charge, momentum, number of molecules, etc. Let be the volume density of this quantity, that is, the amount of per unit volume. The way that this quantity is flowing is described by its flux. The flux of is a vector field, which we denote as j. Here are some examples and properties of flux: The integral form of the continuity equation states that: Mathematically, the integral form of the continuity equation expressing the rate of increase of within a volume is: where In a simple example, could be a building, and could be the number of people in the building. The surface would consist of the walls, doors, roof, and foundation of the building. Then the continuity equation states that the number of people in the building increases when people enter the building (an inward flux through the surface), decreases when people exit the building (an outward flux through the surface), increases when someone in the building gives birth (a source, ), and decreases when someone in the building dies (a sink, ). By the divergence theorem, a general continuity equation can also be written in a "differential form": where This general equation may be used to derive any continuity equation, ranging from as simple as the volume continuity equation to as complicated as the Navier–Stokes equations. This equation also generalizes the advection equation. Other equations in physics, such as Gauss's law of the electric field and Gauss's law for gravity, have a similar mathematical form to the continuity equation, but are not usually referred to by the term "continuity equation", because in those cases does not represent the flow of a real physical quantity. In the case that is a conserved quantity that cannot be created or destroyed (such as energy), and the equations become: In electromagnetic theory, the continuity equation is an empirical law expressing (local) charge conservation. Mathematically it is an automatic consequence of Maxwell's equations, although charge conservation is more fundamental than Maxwell's equations. It states that the divergence of the current density (in amperes per square metre) is equal to the negative rate of change of the charge density (in coulombs per cubic metre), Current is the movement of charge. The continuity equation says that if charge is moving out of a differential volume (i.e. divergence of current density is positive) then the amount of charge within that volume is going to decrease, so the rate of change of charge density is negative. Therefore, the continuity equation amounts to a conservation of charge. If magnetic monopoles exist, there would be a continuity equation for monopole currents as well, see the monopole article for background and the duality between electric and magnetic currents. In fluid dynamics, the continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system plus the accumulation of mass within the system. The differential form of the continuity equation is: where The time derivative can be understood as the accumulation (or loss) of mass in the system, while the divergence term represents the difference in flow in versus flow out. In this context, this equation is also one of the Euler equations (fluid dynamics). The Navier–Stokes equations form a vector continuity equation describing the conservation of linear momentum. If the fluid is incompressible ( is constant, independent of space and time), the mass continuity equation simplifies to a volume continuity equation: which means that the divergence of the velocity field is zero everywhere. Physically, this is equivalent to saying that the local volume dilation rate is zero, hence a flow of water through a converging pipe will adjust solely by increasing its velocity as water is largely incompressible. Conservation of energy says that energy cannot be created or destroyed. (See below for the nuances associated with general relativity.) Therefore, there is a continuity equation for energy flow: where An important practical example is the flow of heat. When heat flows inside a solid, the continuity equation can be combined with Fourier's law (heat flux is proportional to temperature gradient) to arrive at the heat equation. The equation of heat flow may also have source terms: Although "energy" cannot be created or destroyed, "heat" can be created from other types of energy, for example via friction or joule heating. If there is a quantity that moves continuously according to a stochastic (random) process, like the location of a single dissolved molecule with Brownian motion, then there is a continuity equation for its probability distribution. The flux in this case is the probability per unit area per unit time that the particle passes through a surface. According to the continuity equation, the negative divergence of this flux equals the rate of change of the probability density. The continuity equation reflects the fact that the molecule is always somewhere—the integral of its probability distribution is always equal to 1—and that it moves by a continuous motion (no teleporting). Quantum mechanics is another domain where there is a continuity equation related to "conservation of probability". The terms in the equation require the following definitions, and are slightly less obvious than the other examples above, so they are outlined here: With these definitions the continuity equation reads: Either form may be quoted. Intuitively, the above quantities indicate this represents the flow of probability. The "chance" of finding the particle at some position and time flows like a fluid; hence the term "probability current", a vector field. The particle itself does "not" flow deterministically in this vector field. The notation and tools of special relativity, especially 4-vectors and 4-gradients, offer a convenient way to write any continuity equation. The density of a quantity and its current can be combined into a 4-vector called a 4-current: where is the speed of light. The 4-divergence of this current is: where is the 4-gradient and is an index labelling the spacetime dimension. Then the continuity equation is: in the usual case where there are no sources or sinks, that is, for perfectly conserved quantities like energy or charge. This continuity equation is manifestly ("obviously") Lorentz invariant. Examples of continuity equations often written in this form include electric charge conservation where is the electric 4-current; and energy-momentum conservation where is the stress-energy tensor. In general relativity, where spacetime is curved, the continuity equation (in differential form) for energy, charge, or other conserved quantities involves the "covariant" divergence instead of the ordinary divergence. For example, the stress–energy tensor is a second-order tensor field containing energy–momentum densities, energy–momentum fluxes, and shear stresses, of a mass-energy distribution. The differential form of energy-momentum conservation in general relativity states that the "covariant" divergence of the stress-energy tensor is zero: This is an important constraint on the form the Einstein field equations take in general relativity. However, the "ordinary" divergence of the stress-energy tensor does "not" necessarily vanish: The right-hand side strictly vanishes for a flat geometry only. As a consequence, the "integral" form of the continuity equation is difficult to define and not necessarily valid for a region within which spacetime is significantly curved (e.g. around a black hole, or across the whole universe). Quarks and gluons have "color charge", which is always conserved like electric charge, and there is a continuity equation for such color charge currents (explicit expressions for currents are given at gluon field strength tensor). There are many other quantities in particle physics which are often or always conserved: baryon number (proportional to the number of quarks minus the number of antiquarks), electron number, mu number, tau number, isospin, and others. Each of these has a corresponding continuity equation, possibly including source / sink terms. One reason that conservation equations frequently occur in physics is Noether's theorem. This states that whenever the laws of physics have a continuous symmetry, there is a continuity equation for some conserved physical quantity. The three most famous examples are: See Noether's theorem for proofs and details.	A continuity equation in physics is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. 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summarize: The word "lever" entered English about 1300 from Old French, in which the word was "levier". This sprang from the stem of the verb "lever", meaning "to raise". The verb, in turn, goes back to the Latin "levare", itself from the adjective "levis", meaning "light" (as in "not heavy"). The word's primary origin is the Proto-Indo-European (PIE) stem "legwh-", meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light". The earliest evidence of the lever mechanism dates back to the ancient Near East circa 5000 BC, when it was first used in a simple balance scale. In ancient Egypt circa 4400 BC, a foot pedal was used for the earliest horizontal frame loom. In Mesopotamia (modern Iraq) circa 3000 BC, the shadouf, a crane-like device that uses a lever mechanism, was invented. In ancient Egypt technology, workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the handling bosses which could not be used for any purpose other than for levers. The earliest remaining writings regarding levers date from the 3rd century BCE and were provided by Archimedes. He stated, 'Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.' A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the "law of the lever." The mechanical advantage of a lever can be determined by considering the balance of moments or torque, "T", about the fulcrum. If the distance traveled is greater, then the output force is lessened. where F is the input force to the lever and F is the output force. The distances "a" and "b" are the perpendicular distances between the forces and the fulcrum. Since the moments of torque must be balanced, formula_3. So, formula_4. The mechanical advantage of the lever is the ratio of output force to input force, This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming no losses due to friction, flexibility or wear. This remains true even though the "horizontal" distance (perpendicular to the pull of gravity) of both "a" and "b" change (diminish) as the lever changes to any position away from the horizontal. Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force "the effort" and the output force "the load" or "the resistance." This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort: These cases are described by the mnemonic "fre 123" where the "f" fulcrum is between "r" and "e" for the 1st class lever, the "r" resistance is between "f" and "e" for the 2nd class lever, and the "e" effort is between "f" and "r" for the 3rd class lever. A compound lever comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys. The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot. Assuming the lever does not dissipate or store energy, the power into the lever must equal the power out of the lever. As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity. If "a" and "b" are distances from the fulcrum to points "A" and "B" and the force "F" applied to "A" is the input and the force "F" applied at "B" is the output, the ratio of the velocities of points "A" and "B" is given by "a/b", so we have the ratio of the output force to the input force, or mechanical advantage, is given by This is the "law of the lever", which was proven by Archimedes using geometric reasoning. It shows that if the distance "a" from the fulcrum to where the input force is applied (point "A") is greater than the distance "b" from fulcrum to where the output force is applied (point "B"), then the lever amplifies the input force. On the other hand, if the distance "a" from the fulcrum to the input force is less than the distance "b" from the fulcrum to the output force, then the lever reduces the input force. The use of velocity in the static analysis of a lever is an application of the principle of virtual work. A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force F at a point "A" located by the coordinate vector r on the bar. The lever then exerts an output force F at the point "B" located by r. The rotation of the lever about the fulcrum "P" is defined by the rotation angle "θ" in radians. Let the coordinate vector of the point "P" that defines the fulcrum be r, and introduce the lengths which are the distances from the fulcrum to the input point "A" and to the output point "B", respectively. Now introduce the unit vectors e and e from the fulcrum to the point "A" and "B", so The velocity of the points "A" and "B" are obtained as where e and e are unit vectors perpendicular to e and e, respectively. The angle "θ" is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by where "F" and "F" are components of the forces that are perpendicular to the radial segments "PA" and "PB". The principle of virtual work states that at equilibrium the generalized force is zero, that is Thus, the ratio of the output force "F" to the input force "F" is obtained as which is the mechanical advantage of the lever. This equation shows that if the distance "a" from the fulcrum to the point "A" where the input force is applied is greater than the distance "b" from fulcrum to the point "B" where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point "A" is less than from the fulcrum to the output point "B", then the lever reduces the magnitude of the input force.	A lever ( or ) is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into three types. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide leverage. The ratio of the output force to the input force is the mechanical advantage of the lever. 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summarize: Examples of drag include the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of movement of a solid object such as cars, aircraft and boat hulls; or acting in the same geographical direction of motion as the solid, as for sails attached to a down wind sail boat, or in intermediate directions on a sail depending on points of sail. In the case of viscous drag of fluid in a pipe, drag force on the immobile pipe decreases fluid velocity relative to the pipe. In the physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. Types of drag are generally divided into the following categories: The phrase "parasitic drag" is mainly used in aerodynamics, since for lifting wings, drag is generally small compared to lift. For flow around bluff bodies, form drag and skin friction drag dominate, and then the qualifier "parasitic" is meaningless. Further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in aviation or in the design of semi-planing or planing hulls. Wave drag occurs either when a solid object is moving through a gas at or near the speed of sound or when a solid object is moving along a fluid boundary, as in surface waves. Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation: where The drag coefficient depends on the shape of the object and on the Reynolds number where "formula_8" is some characteristic diameter or linear dimension and formula_9 is the kinematic viscosity of the fluid (equal to the viscosity formula_10 divided by the density formula_11). At low formula_12, formula_6 is asymptotically proportional to formula_14, which means that the drag is linearly proportional to the speed. At high formula_12, formula_6 is more or less constant and drag will vary as the square of the speed. The graph to the right shows how formula_6 varies with formula_12 for the case of a sphere. Since the power needed to overcome the drag force is the product of the force times speed, the power needed to overcome drag will vary as the square of the speed at low Reynolds numbers and as the cube of the speed at high numbers. It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the Bejan number. Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of drag force it has been obtained: formula_19 and consequently allows expressing the drag coefficient formula_6as a function of Bejan number and the ratio between wet area formula_21and front area formula_22: formula_23 where formula_24is the Reynold Number related to fluid path length L. As mentioned, the drag equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000). This is also called "quadratic drag". The equation is attributed to Lord Rayleigh, who originally used "L" in place of "A" ("L" being some length). The reference area "A" is often orthographic projection of the object (frontal area)—on a plane perpendicular to the direction of motion—e.g. for objects with a simple shape, such as a sphere, this is the cross sectional area. Sometimes a body is a composite of different parts, each with a different reference areas, in which case a drag coefficient corresponding to each of those different areas must be determined. In the case of a wing the reference areas are the same and the drag force is in the same ratio to the lift force as the ratio of drag coefficient to lift coefficient. Therefore, the reference for a wing is often the lifting area ("wing area") rather than the frontal area. For an object with a smooth surface, and non-fixed separation points—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number "R", even up to very high values ("R" of the order 10). For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for "R" > 3,500. Further the drag coefficient "C" is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere). Under the assumption that the fluid is not moving relative to the currently used reference system, the power required to overcome the aerodynamic drag is given by: Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at may require only to overcome aerodynamic drag, but that same car at requires. With a doubling of speed the drag (force) quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, 4 times the work done in half the time requires 8 times the power. When the fluid is moving relative to the reference system (e.g. a car driving into headwind) the power required to overcome the aerodynamic drag is given by: Where formula_28 is the wind speed and formula_29 is the object speed (both relative to ground). The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity "v" = 0 at time "t" = 0, is roughly given by a function involving a hyperbolic tangent (tanh): The hyperbolic tangent has a limit value of one, for large time "t". In other words, velocity asymptotically approaches a maximum value called the terminal velocity "v": For an object falling and released at relative-velocity "v" = v at time "t" = 0, with v ≤ v, is also defined in terms of the hyperbolic tangent function: Actually, this function is defined by the solution of the following differential equation: Or, more generically (where F(v) are the forces acting on the object beyond drag): For a potato-shaped object of average diameter "d" and of density "ρ", terminal velocity is about For objects of water-like density (raindrops, hail, live objects—mammals, birds, insects, etc.) falling in air near Earth's surface at sea level, the terminal velocity is roughly equal to with "d" in metre and "v" in m/s. For example, for a human body (formula_37 ~ 0.6 m) formula_38 ~ 70 m/s, for a small animal like a cat (formula_37 ~ 0.2 m) formula_38 ~ 40 m/s, for a small bird (formula_37 ~ 0.05 m) formula_38 ~ 20 m/s, for an insect (formula_37 ~ 0.01 m) formula_38 ~ 9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law. Terminal velocity is higher for larger creatures, and thus potentially more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This, combined with the relative ratio of limb cross-sectional area vs. body mass (commonly referred to as the Square-cube law), explains why very small animals can fall from a large height and not be harmed. The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, formula_45). Note that purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity. The equation for viscous resistance is: where: When an object falls from rest, its velocity will be which asymptotically approaches the terminal velocity formula_50. For a given formula_47, heavier objects fall more quickly. For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant: where: The resulting expression for the drag is known as Stokes' drag: For example, consider a small sphere with radius formula_53 = 0.5 micrometre (diameter = 1.0 μm) moving through water at a velocity formula_57 of 10 μm/s. Using 10 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water. In aerodynamics, aerodynamic drag is the fluid drag force that acts on any moving solid body in the direction of the fluid freestream flow. From the body's perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized formula_58, and forces due to skin friction, which is a result of viscosity, denoted formula_59. Alternatively, calculated from the flowfield perspective (far-field approach), the drag force results from three natural phenomena: shock waves, vortex sheet, and viscosity. The pressure distribution acting on a body's surface exerts normal forces on the body. Those forces can be summed and the component of that force that acts downstream represents the drag force, formula_58, due to pressure distribution acting on the body. The nature of these normal forces combines shock wave effects, vortex system generation effects, and wake viscous mechanisms. The viscosity of the fluid has a major effect on drag. In the absence of viscosity, the pressure forces acting to retard the vehicle are canceled by a pressure force further aft that acts to push the vehicle forward; this is called pressure recovery and the result is that the drag is zero. That is to say, the work the body does on the airflow, is reversible and is recovered as there are no frictional effects to convert the flow energy into heat. Pressure recovery acts even in the case of viscous flow. Viscosity, however results in pressure drag and it is the dominant component of drag in the case of vehicles with regions of separated flow, in which the pressure recovery is fairly ineffective. The friction drag force, which is a tangential force on the aircraft surface, depends substantially on boundary layer configuration and viscosity. The net friction drag, formula_61, is calculated as the downstream projection of the viscous forces evaluated over the body's surface. The sum of friction drag and pressure (form) drag is called viscous drag. This drag component is due to viscosity. In a thermodynamic perspective, viscous effects represent irreversible phenomena and, therefore, they create entropy. The calculated viscous drag formula_62 use entropy changes to accurately predict the drag force. When the airplane produces lift, another drag component results. Induced drag, symbolized formula_63, is due to a modification of the pressure distribution due to the trailing vortex system that accompanies the lift production. An alternative perspective on lift and drag is gained from considering the change of momentum of the airflow. The wing intercepts the airflow and forces the flow to move downward. This results in an equal and opposite force acting upward on the wing which is the lift force. The change of momentum of the airflow downward results in a reduction of the rearward momentum of the flow which is the result of a force acting forward on the airflow and applied by the wing to the air flow; an equal but opposite force acts on the wing rearward which is the induced drag. Induced drag tends to be the most important component for airplanes during take-off or landing flight. Another drag component, namely wave drag, formula_64, results from shock waves in transonic and supersonic flight speeds. The shock waves induce changes in the boundary layer and pressure distribution over the body surface. The idea that a moving body passing through air or another fluid encounters resistance had been known since the time of Aristotle. Louis Charles Breguet's paper of 1922 began efforts to reduce drag by streamlining. Breguet went on to put his ideas into practice by designing several record-breaking aircraft in the 1920s and 1930s. Ludwig Prandtl's boundary layer theory in the 1920s provided the impetus to minimise skin friction. A further major call for streamlining was made by Sir Melvill Jones who provided the theoretical concepts to demonstrate emphatically the importance of streamlining in aircraft design. In 1929 his paper ‘The Streamline Airplane’ presented to the Royal Aeronautical Society was seminal. He proposed an ideal aircraft that would have minimal drag which led to the concepts of a 'clean' monoplane and retractable undercarriage. The aspect of Jones's paper that most shocked the designers of the time was his plot of the horse power required versus velocity, for an actual and an ideal plane. By looking at a data point for a given aircraft and extrapolating it horizontally to the ideal curve, the velocity gain for the same power can be seen. When Jones finished his presentation, a member of the audience described the results as being of the same level of importance as the Carnot cycle in thermodynamics. Lift-induced drag (also called induced drag) is drag which occurs as the result of the creation of lift on a three-dimensional lifting body, such as the wing or fuselage of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices (vortex drag); and the presence of additional viscous drag (lift-induced viscous drag) that is not present when lift is zero. The trailing vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air from above and below the body which flows in slightly different directions as a consequence of creation of lift. With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. This means that as the wing's angle of attack increases (up to a maximum called the stalling angle), the lift coefficient also increases, and so too does the lift-induced drag. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow in the wake behind the body. Parasitic drag is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag (form drag), and drag due to surface roughness (skin friction drag). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag, which is sometimes described as a component of parasitic drag. In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the angle of attack can be reduced and the induced drag decreases. Parasitic drag, however, increases because the fluid is flowing more quickly around protruding objects increasing friction or drag. At even higher speeds (transonic), wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance (minimum fuel consumption), or maximize gliding range in the event of an engine failure. The interaction of parasitic and induced drag "vs." airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the "power curve", and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires "more" thrust as speed decreases, rather than less. The consequences of being "behind the curve" in flight are important and are taught as part of pilot training. At the subsonic airspeeds where the "U" shape of this curve is significant, wave drag has not yet become a factor, and so it is not shown in the curve. Wave drag (also called compressibility drag) is drag that is created when a body moves in a compressible fluid and at speeds that are close to the speed of sound in that fluid. In aerodynamics, wave drag consists of multiple components depending on the speed regime of the flight. In transonic flight (Mach numbers greater than about 0.8 and less than about 1.4), wave drag is the result of the formation of shockwaves in the fluid, formed when local areas of supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air increases as it accelerates over the body to speeds above Mach 1.0. However, full supersonic flow over the vehicle will not develop until well past Mach 1.0. Aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as transonic compressibility drag. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at those speeds. In supersonic flight (Mach numbers greater than 1.0), wave drag is the result of shockwaves present in the fluid and attached to the body, typically oblique shockwaves formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large, unattached shockwaves, or bow waves will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic flow regimes, wave drag is commonly separated into two components, supersonic lift-dependent wave drag and supersonic volume-dependent wave drag. The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the Sears-Haack Distribution. Similarly, for a fixed volume, the shape for minimum wave drag is the Von Karman Ogive. The Busemann biplane is not, in principle, subject to wave drag when operated at its design speed, but is incapable of generating lift in this condition. In 1752 d'Alembert proved that potential flow, the 18th century state-of-the-art inviscid flow theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the Navier–Stokes equations for the description of viscous flow were developed by Saint-Venant, Navier and Stokes. Stokes derived the drag around a sphere at very low Reynolds numbers, the result of which is called Stokes' law. In the limit of high Reynolds numbers, the Navier–Stokes equations approach the inviscid Euler equations, of which the potential-flow solutions considered by d'Alembert are solutions. However, all experiments at high Reynolds numbers showed there is drag. Attempts to construct inviscid steady flow solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results. The notion of boundary layers—introduced by Prandtl in 1904, founded on both theory and experiments—explained the causes of drag at high Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important even when the viscosity is very small (or equivalently the Reynolds number is very large).	In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity. Drag force is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. 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summarize: The Halaf culture of 6500–5100 BCE has been credited with the earliest depiction of a wheeled vehicle, but this is doubtful as there is no evidence of Halafians using either wheeled vehicles or even pottery wheels. One of the first applications of the wheel to appear was the potter's wheel, used by prehistoric cultures to fabricate clay pots. The earliest type, known as "tournettes" or "slow wheels", were known in the Middle East by the 5th millennium BCE. One of the earliest examples was discovered at Tepe Pardis, Iran, and dated to 5200–4700 BCE. These were made of stone or clay and secured to the ground with a peg in the center, but required significant effort to turn. True potter's wheels, which are freely-spinning and have a wheel and axle mechanism, were developed in Mesopotamia (Iraq) by 4200–4000 BCE. The oldest surviving example, which was found in Ur (modern day Iraq), dates to approximately 3100 BCE. Evidence of wheeled vehicles appeared by the late 4th millennium BCE. Depictions of wheeled wagons found on clay tablet pictographs at the Eanna district of Uruk, in the Sumerian civilization of Mesopotamia, are dated between 3700–3500 BCE. In the second half of the 4th millennium BCE, evidence of wheeled vehicles appeared near-simultaneously in the Northern Caucasus (Maykop culture) and Eastern Europe (Cucuteni–Trypillian culture). Depictions of a wheeled vehicle appeared between 3500 and 3350 BCE in the Bronocice clay pot excavated in a Funnelbeaker culture settlement in southern Poland. In nearby Olszanica, a 2.2 m wide door was constructed (2.2 wide doors were constructed) for wagon entry; this barn was 40 m long and had 3 doors. Surviving evidence of a wheel–axle combination, from Stare Gmajne near Ljubljana in Slovenia (Ljubljana Marshes Wooden Wheel), is dated within two standard deviations to 3340–3030 BCE, the axle to 3360–3045 BCE. Two types of early Neolithic European wheel and axle are known; a circumalpine type of wagon construction (the wheel and axle rotate together, as in Ljubljana Marshes Wheel), and that of the Baden culture in Hungary (axle does not rotate). They both are dated to c. 3200–3000 BCE. Historians believe that there was a diffusion of the wheeled vehicle from the Near East to Europe around the mid-4th millennium BCE. An early example of a wooden wheel and its axle was found in 2002 at the Ljubljana Marshes some 20 km south of Ljubljana, the capital of Slovenia. According to radiocarbon dating, it is between 5,100 and 5,350 years old. The wheel was made of ash and oak and had a radius of 70 cm and the axle was 120 cm long and made of oak. In Roman Egypt, Hero of Alexandria identified the wheel and axle as one of the simple machines used to lift weights. This is thought to have been in the form of the windlass which consists of a crank or pulley connected to a cylindrical barrel that provides mechanical advantage to wind up a rope and lift a load such as a bucket from the well. The wheel and axle was identified as one of six simple machines by Renaissance scientists, drawing from Greek texts on technology. The simple machine called a "wheel and axle" refers to the assembly formed by two disks, or cylinders, of different diameters mounted so they rotate together around the same axis.The thin rod which needs to be turned is called the axle and the wider object fixed to the axle, on which we apply force is called the wheel. A tangential force applied to the periphery of the large disk can exert a larger force on a load attached to the axle, achieving mechanical advantage. When used as the wheel of a wheeled vehicle the smaller cylinder is the axle of the wheel, but when used in a windlass, winch, and other similar applications (see medieval mining lift to right) the smaller cylinder may be separate from the axle mounted in the bearings. It cannot be used separately. Assuming the wheel and axle does not dissipate or store energy, that is it has no friction or elasticity, the power input by the force applied to the wheel must equal the power output at the axle. As the wheel and axle system rotates around its bearings, points on the circumference, or edge, of the wheel move faster than points on the circumference, or edge, of the axle. Therefore, a force applied to the edge of the wheel must be less than the force applied to the edge of the axle, because power is the product of force and velocity. Let "a" and "b" be the distances from the center of the bearing to the edges of the wheel "A" and the axle "B." If the input force "F" is applied to the edge of the wheel "A" and the force "F" at the edge of the axle "B" is the output, then the ratio of the velocities of points "A" and "B" is given by "a/b", so the ratio of the output force to the input force, or mechanical advantage, is given by The mechanical advantage of a simple machine like the wheel and axle is computed as the ratio of the resistance to the effort. The larger the ratio the greater the multiplication of force (torque) created or distance achieved. By varying the radii of the axle and/or wheel, any amount of mechanical advantage may be gained. In this manner, the size of the wheel may be increased to an inconvenient extent. In this case a system or combination of wheels (often toothed, that is, gears) are used. As a wheel and axle is a type of lever, a system of wheels and axles is like a compound lever. The mechanical advantage of a wheel and axle with no friction is called the ideal mechanical advantage (IMA). It is calculated with the following formula: All actual wheels have friction, which dissipates some of the power as heat. The actual mechanical advantage (AMA) of a wheel and axle is calculated with the following formula: where Basic Machines and How They Work, United States. Bureau of Naval Personnel, Courier Dover Publications 1965, pp. 3–1 and following preview online	The wheel and axle is a machine consisting of a wheel attached to a smaller axle so that these two parts rotate together in which a force is transferred from one to the other. A hinge or bearing supports the axle, allowing rotation. 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summarize: Perhaps the first example of a wedge is the hand axe, also see biface and Olorgesailie. Wedges have existed for thousands of years, they were first made of simple stone. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint. The origin of the wedge is not known. In ancient Egyptian quarries, bronze wedges were used to break away blocks of stone used in construction. Wooden wedges that swelled after being saturated with water, were also used. Some indigenous peoples of the Americas used antler wedges for splitting and working wood to make canoes, dwellings and other objects. Wedges are used to lift heavy objects, separating them from the surface upon which they rest. Consider a block that is to be lifted by a wedge. As the wedge slides under the block, the block slides up the sloped side of a wedge. This lifts the weight "F" of the block. The horizontal force "F" needed to lift the block is obtained by considering the velocity of the wedge "v" and the velocity of the block "v". If we assume the wedge does not dissipate or store energy, then the power into the wedge equals the power out. or The velocity of the block is related to the velocity of the wedge by the slope of the side of the wedge. If the angle of the wedge is "α" then which means that the mechanical advantage Thus, the smaller the angle "α" the greater the ratio of the lifting force to the applied force on the wedge. This is the mechanical advantage of the wedge. This formula for mechanical advantage applies to cutting edges and splitting operations as well as to lifting. They can also be used to separate objects, such as blocks of cut stone. Splitting mauls and splitting wedges are used to split wood along the grain. A narrow wedge with a relatively long taper used to finely adjust the distance between objects is called a shim, and is commonly used in carpentry. The tips of forks and nails are also wedges, as they split and separate the material into which they are pushed or driven; the shafts may then hold fast due to friction. The blade is a compound inclined plane, consisting of two inclined planes placed so that the planes meet at one edge. When the edge where the two planes meet is pushed into a solid or fluid substance it overcomes the resistance of materials to separate by transferring the force exerted against the material into two opposing forces normal to the faces of the blade. The blade's first known use by humans was the sharp edge of a flint stone that was used to cleave or split animal tissue, e.g. cutting meat. The use of iron or other metals led to the development of knives for those kinds of tasks. The blade of the knife allowed humans to cut meat, fibers, and other plant and animal materials with much less force than it would take to tear them apart by simply pulling with their hands. Other examples are plows, which separate soil particles, scissors which separate fabric, axes which separate wood fibers, and chisels and planes which separate wood. Wedges, saws and chisels can separate thick and hard materials, such as wood, solid stone and hard metals and they do so with much less force, waste of material, and with more precision, than crushing, which is the application of the same force over a wider area of the material to be separated. Other examples of wedges are found in drill bits, which produce circular holes in solids. The two edges of a drill bit are sharpened, at opposing angles, into a point and that edge is wound around the shaft of the drill bit. When the drill bit spins on its axis of rotation, the wedges are forced into the material to be separated. The resulting cut in the material is in the direction of rotation of the drill bit while the helical shape of a bit allows the removal of the cut material. Wedges can also be used to hold objects in place, such as engine parts (poppet valves), bicycle parts (stems and eccentric bottom brackets), and doors. A wedge-type door stop (door wedge) functions largely because of the friction generated between the bottom of the door and the wedge, and the wedge and the floor (or other surface). The mechanical advantage of a wedge can be calculated by dividing the height of the wedge by the wedge's width: The more acute, or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical advantage it will yield. A wedge will bind when the wedge included angle is less than the arctangent of the coefficient of friction between the wedge and the material. Therefore, in an elastic material such as wood, friction may bind a narrow wedge more easily than a wide one. This is why the head of a splitting maul has a much wider angle than that of an axe.	A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six classical simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular (normal) to its inclined surfaces. The mechanical advantage of a wedge is given by the ratio of the length of its slope to its width. 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summarize: The only chemical elements that are stable diatomic homonuclear molecules at STP are hydrogen (H), nitrogen (N), oxygen (O), and two halogens: fluorine (F) and chlorine (Cl). When grouped together with the monatomic noble gases – helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn) – these gases are called "elemental gases". The word "gas" was first used by the early 17th-century Flemish chemist Jan Baptist van Helmont. He identified carbon dioxide, the first known gas other than air. Van Helmont's word appears to have been simply a phonetic transcription of the Ancient Greek word χάος "Chaos" – the "g" in Dutch being pronounced like "ch" in "loch" (voiceless velar fricative, ) – in which case Van Helmont was simply following the established alchemical usage first attested in the works of Paracelsus. According to Paracelsus's terminology, "chaos" meant something like "ultra-rarefied water". An alternative story is that Van Helmont's word is corrupted from "gahst" (or "geist"), signifying a ghost or spirit. This was because certain gases suggested a supernatural origin, such as from their ability to cause death, extinguish flames, and to occur in "mines, bottom of wells, churchyards and other lonely places". In contrast, French-American historian Jacques Barzun speculated that Van Helmont had borrowed the word from the German "Gäscht", meaning the froth resulting from fermentation. Because most gases are difficult to observe directly, they are described through the use of four physical properties or macroscopic characteristics: pressure, volume, number of particles (chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below). Gas particles are widely separated from one another, and consequently, have weaker intermolecular bonds than liquids or solids. These intermolecular forces result from electrostatic interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another; gases that contain permanently charged ions are known as plasmas. Gaseous compounds with polar covalent bonds contain permanent charge imbalances and so experience relatively strong intermolecular forces, although the molecule while the compound's net charge remains neutral. Transient, randomly induced charges exist across non-polar covalent bonds of molecules and electrostatic interactions caused by them are referred to as Van der Waals forces. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of "boiling points" for compounds formed by ionic and covalent bonds leads us to this conclusion. The drifting smoke particles in the image provides some insight into low-pressure gas behavior. Compared to the other states of matter, gases have low density and viscosity. Pressure and temperature influence the particles within a certain volume. This variation in particle separation and speed is referred to as "compressibility". This particle separation and size influences optical properties of gases as can be found in the following list of refractive indices. Finally, gas particles spread apart or diffuse in order to homogeneously distribute themselves throughout any container. When observing a gas, it is typical to specify a frame of reference or length scale. A larger length scale corresponds to a macroscopic or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the "average" behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. In contrast, a smaller length scale corresponds to a microscopic or particle point of view. Macroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube manometer which looks like a test tube in the shape of the letter J. Boyle trapped an inert gas in the closed end of the test tube with a column of mercury, thereby making the number of particles and the temperature constant. He observed that when the pressure was increased in the gas, by adding more mercury to the column, the trapped gas' volume decreased (this is known as an inverse relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the product was constant. This relationship held for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field. There are many mathematical tools available for analyzing gas properties. As gases are subjected to extreme conditions, these tools become more complex, from the Euler equations for inviscid flow to the Navier–Stokes equations that fully account for viscous effects. These equations are adapted to the conditions of the gas system in question. Boyle's lab equipment allowed the use of algebra to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an "ideal" manner. These ideal relationships apply to safety calculations for a variety of flight conditions on the materials in use. The high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an "ideal" manner. This advanced math, including statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. An example is the analysis of the space shuttle reentry pictured to ensure the material properties under this loading condition are appropriate. In this flight regime, the gas is no longer behaving ideally. The symbol used to represent pressure in equations is "p" or "P" with SI units of pascals. When describing a container of gas, the term pressure (or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container. Within this volume, it is sometimes easier to visualize the gas particles moving in straight lines until they collide with the container (see diagram at top of the article). The force imparted by a gas particle into the container during this collision is the change in momentum of the particle. During a collision only the normal component of velocity changes. A particle traveling parallel to the wall does not change its momentum. Therefore, the average force on a surface must be the average change in linear momentum from all of these gas particle collisions. Pressure is the sum of all the normal components of force exerted by the particles impacting the walls of the container divided by the surface area of the wall. The symbol used to represent "temperature" in equations is "T" with SI units of kelvins. The speed of a gas particle is proportional to its absolute temperature. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any physical system is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a particle. The methods of storing this energy are dictated by the degrees of freedom of the particle itself (energy modes). Kinetic energy added (endothermic process) to gas particles by way of collisions produces linear, rotational, and vibrational motion. In contrast, a molecule in a solid can only increase its vibrational modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions. These heated gas molecules have a greater speed range which constantly varies due to constant collisions with other particles. The speed range can be described by the Maxwell–Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered. The symbol used to represent specific volume in equations is "v" with SI units of cubic meters per kilogram. The symbol used to represent volume in equations is "V" with SI units of cubic meters. When performing a thermodynamic analysis, it is typical to speak of intensive and extensive properties. Properties which depend on the amount of gas (either by mass or volume) are called "extensive" properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of volume occupied by a "unit of mass" of a gas that is identical throughout a system at equilibrium. 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are incompressible compared to gases. However, volume itself --- not specific --- is an extensive property. The symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the reciprocal of specific volume. Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases. If one could observe a gas under a powerful microscope, one would see a collection of particles (molecules, atoms, ions, electrons, etc.) without any definite shape or volume that are in more or less random motion. These neutral gas particles only change direction when they collide with another particle or with the sides of the container. In an ideal gas, these collisions are perfectly elastic. This particle or microscopic view of a gas is described by the kinetic-molecular theory. The assumptions behind this theory can be found in the postulates section of kinetic theory. Kinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of momentum and kinetic energy, one can use the conservation of momentum and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule. The theory provides averaged values for these two properties. The theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is (in theory) perfectly still, its internal energy (temperature) is increased. As a gas is heated, the particles speed up and its temperature rises. This results in greater numbers of collisions with the container per unit time due to the higher particle speeds associated with elevated temperatures. The pressure increases in proportion to the number of collisions per unit time. Brownian motion is the mathematical model used to describe the random movement of particles suspended in a fluid. The gas particle animation, using pink and green particles, illustrates how this behavior results in the spreading out of gases (entropy). These events are also described by particle theory. Since it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions about how they move, but their motion is different from Brownian motion because Brownian motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as would be expected if an individual gas molecule were examined. As discussed earlier, momentary attractions (or repulsions) between particles have an effect on gas dynamics. In physical chemistry, the name given to these intermolecular forces is "van der Waals force". These forces play a key role in determining physical properties of a gas such as viscosity and flow rate (see physical characteristics section). Ignoring these forces in certain conditions allows a real gas to be treated like an ideal gas. This assumption allows the use of ideal gas laws which greatly simplifies calculations. Proper use of these gas relationships requires the kinetic-molecular theory (KMT). When gas particles experience intermolecular forces they gradually influence one another as the spacing between them is reduced (the hydrogen bond model illustrates one example). In the absence of any charge, at some point when the spacing between gas particles is greatly reduced they can no longer avoid collisions between themselves at normal gas temperatures. Another case for increased collisions among gas particles would include a fixed volume of gas, which upon heating would contain very fast particles. This means that these ideal equations provide reasonable results except for extremely high pressure (compressible) or high temperature (ionized) conditions. All of these excepted conditions allow energy transfer to take place within the gas system. The absence of these internal transfers is what is referred to as ideal conditions in which the energy exchange occurs only at the boundaries of the system. Real gases experience some of these collisions and intermolecular forces. When these collisions are statistically negligible (incompressible), results from these ideal equations are still meaningful. If the gas particles are compressed into close proximity they behave more like a liquid (see fluid dynamics). An "equation of state" (for gases) is a mathematical model used to roughly describe or predict the state properties of a gas. At present, there is no single equation of state that accurately predicts the properties of all gases under all conditions. Therefore, a number of much more accurate equations of state have been developed for gases in specific temperature and pressure ranges. The "gas models" that are most widely discussed are "perfect gas", "ideal gas" and "real gas". Each of these models has its own set of assumptions to facilitate the analysis of a given thermodynamic system. Each successive model expands the temperature range of coverage to which it applies. The equation of state for an ideal or perfect gas is the ideal gas law and reads where "P" is the pressure, "V" is the volume, "n" is amount of gas (in mol units), "R" is the universal gas constant, 8.314 J/(mol K), and "T" is the temperature. Written this way, it is sometimes called the "chemist's version", since it emphasizes the number of molecules "n". It can also be written as where formula_3 is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the "gas dynamicist's" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions. The ideal gas law does not make an assumption about the specific heat of a gas. In the most general case, the specific heat is a function of both temperature and pressure. If the pressure-dependence is neglected (and possibly the temperature-dependence as well) in a particular application, sometimes the gas is said to be a perfect gas, although the exact assumptions may vary depending on the author and/or field of science. For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the compressibility factor "Z" is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the ideal gas law. This approximation is more suitable for applications in engineering although simpler models can be used to produce a "ball-park" range as to where the real solution should lie. An example where the "ideal gas approximation" would be suitable would be inside a combustion chamber of a jet engine. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions. Each one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing "reasonable" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to plasma). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution. One of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different thermodynamic processes by adjusting the equation to read "pV = constant" and then varying the "n" through different values such as the specific heat ratio, "γ". Real gas effects include those adjustments made to account for a greater range of gas behavior: For most applications, such a detailed analysis is excessive. Examples where real gas effects would have a significant impact would be on the Space Shuttle re-entry where extremely high temperatures and pressures were present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt. Boyle's law was perhaps the first expression of an equation of state. In 1662 Robert Boyle performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. The image of Boyle's equipment shows some of the exotic tools used by Boyle during his study of gases. Through these experiments, Boyle noted that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. For example, if the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Given the inverse relationship between pressure and volume, the product of pressure ("P") and volume ("V") is a constant ("k") for a given mass of confined gas as long as the temperature is constant. Stated as a formula, thus is: Because the before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same both equal the constant "k", they can be related by the equation: formula_5 In 1787, the French physicist and balloon pioneer, Jacques Charles, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature: In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments. Gay-Lussac credited Charles' earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature. In 1811, Amedeo Avogadro verified that equal volumes of pure gases contain the same number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal exceptions. For his work with gases a century prior, the number that bears his name Avogadro's constant represents the number of atoms found in 12 grams of elemental carbon-12 (6.022×10 mol). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the molar volume. Avogadro's law states that the volume occupied by an ideal gas is proportional to the number of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 dm (or litres). The relation is given by where n is equal to the number of moles of gas (the number of molecules divided by Avogadro's number). In 1801, John Dalton published the law of partial pressures from his work with ideal gas law relationship: The pressure of a mixture of non reactive gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented for "n" species as: The image of Dalton's journal depicts symbology he used as shorthand to record the path he followed. Among his key journal observations upon mixing unreactive "elastic fluids" (gases) were the following: Thermodynamicists use this factor ("Z") to alter the ideal gas equation to account for compressibility effects of real gases. This factor represents the ratio of actual to ideal specific volumes. It is sometimes referred to as a "fudge-factor" or correction to expand the useful range of the ideal gas law for design purposes. "Usually" this "Z" value is very close to unity. The compressibility factor image illustrates how Z varies over a range of very cold temperatures. In fluid mechanics, the Reynolds number is the ratio of inertial forces ("vρ") to viscous forces ("μ/L"). It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. As such, the Reynolds number provides the link between modeling results (design) and the full-scale actual conditions. It can also be used to characterize the flow. Viscosity, a physical property, is a measure of how well adjacent molecules stick to one another. A solid can withstand a shearing force due to the strength of these sticky intermolecular forces. A fluid will continuously deform when subjected to a similar load. While a gas has a lower value of viscosity than a liquid, it is still an observable property. If gases had no viscosity, then they would not stick to the surface of a wing and form a boundary layer. A study of the delta wing in the Schlieren image reveals that the gas particles stick to one another (see Boundary layer section). In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. The satellite view of weather around Robinson Crusoe Islands illustrates one example. Particles will, in effect, "stick" to the surface of an object moving through it. This layer of particles is called the boundary layer. At the surface of the object, it is essentially static due to the friction of the surface. The object, with its boundary layer is effectively the new shape of the object that the rest of the molecules "see" as the object approaches. This boundary layer can separate from the surface, essentially creating a new surface and completely changing the flow path. The classical example of this is a stalling airfoil. The delta wing image clearly shows the boundary layer thickening as the gas flows from right to left along the leading edge. As the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity. In order to illustrate this principle, observe the skin temperature of a frozen metal bar. Using a thermal image of the skin temperature, note the temperature distribution on the surface. This initial observation of temperature represents a "microstate". At some future time, a second observation of the skin temperature produces a second microstate. By continuing this observation process, it is possible to produce a series of microstates that illustrate the thermal history of the bar's surface. Characterization of this historical series of microstates is possible by choosing the macrostate that successfully classifies them all into a single grouping. When energy transfer ceases from a system, this condition is referred to as thermodynamic equilibrium. Usually, this condition implies the system and surroundings are at the same temperature so that heat no longer transfers between them. It also implies that external forces are balanced (volume does not change), and all chemical reactions within the system are complete. The timeline varies for these events depending on the system in question. A container of ice allowed to melt at room temperature takes hours, while in semiconductors the heat transfer that occurs in the device transition from an on to off state could be on the order of a few nanoseconds.

Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture, such as air, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible, as indicated by the constant velocity vectors in the image.

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summarize: Liquid is one of the four primary states of matter, with the others being solid, gas and plasma. A liquid is a fluid. Unlike a solid, the molecules in a liquid have a much greater freedom to move. The forces that bind the molecules together in a solid are only temporary in a liquid, allowing a liquid to flow while a solid remains rigid. A liquid, like a gas, displays the properties of a fluid. A liquid can flow, assume the shape of a container, and, if placed in a sealed container, will distribute applied pressure evenly to every surface in the container. If liquid is placed in a bag, it can be squeezed into any shape. Unlike a gas, a liquid is nearly incompressible, meaning that it occupies nearly a constant volume over a wide range of pressures; it does not generally expand to fill available space in a container but forms its own surface, and it may not always mix readily with another liquid. These properties make a liquid suitable for applications such as hydraulics. Liquid particles are bound firmly but not rigidly. They are able to move around one another freely, resulting in a limited degree of particle mobility. As the temperature increases, the increased vibrations of the molecules causes distances between the molecules to increase. When a liquid reaches its boiling point, the cohesive forces that bind the molecules closely together break, and the liquid changes to its gaseous state (unless superheating occurs). If the temperature is decreased, the distances between the molecules become smaller. When the liquid reaches its freezing point the molecules will usually lock into a very specific order, called crystallizing, and the bonds between them become more rigid, changing the liquid into its solid state (unless supercooling occurs). Only two elements are liquid at standard conditions for temperature and pressure: mercury and bromine. Four more elements have melting points slightly above room temperature: francium, caesium, gallium and rubidium. Metal alloys that are liquid at room temperature include NaK, a sodium-potassium metal alloy, galinstan, a fusible alloy liquid, and some amalgams (alloys involving mercury). Pure substances that are liquid under normal conditions include water, ethanol and many other organic solvents. Liquid water is of vital importance in chemistry and biology; it is believed to be a necessity for the existence of life. Inorganic liquids include water, magma, inorganic nonaqueous solvents and many acids. Important everyday liquids include aqueous solutions like household bleach, other mixtures of different substances such as mineral oil and gasoline, emulsions like vinaigrette or mayonnaise, suspensions like blood, and colloids like paint and milk. Many gases can be liquefied by cooling, producing liquids such as liquid oxygen, liquid nitrogen, liquid hydrogen and liquid helium. Not all gases can be liquified at atmospheric pressure, however. Carbon dioxide, for example, can only be liquified at pressures above 5.1 atm. Some materials cannot be classified within the classical three states of matter; they possess solid-like and liquid-like properties. Examples include liquid crystals, used in LCD displays, and biological membranes. Liquids have a variety of uses, as lubricants, solvents, and coolants. In hydraulic systems, liquid is used to transmit power. In tribology, liquids are studied for their properties as lubricants. Lubricants such as oil are chosen for viscosity and flow characteristics that are suitable throughout the operating temperature range of the component. Oils are often used in engines, gear boxes, metalworking, and hydraulic systems for their good lubrication properties. Many liquids are used as solvents, to dissolve other liquids or solids. Solutions are found in a wide variety of applications, including paints, sealants, and adhesives. Naphtha and acetone are used frequently in industry to clean oil, grease, and tar from parts and machinery. Body fluids are water based solutions. Surfactants are commonly found in soaps and detergents. Solvents like alcohol are often used as antimicrobials. They are found in cosmetics, inks, and liquid dye lasers. They are used in the food industry, in processes such as the extraction of vegetable oil. Liquids tend to have better thermal conductivity than gases, and the ability to flow makes a liquid suitable for removing excess heat from mechanical components. The heat can be removed by channeling the liquid through a heat exchanger, such as a radiator, or the heat can be removed with the liquid during evaporation. Water or glycol coolants are used to keep engines from overheating. The coolants used in nuclear reactors include water or liquid metals, such as sodium or bismuth. Liquid propellant films are used to cool the thrust chambers of rockets. In machining, water and oils are used to remove the excess heat generated, which can quickly ruin both the work piece and the tooling. During perspiration, sweat removes heat from the human body by evaporating. In the heating, ventilation, and air-conditioning industry (HVAC), liquids such as water are used to transfer heat from one area to another. Similarly, liquids are often used in cooking for their better heat-transfer properties. In addition to better conductivity, because warmer fluids expand and rise while cooler areas contract and sink, liquids with low kinematic viscosity tend to transfer heat through convection at a fairly constant temperature, making a liquid suitable for blanching, boiling, or frying. This phenomenon was also exploited to produce lava lamps. Even higher rates of heat transfer can be achieved by condensing a gas into a liquid. At the liquid's boiling point, all of the heat energy is used to cause the phase change from a liquid to a gas, without an accompanying increase in temperature, and is stored as chemical potential energy. When the gas condenses back into a liquid this excess heat-energy is released at a constant temperature. This phenomenon is used in processes such as steaming. Since liquids often have different boiling points, mixtures or solutions of liquids or gases can typically be separated by distillation, using heat, cold, vacuum, pressure, or other means. Distillation can be found in everything from the production of alcoholic beverages, to oil refineries, to the cryogenic distillation of gases such as argon, oxygen, nitrogen, neon, or xenon by liquefaction (cooling them below their individual boiling points). Liquid is the primary component of hydraulic systems, which take advantage of Pascal's law to provide fluid power. Devices such as pumps and waterwheels have been used to change liquid motion into mechanical work since ancient times. Oils are forced through hydraulic pumps, which transmit this force to hydraulic cylinders. Hydraulics can be found in many applications, such as automotive brakes and transmissions, heavy equipment, and airplane control systems. Various hydraulic presses are used extensively in repair and manufacturing, for lifting, pressing, clamping and forming. Liquids are sometimes used in measuring devices. A thermometer often uses the thermal expansion of liquids, such as mercury, combined with their ability to flow to indicate temperature. A manometer uses the weight of the liquid to indicate air pressure. Quantities of liquids are measured in units of volume. These include the SI unit cubic metre (m) and its divisions, in particular the cubic decimeter, more commonly called the litre (1 dm = 1 L = 0.001 m), and the cubic centimetre, also called millilitre (1 cm = 1 mL = 0.001 L = 10 m). The volume of a quantity of liquid is fixed by its temperature and pressure. Liquids generally expand when heated, and contract when cooled. Water between 0 °C and 4 °C is a notable exception. On the other hand, liquids have little compressibility. Water, for example, will compress by only 46.4 parts per million for every unit increase in atmospheric pressure (bar). At around 4000 bar (400 megapascals or 58,000 psi) of pressure at room temperature water experiences only an 11% decrease in volume. Incompressibility makes liquids suitable for transmitting hydraulic power, because a change in pressure at one point in a liquid is transmitted undiminished to every other part of the liquid and very little energy is lost in the form of compression. However, the negligible compressibility does lead to other phenomena. The banging of pipes, called water hammer, occurs when a valve is suddenly closed, creating a huge pressure-spike at the valve that travels backward through the system at just under the speed of sound. Another phenomenon caused by liquid's incompressibility is cavitation. Because liquids have little elasticity they can literally be pulled apart in areas of high turbulence or dramatic change in direction, such as the trailing edge of a boat propeller or a sharp corner in a pipe. A liquid in an area of low pressure (vacuum) vaporizes and forms bubbles, which then collapse as they enter high pressure areas. This causes liquid to fill the cavities left by the bubbles with tremendous localized force, eroding any adjacent solid surface. In a gravitational field, liquids exert pressure on the sides of a container as well as on anything within the liquid itself. This pressure is transmitted in all directions and increases with depth. If a liquid is at rest in a uniform gravitational field, the pressure formula_1 at depth formula_2 is given by where: For a body of water open to the air, formula_7 would be the atmospheric pressure. Static liquids in uniform gravitational fields also exhibit the phenomenon of buoyancy, where objects immersed in the liquid experience a net force due to the pressure variation with depth. The magnitude of the force is equal to the weight of the liquid displaced by the object, and the direction of the force depends on the average density of the immersed object. If the density is "smaller" than that of the liquid, the buoyant force points "upward" and the object floats, whereas if the density is "larger", the buoyant force points "downward" and the object sinks. This is known as Archimedes' principle. Unless the volume of a liquid exactly matches the volume of its container, one or more surfaces are observed. The presence of a surface introduces new phenomena which are not present in a bulk liquid. This is because a molecule at a surface possesses bonds with other liquid molecules only on the inner side of the surface, which implies a net force pulling surface molecules inward. Equivalently, this force can be described in terms of energy: there is a fixed amount of energy associated with forming a surface of a given area. This quantity is a material property called the surface tension, in units of energy per unit area (SI units: J/m). Liquids with strong intermolecular forces tend to have large surface tensions. A practical implication of surface tension is that liquids tend to minimize their surface area, forming spherical drops and bubbles unless other constraints are present. Surface tension is responsible for a range of other phenomena as well, including surface waves, capillary action, wetting, and ripples. In liquids under nanoscale confinement, surface effects can play a dominating role since – compared with a macroscopic sample of liquid – a much greater fraction of molecules are located near a surface. The surface tension of a liquid directly affects its wettability. Most common liquids have tensions ranging in the tens of mJ/m, so droplets of oil, water, or glue can easily merge and adhere to other surfaces, whereas liquid metals such as mercury may have tensions ranging in the hundreds of mJ/m, thus droplets do not combine easily and surfaces may only wet under specific conditions. The surface tensions of common liquids occupy a relatively narrow range of values, which contrasts strongly with the enormous variation seen in other mechanical properties, such as viscosity. An important physical property characterizing the flow of liquids is viscosity. Intuitively, viscosity describes the resistance of a liquid to flow. More technically, viscosity measures the resistance of a liquid to deformation at a given rate, such as when it is being sheared at finite velocity. A specific example is a liquid flowing through a pipe: in this case the liquid undergoes shear deformation since it flows more slowly near the walls of the pipe than near the center. As a result, it exhibits viscous resistance to flow. In order to maintain flow, an external force must be applied, such as a pressure difference between the ends of the pipe. The viscosity of liquids decreases with increasing temperature. Precise control of viscosity is important in many applications, particularly the lubrication industry. One way to achieve such control is by blending two or more liquids of differing viscosities in precise ratios. In addition, various additives exist which can modulate the temperature-dependence of the viscosity of lubricating oils. This capability is important since machinery often operate over a range of temperatures (see also viscosity index). The viscous behavior of a liquid can be either Newtonian or non-Newtonian. A Newtonian liquid exhibits a linear strain/stress curve, meaning its viscosity is independent of time, shear rate, or shear-rate history. Examples of Newtonian liquids include water, glycerin, motor oil, honey, or mercury. A non-Newtonian liquid is one where the viscosity is not independent of these factors and either thickens (increases in viscosity) or thins (decreases in viscosity) under shear. Examples of non-Newtonian liquids include ketchup, mayonnaise, hair gels, play dough, or starch solutions. The speed of sound in a liquid is given by formula_8 where formula_9 is the bulk modulus of the liquid and formula_10 the density. As an example, water has a bulk modulus of about 2.2 GPa and a density of 1000 kg/m, which gives "c" = 1.5 km/s. At a temperature below the boiling point, any matter in liquid form will evaporate until the condensation of gas above reach an equilibrium. At this point the gas will condense at the same rate as the liquid evaporates. Thus, a liquid cannot exist permanently if the evaporated liquid is continually removed. A liquid at its boiling point will evaporate more quickly than the gas can condense at the current pressure. A liquid at or above its boiling point will normally boil, though superheating can prevent this in certain circumstances. At a temperature below the freezing point, a liquid will tend to crystallize, changing to its solid form. Unlike the transition to gas, there is no equilibrium at this transition under constant pressure, so unless supercooling occurs, the liquid will eventually completely crystallize. Note that this is only true under constant pressure, so e.g. water and ice in a closed, strong container might reach an equilibrium where both phases coexist. For the opposite transition from solid to liquid, see melting. The phase diagram explains why liquids do not exist in space or any other vacuum. Since the pressure is zero (except on surfaces or interiors of planets and moons) water and other liquids exposed to space will either immediately boil or freeze depending on the temperature. In regions of space near the earth, water will freeze if the sun is not shining directly on it and vapourize (sublime) as soon as it is in sunlight. If water exists as ice on the moon, it can only exist in shadowed holes where the sun never shines and where the surrounding rock doesn't heat it up too much. At some point near the orbit of Saturn, the light from the sun is too faint to sublime ice to water vapour. This is evident from the longevity of the ice that composes Saturn's rings. Liquids can form solutions with gases, solids, and other liquids. Two liquids are said to be miscible if they can form a solution in any proportion; otherwise they are immiscible. As an example, water and ethanol (drinking alcohol) are miscible whereas water and gasoline are immiscible. In some cases a mixture of otherwise immiscible liquids can be stabilized to form an emulsion, where one liquid is dispersed throughout the other as microscopic droplets. Usually this requires the presence of a surfactant in order to stabilize the droplets. A familiar example of an emulsion is mayonnaise, which consists of a mixture of water and oil that is stabilized by lecithin, a substance found in egg yolks. The molecules which compose liquids are "disordered" and "strongly interacting", which makes liquids difficult to describe rigorously at the molecular level. This stands in contrast with the other two common phases of matter, gases and solids. Although gases are disordered, they are sufficiently dilute that many-body interactions can be ignored, and molecular interactions can instead be modeled in terms of well-defined binary collision events. Conversely, although solids are dense and strongly interacting, their regular structure at the molecular level (e.g. a crystalline lattice) allows for significant theoretical simplifications. For these reasons, the microscopic theory of liquids is less developed than that of gases and solids. In a liquid, atoms do not form a crystalline lattice, nor do they show any other form of long-range order. This is evidenced by the absence of Bragg peaks in X-ray and neutron diffraction. Under normal conditions, the diffraction pattern has circular symmetry, expressing the isotropy of the liquid. In radial direction, the diffraction intensity smoothly oscillates. This is usually described by the static structure factor "S(q)", with wavenumber "q"=(4π/λ)sinθ given by the wavelength λ of the probe (photon or neutron) and the Bragg angle θ. The oscillations of "S(q)" express the "near order" of the liquid, i.e. the correlations between an atom and a few shells of nearest, second nearest,... neighbors. A more intuitive description of these correlations is given by the radial distribution function "g(r)", which is basically the Fourier transform of "S(q)". It represents a spatial average of a temporal snapshot of pair correlations in the liquid. The above expression for the sound velocity formula_8 contains the bulk modulus "K". If "K" is frequency independent then the liquid behaves as a linear medium, so that sound propagates without dissipation and without mode coupling. In reality, any liquid shows some dispersion: with increasing frequency, "K" crosses over from the low-frequency, liquid-like limit formula_12 to the high-frequency, solid-like limit formula_13. In normal liquids, most of this cross over takes place at frequencies between GHz and THz, sometimes called hypersound. At sub-GHz frequencies, a normal liquid cannot sustain shear waves: the zero-frequency limit of the shear modulus is formula_14. This is sometimes seen as the defining property of a liquid. However, just as the bulk modulus "K", the shear modulus "G" is frequency dependent, and at hypersound frequencies it shows a similar cross over from the liquid-like limit formula_15 to a solid-like, non-zero limit formula_16. According to the Kramers-Kronig relation, the dispersion in the sound velocity (given by the real part of "K" or "G") goes along with a maximum in the sound attenuation (dissipation, given by the imaginary part of "K" or "G"). According to linear response theory, the Fourier transform of "K" or "G" describes how the system returns to equilibrium after an external perturbation; for this reason, the dispersion step in the GHz..THz region is also called structural relaxation. According to the fluctuation-dissipation theorem, relaxation "towards" equilibrium is intimately connected to fluctuations "in" equilibrium. The density fluctuations associated with sound waves can be experimentally observed by Brillouin scattering. On supercooling a liquid towards the glass transition, the crossover from liquid-like to solid-like response moves from GHz to MHz, kHz, Hz,...; equivalently, the characteristic time of structural relaxation increases from ns to μs, ms, s,... This is the microscopic explanation for the above-mentioned viscoelastic behaviour of glass-forming liquids. The mechanisms of atomic/molecular diffusion (or particle displacement) in solids are closely related to the mechanisms of viscous flow and solidification in liquid materials. Descriptions of viscosity in terms of molecular "free space" within the liquid were modified as needed in order to account for liquids whose molecules are known to be "associated" in the liquid state at ordinary temperatures. When various molecules combine together to form an associated molecule, they enclose within a semi-rigid system a certain amount of space which before was available as free space for mobile molecules. Thus, increase in viscosity upon cooling due to the tendency of most substances to become "associated" on cooling. Similar arguments could be used to describe the effects of pressure on viscosity, where it may be assumed that the viscosity is chiefly a function of the volume for liquids with a finite compressibility. An increasing viscosity with rise of pressure is therefore expected. In addition, if the volume is expanded by heat but reduced again by pressure, the viscosity remains the same. The local tendency to orientation of molecules in small groups lends the liquid (as referred to previously) a certain degree of association. This association results in a considerable "internal pressure" within a liquid, which is due almost entirely to those molecules which, on account of their temporary low velocities (following the Maxwell distribution) have coalesced with other molecules. The internal pressure between several such molecules might correspond to that between a group of molecules in the solid form.

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, and plasma), and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is, by far, the most common liquid on Earth.

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summarize: Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the terrestrial sphere contained four elements that come to rest at different "natural places" therein. Aristotle believed that motionless objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground and that they will stay that way if left alone. He distinguished between the innate tendency of objects to find their Sir Isaac Newton described the motion of all objects using the concepts of inertia and force, and in doing so he found they obey certain conservation laws. In 1687, Newton published his thesis "Philosophiæ Naturalis Principia Mathematica". In this work Newton set out three laws of motion that to this day are the way forces are described in physics. Newton's First Law of Motion states that objects continue to move in a state of constant velocity unless acted upon by an external net force (resultant force). This law is an extension of Galileo's insight that constant velocity was associated with a lack of net force (see a more detailed description of this below). Newton proposed that every object with mass has an innate inertia that functions as the fundamental equilibrium "natural state" in place of the Aristotelian idea of the "natural state of rest". That is, Newton's empirical First Law contradicts the intuitive Aristotelian belief that a net force is required to keep an object moving with constant velocity. By making "rest" physically indistinguishable from "non-zero constant velocity", Newton's First Law directly connects inertia with the concept of relative velocities. Specifically, in systems where objects are moving with different velocities, it is impossible to determine which object is "in motion" and which object is "at rest". A modern statement of Newton's Second Law is a vector equation: where formula_2 is the momentum of the system, and formula_3 is the net (vector sum) force. If a body is in equilibrium, there is zero "net" force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an "unbalanced" force acting on an object it will result in the object's momentum changing over time. By the definition of momentum, where "m" is the mass and formula_5 is the velocity. If Newton's second law is applied to a system of constant mass, "m" may be moved outside the derivative operator. The equation then becomes By substituting the definition of acceleration, the algebraic version of Newton's Second Law is derived: Newton never explicitly stated the formula in the reduced form Whenever one body exerts a force on another, the latter simultaneously exerts an equal and opposite force on the first. In vector form, if formula_8 is the force of body 1 on body 2 and formula_9 that of body 2 on body 1, then This law is sometimes referred to as the "action-reaction law", with formula_11 called the "action" and formula_12 the "reaction". Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are "interactions" between different bodies, and thus that there is no such thing as a unidirectional force or a force that acts on only one body. In the special theory of relativity, mass and energy are equivalent (as can be seen by calculating the work required to accelerate an object). When an object's velocity increases, so does its energy and hence its mass equivalent (inertia). It thus requires more force to accelerate it the same amount than it did at a lower velocity. Newton's Second Law remains valid because it is a mathematical definition. But for relativistic momentum to be conserved, it must be redefined as: where formula_19 is the rest mass and formula_20 the speed of light. The relativistic expression relating force and acceleration for a Since forces are perceived as pushes or pulls, this can provide an intuitive understanding for describing forces. As with other physical concepts (e.g. temperature), the intuitive understanding of forces is quantified using precise operational definitions that are consistent with direct observations and compared to a standard measurement scale. Through experimentation, it is determined that laboratory measurements of forces are fully consistent with the conceptual definition of force offered by Newtonian mechanics. Forces act in a particular direction and have sizes dependent upon how strong the push or pull is. Because of these characteristics, forces are classified as "vector quantities". This means that forces follow a different set of mathematical rules than physical quantities that do not have direction (denoted scalar quantities). For example, when determining what happens when two forces act on the same object, it is necessary to know both the magnitude and the direction of both forces to calculate the result. If both of these pieces of information are not known for each force, the situation is ambiguous. For example, if you know that two people are pulling on the same rope with known magnitudes of force but you do not know which direction either person is pulling, it is impossible to determine what the acceleration of the rope will be. The two people could be pulling against each other as in tug of war or the two people could be pulling in the same direction. In this simple one-dimensional example, without knowing the direction of the forces it is impossible to decide whether the net force is the result of adding the two force magnitudes or subtracting one from the other. Associating forces with vectors avoids such problems. Historically, forces were first quantitatively investigated in conditions of static equilibrium where several forces canceled each other out. Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction. When two forces act on a point particle, the resulting force, the "resultant" (also called the "net force"), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. However, if the forces are acting on an extended body, their respective lines of application must also be specified in order to account for their effects on the motion of the body. Free-body diagrams can be used as a convenient way to keep track of forces acting on a system. Ideally, these diagrams are drawn with the angles and relative magnitudes of the force vectors preserved so that graphical vector addition can be done to determine the net force. As well as being added, forces can also be resolved into independent components at right angles to each other. A horizontal force pointing northeast can therefore be split into two forces, one pointing north, and one pointing east. Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other. Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right-angles to the other two. All of the known forces of the universe are classified into four fundamental interactions. The strong and the weak forces are nuclear forces that act only at very short distances, and are responsible for the interactions between subatomic particles, including nucleons and compound nuclei. The electromagnetic force acts between electric charges, and the gravitational force acts between masses. All other forces in nature derive from these four fundamental interactions. For example, friction is a manifestation of the electromagnetic force acting between atoms of two surfaces, and the Pauli exclusion principle, which does not permit atoms to pass through each other. Similarly, the forces in springs, modeled by Hooke's law, are the result of electromagnetic forces and the Pauli exclusion principle acting together to return an object to its equilibrium position. Centrifugal forces are acceleration forces that arise simply from the acceleration of rotating frames of reference. The fundamental theories for forces developed from the unification of different ideas. For example, Sir. Isaac Newton unified, with his universal theory of gravitation, the force responsible for objects falling near the surface of the Earth with the force responsible for the falling of celestial bodies about the Earth (the Moon) and around the Sun (the planets). Michael Faraday and James Clerk Maxwell demonstrated that electric and magnetic forces were unified through a theory of electromagnetism. In the 20th century, the development of quantum mechanics led to a modern understanding that the first three fundamental forces (all except gravity) are manifestations of matter (fermions) interacting by exchanging virtual particles called gauge bosons. This Standard Model of particle physics assumes a similarity between the forces and led scientists to predict the unification of the weak and electromagnetic forces in electroweak theory, which was subsequently confirmed by observation. The complete formulation of the Standard Model predicts an as yet unobserved Higgs mechanism, but observations such as neutrino oscillations suggest that the Standard Model is incomplete. A Grand Unified Theory that allows for the combination of the electroweak interaction with the strong force is held out as a possibility with candidate theories such as supersymmetry proposed to accommodate some of the outstanding unsolved problems in physics. Physicists are still attempting to develop self-consistent unification models that would combine all four fundamental interactions into a theory of everything. Einstein tried and failed at this endeavor, but currently the most popular approach to answering this question is string theory. Some forces are consequences of the fundamental ones. In such situations, idealized models can be utilized to gain physical insight. The normal force is due to repulsive forces of interaction between atoms at close contact. When their electron clouds overlap, Pauli repulsion (due to fermionic nature of electrons) follows resulting in the force that acts in a direction normal Friction is a surface force that opposes relative motion. The frictional force is directly related to the normal force that acts to keep two solid objects separated at the point of contact. There are two broad classifications of frictional forces: static friction and kinetic friction. The static friction force (formula_56) will exactly oppose forces applied to an object Tension forces can be modeled using ideal strings that are massless, frictionless, unbreakable, and unstretchable. They can be combined with ideal pulleys, which allow ideal strings to switch physical direction. Ideal strings transmit tension forces instantaneously in action-reaction pairs so that if two objects are connected by an ideal string, any force directed along the string by the first object is accompanied by a force directed along the string in the opposite direction by An elastic force acts to return a spring to its natural length. An ideal spring is taken to be massless, frictionless, unbreakable, and infinitely stretchable. Such springs exert forces that push when contracted, or pull when extended, in proportion to the displacement of the spring Newton's laws and Newtonian mechanics in general were first developed to describe how forces affect idealized point particles rather than three-dimensional objects. However, in real life, matter has extended structure and forces that act on one part of an object might affect other parts of an object. For situations where lattice holding together the atoms in an object is able to flow, contract, expand, or otherwise change shape, the theories of continuum mechanics describe the way forces affect the material. For example, in extended fluids, differences in pressure result in forces being directed along the pressure gradients as follows: where formula_67 is the volume of the object in the fluid and formula_68 is the scalar function that describes There are forces that are frame dependent, meaning that they appear due to the adoption of non-Newtonian (that is, non-inertial) reference frames. Such forces include the centrifugal force and the Coriolis force. These forces are considered fictitious because they do not exist in frames of reference Forces that cause extended objects to rotate are associated with torques. Mathematically, the torque of a force formula_51 is defined relative to an arbitrary reference point as the cross-product: where Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's First Law of Motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an unbalanced torque. Likewise, Newton's Second Law of Motion can be used to derive an analogous equation for the instantaneous angular acceleration of the rigid body: where This provides a definition for the moment of inertia, which is the rotational equivalent for mass. In more advanced treatments of mechanics, where the rotation over a time interval is described, the moment of inertia must be substituted by the tensor that, when properly analyzed, fully determines the characteristics of rotations including precession and nutation. Equivalently, the differential form of Newton's Second Law provides an alternative definition of torque: Newton's Third Law of Motion requires that all objects exerting torques themselves experience equal and opposite torques, and therefore also directly implies the conservation of angular momentum for closed systems that experience rotations and revolutions through the action of internal torques. For an object accelerating in circular motion, the unbalanced force acting on the object equals: where formula_21 is the mass of the object, formula_28 is the velocity of the object and formula_43 is the distance to the center of the circular path and formula_44 is the unit vector pointing in the radial direction outwards from the center. This means that the unbalanced centripetal force felt by any Forces can be used to define a number of physical concepts by integrating with respect to kinematic variables. For example, integrating with respect to time gives the definition of impulse: which by Newton's Second Law must be equivalent to the change in momentum (yielding Instead of a force, often the mathematically related concept of a potential energy field can be used for convenience. For instance, the gravitational force acting upon an object can be seen as the action of the gravitational field that is present at the object's location. Restating mathematically the definition of energy (via the definition of work), a potential scalar field formula_92 is defined as that field whose gradient is equal and opposite to the force produced at every point: Forces can be classified as conservative or nonconservative. Conservative forces are equivalent to the gradient of a potential while nonconservative forces are not. A conservative force that acts on a closed system has an associated mechanical work that allows energy to convert only between kinetic or potential forms. This means that for a closed system, the net mechanical energy is conserved whenever a conservative force acts on the system. The force, therefore, is related directly to the difference in potential energy between two different locations in space, and can be considered to be an artifact of the potential field in the same For certain physical scenarios, it is impossible to model forces as being due to gradient of potentials. This is often due to macrophysical considerations that yield forces as arising from a macroscopic statistical average of microstates. For example, friction is caused by the gradients of numerous electrostatic potentials between the atoms, but manifests as a force model that is independent of any macroscale position vector. Nonconservative forces other than friction include The SI unit of force is the newton (symbol N), which is the force required to accelerate a one kilogram mass at a rate of one meter per second squared, or. The corresponding CGS unit is the dyne, the force required to accelerate a one gram mass by one centimeter per second squared, or. A newton is thus equal to 100,000 dynes. The gravitational foot-pound-second English unit of force is the pound-force (lbf), defined as the force exerted by gravity on a pound-mass in the standard gravitational field of. The pound-force provides an alternative unit of mass: one slug is the mass that will accelerate by one foot per second squared when acted on by one pound-force. See force gauge, spring scale, load cell

In physics, a force is any interaction that, when unopposed, will change the motion of an object. A force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. It is measured in the SI unit of newtons and represented by the symbol F.

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summarize: For most substances, melting and freezing points are approximately equal. For example, the melting point "and" freezing point of mercury is 234.32 Kelvin (−38.83 °C or −37.89 °F). However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts at 85 °C (185 °F) and solidifies from ; such direction dependence is known as hysteresis. The melting point of ice at 1 atmosphere of pressure is very close to ; this is also known as the ice point. In the presence of nucleating substances, the freezing point of water is not always the same as the melting point. In the absence of nucleators water can exist as a supercooled liquid down to −48.3 °C (−55 °F, 224.8 K) before freezing. The chemical element with the highest melting point is tungsten, at ; this property makes tungsten excellent for use as filaments in light bulbs. The often-cited carbon does not melt at ambient pressure but sublimes at about ; a liquid phase only exists above pressures of and estimated (see ). Tantalum hafnium carbide (TaHfC) is a refractory compound with a very high melting point of 4215 K (3942 °C, 7128 °F). Quantum mechanical computer simulations have predicted that the alloy HfNC will have an even higher melting point (about 4400 K), which would make it the substance with the highest melting point at ambient pressure. This prediction was later confirmed by experiment. At the other end of the scale, helium does not freeze at all at normal pressure even at temperatures arbitrarily close to absolute zero; a pressure of more than twenty times normal atmospheric pressure is necessary. Many laboratory techniques exist for the determination of melting points. A Kofler bench is a metal strip with a temperature gradient (range from room temperature to 300 °C). Any substance can be placed on a section of the strip, revealing its thermal behaviour at the temperature at that point. Differential scanning calorimetry gives information on melting point together with its enthalpy of fusion. A basic melting point apparatus for the analysis of crystalline solids consists of an oil bath with a transparent window (most basic design: a Thiele tube) and a simple magnifier. Several grains of a solid are placed in a thin glass tube and partially immersed in the oil bath. The oil bath is heated (and stirred) and with the aid of the magnifier (and external light source) melting of the individual crystals at a certain temperature can be observed. A metal block might be used instead of an oil bath. Some modern instruments have automatic optical detection. The measurement can also be made continuously with an operating process. For instance, oil refineries measure the freeze point of diesel fuel "online", meaning that the sample is taken from the process and measured automatically. This allows for more frequent measurements as the sample does not have to be manually collected and taken to a remote laboratory. For refractory materials (e.g. platinum, tungsten, tantalum, some carbides and nitrides, etc.) the extremely high melting point (typically considered to be above, say, 1800 °C) may be determined by heating the material in a black body furnace and measuring the black-body temperature with an optical pyrometer. For the highest melting materials, this may require extrapolation by several hundred degrees. The spectral radiance from an incandescent body is known to be a function of its temperature. An optical pyrometer matches the radiance of a body under study to the radiance of a source that has been previously calibrated as a function of temperature. In this way, the measurement of the absolute magnitude of the intensity of radiation is unnecessary. However, known temperatures must be used to determine the calibration of the pyrometer. For temperatures above the calibration range of the source, an extrapolation technique must be employed. This extrapolation is accomplished by using Planck's law of radiation. The constants in this equation are not known with sufficient accuracy, causing errors in the extrapolation to become larger at higher temperatures. However, standard techniques have been developed to perform this extrapolation. Consider the case of using gold as the source (mp = 1063 °C). In this technique, the current through the filament of the pyrometer is adjusted until the light intensity of the filament matches that of a black-body at the melting point of gold. This establishes the primary calibration temperature and can be expressed in terms of current through the pyrometer lamp. With the same current setting, the pyrometer is sighted on another black-body at a higher temperature. An absorbing medium of known transmission is inserted between the pyrometer and this black-body. The temperature of the black-body is then adjusted until a match exists between its intensity and that of the pyrometer filament. The true higher temperature of the black-body is then determined from Planck's Law. The absorbing medium is then removed and the current through the filament is adjusted to match the filament intensity to that of the black-body. This establishes a second calibration point for the pyrometer. This step is repeated to carry the calibration to higher temperatures. Now, temperatures and their corresponding pyrometer filament currents are known and a curve of temperature versus current can be drawn. This curve can then be extrapolated to very high temperatures. In determining melting points of a refractory substance by this method, it is necessary to either have black body conditions or to know the emissivity of the material being measured. The containment of the high melting material in the liquid state may introduce experimental difficulties. Melting temperatures of some refractory metals have thus been measured by observing the radiation from a black body cavity in solid metal specimens that were much longer than they were wide. To form such a cavity, a hole is drilled perpendicular to the long axis at the center of a rod of the material. These rods are then heated by passing a very large current through them, and the radiation emitted from the hole is observed with an optical pyrometer. The point of melting is indicated by the darkening of the hole when the liquid phase appears, destroying the black body conditions. Today, containerless laser heating techniques, combined with fast pyrometers and spectro-pyrometers, are employed to allow for precise control of the time for which the sample is kept at extreme temperatures. Such experiments of sub-second duration address several of the challenges associated with more traditional melting point measurements made at very high temperatures, such as sample vaporization and reaction with the container. For a solid to melt, heat is required to raise its temperature to the melting point. However, further heat needs to be supplied for the melting to take place: this is called the heat of fusion, and is an example of latent heat. From a thermodynamics point of view, at the melting point the change in Gibbs free energy (ΔG) of the material is zero, but the enthalpy ("H") and the entropy ("S") of the material are increasing (ΔH, ΔS > 0). Melting phenomenon happens when the Gibbs free energy of the liquid becomes lower than the solid for that material. At various pressures this happens at a specific temperature. It can also be shown that: Here "T", "ΔS" and "ΔH" are respectively the temperature at the melting point, change of entropy of melting and the change of enthalpy of melting. The melting point is sensitive to extremely large changes in pressure, but generally this sensitivity is orders of magnitude less than that for the boiling point, because the solid-liquid transition represents only a small change in volume. If, as observed in most cases, a substance is more dense in the solid than in the liquid state, the melting point will increase with increases in pressure. Otherwise the reverse behavior occurs. Notably, this is the case of water, as illustrated graphically to the right, but also of Si, Ge, Ga, Bi. With extremely large changes in pressure, substantial changes to the melting point are observed. For example, the melting point of silicon at ambient pressure (0.1 MPa) is 1415 °C, but at pressures in excess of 10 GPa it decreases to 1000 °C. Melting points are often used to characterize organic and inorganic compounds and to ascertain their purity. The melting point of a pure substance is always higher and has a smaller range than the melting point of an impure substance or, more generally, of mixtures. The higher the quantity of other components, the lower the melting point and the broader will be the melting point range, often referred to as the "pasty range". The temperature at which melting begins for a mixture is known as the "solidus" while the temperature where melting is complete is called the "liquidus". Eutectics are special types of mixtures that behave like single phases. They melt sharply at a constant temperature to form a liquid of the same composition. Alternatively, on cooling a liquid with the eutectic composition will solidify as uniformly dispersed, small (fine-grained) mixed crystals with the same composition. In contrast to crystalline solids, glasses do not possess a melting point; on heating they undergo a smooth glass transition into a viscous liquid. Upon further heating, they gradually soften, which can be characterized by certain softening points. The freezing point of a solvent is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This phenomenon is used in technical applications to avoid freezing, for instance by adding salt or ethylene glycol to water. In organic chemistry, Carnelley's rule, established in 1882 by Thomas Carnelley, states that "high molecular symmetry is associated with high melting point". Carnelley based his rule on examination of 15,000 chemical compounds. For example, for three structural isomers with molecular formula CH the melting point increases in the series isopentane −160 °C (113 K) n-pentane −129.8 °C (143 K) and neopentane −16.4 °C (256.8 K). Likewise in xylenes and also dichlorobenzenes the melting point increases in the order meta, ortho and then para. Pyridine has a lower symmetry than benzene hence its lower melting point but the melting point again increases with diazine and triazines. Many cage-like compounds like adamantane and cubane with high symmetry have relatively high melting points. A high melting point results from a high heat of fusion, a low entropy of fusion, or a combination of both. In highly symmetrical molecules the crystal phase is densely packed with many efficient intermolecular interactions resulting in a higher enthalpy change on melting. An attempt to predict the bulk melting point of crystalline materials was first made in 1910 by Frederick Lindemann. The idea behind the theory was the observation that the average amplitude of thermal vibrations increases with increasing temperature. Melting initiates when the amplitude of vibration becomes large enough for adjacent atoms to partly occupy the same space. The Lindemann criterion states that melting is expected when the vibration root mean square amplitude exceeds a threshold value. Assuming that all atoms in a crystal vibrate with the same frequency "ν", the average thermal energy can be estimated using the equipartition theorem as where "m" is the atomic mass, "ν" is the frequency, "u" is the average vibration amplitude, "k" is the Boltzmann constant, and "T" is the absolute temperature. If the threshold value of "u" is "ca" where "c" is the Lindemann constant and "a" is the atomic spacing, then the melting point is estimated as Several other expressions for the estimated melting temperature can be obtained depending on the estimate of the average thermal energy. Another commonly used expression for the Lindemann criterion is From the expression for the Debye frequency for "ν", we have where "θ" is the Debye temperature and "h" is the Planck constant. Values of "c" range from 0.15–0.3 for most materials. In February 2011, Alfa Aesar released over 10,000 melting points of compounds from their catalog as open data. This dataset has been used to create a random forest model for melting point prediction which is now freely available. Open melting point data are also available from "Nature Precedings". High quality data mined from patents and also models developed with these data were published by Tetko "et al".

The melting point (or, rarely, liquefaction point) of a substance is the temperature at which it changes state from solid to liquid. At the melting point the solid and liquid phase exist in equilibrium. The melting point of a substance depends on pressure and is usually specified at a standard pressure such as 1 atmosphere or 100 kPa.

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summarize: Research into the various aspects of the history of interpreting is quite new. For as long as most scholarly interest was given to professional conference interpreting, very little academic work was done on the practice of interpreting in history, and until the 1990s, only a few dozen publications were done on it. Considering the amount of interpreting activities that is assumed to have occurred for thousands of years, historical records are limited. Moreover, interpreters and their work have usually not found their way into the history books. One of the reasons for that is the dominance of the written text over the spoken word (in the sense that those who have left written texts are more likely to be recorded by historians). Another problem is the tendency to view it as an ordinary support activity which does not require any special attention, and the social status of interpreters, who were sometimes treated unfairly by scribes, chroniclers and historians. Our knowledge of the past of interpreting tends to come from letters, chronicles, biographies, diaries and memoirs, along with a variety of other documents and literary works, many of which (and with few exceptions) were only incidentally or marginally related to interpreting. Many Indo-European languages have words for 'interpreting' and 'interpreter'. Expressions in Germanic, Scandinavian and Slavic languages denoting an interpreter can be traced back to Akkadian, around 1900 BCE. The Akkadian root "targumânu"/"turgumânu" also gave rise to the term dragoman via an etymological sideline from Arabic. The English word ‘interpreter’, however, is derived from Latin "interpres" (meaning ‘expounder’, ‘person explaining what is obscure’), whose semantic roots are not clear. Some scholars take the second part of the word to be derived from "partes" or "pretium" (meaning ‘price’, which fits the meaning of a ‘middleman’, ‘intermediary’ or ‘commercial go-between’), but others have suggested a Sanskrit root. In consecutive interpreting (CI), the interpreter starts to interpret after the speaker pauses. Therefore, the time needed is much longer (possibly double the time needed). Traditionally, the interpreter will sit or stand near the speaker. Consecutive interpretation can be conducted in a pattern of short or long segments according to the interpreter's preference. In short CI, the interpreter relies mostly on memory whereas, in long CI, most interpreters will rely on note-taking. The notes must be clear and legible in order to not waste time on reading them. Consecutive interpreting of whole thoughts, rather than in small pieces, is desirable so that the interpreter has the whole meaning before rendering it in the target language. This affords a truer, more accurate, and more accessible interpretation than where short CI or simultaneous interpretation is used. An attempt at consensus about lengths of segments may be reached prior to commencement, depending upon complexity of the subject matter and purpose of the interpretation, though speakers generally face difficulty adjusting to unnatural speech patterns. On occasion, document sight translation is required of the interpreter during consecutive interpretation work. Sight translation combines interpretation and translation; the interpreter must render the source-language document to the target-language as if it were written in the target language. Sight translation occurs usually, but not exclusively, in judicial and medical work. Consecutive interpretation may be the chosen mode when bilingual listeners are present who wish to hear both the original and interpreted speech or where, as in a court setting, a record must be kept of both. When no interpreter is available to interpret directly from source to target, an intermediate interpreter will be inserted in a relay mode, e.g. a Greek source language could be interpreted into English and then from English to another language. This is also commonly known as double-interpretation. Triple-interpretation may even be needed, particularly where rare languages or dialects are involved. Such interpretation can only be effectively conducted using consecutive interpretation. Simultaneous interpretation (SI) suffers the disadvantage that if a person is performing the service the interpreter must do the best he or she can within the time permitted by the pace of source speech. However they also have the advantages of saving time and not disturbing the natural flow of the speaker. SI can also be accomplished by software where the program can simultaneously listen to incoming speech and speak the associated interpretation. The most common form is extempore SI, where the interpreter does not know the message until he or she hears it. Simultaneous interpretation using electronic equipment where the interpreter can hear the speaker's voice as well as the interpreter's own voice was introduced at the Nuremberg trials in 1945. The equipment facilitated large numbers of listeners, and interpretation was offered in French, Russian, German and English. The technology arose in the 1920s and 1930s when American businessman Edward Filene and British engineer Alan Gordon Finlay developed simultaneous interpretation equipment with IBM. Yvonne Kapp attended a conference with simultaneous translation in 1935 in the Soviet Union. As it proved successful, IBM was able to sell the equipment to the United Nations, where it is now widely used in the United Nations Interpretation Service. In the ideal setting for oral language, the interpreter sits in a sound-proof booth and speaks into a microphone, while clearly seeing and hearing the source-language speaker via earphones. The simultaneous interpretation is rendered to the target-language listeners via their earphones. Pavel Palazchenko's "My Years with Gorbachev and Shevardnadze: The Memoir of a Soviet Interpreter" gives a short history of modern interpretation and of the transition from its consecutive to simultaneous forms. He explains that during the nineteenth century interpreters were rarely needed during European diplomatic discussions; these were routinely conducted in French, and all government diplomats were required to be fluent in this language. Most European government leaders and heads of state could also speak French. Historian Harold Nicolson attributes the growing need for interpretation after World War I to the fact that U.S. President Woodrow Wilson and British Prime Minister David Lloyd George "were no linguists". At the time, the concept and special equipment needed for simultaneous interpretation, later patented by Alan Gordon Finlay, had not been developed, so consecutive interpretation was used. Consecutive interpreters, in order be accurate, used a specialized system of note-taking which included symbols abbreviations and acronyms. Because they waited until the speaker was finished to provide translation, the interpreters then had the difficult task of creating from these notes as much as half an hour of free-flowing sentences closely matching the speaker's meaning. Palazchenko cites, Jean Herbert and the Kaminker brothers as skilled interpreters, and notes one unusual case in which André Kaminker interpreted a speech by a French diplomat who spoke for two and a half hours without stopping. After World War II, simultaneous interpretation came into use at the Nuremberg trial, and began to be more accepted. Experienced consecutive interpreters asserted that the difficulties of listening and speaking at the same time, adjusting for differences in sentence structure between languages, and interpreting the beginning of a sentence before hearing its end, would produce an inferior result. As well, these interpreters, who to that point had been prominent speakers, would now be speaking invisibly from booths. In 1951, when the United Nations expanded its number of working languages to five (English, French, Russian, Chinese and Spanish), consecutive translation became impractical in most cases, and simultaneous translation became the most common process for the organization's large meetings. Consecutive interpretation, which provides a more fluent result without the need for specialized equipment, continued to be used for smaller discussions. Since time immemorial, whispering interpretation has been used, known in the trade by the French term "chuchotage". To avoid disturbing the original speaker and those present listening to the original speaker, the interpreter's voice is kept at a low volume. To do this, the interpreter and the person requiring interpretation must sit or stand in close proximity to one another. No actual whispering is involved as this is difficult to decipher as well as being too much of a strain on the voice: the interpreter uses normal 'voiced' speech at a low volume. Only one or at the most two people in need of interpretation can be accommodated, unless portable electronic equipment is used. This form of interpretation puts a strain on the interpreter who has to sit for long periods leaning towards the person in need of interpretation. Conference interpreting refers to interpretation at a conference or large meeting, either simultaneously or consecutively. The advent of multi-lingual meetings has reduced the amount of consecutive interpretation in the last 20 years. Conference interpretation is divided between two markets: institutional and private. International institutions (EU, UN, EPO, et cetera), which hold multilingual meetings, often favor interpreting several foreign languages into the interpreters' mother tongues. Local private markets tend to have bilingual meetings (the local language plus another), and the interpreters work both into and out of their mother tongues. These markets are not mutually exclusive. The International Association of Conference Interpreters (AIIC) is the only worldwide association of conference interpreters. Founded in 1953, its membership includes more than 2,800 professional conference interpreters, in more than 90 countries. Judicial, legal, or court interpreting occurs in courts of justice, administrative tribunals, and wherever a legal proceeding is held (i.e., a police station for an interrogation, a conference room for a deposition, or the locale for taking a sworn statement). Legal interpreting can be the consecutive interpretation of witnesses' testimony, for example, or the simultaneous interpretation of entire proceedings, by electronic means, for one person, or all of the people attending. In a legal context, where ramifications of misinterpretation may be dire, accuracy is paramount. Teams of two or more interpreters, with one actively interpreting and the second monitoring for greater accuracy, may be deployed. The right to a competent interpreter for anyone who does not understand the language of the court (especially for the accused in a criminal trial) is usually considered a fundamental rule of justice. Therefore, this right is often guaranteed in national constitutions, declarations of rights, fundamental laws establishing the justice system or by precedents set by the highest courts. However, it is not a constitutionally required procedure (in the United States) that a certified interpreter be present at police interrogation. This has been especially controversial in cases where illegal immigrants with no English skills are accused of crimes. In the US, depending upon the regulations and standards adhered to per state and venue, court interpreters usually work alone when interpreting consecutively, or as a team, when interpreting simultaneously. In addition to practical mastery of the source and target languages, thorough knowledge of law and legal and court procedures is required of court interpreters. They are often required to have formal authorization from the state to work in the courts – and then are called certified court interpreters. In many jurisdictions, the interpretation is considered an essential part of the evidence. Incompetent interpretation, or simply failure to swear in the interpreter, can lead to a mistrial. In escort interpreting, an interpreter accompanies a person or a delegation on a tour, on a visit, or to a business meeting or interview. An interpreter in this role is called an "escort interpreter" or an "escorting interpreter". An escort interpreter’s work session may run for days, weeks, or even months, depending on the period of the client’s visit. This type of interpreting is often needed in business contexts, during presentations, investor meetings, and business negotiations. As such, and escort interpreter needs to be equipped with some business and financial knowledge in order to best understand and convey messages back and forth. Also known as community interpreting, is the type of interpreting occurring in fields such as legal, health, and federal and local government, social, housing, environmental health, education, and welfare services. In community interpreting, factors exist which determine and affect language and communication production, such as speech's emotional content, hostile or polarized social surroundings, its created stress, the power relationships among participants, and the interpreter's degree of responsibility – in many cases more than extreme; in some cases, even the life of the other person depends upon the interpreter's work. Medical interpreting is a subset of public service interpreting, consisting of communication among Healthcare personnel and the patient and their family or among Healthcare personnel speaking different languages, facilitated by an interpreter, usually formally educated and qualified to provide such interpretation services. In some situations medical employees who are multilingual may participate part-time as members of internal language banks. Depending on country/state specific requirements, the interpreter is often required to have some knowledge of medical terminology, common procedures, the patient interview and exam process. Medical interpreters are often cultural liaisons for people (regardless of language) who are unfamiliar with or uncomfortable in hospital, clinical, or medical settings. For example, in China, there is no mandatory certificate for medical interpreters as of 2012. Most interpretation in hospitals in China is done by doctors, who are proficient in both Chinese and English (mostly) in his/her specialty. They interpret more in academic settings than for communications between doctors and patients. When a patient needs English language service in a Chinese hospital, more often than not the patient will be directed to a staff member in the hospital, who is recognized by his/her colleagues as proficient in English. The actual quality of such service for patients or medical translation for communications between doctors speaking different languages is unknown by the interpreting community as interpreters who lack Healthcare background rarely receive accreditation for medical translation in the medical community. Interpreters working in the Healthcare setting may be considered Allied Health Professionals. In the United States, however, providing a Medical Interpreter is required by law. Title VI of the Civil Rights Act of 1964 prohibits discrimination on the basis of race, color, or national origin in any program or activity that receives Federal funds or other Federal financial assistance. Because hospitals are federally funded, they are required by this law to provide a professional interpreter to any patient that may need one. A sign language interpreter must accurately convey messages between two different languages. An interpreter is there for both deaf and hearing individuals. The act of interpreting occurs when a hearing person speaks, and an interpreter renders the speaker's meaning into sign language, or other forms used by the deaf party(ies). The interpreting also happens in reverse: when a deaf person signs, an interpreter renders the meaning expressed in the signs into the oral language for the hearing party, which is sometimes referred to as voice interpreting or "voicing". This may be performed either as simultaneous or consecutive interpreting. Skilled sign language interpreters will position themselves in a room or space that allows them to be seen by the deaf participants and heard clearly by hearing participants, as well as be in a position to hear and/or see the speaker or speakers clearly. In some circumstances, an interpreter may interpret from one language to another whether that is English to British Sign Language, English to American Sign Language, Spanish to English to American Sign Language and so on. Deaf individuals also have the opportunity to work as interpreters. If they are certified they are referred to as a CDI (Certified Deaf Interpreter), if not they would be called a DI (Deaf Interpreter). The Deaf individual will team with a hearing counterpart to provide interpretation for deaf individuals who may not know the same sign language used in that country, who have minimal language skills, are developmentally delayed, have other mental and/or physical disabilities which make communication a unique challenge, or request one. In other cases the hearing interpreter may interpret in the sign language, whichever kind of sign language the team knows and the deaf team will then interpret into the language in which the individual can understand. They also interpret information from one medium of language into another – for example, when a person is signing visually, the deaf interpreter could be hired to copy those signs into a deaf-blind person's hand and add visual information. Some interpreters have been formally trained in an Interpreter Training Program (ITP), though this is not always required. ITP lengths vary, and are usually two or four years to obtain a degree or certificate. Graduate programs are also available. In the United States, Sign Language interpreters have National and some states have a State level certifications. The Registry of Interpreters for the Deaf (RID), a non-profit organization, is known for its national recognition and certification process. In addition to training requirements and stringent certification testing, RID members must abide by a Code of Professional Conduct, Grievance Process and Continuing Education Requirement. There are many interpreter-training programs in the U.S. The Collegiate Commission on Interpreter Education is the body that accredits Interpreter Preparation Programs. A list of accredited programs can be found on the CCIE web site. European countries and countries elsewhere have their own national associations of Sign Language Interpreters. Some countries have more than one national association due to regional or language differences. The European Forum of Sign Language Interpreters (efsli) is the umbrella organization of sign language interpreters in Europe. In Canada, the professional association that recognizes and nationally certifies sign language interpreters is the Association of Visual Language Interpreters of Canada (AVLIC). Under AVLIC holds several affiliate chapters representing a specified region of Canada. Sign language interpreters encounter a number of linguistic, environmental, interpersonal and intrapersonal factors that can have an effect on their ability to provide accurate interpretation. Studies have found that most interpreter training programs do not sufficiently prepare students for the highly variable day-to-day stresses that an interpreter must manage, and there is an ongoing conversation in the interpreting field as to how to appropriately prepare students for the challenges of the job. Proposed changes include having a more robust definition of what a qualified interpreter should know, as well as a post-graduate internship structure that would allow new interpreters to work with the benefit of supervision from more experienced interpreters, much like the programs in place in medicine, law enforcement, etc. In Israel, Naama Weiss, a board member of Malach, the Organization of the Israeli Sign Language Interpreters, advertised a video which she produced. It was her paraphrase of the video "So-Low", and showed her viewpoint upon the Israeli Sign Language interpreters' jobs. A study which was made in Finland found that, in comparison to the foreign language teachers and non-linguistic experts, a high cooperativeness was found to be more characteristic to simultaneous and consecutive interpreters, and Weiss showed it in her video, although she claimed to be comic. By its very nature, media interpreting has to be conducted in the simultaneous mode. It is provided particularly for live television coverages such as press conferences, live or taped interviews with political figures, musicians, artists, sportsmen or people from the business circle. In this type of interpreting, the interpreter has to sit in a sound-proof booth where ideally he/she can see the speakers on a monitor and the set. All equipment should be checked before recording begins. In particular, satellite connections have to be double-checked to ensure that the interpreter's voice is not sent back and the interpreter gets to hear only one channel at a time. In the case of interviews recorded outside the studio and some current affairs program, the interpreter interprets what he or she hears on a TV monitor. Background noise can be a serious problem. The interpreter working for the media has to sound as slick and confident as a television presenter. Media interpreting has gained more visibility and presence especially after the Gulf War. Television channels have begun to hire staff simultaneous interpreters. The interpreter renders the press conferences, telephone beepers, interviews and similar live coverage for the viewers. It is more stressful than other types of interpreting as the interpreter has to deal with a wide range of technical problems coupled with the control room's hassle and wrangling during live coverage. Interpreting services can be delivered in multiple modalities. The most common modality through which interpreting services are provided is on-site interpreting. Also called "in-person interpreting" or sometimes colloquialized as "face-to-face", this delivery method requires the interpreter to be physically present in order for the interpretation to take place. In on-site interpreting settings, all of the parties who wish to speak to one another are usually located in the same place. This is by far the most common modality used for most public and social service settings. Also referred to as "over-the-phone interpreting," "telephonic interpreting," and "tele-interpreting," telephone interpreting enables interpretation via telephone. Telephone interpreting can be used in community settings as well as conference settings. Telephone interpreting may be used in place of on-site interpreting when no on-site interpreter is readily available at the location where services are needed. However, it is more commonly used for situations in which all parties who wish to communicate are already speaking to one another via telephone (e.g. telephone applications for insurance or credit cards, or telephone inquiries from consumers to businesses). Interpretation services via Video Remote Interpreting (VRI) or a Video Relay Service (VRS) are useful for spoken language barriers where visual-cultural recognition is relevant, and even more applicable where one of the parties is deaf, hard-of-hearing or speech-impaired (mute). In such cases the direction of interpretation is normally within the same principal language, such as French Sign Language (FSL) to spoken French and Spanish Sign Language (SSL) to spoken Spanish. Multilingual sign language interpreters, who can also translate as well across principal languages (such as to and from SSL, to and from spoken English), are also available, albeit less frequently. Such activities involve considerable effort on the part of the translator, since sign languages are distinct natural languages with their own construction and syntax, different from the aural version of the same principal language. With video interpreting, sign language interpreters work remotely with live video and audio feeds, so that the interpreter can see the deaf or mute party, converse with the hearing party and vice versa. Much like telephone interpreting, video interpreting can be used for situations in which no on-site interpreters are available. However, video interpreting cannot be used for situations in which all parties are speaking via telephone alone. VRI and VRS interpretation requires all parties to have the necessary equipment. Some advanced equipment enables interpreters to control the video camera, in order to zoom in and out, and to point the camera toward the party that is signing. The majority of professional full-time conference interpreters work for phone interpreting agencies, health care institutions, courts, school systems and international organizations like the United Nations, (for the United Nations Interpretation Service), the European Union, or the African Union. The world's largest employer of interpreters is currently the European Commission, which employs hundreds of staff and freelance interpreters working into the official languages of the European Union and some others. The European Union's other institutions (the European Parliament and the European Court of Justice) have smaller interpreting services. The United Nations employs interpreters at almost all its sites throughout the world. Because it has only six official languages, however, it is a smaller employer than the European Union. Interpreters may also work as freelance operators in their local, regional and national communities, or may take on contract work under an interpreting business or service. They would typically take on work as described above. Militaries often use interpreters to better communicate with the local population. One notable example is the US military during the war in Iraq and Afghanistan. There are a number of interpreting and translation associations around the world, including NAATI (National Accreditation Authority for Translators and Interpreters), AIIC (The International Association of Conference Interpreters), CATTI (China Accreditation Test for Translators and Interpreters), CTTIC (Canadian Translators, Terminologists and Interpreters Council), and the Institute of Translation & Interpreting, in the UK. No worldwide testing or certification agency exists for all types of interpreters. For conference interpretation, there is the International Association of Conference Interpreters, or AIIC. Specific regions, countries, or even cities will have their own certification standards. In many cases, graduates of a certain caliber university program acts as a de facto certification for conference interpretation. The most recognized interpretation & translation certificate in P.R.C. is China Accreditation Test for Translation and Interpretation, short for CATTI. It is entrusted by the Ministry of Human Resources and Social Security of P.R.C. It is a translation and interpretation professional qualification accreditation test which is implemented throughout the country according to uniform standards, in order to assess examinees' bilingual translation or interpretation capability. CATTI was introduced in 2003. In later 2013, translation and interpreting tests of different levels in English, French, Japanese, Russian, German, Spanish and Arabic were held across the nation. Those examinees who pass CATTI and obtain translation and interpretation certificates acquire corresponding translation and interpretation professional titles. Relevant institutions from Australia, France, Japan, the Republic of Korea, Singapore and other countries as well as Hong Kong Special Administrative Region and the region of Taiwan have established work ties with CATTI.

Interpreting is a translational activity in which one produces a first and final translation on the basis of a one-time exposure to an expression in a source language.

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summarize: In a solid, constituent particles (ions, atoms, or molecules) are closely packed together. The forces between particles are so strong that the particles cannot move freely but can only vibrate. As a result, a solid has a stable, definite shape, and a definite volume. Solids can only change their shape by an outside force, as when broken or cut. In crystalline solids, the particles (atoms, molecules, or ions) are packed in a regularly ordered, repeating pattern. There are various different crystal structures, and the same substance can have more than one structure (or solid phase). For example, iron has a body-centred cubic structure at temperatures below, and a face-centred cubic structure between 912 and. Ice has fifteen known crystal structures, or fifteen solid phases, which exist at various temperatures and pressures. Glasses and other non-crystalline, amorphous solids without long-range order are not thermal equilibrium ground states; therefore they are described below as nonclassical states of matter. Solids can be transformed into liquids by melting, and liquids can be transformed into solids by freezing. Solids can also change directly into gases through the process of sublimation, and gases can likewise change directly into solids through deposition. A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. The volume is definite if the temperature and pressure are constant. When a solid is heated above its melting point, it becomes liquid, given that the pressure is higher than the triple point of the substance. Intermolecular (or interatomic or interionic) forces are still important, but the molecules have enough energy to move relative to each other and the structure is mobile. This means that the shape of a liquid is not definite but is determined by its container. The volume is usually greater than that of the corresponding solid, the best known exception being water, HO. The highest temperature at which a given liquid can exist is its critical temperature. A gas is a compressible fluid. Not only will a gas conform to the shape of its container but it will also expand to fill the container. In a gas, the molecules have enough kinetic energy so that the effect of intermolecular forces is small (or zero for an ideal gas), and the typical distance between neighboring molecules is much greater than the molecular size. A gas has no definite shape or volume, but occupies the entire container in which it is confined. A liquid may be converted to a gas by heating at constant pressure to the boiling point, or else by reducing the pressure at constant temperature. At temperatures below its critical temperature, a gas is also called a vapor, and can be liquefied by compression alone without cooling. A vapor can exist in equilibrium with a liquid (or solid), in which case the gas pressure equals the vapor pressure of the liquid (or solid). A supercritical fluid (SCF) is a gas whose temperature and pressure are above the critical temperature and critical pressure respectively. In this state, the distinction between liquid and gas disappears. A supercritical fluid has the physical properties of a gas, but its high density confers solvent properties in some cases, which leads to useful applications. For example, supercritical carbon dioxide is used to extract caffeine in the manufacture of decaffeinated coffee. Like a gas, plasma does not have definite shape or volume. Unlike gases, plasmas are electrically conductive, produce magnetic fields and electric currents, and respond strongly to electromagnetic forces. Positively charged nuclei swim in a "sea" of freely-moving disassociated electrons, similar to the way such charges exist in conductive metal, where this electron "sea" allows matter in the plasma state to conduct electricity. A gas is usually converted to a plasma in one of two ways, e.g., either from a huge voltage difference between two points, or by exposing it to extremely high temperatures. Heating matter to high temperatures causes electrons to leave the atoms, resulting in the presence of free electrons. This creates a so-called partially ionised plasma. At very high temperatures, such as those present in stars, it is assumed that essentially all electrons are "free", and that a very high-energy plasma is essentially bare nuclei swimming in a sea of electrons. This forms the so-called fully ionised plasma. The plasma state is often misunderstood, and although not freely existing under normal conditions on Earth, it is quite commonly generated by either lightning, electric sparks, fluorescent lights, neon lights or in plasma televisions. The Sun's corona, some types of flame, and stars are all examples of illuminated matter in the plasma state. A state of matter is also characterized by phase transitions. A phase transition indicates a change in structure and can be recognized by an abrupt change in properties. A distinct state of matter can be defined as any set of states distinguished from any other set of states by a phase transition. Water can be said to have several distinct solid states. The appearance of superconductivity is associated with a phase transition, so there are superconductive states. Likewise, ferromagnetic states are demarcated by phase transitions and have distinctive properties. When the change of state occurs in stages the intermediate steps are called mesophases. Such phases have been exploited by the introduction of liquid crystal technology. The state or "phase" of a given set of matter can change depending on pressure and temperature conditions, transitioning to other phases as these conditions change to favor their existence; for example, solid transitions to liquid with an increase in temperature. Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point, boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons are so energized that they leave their parent atoms. Forms of matter that are not composed of molecules and are organized by different forces can also be considered different states of matter. Superfluids (like Fermionic condensate) and the quark–gluon plasma are examples. In a chemical equation, the state of matter of the chemicals may be shown as (s) for solid, (l) for liquid, and (g) for gas. An aqueous solution is denoted (aq). Matter in the plasma state is seldom used (if at all) in chemical equations, so there is no standard symbol to denote it. In the rare equations that plasma is used it is symbolized as (p). Glass is a non-crystalline or amorphous solid material that exhibits a glass transition when heated towards the liquid state. Glasses can be made of quite different classes of materials: inorganic networks (such as window glass, made of silicate plus additives), metallic alloys, ionic melts, aqueous solutions, molecular liquids, and polymers. Thermodynamically, a glass is in a metastable state with respect to its crystalline counterpart. The conversion rate, however, is practically zero. A plastic crystal is a molecular solid with long-range positional order but with constituent molecules retaining rotational freedom; in an orientational glass this degree of freedom is frozen in a quenched disordered state. Similarly, in a spin glass magnetic disorder is frozen. Liquid crystal states have properties intermediate between mobile liquids and ordered solids. Generally, they are able to flow like a liquid, but exhibiting long-range order. For example, the nematic phase consists of long rod-like molecules such as para-azoxyanisole, which is nematic in the temperature range. In this state the molecules flow as in a liquid, but they all point in the same direction (within each domain) and cannot rotate freely. Like a crystalline solid, but unlike a liquid, liquid crystals react to polarized light. Other types of liquid crystals are described in the main article on these states. Several types have technological importance, for example, in liquid crystal displays. Transition metal atoms often have magnetic moments due to the net spin of electrons that remain unpaired and do not form chemical bonds. In some solids the magnetic moments on different atoms are ordered and can form a ferromagnet, an antiferromagnet or a ferrimagnet. In a ferromagnet—for instance, solid iron—the magnetic moment on each atom is aligned in the same direction (within a magnetic domain). If the domains are also aligned, the solid is a permanent magnet, which is magnetic even in the absence of an external magnetic field. The magnetization disappears when the magnet is heated to the Curie point, which for iron is. An antiferromagnet has two networks of equal and opposite magnetic moments, which cancel each other out so that the net magnetization is zero. For example, in nickel(II) oxide (NiO), half the nickel atoms have moments aligned in one direction and half in the opposite direction. In a ferrimagnet, the two networks of magnetic moments are opposite but unequal, so that cancellation is incomplete and there is a non-zero net magnetization. An example is magnetite (FeO), which contains Fe and Fe ions with different magnetic moments. A quantum spin liquid (QSL) is a disordered state in a system of interacting quantum spins which preserves its disorder to very low temperatures, unlike other disordered states. It is not a liquid in physical sense, but a solid whose magnetic order is inherently disordered. The name "liquid" is due to an analogy with the molecular disorder in a conventional liquid. A QSL is neither a ferromagnet, where magnetic domains are parallel, nor an antiferromagnet, where the magnetic domains are antiparallel; instead, the magnetic domains are randomly oriented. This can be realized e.g. by geometrically frustrated magnetic moments that cannot point uniformly parallel or antiparallel. When cooling down and settling to a state, the domain must "choose" an orientation, but if the possible states are similar in energy, one will be chosen randomly. Consequently, despite strong short-range order, there is no long-range magnetic order. Copolymers can undergo microphase separation to form a diverse array of periodic nanostructures, as shown in the example of the styrene-butadiene-styrene block copolymer shown at right. Microphase separation can be understood by analogy to the phase separation between oil and water. Due to chemical incompatibility between the blocks, block copolymers undergo a similar phase separation. However, because the blocks are covalently bonded to each other, they cannot demix macroscopically as water and oil can, and so instead the blocks form nanometre-sized structures. Depending on the relative lengths of each block and the overall block topology of the polymer, many morphologies can be obtained, each its own phase of matter. Ionic liquids also display microphase separation. The anion and cation are not necessarily compatible and would demix otherwise, but electric charge attraction prevents them from separating. Their anions and cations appear to diffuse within compartmentalized layers or micelles instead of freely as in a uniform liquid. Close to absolute zero, some liquids form a second liquid state described as superfluid because it has zero viscosity (or infinite fluidity; i.e., flowing without friction). This was discovered in 1937 for helium, which forms a superfluid below the lambda temperature of. In this state it will attempt to "climb" out of its container. It also has infinite thermal conductivity so that no temperature gradient can form in a superfluid. Placing a superfluid in a spinning container will result in quantized vortices. These properties are explained by the theory that the common isotope helium-4 forms a Bose–Einstein condensate (see next section) in the superfluid state. More recently, Fermionic condensate superfluids have been formed at even lower temperatures by the rare isotope helium-3 and by lithium-6. In 1924, Albert Einstein and Satyendra Nath Bose predicted the "Bose–Einstein condensate" (BEC), sometimes referred to as the fifth state of matter. In a BEC, matter stops behaving as independent particles, and collapses into a single quantum state that can be described with a single, uniform wavefunction. In the gas phase, the Bose–Einstein condensate remained an unverified theoretical prediction for many years. In 1995, the research groups of Eric Cornell and Carl Wieman, of JILA at the University of Colorado at Boulder, produced the first such condensate experimentally. A Bose–Einstein condensate is "colder" than a solid. It may occur when atoms have very similar (or the same) quantum levels, at temperatures very close to absolute zero,. A "fermionic condensate" is similar to the Bose–Einstein condensate but composed of fermions. The Pauli exclusion principle prevents fermions from entering the same quantum state, but a pair of fermions can behave as a boson, and multiple such pairs can then enter the same quantum state without restriction. One of the metastable states of strongly non-ideal plasma is Rydberg matter, which forms upon condensation of excited atoms. These atoms can also turn into ions and electrons if they reach a certain temperature. In April 2009, "Nature" reported the creation of Rydberg molecules from a Rydberg atom and a ground state atom, confirming that such a state of matter could exist. The experiment was performed using ultracold rubidium atoms. A "quantum Hall state" gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow. A "quantum spin Hall state" is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat. This is a derivation of the Quantum Hall state of matter. Photonic matter is a phenomenon where photons interacting with a gas develop apparent mass, and can interact with each other, even forming photonic "molecules". The source of mass is the gas, which is massive. This is in contrast to photons moving in empty space, which have no rest mass, and cannot interact. A "quantum fog" of electrons and holes that flow around each other and even ripple like a liquid, rather than existing as discrete pairs. Under extremely high pressure, as in the cores of dead stars, ordinary matter undergoes a transition to a series of exotic states of matter collectively known as degenerate matter, which are supported mainly by quantum mechanical effects. In physics, "degenerate" refers to two states that have the same energy and are thus interchangeable. Degenerate matter is supported by the Pauli exclusion principle, which prevents two fermionic particles from occupying the same quantum state. Unlike regular plasma, degenerate plasma expands little when heated, because there are simply no momentum states left. Consequently, degenerate stars collapse into very high densities. More massive degenerate stars are smaller, because the gravitational force increases, but pressure does not increase proportionally. Electron-degenerate matter is found inside white dwarf stars. Electrons remain bound to atoms but are able to transfer to adjacent atoms. Neutron-degenerate matter is found in neutron stars. Vast gravitational pressure compresses atoms so strongly that the electrons are forced to combine with protons via inverse beta-decay, resulting in a superdense conglomeration of neutrons. Normally free neutrons outside an atomic nucleus will decay with a half life of just under 15 minutes, but in a neutron star, the decay is overtaken by inverse decay. Cold degenerate matter is also present in planets such as Jupiter and in the even more massive brown dwarfs, which are expected to have a core with metallic hydrogen. Because of the degeneracy, more massive brown dwarfs are not significantly larger. In metals, the electrons can be modeled as a degenerate gas moving in a lattice of non-degenerate positive ions. In regular cold matter, quarks, fundamental particles of nuclear matter, are confined by the strong force into hadrons that consist of 2–4 quarks, such as protons and neutrons. Quark matter or quantum chromodynanamical (QCD) matter is a group of phases where the strong force is overcome and quarks are deconfined and free to move. Quark matter phases occur at extremely high densities or temperatures, and there are no known ways to produce them in equilibrium in the laboratory; in ordinary conditions, any quark matter formed immediately undergoes radioactive decay. Strange matter is a type of quark matter that is suspected to exist inside some neutron stars close to the Tolman–Oppenheimer–Volkoff limit (approximately 2–3 solar masses), although there is no direct evidence of its existence. In strange matter, part of the energy available manifests as strange quarks, a heavier analogue of the common down quark. It may be stable at lower energy states once formed, although this is not known. Quark–gluon plasma is a very high-temperature phase in which quarks become free and able to move independently, rather than being perpetually bound into particles, in a sea of gluons, subatomic particles that transmit the strong force that binds quarks together. This is analogous to the liberation of electrons from atoms in a plasma. This state is briefly attainable in extremely high-energy heavy ion collisions in particle accelerators, and allows scientists to observe the properties of individual quarks, and not just theorize. Quark–gluon plasma was discovered at CERN in 2000. Unlike plasma, which flows like a gas, interactions within QGP are strong and it flows like a liquid. At high densities but relatively low temperatures, quarks are theorized to form a quark liquid whose nature is presently unknown. It forms a distinct color-flavor locked (CFL) phase at even higher densities. This phase is superconductive for color charge. These phases may occur in neutron stars but they are presently theoretical. Color-glass condensate is a type of matter theorized to exist in atomic nuclei traveling near the speed of light. According to Einstein's theory of relativity, a high-energy nucleus appears length contracted, or compressed, along its direction of motion. As a result, the gluons inside the nucleus appear to a stationary observer as a "gluonic wall" traveling near the speed of light. At very high energies, the density of the gluons in this wall is seen to increase greatly. Unlike the quark–gluon plasma produced in the collision of such walls, the color-glass condensate describes the walls themselves, and is an intrinsic property of the particles that can only be observed under high-energy conditions such as those at RHIC and possibly at the Large Hadron Collider as well. Various theories predict new states of matter at very high energies. An unknown state has created the baryon asymmetry in the universe, but little is known about it. In string theory, a Hagedorn temperature is predicted for superstrings at about 10 K, where superstrings are copiously produced. At Planck temperature (10 K), gravity becomes a significant force between individual particles. No current theory can describe these states and they cannot be produced with any foreseeable experiment. However, these states are important in cosmology because the universe may have passed through these states in the Big Bang. The gravitational singularity predicted by general relativity to exist at the center of a black hole is "not" a phase of matter; it is not a material object at all (although the mass-energy of matter contributed to its creation) but rather a property of spacetime at a location. It could be argued, of course, that all particles are properties of spacetime at a location, leaving a half-note of controversy on the subject. A supersolid is a spatially ordered material (that is, a solid or crystal) with superfluid properties. Similar to a superfluid, a supersolid is able to move without friction but retains a rigid shape. Although a supersolid is a solid, it exhibits so many characteristic properties different from other solids that many argue it is another state of matter. In a string-net liquid, atoms have apparently unstable arrangement, like a liquid, but are still consistent in overall pattern, like a solid. When in a normal solid state, the atoms of matter align themselves in a grid pattern, so that the spin of any electron is the opposite of the spin of all electrons touching it. But in a string-net liquid, atoms are arranged in some pattern that requires some electrons to have neighbors with the same spin. This gives rise to curious properties, as well as supporting some unusual proposals about the fundamental conditions of the universe itself. A superglass is a phase of matter characterized, at the same time, by superfluidity and a frozen amorphous structure.

In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates, neutron-degenerate matter, and quark–gluon plasma, which only occur, respectively, in situations of extreme cold, extreme density, and extremely high energy. For a complete list of all exotic states of matter, see the list of states of matter.

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summarize: To Isaac Newton, his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. When looking at the motion of many bodies all interacting with each other, such as the planets in the Solar System, dealing with the force between each pair of bodies separately rapidly becomes computationally inconvenient. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces. This quantity, the gravitational field, gave at each point in space the total gravitational acceleration which would be felt by a small object at that point. This did not change the physics in any way: it did not matter if all the gravitational forces on an object were calculated individually and then added together, or if all the contributions were first added together as a gravitational field and then applied to an object. The development of the independent concept of a field truly began in the nineteenth century with the development of the theory of electromagnetism. In the early stages, André-Marie Ampère and Charles-Augustin de Coulomb could manage with Newton-style laws that expressed the forces between pairs of electric charges or electric currents. However, it became much more natural to take the field approach and express these laws in terms of electric and magnetic fields; in 1849 Michael Faraday became the first to coin the term "field". The independent nature of the field became more apparent with James Clerk Maxwell's discovery that waves in these fields propagated at a finite speed. Consequently, the forces on charges and currents no longer just depended on the positions and velocities of other charges and currents at the same time, but also on their positions and velocities in the past. Maxwell, at first, did not adopt the modern concept of a field as a fundamental quantity that could independently exist. Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. If that were the case, the observed velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Despite much effort, no experimental evidence of such an effect was ever found; the situation was resolved by the introduction of the special theory of relativity by Albert Einstein in 1905. This theory changed the way the viewpoints of moving observers were related to each other. They became related to each other in such a way that velocity of electromagnetic waves in Maxwell's theory would be the same for all observers. By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities. In the late 1920s, the new rules of quantum mechanics were first applied to the electromagnetic field. In 1927, Paul Dirac used quantum fields to successfully explain how the decay of an atom to a lower quantum state led to the spontaneous emission of a photon, the quantum of the electromagnetic field. This was soon followed by the realization (following the work of Pascual Jordan, Eugene Wigner, Werner Heisenberg, and Wolfgang Pauli) that all particles, including electrons and protons, could be understood as the quanta of some quantum field, elevating fields to the status of the most fundamental objects in nature. That said, John Wheeler and Richard Feynman seriously considered Newton's pre-field concept of action at a distance (although they set it aside because of the ongoing utility of the field concept for research in general relativity and quantum electrodynamics). There are several examples of classical fields. Classical field theories remain useful wherever quantum properties do not arise, and can be active areas of research. Elasticity of materials, fluid dynamics and Maxwell's equations are cases in point. Some of the simplest physical fields are vector force fields. Historically, the first time that fields were taken seriously was with Faraday's lines of force when describing the electric field. The gravitational field was then similarly described. A classical field theory describing gravity is Newtonian gravitation, which describes the gravitational force as a mutual interaction between two masses. Any body with mass "M" is associated with a gravitational field g which describes its influence on other bodies with mass. The gravitational field of "M" at a point r in space corresponds to the ratio between force F that "M" exerts on a small or negligible test mass "m" located at r and the test mass itself: Stipulating that "m" is much smaller than "M" ensures that the presence of "m" has a negligible influence on the behavior of "M". According to Newton's law of universal gravitation, F(r) is given by where formula_3 is a unit vector lying along the line joining "M" and "m" and pointing from "M" to "m". Therefore, the gravitational field of M is The experimental observation that inertial mass and gravitational mass are equal to an unprecedented level of accuracy leads to the identity that gravitational field strength is identical to the acceleration experienced by a particle. This is the starting point of the equivalence principle, which leads to general relativity. Because the gravitational force F is conservative, the gravitational field g can be rewritten in terms of the gradient of a scalar function, the gravitational potential Φ(r): Michael Faraday first realized the importance of a field as a physical quantity, during his investigations into magnetism. He realized that electric and magnetic fields are not only fields of force which dictate the motion of particles, but also have an independent physical reality because they carry energy. These ideas eventually led to the creation, by James Clerk Maxwell, of the first unified field theory in physics with the introduction of equations for the electromagnetic field. The modern version of these equations is called Maxwell's equations. A charged test particle with charge "q" experiences a force F based solely on its charge. We can similarly describe the electric field E so that. Using this and Coulomb's law tells us that the electric field due to a single charged particle is The electric field is conservative, and hence can be described by a scalar potential, "V"(r): A steady current "I" flowing along a path "l" will create a field B, that exerts a force on nearby moving charged particles that is quantitatively different from the electric field force described above. The force exerted by "I" on a nearby charge "q" with velocity v is where B(r) is the magnetic field, which is determined from "I" by the Biot–Savart law: The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential. However, it can be written in terms of a vector potential, A(r): In general, in the presence of both a charge density ρ(r, "t") and current density J(r, "t"), there will be both an electric and a magnetic field, and both will vary in time. They are determined by Maxwell's equations, a set of differential equations which directly relate E and B to ρ and J. Alternatively, one can describe the system in terms of its scalar and vector potentials "V" and A. A set of integral equations known as "retarded potentials" allow one to calculate "V" and A from ρ and J, and from there the electric and magnetic fields are determined via the relations At the end of the 19th century, the electromagnetic field was understood as a collection of two vector fields in space. Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in space-time. Einstein's theory of gravity, called general relativity, is another example of a field theory. Here the principal field is the metric tensor, a symmetric 2nd-rank tensor field in space-time. This replaces Newton's law of universal gravitation. Waves can be constructed as physical fields, due to their finite propagation speed and causal nature when a simplified physical model of an isolated closed system is set. They are also subject to the inverse-square law. For electromagnetic waves, there are optical fields, and terms such as near- and far-field limits for diffraction. In practice though, the field theories of optics are superseded by the electromagnetic field theory of Maxwell. It is now believed that quantum mechanics should underlie all physical phenomena, so that a classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory. For example, quantizing classical electrodynamics gives quantum electrodynamics. Quantum electrodynamics is arguably the most successful scientific theory; experimental data confirm its predictions to a higher precision (to more significant digits) than any other theory. The two other fundamental quantum field theories are quantum chromodynamics and the electroweak theory. In quantum chromodynamics, the color field lines are coupled at short distances by gluons, which are polarized by the field and line up with it. This effect increases within a short distance (around 1 fm from the vicinity of the quarks) making the color force increase within a short distance, confining the quarks within hadrons. As the field lines are pulled together tightly by gluons, they do not "bow" outwards as much as an electric field between electric charges. These three quantum field theories can all be derived as special cases of the so-called standard model of particle physics. General relativity, the Einsteinian field theory of gravity, has yet to be successfully quantized. However an extension, thermal field theory, deals with quantum field theory at "finite temperatures", something seldom considered in quantum field theory. In BRST theory one deals with odd fields, e.g. Faddeev–Popov ghosts. There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. As above with classical fields, it is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. The equations governing the quantum fields are in fact PDEs (specifically, relativistic wave equations (RWEs)). Thus one can speak of Yang–Mills, Dirac, Klein–Gordon and Schrödinger fields as being solutions to their respective equations. A possible problem is that these RWEs can deal with complicated mathematical objects with exotic algebraic properties (e.g. spinors are not tensors, so may need calculus for spinor fields), but these in theory can still be subjected to analytical methods given appropriate mathematical generalization. Field theory usually refers to a construction of the dynamics of a field, i.e. a specification of how a field changes with time or with respect to other independent physical variables on which the field depends. Usually this is done by writing a Lagrangian or a Hamiltonian of the field, and treating it as a classical or quantum mechanical system with an infinite number of degrees of freedom. The resulting field theories are referred to as classical or quantum field theories. The dynamics of a classical field are usually specified by the Lagrangian density in terms of the field components; the dynamics can be obtained by using the action principle. It is possible to construct simple fields without any prior knowledge of physics using only mathematics from several variable calculus, potential theory and partial differential equations (PDEs). For example, scalar PDEs might consider quantities such as amplitude, density and pressure fields for the wave equation and fluid dynamics; temperature/concentration fields for the heat/diffusion equations. Outside of physics proper (e.g., radiometry and computer graphics), there are even light fields. All these previous examples are scalar fields. Similarly for vectors, there are vector PDEs for displacement, velocity and vorticity fields in (applied mathematical) fluid dynamics, but vector calculus may now be needed in addition, being calculus for vector fields (as are these three quantities, and those for vector PDEs in general). More generally problems in continuum mechanics may involve for example, directional elasticity (from which comes the term "tensor", derived from the Latin word for stretch), complex fluid flows or anisotropic diffusion, which are framed as matrix-tensor PDEs, and then require matrices or tensor fields, hence matrix or tensor calculus. The scalars (and hence the vectors, matrices and tensors) can be real or complex as both are fields in the abstract-algebraic/ring-theoretic sense. In a general setting, classical fields are described by sections of fiber bundles and their dynamics is formulated in the terms of jet manifolds (covariant classical field theory). In modern physics, the most often studied fields are those that model the four fundamental forces which one day may lead to the Unified Field Theory. A convenient way of classifying a field (classical or quantum) is by the symmetries it possesses. Physical symmetries are usually of two types: Fields are often classified by their behaviour under transformations of space-time. The terms used in this classification are: Fields may have internal symmetries in addition to space-time symmetries. In many situations, one needs fields which are a list of space-time scalars: (φ, φ,... φ). For example, in weather prediction these may be temperature, pressure, humidity, etc. In particle physics, the color symmetry of the interaction of quarks is an example of an internal symmetry, that of the strong interaction. Other examples are isospin, weak isospin, strangeness and any other flavour symmetry. If there is a symmetry of the problem, not involving space-time, under which these components transform into each other, then this set of symmetries is called an "internal symmetry". One may also make a classification of the charges of the fields under internal symmetries. Statistical field theory attempts to extend the field-theoretic paradigm toward many-body systems and statistical mechanics. As above, it can be approached by the usual infinite number of degrees of freedom argument. Much like statistical mechanics has some overlap between quantum and classical mechanics, statistical field theory has links to both quantum and classical field theories, especially the former with which it shares many methods. One important example is mean field theory. Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable functions, but they are in any case almost always twice differentiable. In contrast, generalized functions are not continuous. When dealing carefully with classical fields at finite temperature, the mathematical methods of continuous random fields are used, because thermally fluctuating classical fields are nowhere differentiable. Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions as its index set. In particular, it is often mathematically convenient to take a continuous random field to have a Schwartz space of functions as its index set, in which case the continuous random field is a tempered distribution. We can think about a continuous random field, in a (very) rough way, as an ordinary function that is formula_13 almost everywhere, but such that when we take a weighted average of all the infinities over any finite region, we get a finite result. The infinities are not well-defined; but the finite values can be associated with the functions used as the weight functions to get the finite values, and that can be well-defined. We can define a continuous random field well enough as a linear map from a space of functions into the real numbers.

In physics, a field is a physical quantity, represented by a number or tensor, that has a value for each point in space-time. For example, on a weather map, the surface temperature is described by assigning a real number to each point on a map; the temperature can be considered at a fixed point in time or over some time interval, to study the dynamics of temperature change. A surface wind map, assigning a vector to each point on a map that describes the wind velocity at that point, would be an example of a 1-dimensional tensor field, i.e. a vector field. Field theories, mathematical descriptions of how field values change in space and time, are ubiquitous in physics. For instance, the electric field is another rank-1 tensor field, and the full description of electrodynamics can be formulated in terms of two interacting vector fields at each point in space-time, or as a single-rank 2-tensor field theory.

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summarize: In the hydraulic analogy, current flowing through a wire (or resistor) is like water flowing through a pipe, and the voltage drop across the wire is like the pressure drop that pushes water through the pipe. Conductance is proportional to how much flow occurs for a given pressure, and resistance is proportional to how much pressure is required to achieve a given flow. (Conductance and resistance are reciprocals.) The voltage drop (i.e., difference between voltages on one side of the resistor and the other), not the voltage itself, provides the driving force pushing current through a resistor. In hydraulics, it is similar: The pressure difference between two sides of a pipe, not the pressure itself, determines the flow through it. For example, there may be a large water pressure above the pipe, which tries to push water down through the pipe. But there may be an equally large water pressure below the pipe, which tries to push water back up through the pipe. If these pressures are equal, no water flows. (In the image at right, the water pressure below the pipe is zero.) The resistance and conductance of a wire, resistor, or other element is mostly determined by two properties: Geometry is important because it is more difficult to push water through a long, narrow pipe than a wide, short pipe. In the same way, a long, thin copper wire has higher resistance (lower conductance) than a short, thick copper wire. Materials are important as well. A pipe filled with hair restricts the flow of water more than a clean pipe of the same shape and size. Similarly, electrons can flow freely and easily through a copper wire, but cannot flow as easily through a steel wire of the same shape and size, and they essentially cannot flow at all through an insulator like rubber, regardless of its shape. The difference between copper, steel, and rubber is related to their microscopic structure and electron configuration, and is quantified by a property called resistivity. In addition to geometry and material, there are various other factors that influence resistance and conductance, such as temperature; see below. Substances in which electricity can flow are called conductors. A piece of conducting material of a particular resistance meant for use in a circuit is called a resistor. Conductors are made of high-conductivity materials such as metals, in particular copper and aluminium. Resistors, on the other hand, are made of a wide variety of materials depending on factors such as the desired resistance, amount of energy that it needs to dissipate, precision, and costs. For many materials, the current "I" through the material is proportional to the voltage "V" applied across it: over a wide range of voltages and currents. Therefore, the resistance and conductance of objects or electronic components made of these materials is constant. This relationship is called Ohm's law, and materials which obey it are called "ohmic" materials. Examples of ohmic components are wires and resistors. The current–voltage graph of an ohmic device consists of a straight line through the origin with positive slope. Other components and materials used in electronics do not obey Ohm's law; the current is not proportional to the voltage, so the resistance varies with the voltage and current through them. These are called "nonlinear" or "nonohmic". Examples include diodes and fluorescent lamps. The current-voltage curve of a nonohmic device is a curved line. The resistance of a given object depends primarily on two factors: What material it is made of, and its shape. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The resistance and conductance of a conductor of uniform cross section, therefore, can be computed as where formula_5 is the length of the conductor, measured in metres (m), "A" is the cross-sectional area of the conductor measured in square metres (m2), σ (sigma) is the electrical conductivity measured in siemens per meter (S·m), and ρ (rho) is the electrical resistivity (also called "specific electrical resistance") of the material, measured in ohm-metres (Ω·m). The resistivity and conductivity are proportionality constants, and therefore depend only on the material the wire is made of, not the geometry of the wire. Resistivity and conductivity are reciprocals: formula_6. Resistivity is a measure of the material's ability to oppose electric current. This formula is not exact, as it assumes the current density is totally uniform in the conductor, which is not always true in practical situations. However, this formula still provides a good approximation for long thin conductors such as wires. Another situation for which this formula is not exact is with alternating current (AC), because the skin effect inhibits current flow near the center of the conductor. For this reason, the "geometrical" cross-section is different from the "effective" cross-section in which current actually flows, so resistance is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the proximity effect. At commercial power frequency, these effects are significant for large conductors carrying large currents, such as busbars in an electrical substation, or large power cables carrying more than a few hundred amperes. The resistivity of different materials varies by an enormous amount: For example, the conductivity of teflon is about 10 times lower than the conductivity of copper. Loosely speaking, this is because metals have large numbers of "delocalized" electrons that are not stuck in any one place, so they are free to move across large distances. In an insulator, such as Teflon, each electron is tightly bound to a single molecule so a great force is required to pull it away. Semiconductors lie between these two extremes. More details can be found in the article: Electrical resistivity and conductivity. For the case of electrolyte solutions, see the article: Conductivity (electrolytic). Resistivity varies with temperature. In semiconductors, resistivity also changes when exposed to light. See below. An instrument for measuring resistance is called an ohmmeter. Simple ohmmeters cannot measure low resistances accurately because the resistance of their measuring leads causes a voltage drop that interferes with the measurement, so more accurate devices use four-terminal sensing. Many electrical elements, such as diodes and batteries do "not" satisfy Ohm's law. These are called "non-ohmic" or "non-linear", and their current–voltage curves are "not" straight lines through the origin. Resistance and conductance can still be defined for non-ohmic elements. However, unlike ohmic resistance, non-linear resistance is not constant but varies with the voltage or current through the device; i.e., its operating point. There are two types of resistance: When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their phases. For example, in an ideal resistor, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a capacitor or inductor, the maximum current flow occurs as the voltage passes through zero and vice versa (current and voltage are oscillating 90° out of phase, see image below). Complex numbers are used to keep track of both the phase and magnitude of current and voltage: where: The impedance and admittance may be expressed as complex numbers that can be broken into real and imaginary parts: where "R" and "G" are resistance and conductance respectively, "X" is reactance, and "B" is susceptance. For ideal resistors, "Z" and "Y" reduce to "R" and "G" respectively, but for AC networks containing capacitors and inductors, "X" and "B" are nonzero. formula_12 for AC circuits, just as formula_13 for DC circuits. A key feature of AC circuits is that the resistance and conductance can be frequency-dependent, a phenomenon known as the universal dielectric response. One reason, mentioned above is the skin effect (and the related proximity effect). Another reason is that the resistivity itself may depend on frequency (see Drude model, deep-level traps, resonant frequency, Kramers–Kronig relations, etc.) Resistors (and other elements with resistance) oppose the flow of electric current; therefore, electrical energy is required to push current through the resistance. This electrical energy is dissipated, heating the resistor in the process. This is called "Joule heating" (after James Prescott Joule), also called "ohmic heating" or "resistive heating". The dissipation of electrical energy is often undesired, particularly in the case of transmission losses in power lines. High voltage transmission helps reduce the losses by reducing the current for a given power. On the other hand, Joule heating is sometimes useful, for example in electric stoves and other electric heaters (also called "resistive heaters"). As another example, incandescent lamps rely on Joule heating: the filament is heated to such a high temperature that it glows "white hot" with thermal radiation (also called incandescence). The formula for Joule heating is: where "P" is the power (energy per unit time) converted from electrical energy to thermal energy, "R" is the resistance, and "I" is the current through the resistor. Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system. For the detailed behavior and explanation, see Electrical resistivity and conductivity. As a consequence, the resistance of wires, resistors, and other components often change with temperature. This effect may be undesired, causing an electronic circuit to malfunction at extreme temperatures. In some cases, however, the effect is put to good use. When temperature-dependent resistance of a component is used purposefully, the component is called a resistance thermometer or thermistor. (A resistance thermometer is made of metal, usually platinum, while a thermistor is made of ceramic or polymer.) Resistance thermometers and thermistors are generally used in two ways. First, they can be used as thermometers: By measuring the resistance, the temperature of the environment can be inferred. Second, they can be used in conjunction with Joule heating (also called self-heating): If a large current is running through the resistor, the resistor's temperature rises and therefore its resistance changes. Therefore, these components can be used in a circuit-protection role similar to fuses, or for feedback in circuits, or for many other purposes. In general, self-heating can turn a resistor into a nonlinear and hysteretic circuit element. For more details see Thermistor#Self-heating effects. If the temperature "T" does not vary too much, a linear approximation is typically used: where formula_16 is called the "temperature coefficient of resistance", formula_17 is a fixed reference temperature (usually room temperature), and formula_18 is the resistance at temperature formula_17. The parameter formula_16 is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, formula_16 is different for different reference temperatures. For this reason it is usual to specify the temperature that formula_16 was measured at with a suffix, such as formula_23, and the relationship only holds in a range of temperatures around the reference. The temperature coefficient formula_16 is typically +3×10 K to +6×10 K for metals near room temperature. It is usually negative for semiconductors and insulators, with highly variable magnitude. Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain. By placing a conductor under tension (a form of stress that leads to strain in the form of stretching of the conductor), the length of the section of conductor under tension increases and its cross-sectional area decreases. Both these effects contribute to increasing the resistance of the strained section of conductor. Under compression (strain in the opposite direction), the resistance of the strained section of conductor decreases. See the discussion on strain gauges for details about devices constructed to take advantage of this effect. Some resistors, particularly those made from semiconductors, exhibit "photoconductivity", meaning that their resistance changes when light is shining on them. Therefore, they are called "photoresistors" (or "light dependent resistors"). These are a common type of light detector. Superconductors are materials that have exactly zero resistance and infinite conductance, because they can have V = 0 and I ≠ 0. This also means there is no joule heating, or in other words no dissipation of electrical energy. Therefore, if superconductive wire is made into a closed loop, current flows around the loop forever. Superconductors require cooling to temperatures near 4K with liquid helium for most metallic superconductors like niobium–tin alloys, or cooling to temperatures near 77K with liquid nitrogen for the expensive, brittle and delicate ceramic high temperature superconductors. Nevertheless, there are many technological applications of superconductivity, including superconducting magnets.

In electronics and electromagnetism, the electrical resistance of an object is a measure of its opposition to the flow of electric current. The inverse quantity is, and is the ease with which an electric current passes. Electrical resistance shares some conceptual parallels with the notion of mechanical friction. The SI unit of electrical resistance is the ohm (Ω), while electrical conductance is measured in siemens (S).

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summarize: Even amorphous materials have some shortrange order at the atomic length scale due to the nature of chemical bonding (see structure of liquids and glasses for more information on non-crystalline material structure). Furthermore, in very small crystals a large fraction of the atoms are the crystal; relaxation of the surface and interfacial effects distort the atomic positions, decreasing the structural order. Even the most advanced structural characterization techniques, such as x-ray diffraction and transmission electron microscopy, have difficulty in distinguishing between amorphous and crystalline structures on these length scales. Amorphous phases are important constituents of thin films, which are solid layers of a few nanometres to some tens of micrometres thickness deposited upon a substrate. So-called structure zone models were developed to describe the micro structure and ceramics of thin films as a function of the homologous temperature "T" that is the ratio of deposition temperature over melting temperature. According to these models, a necessary (but not sufficient) condition for the occurrence of amorphous phases is that "T" has to be smaller than 0.3, that is the deposition temperature must be below 30% of the melting temperature. For higher values, the surface diffusion of deposited atomic species would allow for the formation of crystallites with long range atomic order. Regarding their applications, amorphous metallic layers played an important role in the discovery of superconductivity in amorphous metals by Buckel and Hilsch. The superconductivity of amorphous metals, including amorphous metallic thin films, is now understood to be due to phonon-mediated Cooper pairing, and the role of structural disorder can be rationalized based on the strong-coupling Eliashberg theory of superconductivity. Today, optical coatings made from TiO, SiO, TaO etc. and combinations of them in most cases consist of amorphous phases of these compounds. Much research is carried out into thin amorphous films as a gas separating membrane layer. The technologically most important thin amorphous film is probably represented by few nm thin SiO layers serving as isolator above the conducting channel of a metal-oxide semiconductor field-effect transistor (MOSFET). Also, hydrogenated amorphous silicon, a-Si:H in short, is of technical significance for thin-film solar cells. In case of a-Si:H the missing long-range order between silicon atoms is partly induced by the presence by hydrogen in the percent range. The occurrence of amorphous phases turned out as a phenomenon of particular interest for studying thin-film growth. Remarkably, the growth of polycrystalline films is often used and preceded by an initial amorphous layer, the thickness of which may amount to only a few nm. The most investigated example is represented by thin multicrystalline silicon films, where such as the unoriented molecule. An initial amorphous layer was observed in many studies. Wedge-shaped polycrystals were identified by transmission electron microscopy to grow out of the amorphous phase only after the latter has exceeded a certain thickness, the precise value of which depends on deposition temperature, background pressure and various other process parameters. The phenomenon has been interpreted in the framework of Ostwald's rule of stages that predicts the formation of phases to proceed with increasing condensation time towards increasing stability. Experimental studies of the phenomenon require a clearly defined state of the substrate surface and its contaminant density etc., upon which the thin film is deposited.

In condensed matter physics and materials science, an amorphous (from the Greek "a", without, "morphé", shape, form) or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal. In some older books, the term has been used synonymously with glass. Nowadays, "glassy solid" or "amorphous solid" is considered to be the overarching concept, and glass the more special case: Glass is an amorphous solid that exhibits a glass transition. Polymers are often amorphous. Other types of amorphous solids include gels, thin films, and nanostructured materials such as glass. Amorphous materials have an internal structure made of interconnected structural blocks. These blocks can be similar to the basic structural units found in the corresponding crystalline phase of the same compound. Whether a material is liquid or solid depends primarily on the connectivity between its elementary building blocks so that solids are characterized by a high degree of connectivity whereas structural blocks in fluids have lower connectivity.

en

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summarize: EU citizenship was first introduced by the Maastricht Treaty, and was extended by the Treaty of Amsterdam. Prior to the 1992 Maastricht Treaty, the European Communities treaties provided guarantees for the free movement of economically active persons, but not, generally, for others. The 1951 Treaty of Paris establishing the European Coal and Steel Community established a right to free movement for workers in these industries and the 1957 Treaty of Rome provided for the free movement of workers and services. However, the treaty provisions were interpreted by the European Court of Justice not as having a narrow economic purpose, but rather a wider social and economic purpose. In "Levin", the Court found that the "freedom to take up employment was important, not just as a means towards the creation of a single market for the benefit of the member state economies, but as a right for the worker to raise her or his standard of living". Under the ECJ caselaw, the rights of free movement of workers applies regardless of the worker's purpose in taking up employment abroad, to both part-time and full-time work, and whether or not the worker required additional financial assistance from the member state into which he moves. Since the ECJ has held that a recipient of service has free movement rights under the treaty and this criterion is easily fulfilled, effectively every national of an EU country within another member state, whether economically active or not, had a right under Article 12 of the European Community Treaty to non-discrimination even prior to the Maastricht Treaty. In the case of "Martinez Sala", the European Court of Justice held that the citizenship provisions provided substantive equal treatment rights alongside those already granted by union law. The case of Baumbast later established that the right to equal treatment applies equally to both economically active and inactive citizens. Despite these broad interpretations, the landmark case of Dano combined the criteria of freedom to move and equal treatment, citing them as inter-dependant, subsequently limiting the scope of Martinez Sala. Historically, the main benefit of being a citizen of an EU state has been that of free movement. The free movement also applies to the citizens of European Economic Area countries and Switzerland. However, with the creation of EU citizenship, certain political rights came into being. The Treaty on the Functioning of the European Union provides for citizens to be "directly represented at Union level in the European Parliament" and "to participate in the democratic life of the Union" (Treaty on the European Union, Title II, Article 10). Specifically, the following rights are afforded: Article 21 (1) of the Treaty on the Functioning of the European Union states that Every citizen of the Union shall have the right to move and reside freely within the territory of the Member States, subject to the limitations and conditions laid down in this Treaty and by the measures adopted to give it effect. The European Court of Justice has remarked that, EU Citizenship is destined to be the fundamental status of nationals of the Member States The ECJ has held that this Article confers a directly effective right upon citizens to reside in another Member State. Before the case of "Baumbast", it was widely assumed that non-economically active citizens had no rights to residence deriving directly from the EU Treaty, only from directives created under the Treaty. In "Baumbast", however, the ECJ held that (the then) Article 18 of the EC Treaty granted a generally applicable right to residency, which is limited by secondary legislation, but "only" where that secondary legislation is proportionate. Member States can distinguish between nationals and Union citizens but only if the provisions satisfy the test of proportionality. Migrant EU citizens have a "legitimate expectation of a limited degree of financial solidarity... having regard to their degree of integration into the host society" Length of time is a particularly important factor when considering the degree of integration. The ECJ's case law on citizenship has been criticised for subjecting an increasing number of national rules to the proportionality assessment. Article 45 of the Treaty on the Functioning of the European Union states that 1. Freedom of movement for workers shall be secured within the Union.2. Such freedom of movement shall entail the abolition of any discrimination based on nationality between workers of the Member States as regards employment, remuneration and other conditions of work and employment. State employment reserved exclusively for nationals varies between member states. For example, training as a barrister in Britain and Ireland is not reserved for nationals, while the corresponding French course qualifies one as a 'juge' and hence can only be taken by French citizens. However, it is broadly limited to those roles that exercise a significant degree of public authority, such as judges, police, the military, diplomats, senior civil servants or politicians. Note that not all Member States choose to restrict all of these posts to nationals. Much of the existing secondary legislation and case law was consolidated in the Citizens' Rights Directive 2004/38/EC on the right to move and reside freely within the EU. New member states may undergo transitional regimes for Freedom of movement for workers, during which their nationals only enjoy restricted access to labour markets in other member states. EU member states are permitted to keep restrictions on citizens of the newly acceded countries for a maximum of seven years after accession. For the EFTA states (Iceland, Lichtenstein, Norway and Switzerland), the maximum is nine years. Following the 2004 enlargement, three "old" member states—Ireland, Sweden and the United Kingdom—decided to allow unrestricted access to their labour markets. By December 2009, all but two member states—Austria and Germany—had completely dropped controls. These restrictions too expired on 1 May 2011. Following the 2007 enlargement, all pre-2004 member states except Finland and Sweden imposed restrictions on Bulgarian and Romanian citizens, as did two member states that joined in 2004: Malta and Hungary. As of November 2012, all but 8 EU countries have dropped restrictions entirely. These restrictions too expired on 1 January 2014. Norway opened its labour market in June 2012, while Switzerland kept restrictions in place until 2016. Following the 2013 enlargement, some countries implemented restrictions on Croatian nationals following the country's EU accession on 1 July 2013. As of May 2019, all EU countries except Austria have dropped restrictions entirely., the Austrian restrictions are set to expire on 1 July 2020. There is no common EU policy on the acquisition of European citizenship as it is supplementary to national citizenship. (EC citizenship was initially granted to all citizens of European Community member states in 1994 by the Maastricht treaty concluded between the member states of the European community under international law, this changed into citizenship of the European Union in 2007 when the European Community changed its legal identity to be the European Union. Many more people became EU citizens when each new EU member state was added and, at each point, all the existing member states ratified the adjustments to the treaties to allow the creation of those extra citizenship rights for the individual. European citizenship is also generally granted at the same time as national citizenship is granted; likewise it is removed at the point of removal of national citizenship). (1) of the Treaty on the Functioning of the European Union states that: "Citizenship of the Union is hereby established. Every person holding the nationality of a Member State shall be a citizen of the Union. Citizenship of the Union shall be additional to and not replace national citizenship." While nationals of Member States are citizens of the union, "It is for each Member State, having due regard to Union law, to lay down the conditions for the acquisition and loss of nationality." As a result, there is a great variety in rules and practices with regard to the acquisition and loss of citizenship in EU member states. In practice this means that a member state may withhold EU citizenship from certain groups of citizens, most commonly in overseas territories of member states outside the EU. A previous example, was for the United Kingdom. Owing to the complexity of British nationality law, a 1982 declaration by Her Majesty's Government defined who would be deemed to be a British "national" for European Union purposes: This declaration therefore excluded from EU citizenship various historic categories of British citizenship generally associated with former British colonies, such as British Overseas Citizens, British Nationals (Overseas), British protected persons and any British subject who did not have the 'right of abode' under British immigration law. In 2002, with the passing of the British Overseas Territories Act 2002, EU citizenship was extended to almost all British overseas territories citizens when they were automatically granted full British citizenship (with the exception of those with an association to the British sovereign base areas of Akrotiri and Dhekelia on the Island of Cyprus). This had effectively granted them full EU citizenship rights, including free movement rights, although only residents of Gibraltar had the right to vote in European Parliament elections. In contrast, British citizens in the Crown Dependencies of Jersey, Guernsey and the Isle of Man had always been considered to be EU citizens but, unlike residents of the British overseas territories, were prohibited from exercising EU free movement rights under the terms of the UK Accession Treaty if they had no other connection with the UK (e.g. they had lived in the UK for five years, were born in the UK, or had parents or grandparents born in the UK) and had no EU voting rights. (see Guernsey passport, Isle of Man passport, Jersey passport). Another example are the residents of Faroe Islands of Denmark who, though in possession of full Danish citizenship, are outside the EU and are explicitly excluded from EU citizenship under the terms of the Danish Accession Treaty. This is in contrast to residents of the Danish territory of Greenland who, whilst also outside the EU as a result of the 1984 Greenland Treaty, do receive EU citizenship as this was not specifically excluded by the terms of that treaty (see Faroe Islands and the European Union; Greenland and the European Union). This is a summary of nationality laws for each of the twenty-seven EU member states. The general rule for losing EU citizenship is that European citizenship is lost if member state nationality is lost, but the automatic loss of EU citizenship as a result of a member state withdrawing from the EU is the subject of debate. One school of legal thought indicates that the Maastricht treaty created the European Union as a legal entity, it then also created the status of EU citizen which gave an individual relationship between the EU and its citizens, and a status of EU citizen. Clemens Rieder suggests a case can be made that "[n]one of the Member States were forced to confer the status of EU citizenship on their citizens but once they have, according to this argument, they cannot simply withdraw this status.". In this situation, no EU citizen would involuntarily lose their citizenship due to their nation's withdrawal from the EU. It is likely that only a court case before the European Court of Justice would be able to properly determine the correct legal position in this regard, as there is no definitive legal certainty in this area. As of 7 February 2018, the District Court of Amsterdam decided to refer the matter to the European Court of Justice, but the state of the Netherlands has appealed against this referral decision. Although Greenland withdrew from the European Communities in 1985, all citizens of Denmark residing in Greenland are eligible for EU citizenship by virtue of their Danish citizenship. This contrasts with Danish citizens living the Faroe Islands who are excluded from EU citizenship. As a result of the Withdrawal of the United Kingdom from the European Union, the opinion of both the European Union and the British government has been that British citizens would lose their EU citizenship and EU citizens would lose their automatic right to stay in the UK. To account for the problems arising from this, a provisional agreement outlines the right of UK citizens to remain in the EU (and vice versa) where they are resident in the Union on the day of the UK's withdrawal. EU citizens may remain in the UK post-Brexit if and only if they apply to EU Settlement Scheme. The only exception to this is citizens who possess dual citizenship with an EU state. This eligibility includes the majority of British citizens from Northern Ireland, who are automatically entitled to Irish citizenship as part of the Good Friday Agreement. As a result of the Brexit referendum, there were three European Citizens' Initiatives that were registered which sought to protect the rights and/or status of British EU citizens. Out of these three initiatives, the one with the strongest legal argument was registered on 27 March 2017 and officially named "EU Citizenship for Europeans: United in Diversity in Spite of jus soli and jus sanguinis". It is clear that the initiative abides by the first school of thought mentioned above because the annexe that was submitted with the initiative clearly makes reference to Rieder's work. In an article titled "[http://vip.politicsmeanspolitics.com/2017/09/06/extending-full-eu-citizenship-to-uk-nationals-especially-after-brexit/ <nowiki>Extending [full] EU citizenship to UK nationals ESPECIALLY after Brexit</nowiki>]" and published with the online magazine "Politics Means Politics", the creator of the Initiative argues that UK nationals "must" keep their EU citizenship by detaching citizenship of the European Union from Member State nationality. Perhaps the most convincing and authoritative source that is cited in the article is the acting President of the European Court of Justice, Koen Lenaerts who published an article where he explains how the Court analyses and decides cases dealing with citizenship of the European Union. Both Lenaerts and the creator of the Initiative refer to rulings by the European Court of Justice which state that: Based on the argument presented by "EU Citizenship for Europeans" and its creator, Brexit is a textbook definition of a Member State depriving a European citizen of his or her rights as EU citizens, and therefore a legal act is necessary to protect not just rights but the status of EU citizen itself. Despite variances in interpretation of some points of law raised by the Initiative, the European Commission's decision to register the initiative confirms the strength and merit of the initiative's legal argument. A proposal made first by Guy Verhofstadt, the European Parliament's Brexit negotiator, to help cover the rights of UK citizens post-Brexit would see UK citizens able to opt-out of the loss of EU citizenship as a result of the general clauses of the withdrawal agreement. This would allow visa-free working on the basis of their continuing rights as EU citizens. This, he termed, "associate citizenship". This has been discussed with the UK's negotiator David Davis. However, it was made clear by the UK government that there would be no role for EU institutions concerning its citizens, effectively removing the proposal as a possibility. Denmark obtained four opt-outs from the Maastricht Treaty following the treaty's initial rejection in a 1992 referendum. The opt-outs are outlined in the Edinburgh Agreement and concern the EMU (as above), the Common Security and Defence Policy (CSDP), Justice and Home Affairs (JHA) and the citizenship of the European Union. The citizenship opt-out stated that European citizenship did not replace national citizenship; this opt-out was rendered meaningless when the Amsterdam Treaty adopted the same wording for all members. The policy of recent Danish governments has been to hold referendums to abolish these opt-outs, including formally abolishing the citizenship opt-out which is still technically active even if redundant.

Citizenship of the European Union is afforded to qualifying citizens of European Union member states. It was created by the 1992 Maastricht Treaty, at the same time as the creation of the European Union (EU). European Union citizenship is additional to national citizenship, and affords EU citizens with rights, freedoms and legal protections available under EU law.

en

65

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summarize: Braising relies on heat, time, and moisture to break down the tough connective tissue (collagen) that binds together the muscle fibers collectively called "meat", making it an ideal way to cook tougher, more affordable cuts. Many classic braised dishes (e.g., coq au vin) are highly evolved methods of cooking tough and otherwise unpalatable foods. Both pressure cooking and slow cooking (e.g. in a crockpot) are forms of braising. Most braises follow the same basic steps. The food to be braised (meats, vegetables, mushrooms, etc.) is first pan-seared to brown its surface and enhance its flavor (through the Maillard reaction). If the food will not produce enough liquid of its own, a certain amount of cooking liquid that often includes an acidic element (e.g., tomatoes, beer, balsamic vinegar, wine) is added to the pot, often with stock. A classic braise is done with a relatively whole cut of meat, and the braising liquid will cover two-thirds of the food in the pan. The dish is then covered and cooked at a very low simmer until the meat becomes so tender that it can be "cut" with just the gentlest of pressure from a fork (versus a knife). Often the cooking liquid is finished to create a sauce or gravy as well. Sometimes foods with high water content (particularly vegetables) can be cooked in their own juices, making the addition of liquid unnecessary. A successful braise intermingles the flavors of the foods being cooked with those of the cooking liquid. This cooking method dissolves the meat's collagen into gelatin, which can greatly enrich and thicken the liquid. Braising is economical (as it allows the use of tough and inexpensive cuts), and efficient (as it often enables an entire meal to be prepared in a single pot or pan). Familiar braised dishes include pot roast, Swiss steak, chicken cacciatore, goulash, Carbonade Flamande, coq au vin, sauerbraten, beef bourguignon, beef brisket, oxtail, and tajines, among others. Braising is also used extensively in the cuisines of Asia, particularly Chinese cuisine and Vietnamese cuisine, where soy sauce (or in Vietnam, soy sauce and fish sauce) is often the braising liquid. <br

Braising (from the French word "braiser") is a combination-cooking method that uses both wet and dry heats: typically, the food is first sautéed or seared at a high temperature, then finished in a covered pot at a lower temperature while sitting in some (variable) amount of liquid (which may also add flavor). Braising of meat is often referred to as pot roasting, though some authors make a distinction between the two methods, based on whether additional liquid is added.

en

94

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summarize: In Japanese cities, yakitori carts, restaurants, or shops can be found. These contain charcoal-fired grills and marinated grilled meat on a stick. Yakiniku is a type of food where meat and vegetables are grilled directly over small charcoal or gas grills at high temperatures. (This style of cooking has become popular throughout Asia.) In Malaysia, Singapore, Indonesia, and Thailand, a popular food item from food vendors is satay, which is marinated meat on a bamboo skewer grilled over a charcoal fire and served with peanut (sate) sauce. In Germany, the most prominent outdoor form of grilling is using the gridiron over a bed of burning charcoal. Care is taken that the charcoal does not produce flames. Often beer is sprinkled over the sausages or meat and used to suppress flames. The meat is usually marinated before grilling. Besides charcoal, sometimes gas and electric heat sources are used. Other methods are used less frequently. In Northern Mexico, "carne asada" (Spanish for "grilled meat") is a staple food. Popular cuts include arrachera, beefsteak and rib eye, as well as chorizo and chicken, among others. Charcoal, mesquite or firewood are used for the grilling. In Argentina and Uruguay, both "asado" (beef roasted on a fire) and steak "a la parrilla" (beefsteak cooked on traditional grill) are staple dishes and even hailed as national specialties. In Sweden, grilling directly over hot coals is the most prominent form of grilling. Usually the meat is Boston butt, pork chops or pork fillet. It is also common to cook meat and vegetables together on a skewer, this is called "grillspett". In the United Kingdom, Commonwealth countries, and Ireland, grilling generally refers to cooking food directly under a source of direct, dry heat. The "grill" is usually a separate part of an oven where the food is inserted just under the element. This practice is referred to as "broiling" in North America. Sometimes the term grilling may refer to cooking with heat from below, as in the United States. In the 1970s and 1980s the electric, two sided vertical grill marketed by the Sunbeam company achieved cult status because of its quick, clean, and no added fat operation. In electric ovens, grilling may be accomplished by placing the food near the upper heating element, with the lower heating element off and the oven door partially open. Grilling in an electric oven may create a large amount of smoke and cause splattering in the oven. Both gas and electric ovens often have a separate compartment for grilling, such as a drawer below the flame or one of the stove top heating elements. In the United States, the use of the word grill refers to cooking food directly over a source of dry heat, typically with the food sitting on a metal grate that leaves "grill marks." Grilling is usually done outdoors on charcoal grills or gas grills; a recent trend is the concept of infrared grilling. Grilling may also be performed using stove-top "grill pans" which have raised metal ridges for the food to sit on, or using an indoor electric grill. A skewer, brochette, or rotisserie may be used to cook small pieces of food. The resulting food product is often called a "kabob" ("US term") or "kebab" which means "to grill" in Persian. Kebab is short for "shish kebab" (shish = skewer). Mesquite or hickory wood chips (damp) may be added on top of the coals to create a smoldering effect that provides additional flavor to the food. Other hardwoods such as pecan, apple, maple and oak may also be used. As is true of any high-temperature frying or baking, when meat is grilled at high temperatures, the cooking process can generate carcinogenic chemicals. Two processes are thought to be responsible. Heterocyclic amines (HCAs) are formed when amino acids, sugars, and creatine react at high temperatures. Polycyclic aromatic hydrocarbons (PAHs) are formed when fat and juices from meat grilled directly over an open fire drip onto the fire, causing flames. These flames contain PAHs that then adhere to the surface of the meat. However it is possible to significantly reduce carcinogens when grilling meat, or mitigate their effect. Garlic, rosemary, olive oil, cherries, and vitamin E have been shown to reduce formation of both HCAs and PAHs. V-profiled grill elements placed at an angle may help drain much of the meat juices and dripping fat, and transport them away from the heat source. Heat sources on the top (as in many electrical or gas ovens), or on the side (vertical grilling) avoid completely the burning of fat dripping from the meat, and the meat's contact with the flames. Another method is precooking the meat in the microwave, which can reduce HCA formation by reducing the time that meat must be in contact with high heat to finish cooking. Gridironing is the cooking of meats or other foods using a grill suspended above a heat source. Grilling is often performed outdoors using charcoal (real wood or preformed briquettes), wood, or propane gas. Food is cooked using direct radiant heat. Some outdoor grills include a cover so they can be used as smokers or for grill-roasting/barbecue. The suspended metal grate is often referred to as a gridiron.Outdoor grilling on a gridiron may be referred to as "barbecue", though in US usage, the term "barbecue" refers to the cooking of meat through indirect heat and smoke. "Barbecue" may refer to the grilled food itself, to a distinct type of cooked meat called Southern barbecue, to the grilling device used to cook the food (a "barbecue grill"), or to the social event of cooking and eating such food (which may also be called a "cook-out" or "braai"). Charcoal kettle-grilling refers to the process of grilling over a charcoal fire in a kettle, to the point that the edges are charred, or charred grill marks are visible. Some restaurants seek to re-create the charcoal-grilled experience via the use of ceramic lava rocks or infrared heat sources, offering meats that are cooked in this manner as "charcoal-cooked" or "charcoal-grilled". By using a baking sheet pan placed above the grill surface, as well as a drip pan below the surface, it is possible to combine grilling and roasting to cook meats that are stuffed or coated with breadcrumbs or batter, and to bake breads and even casseroles and desserts. When cooking stuffed or coated meats, the foods can be baked first on the sheet pan, and then placed directly on the grilling surface for char marks, effectively cooking twice; the drip pan will be used to capture any crumbs that fall off from the coating or stuffing. It is possible to braise meats and vegetables in a pot on top of a grill. A gas or electric grill would be the best choices for what is known as "barbecue-braising" or "grill-braising", or combining grilling directly on the surface and braising in a pot. To braise on a grill, put a pot on top of the grill, cover it, and let it simmer for a few hours. There are two advantages to barbecue-braising. The first is that this method allows for browning the meat directly on the grill before the braising, and the second is that it also allows for glazing the meat with sauce and finishing it directly over the fire after the braising, effectively cooking the meat three times, which results in a soft textured product that falls right off the bone. This method of cooking is slower than regular grilling but faster than pit-smoking, starting out fast, slowing down, and then speeding up again to finish. If a pressure cooker is used, the cooking time will be much faster. Many restaurants incorporate an indoor grill as part of their cooking apparatus. These grills resemble outdoor grills, in that they are made up of a grid suspended over a heat source. However, indoor grills are more likely to use electric or gas-based heating elements. Some manufacturers of residential cooking appliances now offer indoor grills for home use, either incorporated into a stove top or as a standalone electric device. Sear-grill and gear grilling is a process of searing meat or food items with an infrared grill. In sear grilling, propane or natural gas is used to heat a ceramic plate, which then radiates heat at temperatures over 480 °C (900 °F). Sear-grilling instantly sears the outside of meat to make the food more flavorful. Commonly, grilling heats the surrounding air to cook food. In this method, the infrared grill directly heats the food, not the air. Stove-top pan grilling is an indoor cooking process that uses a grill pan — similar to a frying pan but with raised ridges to emulate the function or look of a gridiron. In pan grilling, heat is applied directly to the food by the raised ridges and indirectly through the heat radiating off the lower pan surface by the stove-top flame. Stove-top grill pans can be used to put sear marks on meat before it is finished by overhead radiant heat. When cooking leaner meats, oil is often applied to the pan ridges to aid in food release. Some griddles designed for stove-top use incorporate raised ridges in addition to a flat cooking area. These are either on half of the cooking surface or, in the case of reversible two-sided griddles, on one side with the flat surface on the other. Foods termed "grilled" may actually be prepared on a hot griddle or flat pan. The griddle or pan may be prepared with oil (or butter), and the food is cooked quickly over a high heat. Griddle-grilling is best for relatively greasy foods such as sausages. Some griddle-grilled foods may have grill marks applied to them during the cooking process with a "branding plate", to mimic the appearance of charbroil-cooked food. A flattop grill is a cooking appliance that resembles a griddle but performs differently because the heating element is circular rather than straight (side to side). This heating technology creates an extremely hot and even cooking surface, as heat spreads in a radial fashion over the surface. The first flattop grills originated in Spain and are known as planchas or la plancha. Food that is cooked a la plancha means grilled on a metal plate. Plancha griddles or flat tops are chrome plated which prevents reaction with the food. Some base metal griddles will impart a subtle flavor to the food being cooked. The flattop grill is a versatile platform for many cooking techniques such as sautéing, toasting, steaming, stir frying, grilling, baking, braising, and roasting, and can also be used in flambéing. In addition, pots and pans can be placed directly on the cooking surface for even more cooking flexibility. In most cases, the steel cooking surface is seasoned like cast iron cookware, providing a natural non-stick surface. Charbroiling, or chargrilling outside North America, refers to grilling on a surface with wide raised ridges, to the point of having the food slightly charred in texture. In the United States, oven pan broiling refers to a method of cooking inside an oven on a broil pan with raised ridges, where the heat can be applied from either above or below. In gas and electric ovens, this is accomplished with a heating element and a broil pan. Sometimes, the food is placed near the upper heating element to intensify the heat. The lower heating element may or may not be left off and the oven door is sometimes opened partially. Gas ovens often have a separate compartment for broiling, sometimes a drawer below the bottom flame. A salamander (also salamander oven or salamander broiler) is a culinary grill characterized by very high temperature overhead electric or gas heating elements. It is used primarily in professional kitchens for overhead grilling. It is also used for toasting, browning of gratin dishes, melting cheeses onto sandwiches, and caramelizing desserts such as crème brûlée. Salamanders are generally similar to an oven without a front door; the heating element is at the top. They are also more compact: typically only half the height and depth of a conventional oven. For convenience, they are often wall mounted at eye level, enabling easy access and close control of the cooking process. Many salamanders can be fitted with a cast iron "branding" plate which is used to make grill marks on the surface of meat. Some grills can also be fitted with a rotisserie accessory for roasting meats. Overhead heat has the advantage of allowing foods containing fats, such as steaks, chops and other cuts of meat, to be grilled without the risk of flare-ups caused by the rendered fat dripping onto the heat source. The salamander's facility for extremely high temperature also takes less cooking time than other grilling techniques, reducing preparation time, which is a benefit in professional kitchens during a busy meal service. Modern salamanders take their name from the 18th century "salamander", the tool of choice for toasting the top of a dish. It consisted of a thick plate of iron attached to the end of a long handle, with two feet, or rests, arranged near the iron plate for propping the plate over the food to be browned. Its name in turn was taken from the legendary salamander, a mythical amphibian that was believed to be immune to fire. Some commercial devices permit the simultaneous grilling of both sides of the meat at the same time. The flame-grilling machine at Burger King, Carl's Jr./Hardee's, and other fast food restaurants is called a 'broiler'. It works by moving meat patties along a chain conveyor belt between top and bottom burners, grilling both sides of the meat patty at the same time. This concept was invented in 1898, when the Bridge and Beach Co. of St. Louis, Missouri, started manufacturing a vertical cast iron stove. These stoves were designed to allow the meat to be flame-broiled (flame-grilled) on both sides at the same time. Custom hinged steel wire gridirons were built for use in the vertical broilers. The hinged gridirons were slid in and out of the stoves holding the meat while it cooked evenly on both sides, like modern day oven racks. These stoves took up a small amount of counter space. They were used in lunch spots to feed factory workers. During the 1990s, double-sided grilling was popular in the USA using consumer electrical grills (e.g., the popular George Foreman Grill). US marketers of electric double-sided grilling appliances opted for the global term 'grill' rather than the geographically isolated term "broiler." Hinged double-sided grills are generically known as contact grills. Whole grilling involves grilling a whole carcass as opposed to grilling individual portion sized cuts. This method is often used in order to avoid the need for complicated grill equipment during, for example, a hunt or expedition in the wild. It is also the traditional method of cooking in several cultures where they do a pig roast, luau, or barbacoa. There are several primitive methods and modern equipment that copies and automates the primitive version:

Grilling is a form of cooking that involves dry heat applied to the surface of food, commonly from above, below or from the side. Grilling usually involves a significant amount of direct, radiant heat, and tends to be used for cooking meat and vegetables quickly. Food to be grilled is cooked on a grill (an open wire grid such as a gridiron with a heat source above or below), using a cast iron/frying pan, or a grill pan (similar to a frying pan, but with raised ridges to mimic the wires of an open grill).

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summarize: Heat is defined in physics as the transfer of thermal energy across a well-defined boundary around a thermodynamic system. The thermodynamic free energy is the amount of work that a thermodynamic system can perform. Enthalpy is a thermodynamic potential, designated by the letter "H", that is the sum of the internal energy of the system (U) plus the product of pressure (P) and volume (V). Joule is a unit to quantify energy, work, or the amount of heat. Heat transfer is a process function (or path function), as opposed to functions of state; therefore, the amount of heat transferred in a thermodynamic process that changes the state of a system depends on how that process occurs, not only the net difference between the initial and final states of the process. Thermodynamic and mechanical heat transfer is calculated with the heat transfer coefficient, the proportionality between the heat flux and the thermodynamic driving force for the flow of heat. Heat flux is a quantitative, vectorial representation of heat-flow through a surface. In engineering contexts, the term "heat" is taken as synonymous to thermal energy. This usage has its origin in the historical interpretation of heat as a fluid ("caloric") that can be transferred by various causes, and that is also common in the language of laymen and everyday life. The transport equations for thermal energy (Fourier's law), mechanical momentum (Newton's law for fluids), and mass transfer (Fick's laws of diffusion) are similar, and analogies among these three transport processes have been developed to facilitate prediction of conversion from any one to the others. Thermal engineering concerns the generation, use, conversion, and exchange of heat transfer. As such, heat transfer is involved in almost every sector of the economy. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. The fundamental modes of heat transfer are: By transferring matter, energy—including thermal energy—is moved by the physical transfer of a hot or cold object from one place to another. This can be as simple as placing hot water in a bottle and heating a bed, or the movement of an iceberg in changing ocean currents. A practical example is thermal hydraulics. This can be described by the formula: where On a microscopic scale, heat conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring particles. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from one atom to another. Conduction is the most significant means of heat transfer within a solid or between solid objects in thermal contact. Fluids—especially gases—are less conductive. Thermal contact conductance is the study of heat conduction between solid bodies in contact. The process of heat transfer from one place to another place without the movement of particles is called conduction, such as when placing a hand on a cold glass of water—heat is conducted from the warm skin to the cold glass, but if the hand is held a few inches from the glass, little conduction would occur since air is a poor conductor of heat. Steady state conduction is an idealized model of conduction that happens when the temperature difference driving the conduction is constant, so that after a time, the spatial distribution of temperatures in the conducting object does not change any further (see Fourier's law). In steady state conduction, the amount of heat entering a section is equal to amount of heat coming out, since the change in temperature (a measure of heat energy) is zero. An example of steady state conduction is the heat flow through walls of a warm house on a cold—inside the house is maintained at a high temperature, and outside the temperature stays low, so the transfer of heat per unit time stays near a constant rate determined by the insulation in the wall, and the spatial distribution of temperature in the walls will be approximately constant over time. "Transient conduction" (see Heat equation) occurs when the temperature within an object changes as a function of time. Analysis of transient systems is more complex, and analytic solutions of the heat equation are only valid for idealized model systems. Practical applications are generally investigated using numerical methods, approximation techniques, or empirical study. The flow of fluid may be forced by external processes, or sometimes (in gravitational fields) by buoyancy forces caused when thermal energy expands the fluid (for example in a fire plume), thus influencing its own transfer. The latter process is often called "natural convection". All convective processes also move heat partly by diffusion, as well. Another form of convection is forced convection. In this case the fluid is forced to flow by using a pump, fan or other mechanical means. Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids, a process that is essentially the transfer of heat via mass transfer. Bulk motion of fluid enhances heat transfer in many physical situations, such as (for example) between a solid surface and the fluid. Convection is usually the dominant form of heat transfer in liquids and gases. Although sometimes discussed as a third method of heat transfer, convection is usually used to describe the combined effects of heat conduction within the fluid (diffusion) and heat transference by bulk fluid flow streaming. The process of transport by fluid streaming is known as advection, but pure advection is a term that is generally associated only with mass transport in fluids, such as advection of pebbles in a river. In the case of heat transfer in fluids, where transport by advection in a fluid is always also accompanied by transport via heat diffusion (also known as heat conduction) the process of heat convection is understood to refer to the sum of heat transport by advection and diffusion/conduction. Free, or natural, convection occurs when bulk fluid motions (streams and currents) are caused by buoyancy forces that result from density variations due to variations of temperature in the fluid. "Forced" convection is a term used when the streams and currents in the fluid are induced by external means—such as fans, stirrers, and pumps—creating an artificially induced convection current. Convective cooling is sometimes described as Newton's law of cooling: In a body of fluid that is heated from underneath its container, conduction and convection can be considered to compete for dominance. If heat conduction is too great, fluid moving down by convection is heated by conduction so fast that its downward movement will be stopped due to its buoyancy, while fluid moving up by convection is cooled by conduction so fast that its driving buoyancy will diminish. On the other hand, if heat conduction is very low, a large temperature gradient may be formed and convection might be very strong. The Rayleigh number (formula_7) is the product of the Grashof (formula_8) and Prandtl (formula_9) numbers. It is a measure which determines the relative strength of conduction and convection. where The Rayleigh number can be understood as the ratio between the rate of heat transfer by convection to the rate of heat transfer by conduction; or, equivalently, the ratio between the corresponding timescales (i.e. conduction timescale divided by convection timescale), up to a numerical factor. This can be seen as follows, where all calculations are up to numerical factors depending on the geometry of the system. The buoyancy force driving the convection is roughly formula_12, so the corresponding pressure is roughly formula_13. In steady state, this is canceled by the shear stress due to viscosity, and therefore roughly equals formula_14, where "V" is the typical fluid velocity due to convection and formula_15 the order of its timescale. The conduction timescale, on the other hand, is of the order of formula_16. Convection occurs when the Rayleigh number is above 1,000–2,000. Thermal radiation occurs through a vacuum or any transparent medium (solid or fluid or gas). It is the transfer of energy by means of photons in electromagnetic waves governed by the same laws. Thermal radiation is energy emitted by matter as electromagnetic waves, due to the pool of thermal energy in all matter with a temperature above absolute zero. Thermal radiation propagates without the presence of matter through the vacuum of space. Thermal radiation is a direct result of the random movements of atoms and molecules in matter. Since these atoms and molecules are composed of charged particles (protons and electrons), their movement results in the emission of electromagnetic radiation, which carries energy away from the surface. The Stefan-Boltzmann equation, which describes the rate of transfer of radiant energy, is as follows for an object in a vacuum : For radiative transfer between two objects, the equation is as follows: where Radiation is typically only important for very hot objects, or for objects with a large temperature difference. Radiation from the sun, or solar radiation, can be harvested for heat and power. Unlike conductive and convective forms of heat transfer, thermal radiation – arriving within a narrow angle i.e. coming from a source much smaller than its distance – can be concentrated in a small spot by using reflecting mirrors, which is exploited in concentrating solar power generation or a burning glass. For example, the sunlight reflected from mirrors heats the PS10 solar power tower and during the day it can heat water to. The reachable temperature at the target is limited by the temperature of the hot source of radiation. (T-law lets the reverse-flow of radiation back to the source rise.) The (on its surface) somewhat 4000 K hot sun allows to reach coarsly 3000 K (or 3000 °C, which is about 3273 K) at a small probe in the focus spot of a big concave, concentrating mirror of the Mont-Louis Solar Furnace in France. Phase transition or phase change, takes place in a thermodynamic system from one phase or state of matter to another one by heat transfer. Phase change examples are the melting of ice or the boiling of water. The Mason equation explains the growth of a water droplet based on the effects of heat transport on evaporation and condensation. Phase transitions involve the four fundamental states of matter: The boiling point of a substance is the temperature at which the vapor pressure of the liquid equals the pressure surrounding the liquid and the liquid evaporates resulting in an abrupt change in vapor volume. Saturation temperature means boiling point. The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition. At standard atmospheric pressure and low temperatures, no boiling occurs and the heat transfer rate is controlled by the usual single-phase mechanisms. As the surface temperature is increased, local boiling occurs and vapor bubbles nucleate, grow into the surrounding cooler fluid, and collapse. This is "sub-cooled nucleate boiling", and is a very efficient heat transfer mechanism. At high bubble generation rates, the bubbles begin to interfere and the heat flux no longer increases rapidly with surface temperature (this is the departure from nucleate boiling, or DNB). At similar standard atmospheric pressure and high temperatures, the hydrodynamically-quieter regime of film boiling is reached. Heat fluxes across the stable vapor layers are low, but rise slowly with temperature. Any contact between fluid and the surface that may be seen probably leads to the extremely rapid nucleation of a fresh vapor layer ("spontaneous nucleation"). At higher temperatures still, a maximum in the heat flux is reached (the critical heat flux, or CHF). The Leidenfrost Effect demonstrates how nucleate boiling slows heat transfer due to gas bubbles on the heater's surface. As mentioned, gas-phase thermal conductivity is much lower than liquid-phase thermal conductivity, so the outcome is a kind of "gas thermal barrier". Condensation occurs when a vapor is cooled and changes its phase to a liquid. During condensation, the latent heat of vaporization must be released. The amount of the heat is the same as that absorbed during vaporization at the same fluid pressure. There are several types of condensation: Melting is a thermal process that results in the phase transition of a substance from a solid to a liquid. The internal energy of a substance is increased, typically with heat or pressure, resulting in a rise of its temperature to the melting point, at which the ordering of ionic or molecular entities in the solid breaks down to a less ordered state and the solid liquefies. Molten substances generally have reduced viscosity with elevated temperature; an exception to this maxim is the element sulfur, whose viscosity increases to a point due to polymerization and then decreases with higher temperatures in its molten state. Heat transfer can be modeled in various ways. The heat equation is an important partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. In some cases, exact solutions of the equation are available; in other cases the equation must be solved numerically using computational methods such as DEM-based models for thermal/reacting particulate systems (as critically reviewed by Peng et al. ). Lumped system analysis often reduces the complexity of the equations to one first-order linear differential equation, in which case heating and cooling are described by a simple exponential solution, often referred to as Newton's law of cooling. System analysis by the lumped capacitance model is a common approximation in transient conduction that may be used whenever heat conduction within an object is much faster than heat conduction across the boundary of the object. This is a method of approximation that reduces one aspect of the transient conduction system—that within the object—to an equivalent steady state system. That is, the method assumes that the temperature within the object is completely uniform, although its value may be changing in time. In this method, the ratio of the conductive heat resistance within the object to the convective heat transfer resistance across the object's boundary, known as the "Biot number", is calculated. For small Biot numbers, the approximation of "spatially uniform temperature within the object" can be used: it can be presumed that heat transferred into the object has time to uniformly distribute itself, due to the lower resistance to doing so, as compared with the resistance to heat entering the object. Climate models study the radiant heat transfer by using quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice. Heat transfer has broad application to the functioning of numerous devices and systems. Heat-transfer principles may be used to preserve, increase, or decrease temperature in a wide variety of circumstances. Heat transfer methods are used in numerous disciplines, such as automotive engineering, thermal management of electronic devices and systems, climate control, insulation, materials processing, and power station engineering. Thermal insulators are materials specifically designed to reduce the flow of heat by limiting conduction, convection, or both. Thermal resistance is a heat property and the measurement by which an object or material resists to heat flow (heat per time unit or thermal resistance) to temperature difference. Radiance or spectral radiance are measures of the quantity of radiation that passes through or is emitted. Radiant barriers are materials that reflect radiation, and therefore reduce the flow of heat from radiation sources. Good insulators are not necessarily good radiant barriers, and vice versa. Metal, for instance, is an excellent reflector and a poor insulator. The effectiveness of a radiant barrier is indicated by its reflectivity, which is the fraction of radiation reflected. A material with a high reflectivity (at a given wavelength) has a low emissivity (at that same wavelength), and vice versa. At any specific wavelength, reflectivity=1 - emissivity. An ideal radiant barrier would have a reflectivity of 1, and would therefore reflect 100 percent of incoming radiation. Vacuum flasks, or Dewars, are silvered to approach this ideal. In the vacuum of space, satellites use multi-layer insulation, which consists of many layers of aluminized (shiny) Mylar to greatly reduce radiation heat transfer and control satellite temperature. A heat engine is a system that performs the conversion of a flow of thermal energy (heat) to mechanical energy to perform mechanical work. A thermocouple is a temperature-measuring device and widely used type of temperature sensor for measurement and control, and can also be used to convert heat into electric power. A thermoelectric cooler is a solid state electronic device that pumps (transfers) heat from one side of the device to the other when electric current is passed through it. It is based on the Peltier effect. A thermal diode or thermal rectifier is a device that causes heat to flow preferentially in one direction. A heat exchanger is used for more efficient heat transfer or to dissipate heat. Heat exchangers are widely used in refrigeration, air conditioning, space heating, power generation, and chemical processing. One common example of a heat exchanger is a car's radiator, in which the hot coolant fluid is cooled by the flow of air over the radiator's surface. Common types of heat exchanger flows include parallel flow, counter flow, and cross flow. In parallel flow, both fluids move in the same direction while transferring heat; in counter flow, the fluids move in opposite directions; and in cross flow, the fluids move at right angles to each other. Common types of heat exchangers include shell and tube, double pipe, extruded finned pipe, spiral fin pipe, u-tube, and stacked plate. Each type has certain advantages and disadvantages over other types. A heat sink is a component that transfers heat generated within a solid material to a fluid medium, such as air or a liquid. Examples of heat sinks are the heat exchangers used in refrigeration and air conditioning systems or the radiator in a car. A heat pipe is another heat-transfer device that combines thermal conductivity and phase transition to efficiently transfer heat between two solid interfaces. Efficient energy use is the goal to reduce the amount of energy required in heating or cooling. In architecture, condensation and air currents can cause cosmetic or structural damage. An energy audit can help to assess the implementation of recommended corrective procedures. For instance, insulation improvements, air sealing of structural leaks or the addition of energy-efficient windows and doors. Climate engineering consists of carbon dioxide removal and solar radiation management. Since the amount of carbon dioxide determines the radiative balance of Earth atmosphere, carbon dioxide removal techniques can be applied to reduce the radiative forcing. Solar radiation management is the attempt to absorb less solar radiation to offset the effects of greenhouse gases. The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface and the lower atmosphere, it results in an elevation of the average surface temperature above what it would be in the absence of the gases. The principles of heat transfer in engineering systems can be applied to the human body in order to determine how the body transfers heat. Heat is produced in the body by the continuous metabolism of nutrients which provides energy for the systems of the body. The human body must maintain a consistent internal temperature in order to maintain healthy bodily functions. Therefore, excess heat must be dissipated from the body to keep it from overheating. When a person engages in elevated levels of physical activity, the body requires additional fuel which increases the metabolic rate and the rate of heat production. The body must then use additional methods to remove the additional heat produced in order to keep the internal temperature at a healthy level. Heat transfer by convection is driven by the movement of fluids over the surface of the body. This convective fluid can be either a liquid or a gas. For heat transfer from the outer surface of the body, the convection mechanism is dependent on the surface area of the body, the velocity of the air, and the temperature gradient between the surface of the skin and the ambient air. The normal temperature of the body is approximately 37 °C. Heat transfer occurs more readily when the temperature of the surroundings is significantly less than the normal body temperature. This concept explains why a person feels cold when not enough covering is worn when exposed to a cold environment. Clothing can be considered an insulator which provides thermal resistance to heat flow over the covered portion of the body. This thermal resistance causes the temperature on the surface of the clothing to be less than the temperature on the surface of the skin. This smaller temperature gradient between the surface temperature and the ambient temperature will cause a lower rate of heat transfer than if the skin were not covered. In order to ensure that one portion of the body is not significantly hotter than another portion, heat must be distributed evenly through the bodily tissues. Blood flowing through blood vessels acts as a convective fluid and helps to prevent any buildup of excess heat inside the tissues of the body. This flow of blood through the vessels can be modeled as pipe flow in an engineering system. The heat carried by the blood is determined by the temperature of the surrounding tissue, the diameter of the blood vessel, the thickness of the fluid, velocity of the flow, and the heat transfer coefficient of the blood. The velocity, blood vessel diameter, and the fluid thickness can all be related with the Reynolds Number, a dimensionless number used in fluid mechanics to characterize the flow of fluids. Latent heat loss, also known as evaporative heat loss, accounts for a large fraction of heat loss from the body. When the core temperature of the body increases, the body triggers sweat glands in the skin to bring additional moisture to the surface of the skin. The liquid is then transformed into vapor which removes heat from the surface of the body. The rate of evaporation heat loss is directly related to the vapor pressure at the skin surface and the amount of moisture present on the skin. Therefore, the maximum of heat transfer will occur when the skin is completely wet. The body continuously loses water by evaporation but the most significant amount of heat loss occurs during periods of increased physical activity. Evaporative cooling happens when water vapor is added to the surrounding air. The energy needed to evaporate the water is taken from the air in the form of sensible heat and converted into latent heat, while the air remains at a constant enthalpy. Latent heat describes the amount of heat that is needed to evaporate the liquid; this heat comes from the liquid itself and the surrounding gas and surfaces. The greater the difference between the two temperatures, the greater the evaporative cooling effect. When the temperatures are the same, no net evaporation of water in air occurs; thus, there is no cooling effect. In quantum physics, laser cooling is used to achieve temperatures of near absolute zero (−273.15 °C, −459.67 °F) of atomic and molecular samples to observe unique quantum effects that can only occur at this heat level. Magnetic evaporative cooling is a process for lowering the temperature of a group of atoms, after pre-cooled by methods such as laser cooling. Magnetic refrigeration cools below 0.3K, by making use of the magnetocaloric effect. Radiative cooling is the process by which a body loses heat by radiation. Outgoing energy is an important effect in the Earth's energy budget. In the case of the Earth-atmosphere system, it refers to the process by which long-wave (infrared) radiation is emitted to balance the absorption of short-wave (visible) energy from the Sun. Convective transport of heat and evaporative transport of latent heat both remove heat from the surface and redistribute it in the atmosphere. Thermal energy storage includes technologies for collecting and storing energy for later use. It may be employed to balance energy demand between day and nighttime. The thermal reservoir may be maintained at a temperature above or below that of the ambient environment. Applications include space heating, domestic or process hot water systems, or generating electricity.

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

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summarize: Frying is believed to have first appeared in the Ancient Egyptian kitchen, during the Old Kingdom, around 2500 BCE. Fats can reach much higher temperatures than water at normal atmospheric pressure. Through frying, one can sear or even carbonize the surface of foods while caramelizing sugars. The food is cooked much more quickly and has a characteristic crispness and texture. Depending on the food, the fat will penetrate it to varying degrees, contributing richness, lubricity, its own flavor, and calories. Frying techniques vary in the amount of fat required, the cooking time, the type of cooking vessel required, and the manipulation of the food. Sautéing, stir frying, pan frying, shallow frying, and deep frying are all standard frying techniques. Pan frying, sautéing and stir-frying involve cooking foods in a thin layer of fat on a hot surface, such as a frying pan, griddle, wok, or sauteuse. Stir frying involves frying quickly at very high temperatures, requiring that the food be stirred continuously to prevent it from adhering to the cooking surface and burning. Shallow frying is a type of pan frying using only enough fat to immerse approximately one-third to one-half of each piece of food; fat used in this technique is typically only used once. Deep-frying, on the other hand, involves totally immersing the food in hot oil, which is normally topped up and used several times before being disposed. Deep-frying is typically a much more involved process, and may require specialized oils for optimal results. Deep frying is now the basis of a very large and expanding worldwide industry. Fried products have consumer appeal in all age groups and in virtually all cultures, and the process is quick, can easily be made continuous for mass production, and the food emerges sterile and dry, with a relatively long shelf life. The end products can then be easily packaged for storage and distribution. Some include potato chips, french fries, nuts, doughnuts, and instant noodles.

Frying is the cooking of food in oil or another fat. Similar to sautéing, pan-fried foods are generally turned over once or twice during cooking, using tongs or a spatula, while sautéed foods are cooked by "tossing in the pan". A large variety of foods may be fried.

en

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summarize: "Aung San Suu Kyi", like other Burmese names, includes no surname, but is only a personal name, in her case derived from three relatives: "Aung San" from her father, "Suu" from her paternal grandmother, and Aung San Suu Kyi was born on 19 June 1945 in Rangoon (now Yangon), British Burma. According to Peter Popham, she was born in a small village outside Rangoon called Hmway Saung. Her father, Aung San, allied with the Japanese during World War II. Aung San founded the modern Burmese army and negotiated Burma's independence from the United Kingdom in 1947; he was assassinated by his rivals in the same year. She grew up with her mother, Khin Kyi, and two brothers, Aung San Lin and Aung San Oo, in Rangoon. Aung San Lin died at the age of eight, when he drowned in an ornamental lake on the grounds of the house. Her elder brother emigrated to San Diego, California, becoming a United States citizen. After Aung San Lin's death, the family moved to a house by Inya Lake where Aung San Suu Kyi met people of various backgrounds, political views and religions. She was educated in Methodist English High School (now Basic Education High School No. 1 Dagon) for much of her childhood in Burma, where she was noted as having a talent for learning languages. She speaks four languages: Burmese, English, French and Japanese. She is a Theravada Buddhist. Suu Kyi's mother, Khin Kyi, gained prominence as a political figure in the newly formed Burmese government. She was appointed Burmese ambassador to India and Nepal in 1960, and Aung San Suu Kyi followed her there. She studied in the Convent of Jesus and Mary School in New Delhi, and graduated from Lady Shri Ram College, a constituent college of the University of Delhi in New Delhi, with a degree in politics in 1964. Suu Kyi continued her education at St Hugh's College, Oxford, obtaining a B.A. degree in Philosophy, Politics and Economics in 1967, graduating with a third-class degree and M.A. degree Coincidentally, when Aung San Suu Kyi returned to Burma in 1988, the long-time military leader of Burma and head of the ruling party, General Ne Win, stepped down. Mass demonstrations for democracy followed that event on 8 August 1988 (8–8–88, a day seen as auspicious), which were violently suppressed in what came to be known as the 8888 Uprising. On 26 August 1988, she addressed half a million people at a mass rally in front of the Shwedagon Pagoda in the capital, calling for a democratic government. However, in September, a new military junta took power. Influenced by both Mahatma Gandhi's philosophy of non-violence and more specifically by Buddhist concepts, Aung San Suu Kyi entered politics to work for democratization, helped found the National League for Democracy on 27 September 1988, but was put under house arrest on 20 July 1989. She was offered freedom if she left the country, but she In 1990, the military junta called a general election, in which the National League for Democracy (NLD) received 59% of the votes, guaranteeing NLD 80% of the parliament seats. Some claim that Aung San Suu Kyi would have assumed the office of Prime Minister. Instead, the results were nullified and the military refused to hand over power, resulting in an international outcry. Aung San Suu Kyi was placed under house arrest at her home on University Avenue () in Rangoon, during which time she was On 9 November 1996, the motorcade that Aung San Suu Kyi was traveling in with other National League for Democracy leaders Tin Oo and Kyi Maung, was attacked in Yangon. About 200 men swooped down on the motorcade, wielding metal chains, metal batons, stones and other weapons. The car that Aung San Suu Aung San Suu Kyi was placed under house arrest for a total of 15 years over a 21-year period, on numerous occasions, since she began her political career, during which time she was prevented from meeting her party supporters and international visitors. In an interview, she said that while under house arrest she spent her time reading philosophy, politics and biographies that her husband had sent her. She also passed the time playing the piano, and was occasionally allowed visits from foreign diplomats as well as from her personal physician. Although under house arrest, Aung San Suu Kyi was granted permission to leave Burma under the condition that she never return, which she refused: "As a mother, the greater sacrifice was giving up my sons, but I was always aware of the fact that others had given up more than me. I never forget that my colleagues who are in prison suffer not only physically, but mentally for their families who have no security outside- in the larger prison of Burma under authoritarian rule." The United Nations (UN) has attempted to facilitate dialogue between the junta and Aung San Suu Kyi. On 6 May 2002, following secret confidence-building negotiations led by the UN, the government released her; a government spokesman said that she was free to move "because we are confident that we can trust each other". Aung San Suu Kyi proclaimed "a new dawn for the country". However, on 30 May 2003 in an incident similar to the 1996 attack on her, a government-sponsored mob attacked her caravan in the northern village of Depayin, murdering and wounding many of her supporters. Aung San Suu Kyi fled the Protests led by Buddhist monks began on 19 August 2007 following steep fuel price increases, and continued each day, despite the threat of a crackdown by the military. On 22 September 2007, although still under house arrest, Aung San Suu Kyi made a brief public On 3 May 2009, an American man, identified as John Yettaw, swam across Inya Lake to her house uninvited and was arrested when he made his return trip three days later. He had attempted to make a similar trip two years earlier, but for unknown reasons was turned away. He later claimed at trial that he was motivated by a divine vision requiring him to notify her of an impending terrorist assassination attempt. On 13 May, Aung San Suu Kyi was arrested for violating the terms of her house arrest because the swimmer, who pleaded exhaustion, was allowed to stay in her house for two days before he attempted the swim back. Aung San Aung San Suu Kyi has received vocal support from Western nations in Europe, Australia and North and South America, as well as India, Israel, Japan the Philippines and South Korea. In December 2007, the US House of Representatives voted unanimously 400–0 to award Aung San Suu Kyi the Congressional Gold Medal; the Senate concurred on 25 April 2008. On 6 May 2008, President George W. Bush signed legislation awarding Aung San Suu Kyi the Congressional Gold Medal. She is the first recipient in American history to receive the prize while imprisoned. More recently, there has been growing criticism of her detention by Burma's neighbours in the Association of Southeast Asian Nations, particularly from Indonesia, Thailand, the Philippines and Singapore. At On the evening of 13 November 2010, Aung San Suu Kyi was released from house arrest. This was the date her detention had been set to expire according to a court ruling in August 2009 and came six days after a widely criticised general election. She appeared in front of a crowd of her supporters, who rushed to her house in Rangoon when nearby barricades were removed by the security forces. Aung San Suu Kyi had been detained for 15 of the past 21 years. The government newspaper "New Light of Myanmar" reported the release positively, saying she had been granted a pardon after serving her sentence "in good conduct". The New York Times suggested that the military government may have released Suu Kyi because it felt it was in a confident position to control her supporters after the election. Her son Kim Aris was granted a visa in November 2010 to see his mother shortly after her release, for the first time in 10 years. He visited again on 5 July 2011, to accompany her on a trip to Bagan, her first In December 2011, there was speculation that Aung San Suu Kyi would run in the 2012 national by-elections to fill vacant seats. On 18 January 2012, Aung San Suu Kyi formally registered to contest a Pyithu Hluttaw (lower house) seat in the Kawhmu Township constituency in special parliamentary elections to be held on 1 April 2012. The seat was previously held by Soe Tint, who vacated it after being appointed Construction Deputy Minister, in the 2010 election. She ran against Union Solidarity and Development Party candidate Soe Min, On 16 June 2012, Aung San Suu Kyi was finally able to deliver her Nobel acceptance speech (Nobel lecture) at Oslo's City Hall, two decades after being awarded the peace prize. In September 2012, Aung San Suu Kyi received in person the United States Congressional Gold Medal, which is the highest Congressional award. Although she was awarded this medal in 2008, at the time she was under house arrest, and was unable to receive the medal. Aung San Suu Kyi was greeted with bipartisan support at Congress, as part of a coast-to-coast tour in the United States. In addition, Aung San Suu Kyi met President Barack Obama at the White House. The experience was described by Aung San Suu Kyi as "one of the most moving days of my life." In 2014, she was listed as the 61st most powerful woman in the world by "Forbes". On 6 July 2012, Aung San Suu Kyi announced on As soon as she became foreign minister, she invited Chinese Foreign Minister Wang Yi, Canadian Foreign Minister Stephane Dion and Italian Foreign Minister Paolo Gentiloni in April and Japanese Foreign Minister Fumio Kishida in May and discussed to have good diplomatic relationships with these countries. Initially, upon accepting the State Counsellor position, she granted amnesty to the students who were arrested for opposing the National Education Bill, and announced a creation of the commission on Rakhine state, which had a long record of persecution of the Muslim Rohingya minority. However, soon Aung San Suu Kyi's government did not manage with the ethnic In 2017, critics have called for Aung San Suu Kyi's Nobel prize to be revoked, citing her silence over the persecution of Rohingya people in Myanmar. Some activists criticised Aung San Suu Kyi for her silence on the 2012 Rakhine State riots (later repeated during the 2015 Rohingya refugee crisis), and her perceived indifference to the plight of the Rohingya, Myanmar's persecuted Muslim minority. In 2012, she told reporters she did not know if the Rohingya could be regarded as Burmese citizens. In a 2013 interview with the BBC's Mishal Husain, Aung San Suu Kyi did not condemn violence against the Rohingya and denied that Muslims in Myanmar have been subject to ethnic cleansing, insisting that the tensions were due to a "climate of fear" caused by "a worldwide perception that global Muslim power is'very great. She did condemn "hate of any kind" in the interview. According to Peter Popham, in the aftermath of the interview, she expressed anger at being interviewed by a Muslim. Husain had challenged Suu Kyi that almost all of the impact of violence was against the Rohingya, in response to Aung San Suu Kyi's claim that violence was happening on both sides, and Peter Popham described her position on the issue as one of purposeful ambiguity for political gain. However, she said that she wanted to work towards reconciliation and she cannot take sides as violence has been committed by both sides. According to "The Economist", her "halo In December 2017, two Reuters journalists, Wa Lone and Kyaw Soe Oo, were arrested while investigating the Inn Din massacre of Rohingyas alleged to have been carried out by Myanmar's security forces. Suu Kyi publicly commented in June 2018 that the journalists "weren't arrested for covering the Rakhine issue", but because they had broken Myanmar's Official Secrets Act. As the journalists were then on trial for violating the Official Secrets Act, Aung San Suu Kyi's presumption of their guilt were criticized by rights groups for potentially influencing the verdict. American diplomat Bill Richardson said that he had privately discussed the arrest with Suu Kyi, and he alleged that Aung San Suu Kyi reacted angrily and labelled the journalists "traitors". A police officer testified Asked what democratic models Myanmar could look to, she said: "We have many, many lessons to learn from various places, not just the Asian countries like South Korea, Taiwan, Mongolia, and Indonesia." She also cited "the eastern European countries, which made the transition from communist autocracy to democracy in the 1980s and 1990s, and the Latin American countries, which made the transition from military governments. "And we cannot of The life of Aung San Suu Kyi and her husband Michael Aris is portrayed in Luc Besson's 2011 film "The Lady", in which they are played by Michelle Yeoh and David Thewlis. Yeoh visited Suu Kyi in 2011 before the film's release in November. In the John Boorman's 1995 film "Beyond Rangoon", Aung San Suu Kyi was played by Adelle Lutz. Since 2009, Indian actress and Bharathanatyam dancer Rukmini Vijayakumar has been portraying She had surgery for a gynecological condition in September 2003 at Asia Royal Hospital during her house arrest. She underwent minor foot surgery in December 2013 and eye surgery in April 2016. Her doctor said that she had no serious health problems but weighed only 48 kg, had low blood pressure and could become weak easily.

Aung San Suu Kyi (; ; born 19 June 1945) is a Burmese politician, diplomat, author, and a 1991 Nobel Peace Prize laureate. The first and incumbent State Counsellor (a position akin to a prime minister leader) of Myanmar, she is also the leader of the National League for Democracy and played a vital role in the state's transition from military junta to partial democracy.

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summarize: The area was long a part of the Austro-Hungarian Empire until the empire collapsed at the end of World War I. The new state was founded by Tomáš Garrigue Masaryk (1850–1937), who served as its first president from 14 November 1918 to 14 December 1935. He was succeeded by his close ally, Edvard Beneš (1884–1948). The roots of Czech nationalism go back to the 19th century, when philologists and educators, influenced by Romanticism, promoted the Czech language and pride in the Czech people. Nationalism became a mass movement in the second half of the 19th century. Taking advantage of the limited opportunities for participation in political life under Austrian rule, Czech leaders such as historian František Palacký (1798–1876) founded many patriotic, self-help organizations which provided a chance for many of their compatriots to participate in communal life prior to independence. Palacký supported Austro-Slavism and worked for a reorganized and federal Austrian Empire, which would protect the Slavic speaking peoples of Central Europe against Russian and German threats. An advocate of democratic reform and Czech autonomy within Austria-Hungary, Masaryk was elected twice to the "Reichsrat" (Austrian Parliament), first from 1891 to 1893 for the Young Czech Party, and again from 1907 to 1914 for the Czech Realist Party, which he had founded in 1889 with Karel Kramář and Josef Kaizl. During World War I small numbers of Czechs and Slovaks, the Czechoslovak Legions, fought with the Allies in France and Italy, while large numbers deserted to Russia in exchange for its support for the independence of Czechoslovakia from the Austrian Empire. With the outbreak of World War I, Masaryk began working for Czech independence in a union with Slovakia. With Edvard Beneš and Milan Rastislav Štefánik, Masaryk visited several Western countries and won support from influential publicists. The Bohemian Kingdom ceased to exist in 1918 when it was incorporated into Czechoslovakia. Czechoslovakia was founded in October 1918, as one of the successor states of the Austro-Hungarian Empire at the end of World War I and as part of the Treaty of Saint-Germain-en-Laye. It consisted of the present day territories of Bohemia, Moravia, Slovakia and Carpathian Ruthenia. Its territory included some of the most industrialized regions of the former Austria-Hungary. The new country was a multi-ethnic state, with Czechs and Slovaks as "constituent peoples". The population consisted of Czechs (51%), Slovaks (16%), Germans (22%), Hungarians (5%) and Rusyns (4%). Many of the Germans, Hungarians, Ruthenians and Poles and some Slovaks, felt oppressed because the political elite did not generally allow political autonomy for minority ethnic groups. This policy led to unrest among the non-Czech population, particularly in German-speaking Sudetenland, which initially had proclaimed itself part of the Republic of German-Austria in accordance with the self-determination principle. The state proclaimed the official ideology that there were no separate Czech and Slovak nations, but only one nation of Czechoslovaks (see Czechoslovakism), to the disagreement of Slovaks and other ethnic groups. Once a unified Czechoslovakia was restored after World War II (after the country had been divided during the war), the conflict between the Czechs and the Slovaks surfaced again. The governments of Czechoslovakia and other eastern European nations deported ethnic Germans to the West, reducing the presence of minorities in the nation. Most of the Jews had been killed during the war by the Nazis and their allies. During the period between the two world wars, democracy thrived in Czechoslovakia. Of all the new states established in central Europe after 1918, only Czechoslovakia preserved a democratic government until the war broke out. Thus, despite regional disparities, its level of development was much higher than that of neighboring states. The population was generally literate, and contained fewer alienated groups. The influence of these conditions was augmented by the political values of Czechoslovakia's leaders and the policies they adopted. Under Tomas Masaryk, Czech and Slovak politicians promoted progressive social and economic conditions that served to defuse discontent. Foreign minister Beneš became the prime architect of the Czechoslovak-Romanian-Yugoslav alliance (the "Little Entente", 1921–38) directed against Hungarian attempts to reclaim lost areas. Beneš worked closely with France. Far more dangerous was the German element, which after 1933 became allied with the Nazis in Germany. The increasing feeling of inferiority among the Slovaks, who were hostile to the more numerous Czechs, weakened the country in the late 1930s. Many Slovaks supported an extreme nationalist movement and welcomed the puppet Slovak state set up under Hitler's control in 1939. After 1933, Czechoslovakia remained the only democracy in central and eastern Europe. In September 1938, Adolf Hitler demanded control of the Sudetenland. On 29 September 1938, Britain and France ceded control in the Appeasement at the Munich Conference; France ignored the military alliance it had with Czechoslovakia. During October 1938, Nazi Germany occupied and annexed the Sudetenland border region, effectively crippling Czechoslovak defences. On 15 March 1939, the remainder ("rump") of Czechoslovakia was invaded and divided into the Protectorate of Bohemia and Moravia and the puppet Slovak State. Much of Slovakia and all of Carpathian Ruthenia were annexed by Hungary. Poland occupied Zaolzie, an area whose population was majority Polish, in October 1938. The eventual goal of the German state under Nazi leadership was to eradicate Czech nationality through assimilation, deportation, and extermination of the Czech intelligentsia; the intellectual elites and middle class made up a considerable number of the 200,000 people who passed through concentration camps and the 250,000 who died during German occupation. Under Generalplan Ost, it was assumed that around 50% Czechs would be fit for Germanization. The Czech intellectual elites were to be removed not only from Czech territories but from Europe completely. The authors of Generalplan Ost believed it would be best if they emigrated overseas, as even in Siberia they were considered a threat to German rule. Just like Jews, Poles, Serbs, and several other nations, Czechs were considered to be untermenschen by the Nazi state. In 1940, in a secret Nazi plan for the Germanization of the Protectorate of Bohemia and Moravia it was declared that those considered to be of racially Mongoloid origin and the Czech intelligentsia were not to be Germanized. The deportation of Jews to concentration camps was organized under the direction of Reinhard Heydrich, and the fortress town of Terezín was made into a ghetto way station for Jewish families. On 4 June 1942 Heydrich died after being wounded by an assassin in Operation Anthropoid. Heydrich's successor, Colonel General Kurt Daluege, ordered mass arrests and executions and the destruction of the villages of Lidice and Ležáky. In 1943 the German war effort was accelerated. Under the authority of Karl Hermann Frank, German minister of state for Bohemia and Moravia, some 350,000 Czech laborers were dispatched to the Reich. Within the protectorate, all non-war-related industry was prohibited. Most of the Czech population obeyed quiescently up until the final months preceding the end of the war, while thousands were involved in the resistance movement. For the Czechs of the Protectorate Bohemia and Moravia, German occupation was a period of brutal oppression. Czech losses resulting from political persecution and deaths in concentration camps totaled between 36,000 and 55,000. The Jewish population of Bohemia and Moravia (118,000 according to the 1930 census) was virtually annihilated. Many Jews emigrated after 1939; more than 70,000 were killed; 8,000 survived at Terezín. Several thousand Jews managed to live in freedom or in hiding throughout the occupation. Despite the estimated 136,000 deaths at the hands of the Nazi regime, the population in the Reichsprotektorate saw a net increase during the war years of approximately 250,000 in line with an increased birth rate. On 6 May 1945, the third US Army of General Patton entered Pilsen from the south west. On 9 May 1945, Soviet Red Army troops entered Prague. After World War II, pre-war Czechoslovakia was re-established, with the exception of Subcarpathian Ruthenia, which was annexed by the Soviet Union and incorporated into the Ukrainian Soviet Socialist Republic. The Beneš decrees were promulgated concerning ethnic Germans (see Potsdam Agreement) and ethnic Hungarians. Under the decrees, citizenship was abrogated for people of German and Hungarian ethnic origin who had accepted German or Hungarian citizenship during the occupations. In 1948, this provision was cancelled for the Hungarians, but only partially for the Germans. The government then confiscated the property of the Germans and expelled about 90% of the ethnic German population, over 2 million people. Those who remained were collectively accused of supporting the Nazis after the Munich Agreement, as 97.32% of Sudeten Germans had voted for the NSDAP in the December 1938 elections. Almost every decree explicitly stated that the sanctions did not apply to antifascists. Some 250,000 Germans, many married to Czechs, some antifascists, and also those required for the post-war reconstruction of the country, remained in Czechoslovakia. The Beneš Decrees still cause controversy among nationalist groups in the Czech Republic, Germany, Austria and Hungary. Carpathian Ruthenia (Podkarpatská Rus) was occupied by (and in June 1945 formally ceded to) the Soviet Union. In the 1946 parliamentary election, the Communist Party of Czechoslovakia was the winner in the Czech lands, and the Democratic Party won in Slovakia. In February 1948 the Communists seized power. Although they would maintain the fiction of political pluralism through the existence of the National Front, except for a short period in the late 1960s (the Prague Spring) the country had no liberal democracy. Since citizens lacked significant electoral methods of registering protest against government policies, periodically there were street protests that became violent. For example, there were riots in the town of Plzeň in 1953, reflecting economic discontent. Police and army units put down the rebellion, and hundreds were injured but no one was killed. While its economy remained more advanced than those of its neighbors in Eastern Europe, Czechoslovakia grew increasingly economically weak relative to Western Europe. The currency reform of 1953 caused dissatisfaction among Czechoslovak laborers. Prior to World War II, the Czech purchasing power surpassed that of the Soviet Union by 115–144%. This disparity was noted after Czechoslovakia came under the Soviet Bloc. To equalize the wage rate, Czechoslovaks had to turn in their old money for new at a decreased value. This lowered the real value of wages by about 11%. The banks also confiscated savings and bank deposits to control the amount of money in circulation. The economy continued to suffer as production achievements of bituminous coal was less than anticipated. Bituminous coal powered 85% of Czechoslovakia's economy. Because of low production, coal was utilized in industry only. Pre-war years, consumers used both coal and lignite for fuel, however due to low production, coal was for industrial use only which meant the consumer was only able to utilize lignite. In 1929, a typical family of four consumed approximately 2.34 tons of lignite, but by 1953 it was allowed to use only 1.6–1.8 tons per year. In 1968, when the reformer Alexander Dubček was appointed to the key post of First Secretary of the Czechoslovak Communist Party, there was a brief period of liberalization known as the Prague Spring. In response, after failing to persuade the Czechoslovak leaders to change course, five other members of the Warsaw Pact invaded. Soviet tanks rolled into Czechoslovakia on the night of 20–21 August 1968. Soviet Communist Party General Secretary Leonid Brezhnev viewed this intervention as vital for the preservation of the Soviet, socialist system and vowed to intervene in any state that sought to replace Marxism-Leninism with capitalism. In the week after the invasion there was a spontaneous campaign of civil resistance against the occupation. This resistance involved a wide range of acts of non-cooperation and defiance: this was followed by a period in which the Czechoslovak Communist Party leadership, having been forced in Moscow to make concessions to the Soviet Union, gradually put the brakes on their earlier liberal policies. In April 1969 Dubček was finally dismissed from the First Secretaryship of the Czechoslovak Communist Party. Meanwhile, one plank of the reform program had been carried out: in 1968–69, Czechoslovakia was turned into a federation of the Czech Socialist Republic and Slovak Socialist Republic. The theory was that under the federation, social and economic inequities between the Czech and Slovak halves of the state would be largely eliminated. A number of ministries, such as education, now became two formally equal bodies in the two formally equal republics. However, the centralized political control by the Czechoslovak Communist Party severely limited the effects of federalization. The 1970s saw the rise of the dissident movement in Czechoslovakia, represented among others by Václav Havel. The movement sought greater political participation and expression in the face of official disapproval, manifested in limitations on work activities, which went as far as a ban on professional employment, the refusal of higher education for the dissidents' children, police harassment and prison. In 1989, the Velvet Revolution restored democracy. This occurred at around the same time as the fall of communism in Romania, Bulgaria, Hungary and Poland. The word "socialist" was removed from the country's full name on 29 March 1990 and replaced by "federal". In 1992, because of growing nationalist tensions in the government, Czechoslovakia was peacefully dissolved by parliament. On 1 January 1993 it formally separated into two independent countries, the Czech Republic and the Slovak Republic. After World War II, a political monopoly was held by the Communist Party of Czechoslovakia (KSČ). Gustáv Husák was elected first secretary of the KSČ in 1969 (changed to general secretary in 1971) and president of Czechoslovakia in 1975. Other parties and organizations existed but functioned in subordinate roles to the KSČ. All political parties, as well as numerous mass organizations, were grouped under umbrella of the National Front. Human rights activists and religious activists were severely repressed. Czechoslovakia had the following constitutions during its history (1918–1992): In the 1930s, the nation formed a military alliance with France, which collapsed in the Munich Agreement of 1938. After World War II, active participant in Council for Mutual Economic Assistance (Comecon), Warsaw Pact, United Nations and its specialized agencies; signatory of conference on Security and Cooperation in Europe. Before World War II, the economy was about the fourth in all industrial states in Europe. The state was based on strong economy, manufacturing cars (Škoda, Tatra), trams, aircraft (Aero, Avia), ships, ship engines (Škoda), canons, shoes (Baťa), turbines, guns (Zbrojovka Brno). It was the industrial workshop for Austro-Hungarian empire. The Slovak lands were more in agriculture. After World War II, the economy was centrally planned, with command links controlled by the communist party, similarly to the Soviet Union. The large metallurgical industry was dependent on imports of iron and non-ferrous ores. After World War II, the country was short of energy, relying on imported crude oil and natural gas from Soviet Union, domestic brown coal, and nuclear and hydroelectric energy. Energy constraints were a major factor in the 1980s. Slightly after the foundation of Czechoslovakia in 1918, there was a lack of needful infrastructure in many areas – paved roads, railways, bridges etc. Massive improvement in the following years enabled Czechoslovakia to develop its industry. Prague's civil airport in Ruzyně became one of the most modern terminals in the world, when it was finished in 1937. Tomáš Baťa, Czech entrepreneur and visionary outlined his ideas in the publication "Budujme stát pro 40 milionů lidí", where he described the future motorway system. Construction of the first motorways in Czechoslovakia begun in 1939, nevertheless, they were stopped after Nazi occupation during the World War II. Education was free at all levels and compulsory from age 6 to 15. The vast majority of the population was literate. There was a highly developed system of apprenticeship training and vocational schools supplemented general secondary schools and institutions of higher education. In 1991: Roman Catholics 46%, Evangelical Lutheran 5.3%, Atheist 30%, n/a 17%, but there were huge differences in religious practices between the two constituent republics; see Czech Republic and Slovakia. After World War II, free health care was available to all citizens. National health planning emphasized preventive medicine; factory and local health care centres supplemented hospitals and other inpatient institutions. There was substantial improvement in rural health care during the 1960s and 1970s. During the era between the World Wars, Czechoslovak democracy and liberalism facilitated conditions for free publication. The most significant daily newspapers in these times were Lidové noviny, Národní listy, Český deník and Československá republika. During Communist rule, the mass media in Czechoslovakia were controlled by the Communist Party. Private ownership of any publication or agency of the mass media was generally forbidden, although churches and other organizations published small periodicals and newspapers. Even with this information monopoly in the hands of organizations under KSČ control, all publications were reviewed by the government's Office for Press and Information. The Czechoslovakia national football team was a consistent performer on the international scene, with eight appearances in the FIFA World Cup Finals, finishing in second place in 1934 and 1962. The team also won the European Football Championship in 1976, came in third in 1980 and won the Olympic gold in 1980. Well-known football players such as Pavel Nedvěd, Antonín Panenka, Milan Baroš, Tomáš Rosický, Vladimír Šmicer or Petr Čech were all born in Czechoslovakia. The International Olympic Committee code for Czechoslovakia is TCH, which is still used in historical listings of results. The Czechoslovak national ice hockey team won many medals from the world championships and Olympic Games. Peter Šťastný, Jaromír Jágr, Dominik Hašek, Peter Bondra, Petr Klíma, Marián Gáborík, Marián Hossa, Miroslav Šatan and Pavol Demitra all come from Czechoslovakia. Emil Zátopek, winner of four Olympic gold medals in athletics, is considered one of the top athletes in Czechoslovak history. Věra Čáslavská was an Olympic gold medallist in gymnastics, winning seven gold medals and four silver medals. She represented Czechoslovakia in three consecutive Olympics. Several accomplished professional tennis players including Ivan Lendl, Jan Kodeš, Miloslav Mečíř, Hana Mandlíková, Martina Hingis, Martina Navratilova, Jana Novotna, Petra Kvitová and Daniela Hantuchová were born in Czechoslovakia. Maps with Hungarian-language rubrics:

Czechoslovakia, or Czecho-Slovakia (; Czech and, "Česko-Slovensko"), was a sovereign state in Central Europe that existed from October 1918, when it declared its independence from the Austro-Hungarian Empire, until its peaceful dissolution into the Czech Republic and Slovakia on 1 January 1993.

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summarize: The Parliament, like the other institutions, was not designed in its current form when it first met on 10 September 1952. One of the oldest common institutions, it began as the "Common Assembly" of the European Coal and Steel Community (ECSC). It was a consultative assembly of 78 appointed parliamentarians drawn from the national parliaments of member states, having no legislative powers. The change since its foundation was highlighted by Professor David Farrell of the University of Manchester: "For much of its life, the European Parliament could have been justly labelled a'multi-lingual talking shop'." Its development since its foundation shows how the European Union's structures have evolved without a clear ‘master plan’. Some, such as Tom Reid of the "Washington Post", said of the union: "nobody would have deliberately designed a government as complex and as redundant as the EU". Even the Parliament's two seats, which have switched several times, are a result of various agreements or lack of agreements. Although most MEPs would prefer to be based just in Brussels, at John Major's 1992 Edinburgh summit, France engineered a treaty amendment to maintain Parliament's plenary seat permanently at Strasbourg. The body was not mentioned in the original Schuman Declaration. It was assumed or hoped that difficulties with the British would be resolved to allow the Parliamentary Assembly of the Council of Europe to perform the task. A separate Assembly was introduced during negotiations on the Treaty as an institution which would counterbalance and monitor the executive while providing democratic legitimacy. The wording of the ECSC Treaty demonstrated the leaders' desire for more than a normal consultative assembly by using the term "representatives of the people" and allowed for direct election. Its early importance was highlighted when the Assembly was given the task of drawing up the draft treaty to establish a European Political Community. By this document, the Ad Hoc Assembly was established on 13 September 1952 with extra members, but after the failure of the proposed European Defence Community the project was In 1979, its members were directly elected for the first time. This sets it apart from similar institutions such as those of the Parliamentary Assembly of the Council of Europe or Pan-African Parliament which are appointed. After that first election, the parliament held its first session on 11 July 1979, electing Simone Veil MEP as its president. Veil was also the first female president of the Parliament since it was formed as the Common Assembly. As an elected body, the Parliament began to draft proposals addressing the functioning of the EU. For example, in 1984, inspired by its previous work on the Political Community, it drafted the "draft Treaty establishing the European Union" (also known as the 'Spinelli Plan' after its rapporteur Altiero Spinelli MEP). Although it was not adopted, many ideas were later implemented by other treaties. Furthermore, the Parliament began holding votes on proposed Commission Presidents from the 1980s, before it was given any formal right to veto. Since it became an elected body, the membership of the In 2004, following the largest trans-national election in history, despite the European Council choosing a President from the largest political group (the EPP), the Parliament again exerted pressure on the Commission. During the Parliament's hearings of the proposed Commissioners MEPs raised doubts about some nominees with the Civil Liberties committee rejecting Rocco Buttiglione from the post of Commissioner for Justice, Freedom and Security over his views on homosexuality. That was the first time the Parliament had ever voted against an incoming Commissioner and despite Barroso's insistence upon Buttiglione the Parliament forced Buttiglione to be withdrawn. A number of other Commissioners also had to be withdrawn or reassigned before Parliament allowed the The Lisbon Treaty finally came into force on 1 December 2009, granting Parliament powers over the entire EU budget, making Parliament's legislative powers equal to the Council's in nearly all areas and linking the appointment of the Commission President to Parliament's own elections. Despite some calls for the parties to put forward candidates beforehand, only the EPP (which had re-secured their position as largest party) had one in re-endorsing Barroso. Barroso gained the support of the European Council for a second term and secured majority support from the Parliament in September 2009. Parliament voted 382 votes in favour and 219 votes against (117 abstentions ) with support of the European People's Party, European Conservatives and Reformists and the Alliance of Liberals and Democrats for Europe. The liberals gave support after Barroso gave them a number of concessions; the liberals previously joined the socialists' call for a delayed vote (the EPP had wanted to approve Barroso in July of that year). Once Barroso put forward the candidates for his next Commission, another opportunity to gain concessions arose. Bulgarian nominee Rumiana Jeleva The Parliament and Council have been compared to the two chambers of a bicameral legislature. However, there are some differences from national legislatures; for example, neither the Parliament nor the Council have the power of legislative initiative (except for the fact that the Council has the power in some intergovernmental matters). In Community matters, this is a power uniquely reserved for the European Commission (the executive). Therefore, while Parliament can amend and reject legislation, to make a proposal for legislation, it needs the Commission to draft a bill before anything can become law. The value of such a power has been questioned by noting that in the national legislatures of the member states 85% of initiatives introduced without executive support fail to become law. Yet it has been argued by former Parliament president Hans-Gert Pöttering that as the Parliament does have the right to ask the Commission to draft such legislation, and as the Commission is following Parliament's proposals more and more Parliament does have a "de facto" right of legislative initiative. The Parliament also has a great deal of indirect influence, through non-binding resolutions and committee hearings, as a "pan-European soapbox" with the ear of thousands of Brussels-based journalists. There is also an indirect effect on foreign policy; the Parliament must approve all development grants, including those overseas. For example, the support for post-war Iraq reconstruction, or incentives for the cessation of Iranian nuclear development, must be supported by the Parliament. Parliamentary support was also required for the transatlantic passenger data-sharing deal with the United States. Finally, Parliament holds a non-binding vote on new EU treaties but cannot veto it. However, when Parliament threatened to vote down the Nice Treaty, the Belgian and Italian Parliaments said they would veto the treaty on the European Parliament's behalf. With each new treaty, the powers of the Parliament, in terms of its role in the Union's legislative procedures, have expanded. The procedure which has slowly become dominant is the "ordinary legislative procedure" (previously named "codecision procedure"), which provides an equal footing between Parliament and Council. In particular, under the procedure, the Commission presents a proposal to Parliament and the Council which can only become law if both agree on a text, which they do (or not) through successive readings up to a maximum of three. In its first reading, Parliament may send amendments to the Council which can either adopt the text with those amendments or send back a "common position". That position may either be approved by Parliament, or it may reject the text by an absolute majority, causing it to fail, or it may adopt further amendments, also by an absolute majority. If the Council does not approve these, then a "Conciliation Committee" is formed. The Committee is composed of the Council members plus an equal number of MEPs who seek to agree a compromise. Once a position is agreed, it has to The legislative branch officially holds the Union's budgetary authority with powers gained through the Budgetary Treaties of the 1970s and the Lisbon Treaty. The EU budget is subject to a form of the ordinary legislative procedure with a single reading giving Parliament power over the entire budget (before 2009, its influence was limited to certain areas) on an equal footing to the Council. If there is a disagreement between them, it is taken to a conciliation committee as it is for legislative proposals. The President of the European Commission is proposed by the European Council on the basis of the European elections to Parliament. That proposal has to be approved by the Parliament (by a simple majority) who "elect" the President according to the treaties. Following the approval of the Commission President, the members of the Commission are proposed by the President in accord with the member states. Each Commissioner comes before a relevant parliamentary committee hearing covering the proposed portfolio. They are then, as a body, approved or rejected by the Parliament. In practice, the Parliament has never voted against a President or his Commission, but it did seem likely when the Barroso Commission was put forward. The resulting pressure forced the proposal to be withdrawn and changed to be more acceptable to parliament. That pressure was seen as an important sign by some of the evolving nature of the Parliament and its ability to make the Commission accountable, The Parliament also has other powers of general supervision, mainly granted by the Maastricht Treaty. The Parliament has the power to set up a Committee of Inquiry, for example over mad cow disease or CIA detention flights the former led to the creation of the European veterinary agency. The Parliament can call other institutions to answer questions and if necessary to take them to court if they break EU law or treaties. Furthermore, it has powers over The parliamentarians are known in English as Members of the European Parliament (MEPs). They are elected every five years by universal adult suffrage and sit according to political allegiance; about a third are women. Before 1979 they were appointed by their national parliaments. In 2017, an estimated 17 MEPs were not white. Of these, three were black; if the numbers were proportionate to the EU population, then 22 would be black. Under the Lisbon Treaty, seats are allocated to each state according to population and the maximum number of members is set at 751 (however, as the President cannot vote while in the chair there will only be 750 voting members at any one time). Since 1 February 2020, 705 MEPs (including the president of the Parliament) sit in the European Parliament, as there is no EU citizens' représentative of the United Kingdom anymore due to Brexit. Representation is currently limited to a maximum of 96 seats and a minimum of 6 seats per state and the seats are distributed according to "degressive proportionality", i.e., the larger the state, the more citizens are represented per MEP. As a result, Maltese and Luxembourgish voters have roughly 10x more influence per voter than citizens of the six large countries. , Germany (80.9 million inhabitants) has 96 seats (previously 99 seats), i.e. one seat for 843,000 inhabitants. Malta (0.4 million inhabitants) has 6 seats, i.e. one seat for 70,000 inhabitants. The new system implemented under the Lisbon Treaty, including revising the seating well before elections, was intended to avoid political horse trading when the allocations have to be revised to reflect demographic changes. Pursuant to this apportionment, the constituencies are formed. In four EU member states (Belgium, Ireland, Italy and Poland), the national territory is divided into a number of constituencies. In the remaining member states, the whole country forms a single constituency. All member states hold elections to the European Parliament using various forms of proportional representation. Due to the delay in ratifying the Lisbon Treaty, the seventh parliament was elected under the lower Nice Treaty cap. A small scale treaty amendment was ratified on 29 November 2011. This amendment brought Before 2009, members received the same salary as members of their national parliament. However, from 2009 a new members statute came into force, after years of attempts, which gave all members an equal monthly pay, of €8,484.05 each in 2016, subject to a European Union tax and which can also be taxed nationally. MEPs are entitled to a pension, paid by Parliament, from the age of 63. Members are also entitled to allowances for office MEPs in Parliament are organised into eight different parliamentary groups, including thirty non-attached members known as "non-inscrits". The two largest groups are the European People's Party (EPP) and the Socialists & Democrats (S&D). These two groups have dominated the Parliament for much of its life, continuously holding between 50 and 70 percent of the seats between them. No single group has ever held a majority in Parliament. As a result of being broad alliances of national parties, European group parties are very decentralised and hence have more in common with parties in federal states like Germany or the United States than unitary states like the majority of the EU states. Nevertheless, the European groups were actually more cohesive than their Given that the Parliament does not form the government in the traditional sense of a Parliamentary system, its politics have developed along more consensual lines rather than majority rule of competing parties and coalitions. Indeed, for much of its life it has been dominated by a grand coalition of the European People's Party and the Party of European Socialists. The two major parties tend to co-operate to find a compromise between their two groups leading to proposals endorsed by huge majorities. However, this does not always produce agreement, and each may instead try to build other alliances, the EPP normally with other centre-right or right wing Groups and the PES with centre-left or left wing groups. Sometimes, the Liberal Group is then in the pivotal position. There are also occasions where very sharp party political divisions have emerged, for example over the resignation of the Santer Elections have taken place, directly in every member state, every five years since 1979. there have been nine elections. When a nation joins mid-term, a by-election will be held to elect their representatives. This has happened six times, most recently when Croatia joined in 2013. Elections take place across four days according to local custom and, apart from having to be proportional, the electoral system is chosen by the member state. This includes allocation of sub-national constituencies; while most members have a national list, some, like the UK and Poland, divide their allocation between regions. Seats are allocated to member states according to their population, since 2014 with no state having more than 96, but no fewer than 6, to maintain proportionality. The most recent Union-wide elections to the European Parliament were the European elections of 2019, held from 23 to 26 May 2019. They were the largest simultaneous transnational elections ever held anywhere in the world. The first session of the ninth parliament started 2 July 2019. European political parties have the exclusive right to campaign during the European elections (as opposed to their corresponding EP groups). There have been a number of proposals Each year the activities of the Parliament cycle between committee weeks where reports are discussed in committees and interparliamentary delegations meet, political group weeks for members to discuss work within their political groups and session weeks where members spend 31⁄2 days in Strasbourg for part-sessions. In addition six 2-day part-sessions are organised in Brussels throughout the year. Four weeks are allocated as constituency week to allow members to do exclusively constituency work. Finally there are no meetings planned during the summer weeks. The Parliament has the power to meet without being convened by another authority. Its meetings are partly controlled by the treaties but are otherwise up to Parliament according to its own "Rules of Procedure" (the regulations governing the parliament). During sessions, members may speak after being called on by the President. Members of the Council or Commission may also attend and speak in debates. Partly due to the need for translation, and the politics of consensus in the chamber, debates tend to be calmer and more polite than, say, the Westminster system. Voting is conducted primarily by a show of hands, that may be checked on request by electronic voting. Votes of MEPs are not recorded in either case, however; that only occurs when there is a roll-call ballot. This is required for the final votes on legislation and also whenever a political group or 30 MEPs request it. The number of roll-call votes has increased with time. Votes can also be a completely secret ballot (for example, when the president is elected). All recorded votes, along with minutes and legislation, are recorded in the "Official Journal of the European Union" and can be accessed online. Votes usually do not follow a debate, but rather they are grouped with other due votes on specific occasions, usually at noon on Tuesdays, Wednesdays or Thursdays. This is because the length of the vote is unpredictable and if it continues for longer than allocated it can disrupt other debates and meetings later in the day. Members are arranged in a hemicycle according to their political groups (in the Common Assembly, prior to 1958, members sat alphabetically) who are ordered mainly by left to right, but some smaller groups are placed towards the outer ring of the Parliament. All desks are equipped with microphones, headphones for translation and electronic voting equipment. The leaders of the groups sit on the front benches at the centre, and in the very centre is a podium for guest speakers. The remaining half of the circular chamber is primarily composed of the raised area where the President and staff sit. Further benches are provided between the sides of this area and the MEPs, these are taken up by the Council on the far left and the Commission on the far right. Both the Brussels and Strasbourg hemicycle roughly follow this layout with only minor differences. The hemicycle design is a compromise between the different Parliamentary systems. The British-based system has the different groups directly facing each other while the French-based system is a semicircle (and the traditional German system had all members in rows facing a rostrum for speeches). Although the design is mainly based on a semicircle, the opposite ends of the spectrum do still face each other. With access to the chamber limited, entrance is controlled by ushers who aid MEPs in the chamber (for example in delivering documents). The ushers can also occasionally act as a form of police in enforcing the President, for example in ejecting an MEP who is disrupting the session (although this is rare). The first head of protocol in the Parliament was French, so many of the duties in the Parliament are based on the French model first developed following the French Revolution. The 180 ushers are highly visible in the Parliament, dressed in black tails and wearing a silver chain, and are recruited in the same manner as the European civil service. The President is allocated a personal usher. According to the European Parliament website, the annual parliament budget for 2016 was €1.838 billion. The main cost categories were: According to a European Parliament study prepared in 2013, the Strasbourg seat costs an extra €103 million over maintaining a single location and according to the Court of Auditors an additional €5 million is related to travel expenses caused by having two seats. As a comparison, the German lower house of parliament (Bundestag) is estimated to cost €517 million in total for 2018, for a parliament with The Parliament is based in three different cities with numerous buildings. A protocol attached to the Treaty of Amsterdam requires that 12 plenary sessions be held in Strasbourg (none in August but two in September), which is the Parliament's official seat, while extra part sessions as well as committee meetings are held in Brussels. Luxembourg City hosts the Secretariat of the European Parliament. The European Parliament is one of at least two assemblies in the world with more than one meeting place (another being the parliament of the Isle of Man, Tynwald) and one of the few that does not have the power to decide its own location. The Strasbourg seat is seen as a symbol of reconciliation between France and Germany, the Strasbourg region having been fought over by the two countries in the past. However, the cost and inconvenience of having two seats is questioned. While Strasbourg is the official seat, and sits alongside the Council of Europe, Brussels is home to nearly all other major EU institutions, with the majority of Parliament's work being carried out there. Critics have described the two-seat arrangement as a "travelling circus", and there is a strong movement to establish Brussels as the sole seat. This is because the other political institutions (the Commission, Council and European Council) are located there, and hence Brussels is treated as the 'capital' of the EU. This movement has received Over the last few years, European institutions have committed to promoting transparency, openness, and the availability of information about their work. In particular, transparency is regarded as pivotal to the action of European institutions and a general principle of EU law, to be applied to the activities of EU institutions in order to strengthen the Union's democratic foundation. The general principles of openness and transparency are reaffirmed in the articles 8 A, point 3 and 10.3 of the Treaty of Lisbon and the Maastricht Treaty respectively, stating that "every citizen shall have the right to participate in the democratic life of the Union. Decisions shall be taken as openly and as closely as possible to the citizen". Furthermore, both treaties acknowledge the value of dialogue between citizens, representative associations, civil society, and European institutions. Article 17 of the Treaty on the Functioning of the European Union (TFEU) lays the juridical foundation for an open, transparent dialogue between European institutions and churches, religious associations, and non-confessional and philosophical organisations. In July 2014, in The chair of European Parliament Mediator for International Parental Child Abduction was established in 1987 by initiative of British MEP Charles Henry Plumb, with the goal of helping minor children of international couples victim of parental abduction. The Mediator finds negotiated solutions in the higher interest of the minor when said minor is abducted by a parent following separation of the couple, regardless whether married or unmarried. Since its institution, the chair has been held by Mairead McGuinness (since 2014), Roberta Angelilli (2009-2014), Evelyne Gebhardt (2004-2009), The European Parliamentary Research Service (EPRS) is the European Parliament's in-house research department and think tank. It provides Members of the European Parliament and, where appropriate, parliamentary committees with independent, objective and authoritative analysis of, and research on, policy issues relating to the European Union, in order to assist them in their parliamentary work. It is also designed to increase Members' and EP committees' The European Parliament periodically commissions opinion polls and studies on public opinion trends in Member States to survey perceptions and expectations of citizens about its work and the overall activities of the European Union. Topics include citizens' perception of the Annually, the European Parliament awards four prizes to individuals and organisations that distinguished themselves in the areas of human rights, film, youth projects, and European participation and citizenship. With the Sakharov Prize for Freedom of Thought, created in 1998, the European Parliament supports human rights by awarding individuals that contribute to promoting human rights worldwide, The European Charlemagne Youth Prize seeks to encourage youth participation in the European integration process. It is awarded The European Citizens' Prize is awarded by the European Parliament to activities and actions carried Since 2007, the LUX Prize is awarded by the European Parliament to films dealing with current topics of public European

The European Parliament (EP) is the legislative branch of the European Union and one of its seven institutions. Together with the Council of the European Union, it adopts European legislation, normally on a proposal from the European Commission. The Parliament is composed of 705 members (MEPs). The Parliament represents the second-largest democratic electorate in the world (after the Parliament of India) and the largest trans-national democratic electorate in the world (375 million eligible voters in 2009).

en

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summarize: The first written mention of name "Slovakia" is in 1586 (). It derives from the Czech word "Slováky"; previous German forms were "Windischen landen" and "Windenland" (the 15th century). The native name Radiocarbon dating puts the oldest surviving human artefacts from Slovakia—found near Nové Mesto nad Váhom—at 270,000 BCE, in the Early Paleolithic era. These ancient tools, made by the Clactonian technique, bear witness to the ancient habitation of Slovakia. Other stone tools from the Middle Paleolithic era (200,000–80,000 BCE) come from the Prévôt (Prepoštská) cave in Bojnice and from other nearby sites. The most important discovery from that era is a Neanderthal cranium (c. 200,000 BCE), discovered near Gánovce, a village in northern Slovakia. Archaeologists have found prehistoric human skeletons in the region, as well as numerous objects and vestiges of the Gravettian culture, principally in the river valleys of Nitra, Hron, Ipeľ, Váh and as far as the city of Žilina, and near the foot of the Vihorlat, Inovec, and Tribeč mountains, as well as in the Myjava Mountains. The most well-known finds include the oldest female statue made of mammoth bone (22,800 BCE), the famous Venus of Moravany. The statue was found in the 1940s in Moravany nad Váhom near Piešťany. Numerous necklaces made of shells from Cypraca thermophile gastropods of the Tertiary period have come from the sites of Zákovská, Podkovice, Hubina, and Radošina. These findings provide the most ancient evidence of commercial exchanges carried out between the Mediterranean and Central Europe. During the Bronze Age, the geographical territory of modern-day Slovakia went through three stages of development, stretching from 2000 to 800 BCE. Major cultural, economic, and political development can be attributed to the significant growth in production of copper, especially in central Slovakia (for example in Špania Dolina) and northwest The arrival of tribes from Thrace disrupted the people of the Kalenderberg culture, who lived in the hamlets located on the plain (Sereď) and in the hill forts like Molpír, near Smolenice, in the Little Carpathians. During Hallstatt times, monumental burial mounds were erected in western Slovakia, with princely equipment consisting of richly decorated vessels, ornaments and decorations. The burial rites consisted From around 500 BCE, the territory of modern-day Slovakia was settled by Celts, who built powerful "oppida" on the sites of modern-day Bratislava and Devín. Biatecs, silver coins with inscriptions in the Latin alphabet, represent the first known use of writing in Slovakia. At the northern regions, From 2 AD, the expanding Roman Empire established and maintained a series of outposts around and just south of the Danube, the largest of which were known as Carnuntum (whose remains are on the main road halfway between Vienna and Bratislava) and Brigetio (present-day Szőny at the Slovak-Hungarian border). Such Roman border settlements were built on the present area of Rusovce, currently a suburb of Bratislava. The military fort was surrounded by a civilian vicus and several farms of the villa rustica type. The name of this In the 2nd and 3rd centuries AD, the Huns began to leave the Central Asian steppes. They crossed the Danube in 377 AD and occupied Pannonia, which they used for 75 years as their base for launching looting-raids into Western Europe. However, Attila's death in 453 brought about the disappearance of The Slavic tribes settled in the territory of present-day Slovakia in the 5th century. Western Slovakia was the centre of Samo's empire in the 7th century. A Slavic state known as the Principality of Nitra arose in the 8th century and its ruler Great Moravia arose around 830 when Mojmír I unified the Slavic tribes settled north of the Danube and extended the Moravian supremacy over them. When Mojmír I endeavoured to secede from the supremacy of the king of East Francia in 846, King Louis the German deposed him and assisted Mojmír's nephew Rastislav (846–870) in acquiring the throne. The new monarch pursued an independent policy: after stopping a Frankish attack in 855, he also sought to weaken the influence of Frankish priests preaching in his realm. Duke Rastislav asked the Byzantine Emperor Michael III to Following the disintegration of the Great Moravian Empire at the turn of the 10th century, the Hungarians annexed the territory comprising modern Slovakia. After their defeat on the Lech River they abandoned their nomadic ways; they settled in the centre of the Carpathian valley, adopted Christianity and began to build a new state—the Hungarian kingdom. From the 11th century, when the territory inhabited by the Slavic-speaking population of Danubian Basin was incorporated into the Kingdom of Hungary, until 1918, when the Austro-Hungarian empire collapsed, the territory of modern Slovakia was an integral part of the Hungarian state. The In late October 1918, the Czech nationalist Tomáš Masaryk declared the "independence" for the territories of Bohemia, Moravia, Silesia, Upper Hungary and Carpathian Ruthenia and proclaimed a common state, Czechoslovakia. The Slovaks were not consulted. In 1919, during the chaos following the break-up of Austria-Hungary, Czechoslovakia was formed with numerous Germans, Slovaks, Hungarians and Ruthenians within the newly set borders. The borders were set by the Treaty of Saint Germain and Treaty of Trianon. In the peace following the World War, Czechoslovakia emerged as a sovereign European state. It provided what were at the time rather extensive rights to its minorities, at least on paper. During the Interwar period, democratic Czechoslovakia was allied with France, and also with Romania and Yugoslavia (Little Entente); however, After the Munich Agreement and its Vienna Award, Nazi Germany threatened to annex part of Slovakia and allow the remaining regions to be partitioned by Hungary or Poland unless independence was declared. Thus, Slovakia seceded from Czecho-Slovakia in March 1939 and allied itself, as demanded by Germany, with Hitler's coalition. Secession had created the first Slovak state in history. The government of the First Slovak Republic, led by Jozef Tiso and Vojtech Tuka, was strongly influenced by Germany and gradually became a puppet regime in many respects. Meanwhile, the Czechoslovak government-in-exile sought to reverse the Munich Agreement and the subsequent German occupation of Czechoslovakia and to return the Republic to its 1937 boundaries. The government operated from London and it was ultimately considered, by those countries that recognised it, the legitimate government for Czechoslovakia throughout the Second World War. As part After World War II, Czechoslovakia was reconstituted and Jozef Tiso was executed in 1947 for collaboration with the Nazis. More than 80,000 Hungarians and 32,000 Germans were forced to leave Slovakia, in a series of population transfers initiated by the Allies at the Potsdam Conference. Out of about 130,000 Carpathian Germans in Slovakia in 1938, by 1947 only some 20,000 remained. As a result of the Yalta Conference, Czechoslovakia came under the influence and later under direct occupation of the Soviet Union and its Warsaw Pact, after a coup in 1948. Eight thousand two hundred and forty The end of Communist rule in Czechoslovakia in 1989, during the peaceful Velvet Revolution, was followed once again by the country's dissolution, this time into two successor states. The word "socialist" was dropped in the names of the two republics, with the Slovak Socialist Republic renamed as Slovak Republic. On 17 July 1992, Slovakia, led by Prime Minister Vladimír Mečiar, declared itself a sovereign state, meaning that its laws took precedence over those of the Slovakia lies between latitudes 47° and 50° N, and longitudes 16° and 23° E. The Slovak landscape is noted primarily for its mountainous nature, with the Carpathian Mountains extending across most of the northern half of the country. Among these mountain ranges are the high peaks of the Fatra-Tatra Area (including Tatra Mountains, Greater Fatra and Lesser Fatra), Slovak Ore Mountains, Slovak Central Mountains or Beskids. The largest lowland is the fertile Danubian Lowland in the southwest, followed by the Eastern Slovak Lowland in the southeast. Forests cover 41% of Slovak land surface. The Tatra Mountains, with 29 peaks higher than AMSL, are the highest mountain range in the Carpathian Mountains. The Tatras occupy an area of, of which the greater part lies in Slovakia. They are divided into several parts. To the north, close to the Polish border, are the High Tatras which are a popular hiking and skiing destination and home to There are 9 national parks Slovakia has hundreds of caves and caverns under its mountains, of which 30 are open to the public. Most of the caves have stalagmites rising from the ground and stalactites hanging Most of the rivers arise in the Slovak mountains. Some only pass through Slovakia, while others make a natural border with surrounding countries (more than ). For example, the Dunajec () to the north, the Danube () to the south or the Morava () to the West. The total length of the rivers on Slovak territory is. The longest river in Slovakia is The Slovak climate lies between the temperate and continental climate zones with relatively warm summers and cold, cloudy and humid winters. Temperature extremes are between although temperatures below are rare. The weather differs from the mountainous north to the plains in the south. The warmest region is Bratislava and Southern Slovakia where the temperatures may reach in summer, occasionally to in Hurbanovo. During night, the temperatures drop to. The daily temperatures in winter average in the range of to. During night it may be freezing, but usually not below. In Slovakia, there are four seasons, each season (spring, summer, autumn and winter) lasts three months. The dry continental air brings in the summer heat and winter frosts. In contrast, oceanic air brings rainfalls and reduces summer temperatures. In the lowlands and valleys, there is often fog, especially in winter. Spring starts with 21 March and is Slovakia signed the Rio Convention on Biological Diversity on 19 May 1993, and became a party to the convention on 25 August 1994. It has subsequently produced a National Biodiversity Strategy and Action Plan, which was received by the convention on 2 November 1998. The biodiversity of Slovakia comprises animals (such as annelids, arthropods, molluscs, nematodes and vertebrates), fungi (Ascomycota, Basidiomycota, Chytridiomycota, Glomeromycota and Zygomycota), micro-organisms (including Mycetozoa), and plants. The geographical position of Slovakia determines the richness of the diversity of fauna and flora. More than 11,000 plant species have been described throughout its territory, nearly 29,000 animal species and over 1,000 species of protozoa. Endemic biodiversity is also common. Slovakia is located in the biome of temperate broadleaf and mixed forests. As the altitude changes, the vegetation associations and animal communities are forming height levels (oak, beech, spruce, scrub pine, alpine meadows and subsoil). Forests cover 44% of the territory of Slovakia. In terms of forest stands, 60% are broadleaf trees and 40% are coniferous trees. The occurrence of animal species is strongly connected to the appropriate types of plant associations and biotopes. Over 4,000 species of fungi have been recorded from Slovakia. Of these, nearly 1,500 are lichen-forming species. Some of these fungi are undoubtedly endemic, but not enough is known to say how Slovakia is a parliamentary democratic republic with a multi-party system. The last parliamentary elections were held on 29 February 2020 and two rounds of presidential elections took place on 16 and 30 March 2019. The Slovak head of state and the formal head of the executive is the president (currently Zuzana Čaputová, the first female president), though with very limited powers. The president is elected by direct, popular vote under the two-round system for a five-year term. Most executive power lies with the head of government, the prime minister (currently Igor Matovič), who is usually the leader of the winning party, but he or she needs to form a majority coalition in the parliament. The prime minister is appointed by the president. The remainder of the cabinet is appointed by the president on the recommendation of the prime minister. Slovakia's highest legislative body is the 150-seat unicameral National Council of the Slovak Republic ("Národná rada Slovenskej republiky"). Delegates are elected for a four-year term on the basis of proportional representation. Slovakia's highest judicial body is the Constitutional Court of Slovakia ("Ústavný súd"), which rules on constitutional issues. The 13 members of this court are appointed by the president from a slate of candidates nominated by parliament. The Constitution of the Slovak Republic was ratified 1 September 1992, and became effective 1 January 1993. It was amended in September 1998 to allow direct election of the president and again in February 2001 due to EU admission requirements. The civil law system is based on Austro-Hungarian codes. The legal code was modified to comply with the obligations of Organization on Security and Cooperation in Europe (OSCE) and to expunge the Marxist–Leninist legal theory. Slovakia accepts the compulsory International Court of Justice jurisdiction with reservations. The Ministry of Foreign and European Affairs () is responsible for maintaining the Slovak Republic's external relations and the management of its international diplomatic missions. The ministry's director is Miroslav Lajčák. The ministry oversees Slovakia's affairs with foreign entities, including bilateral relations with individual nations and its representation in international organizations. Slovakia joined the European Union and NATO in 2004 and the Eurozone in 2009. Slovakia is a member of the United Nations (since 1993) and participates in its specialized agencies. The country was, on 10 October 2005, elected to a two-year term on the UN Security Council from 2006 to 2007. It is also a member of the Schengen Area, the Council of Europe (CoE), the Organization for Security and Cooperation in Europe (OSCE), The Armed Forces of the Slovak Republic number 14,000 uniformed personnel. Slovakia joined NATO in March 2004. The country has been an active participant in US- and NATO-led military actions. There is a joint Czech-Slovak peacekeeping force in Kosovo. From 2006 the army transformed into a fully professional organisation and compulsory military service was abolished. The US State Department in 2017 reported: The government generally respected the human rights of its citizens; however, there were problems in some areas. The most significant human rights issues included incidents of interference with privacy; corruption; widespread discrimination against Roma minority; and security force violence against ethnic and racial minorities government actions and rhetoric did little to discourage. The government investigated reports of abuses by members of the Slovakia is divided into 8 "krajov" (singular—"kraj", usually translated as "region"), each of which is named after its principal city. Regions have enjoyed a certain degree of autonomy since 2002. Their self-governing bodies are referred to as Self-governing (or autonomous) Regions (sg. "samosprávny kraj", pl. "samosprávne kraje") or Upper-Tier Territorial Units (sg. "vyšší územný celok", pl. "vyššie územné celky", abbr. The Slovak economy is a developed, high-income economy, with the GDP per capita equalling 78% of the average of the European Union in 2018. The country has difficulties addressing regional imbalances in wealth and employment. GDP per capita ranges from 188% of EU average in Bratislava to 54% in Eastern Slovakia. Although regional income inequality is high, 90% of citizens own their homes. The OECD in 2017 reported: The Slovak Republic continues exhibiting robust economic performance, with strong growth backed by a sound financial sector, low public debt and high international competitiveness drawing on large inward investment. In 2020, Slovakia was ranked by the International Monetary Fund as the 38th richest country in the world (out of 187 countries), with purchasing power parity per capita GDP of $38,321. The country used to be dubbed the "Tatra Tiger". Slovakia successfully transformed from a centrally planned economy to a market-driven economy. Major privatisations are completed, the banking sector is almost completely in private hands, and foreign investment has risen. The Slovak economy is one of the fastest-growing economies in Europe and 3rd-fastest in eurozone (2017). In 2007, 2008 and 2010 (with GDP growth of 10.5%, 6% and 4%, retrospectively). In 2016, more than 86% of Slovak exports went to European Union, and more than 50% of Slovak imports came from other European Union member states. The ratio of government debt to GDP in Slovakia reached 49.4% by the end of 2018, far below the OECD average. Unemployment, peaking at 19% at the end of 1999, decreased to 4,9% in 2019, lowest recorded rate in Slovak history. Slovakia adopted the Euro currency on 1 January 2009 as the 16th member of the Eurozone. The euro in Slovakia was approved by the European commission on 7 May 2008. The Slovak koruna was revalued on 28 May 2008 to 30.126 for 1 euro, which was also the exchange rate for the euro. The Slovak government encourages foreign investment since it is one of the driving forces of the economy. Slovakia is an attractive country for foreign investors mainly because of its low wages, low tax rates, well educated labour force, favourable geographic location in the heart of Central Europe, strong political stability and good international relations reinforced by the country's accession to the European Union. Some regions, mostly at the east of Slovakia have failed to attract major investment, which has aggravated regional disparities in many economic and social areas. Foreign direct investment inflow grew more than 600% from 2000 and cumulatively reached an all-time high of $17.3 billion in 2006, or around $22,000 per capita by the end of 2008. Slovakia ranks 45th out of 190 economies in terms of ease of doing business, according to the 2020 World Bank Doing Business Report and 57th out of the 63 countries in terms of competitive economy, according to the 2020 World Competitiveness Yearbook Report. The population is over 5.4 million and consists mostly of Slovaks. The average population density is 110 inhabitants per km2. According to the 2011 census, the majority of the inhabitants of Slovakia are Slovaks (80.7%). Hungarians are the largest ethnic minority (8.5%). Other ethnic groups include Roma (2%), Czechs (0.6%), Rusyns (0.6%) and others or unspecified (7.6%). Unofficial estimates on the Roma population are much higher, around 5.6%. In 2018 the median age of the Slovak population was 41 years. The largest waves of Slovak emigration occurred in the 19th and early 20th centuries. In the 1990 US census, 1.8 million people self-identified as having Slovak ancestry. The official language is Slovak, a member of the Slavic language family. Hungarian is widely spoken in the southern regions, and Rusyn is used in some parts of the Northeast. Minority languages hold co-official status in the municipalities in which the size of the minority population meets the legal threshold of 15% in two consecutive censuses. Slovakia is ranked among the top EU countries regarding The Slovak constitution guarantees freedom of religion. In 2011, 62.0% of Slovaks identified themselves as Roman Catholics, 8.9% as Protestants, 3.8% as Greek Catholics, 0.9% as Orthodox, 13.4% identified themselves as atheists or non-religious, and 10.6% did not answer the question about their belief. In 2004, about one third of the church members regularly attended church services. The Slovak Greek Catholic Church is an Eastern rite sui iuris Catholic Church. Before World War II, an estimated 90,000 Jews lived in Slovakia (1.6% The Programme for International Student Assessment, coordinated by the OECD, currently ranks Slovak secondary education the 30th in the world (placing it just below the United States and just above Spain). Education in Slovakia is compulsory from age 6 to 16. The education system consists of elementary school which is divided into two parts, the first grade (age 6–10) and the second grade (age 10–15) which is finished by taking nationwide testing called Monitor, from Slovak language and math. Parents may apply for social assistance for a child that is studying on an elementary school or a high-school. If approved, the state provides basic study necessities for the Folk tradition has rooted strongly in Slovakia and is reflected in literature, music, dance and architecture. The prime example is a Slovak national anthem, ""Nad Tatrou sa blýska"", which is based on a melody from ""Kopala studienku"" folk song. The manifestation of Slovak folklore culture is the ""Východná"" Folklore Festival. It is the oldest and largest nationwide festival with international participation, which takes place in Východná annually. Slovakia is usually represented by many groups but mainly by SĽUK ("Slovenský ľudový umelecký kolektív—Slovak folk art collective"). SĽUK is the largest Slovak folk art group, Visual art in Slovakia is represented through painting, drawing, printmaking, illustration, arts and crafts, sculpture, photography or conceptual art. The Slovak National Gallery founded in 1948, is the biggest network of galleries in Slovakia. Two displays in Bratislava are situated in Esterházy Palace ("Esterházyho palác") and the Water Barracks ("Vodné kasárne"), adjacent one to another. They are located on the For a list of notable Slovak writers and poets, see List of Slovak authors. Christian topics include poem Proglas as a foreword to the four Gospels, partial translations of the Bible into Old Church Slavonic, "Zakon sudnyj ljudem". Medieval literature, in the period from the 11th to the 15th centuries, was written in Latin, Czech and Slovakised Czech. Lyric (prayers, songs and formulas) was still controlled by the Church, while epic was concentrated on legends. Authors Traditional Slovak cuisine is based mainly on pork, poultry (chicken is the most widely eaten, followed by duck, goose, and turkey), flour, potatoes, cabbage, and milk products. It is relatively closely related to Hungarian, Czech, Polish and Austrian cuisine. On the east it is also influenced by Ukrainian, including Lemko and Rusyn. In comparison with other European countries, "game meat" is more accessible in Slovakia due to vast resources of forest and because hunting is relatively popular. Boar, rabbit, and venison are generally available throughout the year. Lamb and goat are eaten but are not widely popular. The traditional Slovak meals are Sporting activities are practised widely in Slovakia, many of them on a professional level. Ice hockey and football have traditionally been regarded as the most popular sports in Slovakia, though tennis, handball, basketball, volleyball, whitewater slalom, cycling and athletics are also popular. One of the most popular team sports in Slovakia is ice hockey. Slovakia became a member of the IIHF on 2 February 1993 and since then has won 4 medals in Ice Hockey World Championships, consisting of 1 gold, 2 silver and 1 bronze. The most recent success was a silver medal at the 2012 IIHF World Championship in Helsinki. The Slovak national hockey team made five appearances in the Olympic games, finishing 4th in the 2010 Winter Olympics in Vancouver. The country has 8,280 registered players and is ranked 7th in the IIHF World Ranking at present. Before 2012, the Slovak

Slovakia (; ), officially the Slovak Republic (, ), is a landlocked country in Central Europe. It is bordered by Poland to the north, Ukraine to the east, Hungary to the south, Austria to the southwest, and the Czech Republic to the northwest. Slovakia's territory spans about and is mostly mountainous. The population is over 5.4 million and consists mostly of ethnic Slovaks. The capital and largest city is Bratislava, and the second-largest city is Košice. The official language is Slovak.

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summarize: In the mid-19th century, a 16th-century Aztec statue of Xochipilli was unearthed on the side of the volcano Popocatépetl near Tlalmanalco. The statue is of a single figure seated upon a temple-like base. Both the statue and the base upon which it sits are covered in carvings of sacred and psychoactive organisms including mushrooms ("Psilocybe aztecorum"), tobacco ("Nicotiana tabacum"), "Ololiúqui" ("Turbina corymbosa"), "sinicuichi" ("Heimia salicifolia"), possibly "cacahuaxochitl" ("Quararibea funebris"), and one unidentified flower. "The texts always use the flower in an entirely spiritual sense, and the aim of the religious colleges was to cause the flower of the body to bloom: This flower can be no other than the soul. The association of the flower with the sun is also evident. One of the hieroglyphs for the sun is a four-petalled flower, and the feasts of the ninth month, dedicated to Huitzilopochtliupo, were entirely given over to flower offerings." - Paul Pettennude, Ph.D. The figure himself sits on the base, head tilted up, eyes open, jaw tensed, with his mouth half open and his arms opened to the heavens. The statue is currently housed in the Aztec hall of the Museo Nacional de Antropología in Mexico City. In the popular reality television show, "Survivor", a statue of Xochipilli was used as the Immunity Idol for the. It has been suggested by Wasson, Schultes, and Hofmann that the statue of Xochipilli represents a figure in the throes of entheogenic ecstasy. The position and expression of the body, in combination with the very clear representations of hallucinogenic plants which are known to have been used in sacred contexts by the Aztec support this interpretation. Wasson says that in the statue's depiction Xochipilli "is absorbed by "temicxoch", 'dream flowers', as the Nahua say describing the awesome experience that follows the ingestion of an entheogen. I can think of nothing like it in the long and rich history of European art: Xochipilli absorbed in "temicxoch"".

' is the god of art, games, dance, flowers, and song in Aztec mythology. His name contains the Nahuatl words ("flower") and (either "prince" or "child") and hence means "flower prince". As the patron of writing and painting, he was called'the "Seven-flower", but he could also be referred to as "Five-flower".

en

76

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summarize: In a speech in 1929, French Foreign Minister Aristide Briand floated the idea of an organisation which would gather European nations together in a "federal union" to resolve common problems. But it was Britain's wartime leader Sir Winston Churchill who first publicly suggested the creation of "a Council of Europe" in a BBC radio broadcast on 21 March 1943, while the second world war was still raging. In his own words, he tried to "peer through the mists of the future to the end of the war," once victory had been achieved, and think about how to re-build and maintain peace on a shattered continent. Given that Europe had been at the origin of two world wars, the creation of such a body would be, he suggested, "a stupendous business". He returned to the idea during a well-known speech at the University of Zurich on 19 September 1946, throwing the full weight of his considerable post-war prestige behind it. The future structure of the Council of Europe was discussed at a specific congress of several hundred leading politicians, government representatives and civil society in The Hague, Netherlands, in 1948. There were two schools of thought competing: some favoured a classical international organisation with representatives of governments, while others preferred a political forum with parliamentarians. Both approaches were finally combined through the creation of a Committee of Ministers (in which governments were represented) and a Consultative Assembly (in which parliaments were represented), the two main bodies mentioned in the Statute of the Council of Europe. This dual intergovernmental and inter-parliamentary structure was later copied for the European Communities, North Atlantic Treaty Organization and the Organization for Security and Co-operation in Europe. The Council of Europe was founded on 5 May 1949 by the Treaty of London. The Statute was signed in London on that day by ten states: Belgium, Denmark, France, Ireland, Italy, Luxembourg, the Netherlands, Norway, Sweden and the United Kingdom, though Turkey and Greece joined three months later. On 10 August 1949, 100 members of the Council's Consultative Assembly, parliamentarians drawn from the twelve member nations, met in Strasbourg for its first plenary session, held over 18 sittings and lasting nearly a month. They debated how to reconcile and reconstruct a continent still reeling from war, yet already facing a new East-West divide, launched the concept of a trans-national court to protect the basic human rights of every European citizen, and took the first steps towards what would in time become the European Union. In August 1949, Paul-Henri Spaak of Belgium was elected as the first president of the Assembly, steering its early work. However, in December 1951, after nearly three years in the role, Spaak resigned in disappointment after the Assembly rejected proposals for a "European political authority". Convinced the Council of Europe was never going to be strong enough to achieve his long-term goal of European unification, he soon tried again in a different format, becoming one of the founders of the European Union. In 2018 an archive of all speeches made to the Parliamentary Assembly of the Council of Europe by heads of state or government since the Council of Europe's creation in 1949 appeared online, the fruit of a two-year project entitled "Voices of Europe". At the time of its launch, the archive comprised 263 speeches delivered over a 70-year period by some 216 Presidents, Prime Ministers, monarchs and religious leaders from 45 countries - though it continues to expand, as new speeches are added every few months. Some very early speeches by individuals considered to be "founding figures" of the European institutions, even if they were not heads of state or government at the time, are also included (such as Sir Winston Churchill or Robert Schuman). Addresses by eight monarchs appear in the list (such as King Juan Carlos I of Spain, King Albert II of Belgium and Grand Duke Henri of Luxembourg) as well as the speeches given by religious figures (such as Pope John Paul II, and Pope Francis) and several leaders from countries in the Middle East and North Africa (such as Shimon Peres, Yasser Arafat, Hosni Mubarak, Léopold Sédar Senghor or King Hussein of Jordan). The full text of the speeches is given in both English and French, regardless of the original language used. The archive is searchable by country, by name, and chronologically. Article 1(a) of the Statute states that "The aim of the Council of Europe is to achieve a greater unity between its members for the purpose of safeguarding and realising the ideals and principles which are their common heritage and facilitating their economic and social progress." Membership is open to all European states who seek harmony, cooperation, good governance and human rights, accepting the principle of the rule of law and are able and willing to guarantee democracy, fundamental human rights and freedoms. Whereas the member states of the European Union transfer part of their national legislative and executive powers to the European Commission and the European Parliament, Council of Europe member states maintain their sovereignty but commit themselves through conventions/treaties (international law) and co-operate on the basis of common values and common political decisions. Those conventions and decisions are developed by the member states working together at the Council of Europe. Both organisations function as concentric circles around the common foundations for European co-operation and harmony, with the Council of Europe being the geographically wider circle. The European Union could be seen as the smaller circle with a much higher level of integration through the transfer of powers from the national to the EU level. "The Council of Europe and the European Union: different roles, shared values." Council of Europe conventions/treaties are also open for signature to non-member states, thus facilitating equal co-operation with countries outside Europe. The Council of Europe's most famous achievement is the European Convention on Human Rights, which was adopted in 1950 following a report by the Council of Europe's Parliamentary Assembly, and followed on from the United Nations 'Universal Declaration of Human Rights' (UDHR). The Convention created the European Court of Human Rights in Strasbourg. The Court supervises compliance with the European Convention on Human Rights and thus functions as the highest European court. It is to this court that Europeans can bring cases if they believe that a member country has violated their fundamental rights and freedoms. The various activities and achievements of the Council of Europe can be found in detail on its official website. The Council of Europe works in the following areas: The institutions of the Council of Europe are: The CoE system also includes a number of semi-autonomous structures known as "Partial Agreements", some of which are also open to non-member states: The seat of the Council of Europe is in Strasbourg, France. First meetings were held in Strasbourg's University Palace in 1949, but the Council of Europe soon moved into its own buildings. The Council of Europe's eight main buildings are situated in the "Quartier européen", an area in the northeast of Strasbourg spread over the three districts of Le Wacken, La Robertsau and Quartier de l'Orangerie, where are also located the four buildings of the seat of the European Parliament in Strasbourg, the Arte headquarters and the seat of the International Institute of Human Rights. Building in the area started in 1949 with the predecessor of the Palais de l'Europe, the House of Europe (demolished in 1977), and came to a provisional end in 2007 with the opening of the New General Office Building, later named "Agora", in 2008. The Palais de l'Europe (Palace of Europe) and the Art Nouveau Villa Schutzenberger (seat of the European Audiovisual Observatory) are in the Orangerie district, and the European Court of Human Rights, the European Directorate for the Quality of Medicines and the Agora Building are in the Robertsau district. The Agora building has been voted "best international business center real estate project of 2007" on 13 March 2008, at the MIPIM 2008. The European Youth Centre is located in the Wacken district. Besides its headquarters in Strasbourg, the Council of Europe is also present in other cities and countries. The Council of Europe Development Bank has its seat in Paris, the North-South Centre of the Council of Europe is established in Lisbon, Portugal, and the Centre for Modern Languages is in Graz, Austria. There are European Youth Centres in Budapest, Hungary, and in Strasbourg. The European Wergeland Centre, a new Resource Centre on education for intercultural dialogue, human rights and democratic citizenship, operated in cooperation with the Norwegian Government, opened in Oslo, Norway, in February 2009. The Council of Europe has offices in Albania, Armenia, Azerbaijan, Bosnia and Herzegovina, Georgia, Moldova, Montenegro, Serbia, and Ukraine; information offices in Albania, Armenia, Azerbaijan, Bulgaria, Czech Republic, Estonia, Georgia, Hungary, Latvia, Lithuania, Moldova, North Macedonia, Poland, Romania, Russian Federation, Slovakia, Slovenia, and Ukraine; and a projects office in Turkey. All these offices are establishments of the Council of Europe and they share its juridical personality with privileges and immunities. The Council of Europe was founded on 5 May 1949 by Belgium, Denmark, France, Ireland, Italy, Luxembourg, Netherlands, Norway, Sweden and the United Kingdom. Greece joined three months later, and Iceland, Turkey and West Germany the next year. It now has 47 member states, with Montenegro being the latest to join. Article 4 of the Council of Europe Statute specifies that membership is open to any "European" State. This has been interpreted liberally from the beginning, when Turkey was admitted, to include transcontinental states (such as Georgia and Azerbaijan) and states that are geographically Asian but socio-politically European (such as Armenia and Cyprus). Nearly all European states have acceded to the Council of Europe, with the exceptions of Belarus (human rights concerns including active use of the death penalty), Kazakhstan (human rights concerns), and the Vatican City (a theocracy), as well as some of the territories with limited recognition. Besides the status as a full member, the Council of Europe has established other instruments for cooperation and participation of non-member states: observer, applicant, special guest, and partner for democracy. The Council of Europe works mainly through conventions. By drafting conventions or international treaties, common legal standards are set for its member states. However, several conventions have also been opened for signature to non-member states. Important examples are the Convention on Cybercrime (signed for example, by Canada, Japan, South Africa and the United States), the Lisbon Recognition Convention on the recognition of study periods and degrees (signed for example, by Australia, Belarus, Canada, the Holy See, Israel, Kazakhstan, Kyrgyzstan, New Zealand and the United States), the Anti-doping Convention (signed, for example, by Australia, Belarus, Canada and Tunisia) and the Convention on the Conservation of European Wildlife and Natural Habitats (signed for example, by Burkina Faso, Morocco, Tunisia and Senegal as well as the European Community). Non-member states also participate in several partial agreements, such as the Venice Commission, the Group of States Against Corruption (GRECO), the European Pharmacopoeia Commission and the North-South Centre. Invitations to sign and ratify relevant conventions of the Council of Europe on a case-by-case basis are sent to three groups of non-member entities: The Council of Europe is not to be confused with the Council of the European Union (the "Council of Ministers") or the European Council. These belong to the European Union, which is separate from the Council of Europe, although they have shared the same European flag and anthem since the 1980s since they both work for European integration. Nor is the Council of Europe to be confused with the European Union itself. The Council of Europe is an entirely separate body from the European Union. It is not controlled by it. Cooperation between the European Union and the Council of Europe has recently been reinforced, notably on culture and education as well as on the international enforcement of justice and Human Rights. The European Union is expected to accede to the European Convention on Human Rights (the Convention). There are also concerns about consistency in case law – the European Court of Justice (the EU's court in Luxembourg) is treating the Convention as part of the legal system of all EU member states in order to prevent conflict between its judgements and those of the European Court of Human Rights (the court in Strasbourg interpreting the Convention). Protocol No. 14 of the Convention is designed to allow the EU to accede to it and the EU Treaty of Lisbon contains a protocol binding the EU to join. The EU would thus be subject to its human rights law and external monitoring as its member states currently are. The Council of Europe Schools of political studies were established to train future generations of political, economic, social and cultural leaders in countries in transition. With the participation of national and international experts, they run annual series of seminars and conferences on topics such as European integration, democracy, human rights, the rule of law and globalisation. The first School of Political Studies was created in Moscow in 1992. Since then, 20 other schools have been set up along the same lines and now form an Association; a genuine network now covering the whole of Eastern and South-Eastern Europe and the Caucasus, as well as some countries in the Southern Mediterranean region. The Council of Europe Schools of political studies is part of the Education Department which is part of the Directorate of Democratic Participation within the Directorate General of Democracy (“DGII”) of the Council of Europe. The beginning of co-operation between the CoE and the UN started with the agreement signed by the Secretariats of these institutions on 15 December 1951. On 17 October 1989, the General Assembly of the United Nations approved a resolution on granting observer status to the Council of Europe which was proposed by several member states of the CoE. Currently Council of Europe holds observer status with the United Nations and is regularly represented in the UN General Assembly. It has organised the regional UN conferences against racism and on women and co-operates with the United Nations at many levels, in particular in the areas of human rights, minorities, migration and counter-terrorism. In November 2016, the UN General Assembly adopted by consensus Resolution (A/Res/71/17) on Cooperation between the United Nations and the Council of Europe whereby it acknowledged the contribution of Council of Europe to the protection and strengthening of human rights and fundamental freedoms, democracy and the rule of law, welcomed the ongoing co-operation in a variety of fields. Non-governmental organisations (NGOs) can participate in the INGOs Conference of the Council of Europe and become observers to inter-governmental committees of experts. The Council of Europe drafted the European Convention on the Recognition of the Legal Personality of International Non-Governmental Organisations in 1986, which sets the legal basis for the existence and work of NGOs in Europe. Article 11 of the European Convention on Human Rights protects the right to freedom of association, which is also a fundamental norm for NGOs. The rules for Consultative Status for INGOs appended to the resolution (93)38 "On relation between the Council of Europe and non-governmental organisations", adopted by the Committee of Ministers on 18 October 1993 at the 500th meeting of the Ministers' Deputies. On 19 November 2003 the Committee of Ministers changed the consultative status into a participatory status, "considering that it is indispensable that the rules governing the relations between the Council of Europe and NGOs evolve to reflect the active participation of international non-governmental organisations (INGOs) in the Organisation's policy and work programme". On 30 May 2018, the Council of Europe signed a Memorandum of understanding with the European football confederation UEFA. The Council of Europe also signed an agreement with FIFA in which the two agreed to strengthen future cooperation in areas of common interests. The deal which included cooperation between member states in the sport of football and safety and security at football matches, was finalized in October 2018. The General Agreement on Privileges and Immunities of the Council of Europe grants the organisation certain privileges and immunities. The working conditions of staff are governed by the Council's staff regulations, which are public. Salaries and emoluments paid by the Council of Europe to its officials are tax-exempt on the basis of Article 18 of the General Agreement on Privileges and Immunities of the Council of Europe. The Council of Europe created, and has since 1955 used as its official symbol, the European Flag with 12 golden stars arranged in a circle on a blue background. Its musical anthem since 1972, the "European Anthem", is based on the "Ode to Joy" theme from Ludwig van Beethoven's ninth symphony. On 5 May 1964, the 15th anniversary of its founding, the Council of Europe established 5 May as Europe Day. The wide private and public use of the European Flag is encouraged to symbolise a European dimension. To avoid confusion with the European Union which subsequently adopted the same flag in the 1980s, as well as other European institutions, the Council of Europe often uses a modified version with a lower-case "e" surrounding the stars which is referred to as the "Council of Europe Logo". The Council of Europe has been accused of institutional corruption and of not having any meaningful purpose, being superfluous in its aims to other pan-European bodies, including the European Union and the Organization for Security and Cooperation in Europe (OSCE). In 2013 "The Economist" agreed, saying that the "Council of Europe's credibility is on the line". Both Human Rights Watch and the European Stability Initiative have called on the Council of Europe to undertake concrete actions to show that it is willing and able to return to its "original mission to protect and ensure human rights". Issues have been raised regarding Azerbaijan's relationship to the Council of Europe, including allegations that Azerbaijan has, over a sustained period, provided bribes to Council members to vote down criticism of the authoritarian rule of the Aliyev regime and support motions advantageous to Azerbaijan. Azerbaijan joined the Council of Europe in 2001. Since September 2014 Human Rights Watch said that Azerbaijan's "systematic crackdown on human rights defenders and other perceived government critics shows sheer contempt for its commitments to the Council of Europe". In 2017 Council member and Italian politician Luca Volontè was accused by Italian prosecutors of receiving over 2.3 million euros in bribes in exchange for working for Azerbaijan in the parliamentary assembly, and that in 2013 he played a key role in orchestrating the defeat of a highly critical report on the abuse of political prisoners in Azerbaijan. The money was paid to Volontè in monthly instalments of 100,000 euros, starting in 2013, via four anonymous offshore companies. The payments stopped in 2014 when Volontè's bank reported them as suspicious transactions to the Milan prosecutor's office. Arif Mammadov, former head of the Azerbaijan representation at the Council of Europe, has stated that Azerbaijan's delegation at the Council had 25 million dollars available to "bribe members of the delegations and PACE generally". From 2014, Russia's voting rights were temporarily suspended by the Council due to the annexation of Crimea by the Russian Federation from Ukraine. In response, Russia withheld its annual membership dues in the amount of 33 million euros, placing the institution under financial strain. Russia claimed that its suspension by the Council was unfair, and demanded the restoration of voting rights. European Council secretary-general Thorbjørn Jagland organized a special committee to find a compromise with Russia in early 2018, a move that was criticized as giving in to alleged Russian pressure by Council members and academic observers, especially if voting sanctions were lifted. In May 2019, Russia's voting rights were restored after members of the human rights watchdog reached agreement to resolve dispute and the overwhelming majority of the Council voted in favour of the restoration.

The Council of Europe (CoE) ( (CdE), ) is an international organisation whose stated aim is to uphold human rights, democracy and the rule of law in Europe. Founded in 1949, it has 47 member states, with a population of approximately 820 million, and operates with an annual budget of approximately 500 million euros.

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summarize: The word "convection" may have slightly different but related usages in different scientific or engineering contexts or applications. The broader sense is in fluid mechanics, where "convection" refers to the motion of fluid regardless of cause. However, in thermodynamics "convection" often refers specifically to heat transfer by convection. Convection occurs on a large scale in atmospheres, oceans, planetary mantles, and it provides the mechanism of heat transfer for a large fraction of the outermost interiors of our sun and all stars. Fluid movement during convection may be invisibly slow, or it may be obvious and rapid, as in a hurricane. On astronomical scales, convection of gas and dust is thought to occur in the accretion disks of black holes, at speeds which may closely approach that of light. Convective heat transfer is a mechanism of heat transfer occurring because of bulk motion (observable movement) of fluids. Heat is the entity of interest being advected (carried), and diffused (dispersed). This can be contrasted with conductive heat transfer, which is the transfer of energy by vibrations at a molecular level through a solid or fluid, and radiative heat transfer, the transfer of energy through electromagnetic waves. Heat is transferred by convection in numerous examples of naturally occurring fluid flow, such as wind, oceanic currents, and movements within the Earth's mantle. Convection is also used in engineering practices of homes, industrial processes, cooling of equipment, etc. The rate of convective heat transfer may be improved by the use of a heat sink, often in conjunction with a fan. For instance, a typical computer CPU will have a purpose-made fan to ensure its operating temperature is kept within tolerable limits. A convection cell, also known as a Bénard cell is a characteristic fluid flow pattern in many convection systems. A rising body of fluid typically loses heat because it encounters a colder surface. In liquid, this occurs because it exchanges heat with colder liquid through direct exchange. In the example of the Earth's atmosphere, this occurs because it radiates heat. Because of this heat loss the fluid becomes denser than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance, its downward force overcomes the rising force beneath it, and the fluid begins to descend. As it descends, it warms again and the cycle repeats itself. Atmospheric circulation is the large-scale movement of air, and is a means by which thermal energy is distributed on the surface of the Earth, together with the much slower (lagged) ocean circulation system. The large-scale structure of the atmospheric circulation varies from year to year, but the basic climatological structure remains fairly constant. Latitudinal circulation occurs because incident solar radiation per unit area is highest at the heat equator, and decreases as the latitude increases, reaching minima at the poles. It consists of two primary convection cells, the Hadley cell and the polar vortex, with the Hadley cell experiencing stronger convection due to the release of latent heat energy by condensation of water vapor at higher altitudes during cloud formation. Longitudinal circulation, on the other hand, comes about because the ocean has a higher specific heat capacity than land (and also thermal conductivity, allowing the heat to penetrate further beneath the surface ) and thereby absorbs and releases more heat, but the temperature changes less than land. This brings the sea breeze, air cooled by the water, ashore in the day, and carries the land breeze, air cooled by contact with the ground, out to sea during the night. Longitudinal circulation consists of two cells, the Walker circulation and El Niño / Southern Oscillation. Some more localized phenomena than global atmospheric movement are also due to convection, including wind and some of the hydrologic cycle. For example, a foehn wind is a down-slope wind which occurs on the downwind side of a mountain range. It results from the adiabatic warming of air which has dropped most of its moisture on windward slopes. Because of the different adiabatic lapse rates of moist and dry air, the air on the leeward slopes becomes warmer than at the same height on the windward slopes. A thermal column (or thermal) is a vertical section of rising air in the lower altitudes of the Earth's atmosphere. Thermals are created by the uneven heating of the Earth's surface from solar radiation. The Sun warms the ground, which in turn warms the air directly above it. The warmer air expands, becoming less dense than the surrounding air mass, and creating a thermal low. The mass of lighter air rises, and as it does, it cools by expansion at lower air pressures. It stops rising when it has cooled to the same temperature as the surrounding air. Associated with a thermal is a downward flow surrounding the thermal column. The downward moving exterior is caused by colder air being displaced at the top of the thermal. Another convection-driven weather effect is the sea breeze. Warm air has a lower density than cool air, so warm air rises within cooler air, similar to hot air balloons. Clouds form as relatively warmer air carrying moisture rises within cooler air. As the moist air rises, it cools, causing some of the water vapor in the rising packet of air to condense. When the moisture condenses, it releases energy known as latent heat of condensation which allows the rising packet of air to cool less than its surrounding air, continuing the cloud's ascension. If enough instability is present in the atmosphere, this process will continue long enough for cumulonimbus clouds to form, which support lightning and thunder. Generally, thunderstorms require three conditions to form: moisture, an unstable airmass, and a lifting force (heat). All thunderstorms, regardless of type, go through three stages: the developing stage, the mature stage, and the dissipation stage. The average thunderstorm has a diameter. Depending on the conditions present in the atmosphere, these three stages take an average of 30 minutes to go through. Solar radiation affects the oceans: warm water from the Equator tends to circulate toward the poles, while cold polar water heads towards the Equator. The surface currents are initially dictated by surface wind conditions. The trade winds blow westward in the tropics, and the westerlies blow eastward at mid-latitudes. This wind pattern applies a stress to the subtropical ocean surface with negative curl across the Northern Hemisphere, and the reverse across the Southern Hemisphere. The resulting Sverdrup transport is equatorward. Because of conservation of potential vorticity caused by the poleward-moving winds on the subtropical ridge's western periphery and the increased relative vorticity of poleward moving water, transport is balanced by a narrow, accelerating poleward current, which flows along the western boundary of the ocean basin, outweighing the effects of friction with the cold western boundary current which originates from high latitudes. The overall process, known as western intensification, causes currents on the western boundary of an ocean basin to be stronger than those on the eastern boundary. As it travels poleward, warm water transported by strong warm water current undergoes evaporative cooling. The cooling is wind driven: wind moving over water cools the water and also causes evaporation, leaving a saltier brine. In this process, the water becomes saltier and denser. and decreases in temperature. Once sea ice forms, salts are left out of the ice, a process known as brine exclusion. These two processes produce water that is denser and colder. The water across the northern Atlantic ocean becomes so dense that it begins to sink down through less salty and less dense water. (The convective action is not unlike that of a lava lamp.) This downdraft of heavy, cold and dense water becomes a part of the North Atlantic Deep Water, a southgoing stream. Mantle convection is the slow creeping motion of Earth's rocky mantle caused by convection currents carrying heat from the interior of the earth to the surface. It is one of 3 driving forces that causes tectonic plates to move around the Earth's surface. The Earth's surface is divided into a number of tectonic plates that are continuously being created and consumed at their opposite plate boundaries. Creation (accretion) occurs as mantle is added to the growing edges of a plate. This hot added material cools down by conduction and convection of heat. At the consumption edges of the plate, the material has thermally contracted to become dense, and it sinks under its own weight in the process of subduction at an ocean trench. This subducted material sinks to some depth in the Earth's interior where it is prohibited from sinking further. The subducted oceanic crust triggers volcanism. The Stack effect or chimney effect is the movement of air into and out of buildings, chimneys, flue gas stacks, or other containers due to buoyancy. Buoyancy occurs due to a difference in indoor-to-outdoor air density resulting from temperature and moisture differences. The greater the thermal difference and the height of the structure, the greater the buoyancy force, and thus the stack effect. The stack effect helps drive natural ventilation and infiltration. Some cooling towers operate on this principle; similarly the solar updraft tower is a proposed device to generate electricity based on the stack effect. The convection zone of a star is the range of radii in which energy is transported primarily by convection. Granules on the photosphere of the Sun are the visible tops of convection cells in the photosphere, caused by convection of plasma in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours. A convection oven is an oven that has fans to circulate air around food, using the convection mechanism to cook food faster than a conventional oven. Convection ovens distribute heat evenly around the food, removing the blanket of cooler air that surrounds food when it is first placed in an oven and allowing food to cook more evenly in less time and at a lower temperature than in a conventional oven. A convection oven has a fan with a heating element around it. A small fan circulates the air in the cooking chamber. Convection may happen in fluids at all scales larger than a few atoms. There are a variety of circumstances in which the forces required for natural and forced convection arise, leading to different types of convection, described below. In broad terms, convection arises because of body forces acting within the fluid, such as gravity. The causes of convection are generally described as one of either "natural" ("free") or "forced", although other mechanisms also exist (discussed below). However, the distinction between natural and forced convection is particularly important for convective heat transfer. Natural convection, or free convection, occurs due to temperature differences which affect the density, and thus relative buoyancy, of the fluid. Heavier (denser) components will fall, while lighter (less dense) components rise, leading to bulk fluid movement. Natural convection can only occur, therefore, in a gravitational field. A common example of natural convection is the rise of smoke from a fire. It can be seen in a pot of boiling water in which the hot and less-dense water on the bottom layer moves upwards in plumes, and the cool and more dense water near the top of the pot likewise sinks. Natural convection will be more likely and more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection or a larger distance through the convecting medium. Natural convection will be less likely and less rapid with more rapid diffusion (thereby diffusing away the thermal gradient that is causing the convection) or a more viscous (sticky) fluid. The onset of natural convection can be determined by the Rayleigh number (Ra). Note that differences in buoyancy within a fluid can arise for reasons other than temperature variations, in which case the fluid motion is called gravitational convection (see below). However, all types of buoyant convection, including natural convection, do not occur in microgravity environments. All require the presence of an environment which experiences g-force (proper acceleration). In forced convection, also called heat advection, fluid movement results from external surface forces such as a fan or pump. Forced convection is typically used to increase the rate of heat exchange. Many types of mixing also utilize forced convection to distribute one substance within another. Forced convection also occurs as a by-product to other processes, such as the action of a propeller in a fluid or aerodynamic heating. Fluid radiator systems, and also heating and cooling of parts of the body by blood circulation, are other familiar examples of forced convection. Forced convection may happen by natural means, such as when the heat of a fire causes expansion of air and bulk air flow by this means. In microgravity, such flow (which happens in all directions) along with diffusion is the only means by which fires are able to draw in fresh oxygen to maintain themselves. The shock wave that transfers heat and mass out of explosions is also a type of forced convection. Although forced convection from thermal gas expansion in zero-g does not fuel a fire as well as natural convection in a gravity field, some types of artificial forced convection are far more efficient than free convection, as they are not limited by natural mechanisms. For instance, a convection oven works by forced convection, as a fan which rapidly circulates hot air forces heat into food faster than would naturally happen due to simple heating without the fan. Gravitational convection is a type of natural convection induced by buoyancy variations resulting from material properties other than temperature. Typically this is caused by a variable composition of the fluid. If the varying property is a concentration gradient, it is known as solutal convection. For example, gravitational convection can be seen in the diffusion of a source of dry salt downward into wet soil due to the buoyancy of fresh water in saline. Variable salinity in water and variable water content in air masses are frequent causes of convection in the oceans and atmosphere which do not involve heat, or else involve additional compositional density factors other than the density changes from thermal expansion (see "thermohaline circulation"). Similarly, variable composition within the Earth's interior which has not yet achieved maximal stability and minimal energy (in other words, with densest parts deepest) continues to cause a fraction of the convection of fluid rock and molten metal within the Earth's interior (see below). Gravitational convection, like natural thermal convection, also requires a g-force environment in order to occur. Vibration-induced convection occurs in powders and granulated materials in containers subject to vibration where an axis of vibration is parallel to the force of gravity. When the container accelerates upward, the bottom of the container pushes the entire contents upward. In contrast, when the container accelerates downward, the sides of the container push the adjacent material downward by friction, but the material more remote from the sides is less affected. The net result is a slow circulation of particles downward at the sides, and upward in the middle. If the container contains particles of different sizes, the downward-moving region at the sides is often narrower than the largest particles. Thus, larger particles tend to become sorted to the top of such a mixture. This is one possible explanation of the Brazil nut effect. Ice convection on Pluto is believed to occur in a soft mixture of nitrogen ice and carbon monoxide ice. It has also been proposed for Europa, and other bodies in the outer solar system. Thermomagnetic convection can occur when an external magnetic field is imposed on a ferrofluid with varying magnetic susceptibility. In the presence of a temperature gradient this results in a nonuniform magnetic body force, which leads to fluid movement. A ferrofluid is a liquid which becomes strongly magnetized in the presence of a magnetic field. This form of heat transfer can be useful for cases where conventional convection fails to provide adequate heat transfer, e.g., in miniature microscale devices or under reduced gravity conditions. Capillary action is a phenomenon where liquid spontaneously rises in a narrow space such as a thin tube, or in porous materials. This effect can cause liquids to flow against the force of gravity. It occurs because of inter-molecular attractive forces between the liquid and solid surrounding surfaces; If the diameter of the tube is sufficiently small, then the combination of surface tension and forces of adhesion between the liquid and container act to lift the liquid. The Marangoni effect is the convection of fluid along an interface between dissimilar substances because of variations in surface tension. Surface tension can vary because of inhomogeneous composition of the substances or the temperature-dependence of surface tension forces. In the latter case the effect is known as thermo-capillary convection. A well-known phenomenon exhibiting this type of convection is the "tears of wine". The Weissenberg effect is a phenomenon that occurs when a spinning rod is placed into a solution of liquid polymer. Entanglements cause the polymer chains to be drawn towards the rod instead of being thrown outward as would happen with an ordinary fluid (i.e., water). In a zero-gravity environment, there can be no buoyancy forces, and thus no natural (free) convection possible, so flames in many circumstances without gravity smother in their own waste gases. However, flames may be maintained with any type of forced convection (breeze); or (in high oxygen environments in "still" gas environments) entirely from the minimal forced convection that occurs as heat-induced "expansion" (not buoyancy) of gases allows for ventilation of the flame, as waste gases move outward and cool, and fresh high-oxygen gas moves in to take up the low pressure zones created when flame-exhaust water condenses. Mathematically, convection can be described by the convection–diffusion equation, also known as the generic scalar transport equation. In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system. The relative magnitudes of the Grashof number and the square of the Reynolds number determine which form of convection dominates. If formula_1, forced convection may be neglected, whereas if formula_2, natural convection may be neglected. If the ratio, known as the Richardson number, is approximately one, then both forced and natural convection need to be taken into account.

Convection is the heat transfer due to the bulk movement of molecules within fluids such as gases and liquids, including molten rock (rheid). Convection includes sub-mechanisms of advection (directional bulk-flow transfer of heat), and diffusion (non-directional transfer of energy or mass particles along a concentration gradient).

en

56

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summarize: On a microscopic scale, conduction occurs within a body considered as being stationary; this means that the kinetic and potential energies of the bulk motion of the body are separately accounted for. Internal energy diffuses as rapidly moving or vibrating atoms and molecules interact with neighbouring particles, transferring some of their microscopic kinetic and potential energies, these quantities being defined relative to the bulk of the body considered as being stationary. Heat is transferred by conduction when adjacent atoms or molecules collide, or as several electrons move backwards and forwards from atom to atom in a disorganized way so as not to form a macroscopic electric current, or as photons collide and scatter. Conduction is the most significant means of heat transfer within a solid or between solid objects in thermal contact. Conduction is greater in solids because the network of relatively close fixed spatial relationships between atoms helps to transfer energy between them by vibration. Thermal contact conductance is the study of heat conduction between solid bodies in contact. A temperature drop is often observed at the interface between the two surfaces in contact. This phenomenon is said to be a result of a thermal contact resistance existing between the contacting surfaces. Interfacial thermal resistance is a measure of an interface's resistance to thermal flow. This thermal resistance differs from contact resistance, as it exists even at atomically perfect interfaces. Understanding the thermal resistance at the interface between two materials is of primary significance in the study of its thermal properties. Interfaces often contribute significantly to the observed properties of the materials. The inter-molecular transfer of energy could be primarily by elastic impact, as in fluids, or by free electron diffusion, as in metals, or phonon vibration, as in insulators. In insulators, the heat flux is carried almost entirely by phonon vibrations. Metals (e.g., copper, platinum, gold, etc.) are usually good conductors of thermal energy. This is due to the way that metals bond chemically: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons that transfer thermal energy rapidly through the metal. The "electron fluid" of a conductive metallic solid conducts most of the heat flux through the solid. Phonon flux is still present, but carries less of the energy. Electrons also conduct electric current through conductive solids, and the thermal and electrical conductivities of most metals have about the same ratio. A good electrical conductor, such as copper, also conducts heat well. Thermoelectricity is caused by the interaction of heat flux and electric current. Heat conduction within a solid is directly analogous to diffusion of particles within a fluid, in the situation where there are no fluid currents. In gases, heat transfer occurs through collisions of gas molecules with one another. In the absence of convection, which relates to a moving fluid or gas phase, thermal conduction through a gas phase is highly dependent on the composition and pressure of this phase, and in particular the mean free path of gas molecules relative to the size of the gas gap, as given by the Knudsen number formula_1. To quantify the ease with which a particular medium conducts, engineers employ the thermal conductivity, also known as the conductivity constant or conduction coefficient, "k". In thermal conductivity, "k" is defined as "the quantity of heat, "Q", transmitted in time ("t") through a thickness ("L"), in a direction normal to a surface of area ("A"), due to a temperature difference (Δ"T") [...]". Thermal conductivity is a material "property" that is primarily dependent on the medium's phase, temperature, density, and molecular bonding. Thermal effusivity is a quantity derived from conductivity, which is a measure of its ability to exchange thermal energy with its surroundings. Steady state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant, so that (after an equilibration time), the spatial distribution of temperatures (temperature field) in the conducting object does not change any further. Thus, all partial derivatives of temperature "with respect to space" may either be zero or have nonzero values, but all derivatives of temperature at any point "with respect to time" are uniformly zero. In steady state conduction, the amount of heat entering any region of an object is equal to amount of heat coming out (if this were not so, the temperature would be rising or falling, as thermal energy was tapped or trapped in a region). For example, a bar may be cold at one end and hot at the other, but after a state of steady state conduction is reached, the spatial gradient of temperatures along the bar does not change any further, as time proceeds. Instead, the temperature remains constant at any given cross-section of the rod normal to the direction of heat transfer, and this temperature varies linearly in space in the case where there is no heat generation in the rod. In steady state conduction, all the laws of direct current electrical conduction can be applied to "heat currents". In such cases, it is possible to take "thermal resistances" as the analog to electrical resistances. In such cases, temperature plays the role of voltage, and heat transferred per unit time (heat power) is the analog of electric current. Steady state systems can be modelled by networks of such thermal resistances in series and in parallel, in exact analogy to electrical networks of resistors. See purely resistive thermal circuits for an example of such a network. During any period in which temperatures changes "in time" at any place within an object, the mode of thermal energy flow is termed "transient conduction." Another term is "non steady-state" conduction, referring to time-dependence of temperature fields in an object. Non-steady-state situations appear after an imposed change in temperature at a boundary of an object. They may also occur with temperature changes inside an object, as a result of a new source or sink of heat suddenly introduced within an object, causing temperatures near the source or sink to change in time. When a new perturbation of temperature of this type happens, temperatures within the system change in time toward a new equilibrium with the new conditions, provided that these do not change. After equilibrium, heat flow into the system once again equals the heat flow out, and temperatures at each point inside the system no longer change. Once this happens, transient conduction is ended, although steady-state conduction may continue if heat flow continues. If changes in external temperatures or internal heat generation changes are too rapid for the equilibrium of temperatures in space to take place, then the system never reaches a state of unchanging temperature distribution in time, and the system remains in a transient state. An example of a new source of heat "turning on" within an object, causing transient conduction, is an engine starting in an automobile. In this case, the transient thermal conduction phase for the entire machine is over, and the steady state phase appears, as soon as the engine reaches steady-state operating temperature. In this state of steady-state equilibrium, temperatures vary greatly from the engine cylinders to other parts of the automobile, but at no point in space within the automobile does temperature increase or decrease. After establishing this state, the transient conduction phase of heat transfer is over. New external conditions also cause this process: for example the copper bar in the example steady-state conduction experiences transient conduction as soon as one end is subjected to a different temperature from the other. Over time, the field of temperatures inside the bar reach a new steady-state, in which a constant temperature gradient along the bar is finally set up, and this gradient then stays constant in space. Typically, such a new steady state gradient is approached exponentially with time after a new temperature-or-heat source or sink, has been introduced. When a "transient conduction" phase is over, heat flow may still continue at high power, so long as temperatures do not change. An example of transient conduction that does not end with steady-state conduction, but rather no conduction, occurs when a hot copper ball is dropped into oil at a low temperature. Here, the temperature field within the object begins to change as a function of time, as the heat is removed from the metal, and the interest lies in analyzing this spatial change of temperature within the object over time, until all gradients disappear entirely (the ball has reached the same temperature as the oil). Mathematically, this condition is also approached exponentially; in theory it takes infinite time, but in practice it is over, for all intents and purposes, in a much shorter period. At the end of this process with no heat sink but the internal parts of the ball (which are finite), there is no steady state heat conduction to reach. Such a state never occurs in this situation, but rather the end of the process is when there is no heat conduction at all. The analysis of non steady-state conduction systems is more complex than that of steady-state systems. If the conducting body has a simple shape, then exact analytical mathematical expressions and solutions may be possible (see heat equation for the analytical approach). However, most often, because of complicated shapes with varying thermal conductivities within the shape (i.e., most complex objects, mechanisms or machines in engineering) often the application of approximate theories is required, and/or numerical analysis by computer. One popular graphical method involves the use of Heisler Charts. Occasionally, transient conduction problems may be considerably simplified if regions of the object being heated or cooled can be identified, for which thermal conductivity is very much greater than that for heat paths leading into the region. In this case, the region with high conductivity can often be treated in the lumped capacitance model, as a "lump" of material with a simple thermal capacitance consisting of its aggregate heat capacity. Such regions warm or cool, but show no significant temperature "variation" across their extent, during the process (as compared to the rest of the system). This is due to their far higher conductance. During transient conduction, therefore, the temperature across their conductive regions changes uniformly in space, and as a simple exponential in time. An example of such systems are those that follow Newton's law of cooling during transient cooling (or the reverse during heating). The equivalent thermal circuit consists of a simple capacitor in series with a resistor. In such cases, the remainder of the system with high thermal resistance (comparatively low conductivity) plays the role of the resistor in the circuit. The theory of relativistic heat conduction is a model that is compatible with the theory of special relativity. For most of the last century, it was recognized that the Fourier equation is in contradiction with the theory of relativity because it admits an infinite speed of propagation of heat signals. For example, according to the Fourier equation, a pulse of heat at the origin would be felt at infinity instantaneously. The speed of information propagation is faster than the speed of light in vacuum, which is physically inadmissible within the framework of relativity. Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Heat takes the place of pressure in normal sound waves. This leads to a very high thermal conductivity. It is known as "second sound" because the wave motion of heat is similar to the propagation of sound in air. The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. We can state this law in two equivalent forms: the integral form, in which we look at the amount of energy flowing into or out of a body as a whole, and the differential form, in which we look at the flow rates or fluxes of energy locally. Newton's law of cooling is a discrete analogue of Fourier's law, while Ohm's law is the electrical analogue of Fourier's law. The differential form of Fourier's law of thermal conduction shows that the local heat flux density, formula_2, is equal to the product of thermal conductivity, formula_3, and the negative local temperature gradient, formula_4. The heat flux density is the amount of energy that flows through a unit area per unit time. where (including the SI units) The thermal conductivity, formula_3, is often treated as a constant, though this is not always true. While the thermal conductivity of a material generally varies with temperature, the variation can be small over a significant range of temperatures for some common materials. In anisotropic materials, the thermal conductivity typically varies with orientation; in this case formula_3 is represented by a second-order tensor. In non-uniform materials, formula_3 varies with spatial location. For many simple applications, Fourier's law is used in its one-dimensional form. In the "x"-direction, In an isotropic medium, Fourier's law leads to Heat equation: formula_13 with a Fundamental solution famously known as Heat kernel. By integrating the differential form over the material's total surface formula_14, we arrive at the integral form of Fourier's law: where (including the SI units): The above differential equation, when integrated for a homogeneous material of 1-D geometry between two endpoints at constant temperature, gives the heat flow rate as: where This law forms the basis for the derivation of the heat equation. Writing where "U" is the conductance, in W/(m K). Fourier's law can also be stated as: The reciprocal of conductance is resistance, formula_25 is given by: Resistance is additive when several conducting layers lie between the hot and cool regions, because "A" and "Q" are the same for all layers. In a multilayer partition, the total conductance is related to the conductance of its layers by: So, when dealing with a multilayer partition, the following formula is usually used: For heat conduction from one fluid to another through a barrier, it is sometimes important to consider the conductance of the thin film of fluid that remains stationary next to the barrier. This thin film of fluid is difficult to quantify because its characteristics depend upon complex conditions of turbulence and viscosity—but when dealing with thin high-conductance barriers it can sometimes be quite significant. The previous conductance equations, written in terms of extensive properties, can be reformulated in terms of intensive properties. Ideally, the formulae for conductance should produce a quantity with dimensions independent of distance, like Ohm's Law for electrical resistance, formula_29, and conductance, formula_30. From the electrical formula: formula_31, where "ρ" is resistivity, "x" is length, and "A" is cross-sectional area, we have formula_32, where "G" is conductance, "k" is conductivity, "x" is length, and "A" is cross-sectional area. For Heat, where "U" is the conductance. Fourier's law can also be stated as: analogous to Ohm's law, formula_35 or formula_36 The reciprocal of conductance is resistance, "R", given by: analogous to Ohm's law, formula_38 The rules for combining resistances and conductances (in series and in parallel) are the same for both heat flow and electric current. Conduction through cylindrical shells (e.g. pipes) can be calculated from the internal radius, formula_39, the external radius, formula_40, the length, formula_41, and the temperature difference between the inner and outer wall, formula_42. The surface area of the cylinder is formula_43 When Fourier's equation is applied: and rearranged: then the rate of heat transfer is: the thermal resistance is: and formula_48, where formula_49. It is important to note that this is the log-mean radius. The conduction through a spherical shell with internal radius, formula_39, and external radius, formula_40, can be calculated in a similar manner as for a cylindrical shell. The surface area of the sphere is: formula_52 Solving in a similar manner as for a cylindrical shell (see above) produces: formula_53 The heat transfer at an interface is considered a transient heat flow. To analyze this problem, the Biot number is important to understand how the system behaves. The Biot number is determined by: formula_54 The heat transfer coefficient formula_55, is introduced in this formula, and is measured in formula_56. If the system has a Biot number of less than 0.1, the material behaves according to Newtonian cooling, i.e. with negligible temperature gradient within the body. If the Biot number is greater than 0.1, the system behaves as a series solution. The temperature profile in terms of time can be derived from the equation which becomes The heat transfer coefficient, "h", is measured in formula_59, and represents the transfer of heat at an interface between two materials. This value is different at every interface, and is an important concept in understanding heat flow at an interface. The series solution can be analyzed with a nomogram. A nomogram has relative temperature as the "y" coordinate and the Fourier number, which is calculated by The Biot number increases as the Fourier number decreases. There are five steps to determine a temperature profile in terms of time. Splat cooling is a method for quenching small droplets of molten materials by rapid contact with a cold surface. The particles undergo a characteristic cooling process, with the heat profile at formula_62 for initial temperature as the maximum at formula_63 and formula_64 at formula_65 and formula_66, and the heat profile at formula_67 for formula_68 as the boundary conditions. Splat cooling rapidly ends in a steady state temperature, and is similar in form to the Gaussian diffusion equation. The temperature profile, with respect to the position and time of this type of cooling, varies with: formula_69 Splat cooling is a fundamental concept that has been adapted for practical use in the form of thermal spraying. The thermal diffusivity coefficient, represented as formula_70, can be written as formula_71. This varies according to the material. Metal quenching is a transient heat transfer process in terms of the time temperature transformation (TTT). It is possible to manipulate the cooling process to adjust the phase of a suitable material. For example, appropriate quenching of steel can convert a desirable proportion of its content of austenite to martensite, creating a very tough product. To achieve this, it is necessary to quench at the "nose" (or eutectic) of the TTT diagram. Since materials differ in their Biot numbers, the time it takes for the material to quench, or the Fourier number, varies in practice. In steel, the quenching temperature range is generally from 600 °C to 200 °C. To control the quenching time and to select suitable quenching media, it is necessary to determine the Fourier number from the desired quenching time, the relative temperature drop, and the relevant Biot number. Usually, the correct figures are read from a standard nomogram. By calculating the heat transfer coefficient from this Biot number, one can find a liquid medium suitable for the application. One statement of the so-called zeroth law of thermodynamics is directly focused on the idea of conduction of heat. Bailyn (1994) writes that "... the zeroth law may be stated: A diathermal wall is a physical connection between two bodies that allows the passage of heat between them. Bailyn is referring to diathermal walls that exclusively connect two bodies, especially conductive walls. This statement of the 'zeroth law' belongs to an idealized theoretical discourse, and actual physical walls may have peculiarities that do not conform to its generality. For example, the material of the wall must not undergo a phase transition, such as evaporation or fusion, at the temperature at which it must conduct heat. But when only thermal equilibrium is considered and time is not urgent, so that the conductivity of the material does not matter too much, one suitable heat conductor is as good as another. Conversely, another aspect of the zeroth law is that, subject again to suitable restrictions, a given diathermal wall is indifferent to the nature of the heat bath to which it is connected. For example, the glass bulb of a thermometer acts as a diathermal wall whether exposed to a gas or to a liquid, provided they do not corrode or melt it. These differences are amongst the defining characteristics of heat transfer. In a sense, they are symmetries of heat transfer. Thermal conduction property of any gas under standard conditions of pressure and temperature is a fixed quantity. This property of a known reference gas or known reference gas mixtures can, therefore, be used for certain sensory applications, such as the thermal conductivity analyzer. The working of this instrument is by principle based on the Wheatstone bridge containing four filaments whose resistances are matched. Whenever a certain gas is passed over such network of filaments, their resistance changes due to the altered thermal conductivity of the filaments and thereby changing the net voltage output from the Wheatstone Bridge. This voltage output will be correlated with the database to identify the gas sample. The principle of thermal conductivity of gases can also be used to measure the concentration of a gas in a binary mixture of gases. Working: if the same gas is present around the all the Wheatstone bridge filaments, then the same temperature is maintained in all the filaments and hence same resistances are also maintained; resulting in a balanced Wheatstone bridge. However, If dissimilar gas sample (or gas mixture) is passed over one set of two filaments and the reference gas on the other set of two filaments, then the Wheatstone bridge becomes unbalanced. And the resulting net voltage output of the circuit will be correlated with the database to identify the constituents of the sample gas. Using this technique many unknown gas samples can be identified by comparing their thermal conductivity with other reference gas of known thermal conductivity. The most commonly used reference gas is nitrogen; as the thermal conductivity of most common gases (except hydrogen and helium) are similar to that of nitrogen.

Thermal conduction is the transfer of internal energy by microscopic collisions of particles and movement of electrons within a body. The colliding particles, which include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. Conduction takes place in all phases: solid, liquid, and gas. The rate at which energy is conducted as heat between two bodies depends on the temperature difference (and hence temperature gradient) between the two bodies and the properties of the conductive interface through which the heat is transferred.

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summarize: "Central America" may mean different things to various people, based upon different contexts: In the Pre-Columbian era, the northern areas of Central America were inhabited by the indigenous peoples of Mesoamerica. Most notable among these were the Mayans, who had built numerous cities throughout the region, and the Aztecs, who had created a vast empire. The pre-Columbian cultures of eastern El Salvador, eastern Honduras, Caribbean Nicaragua, most of Costa Rica and Panama were predominantly speakers of the Chibchan languages at the time of European contact and are considered by some culturally different and grouped in the Isthmo-Colombian Area. Following the Spanish expedition of Christopher Columbus's voyages to the Americas, the Spanish sent many expeditions to the region, and they began their conquest of Maya territory in 1523. Soon after the conquest of the Aztec Empire, Spanish conquistador Pedro de Alvarado commenced the conquest of northern Central America for the Spanish Empire. Beginning with his arrival in Soconusco in 1523, Alvarado's forces systematically conquered and subjugated most of the major Maya kingdoms, including the K'iche', Tz'utujil, Pipil, and the Kaqchikel. By 1528, the conquest of Guatemala was nearly complete, with only the Petén Basin remaining outside the Spanish sphere of influence. The last independent Maya kingdoms – the Kowoj and the Itza people – were finally defeated in 1697, as part of the Spanish conquest of Petén. In 1538, Spain established the Real Audiencia of Panama, which had jurisdiction over all land from the Strait of Magellan to the Gulf of Fonseca. This entity was dissolved in 1543, and most of the territory within Central America then fell under the jurisdiction of the "Audiencia Real de Guatemala". This area included the current territories of Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Mexican state of Chiapas, but excluded the lands that would become Belize and Panama. The president of the Audiencia, which had its seat in Antigua Guatemala, was the governor of the entire area. In 1609 the area became a captaincy general and the governor was also granted the title of captain general. The Captaincy General of Guatemala encompassed most of Central America, with the exception of present-day Belize and Panama. The Captaincy General of Guatemala lasted for more than two centuries, but began to fray after a rebellion in 1811 which began in the intendancy of San Salvador. The Captaincy General formally ended on 15 September 1821, with the signing of the Act of Independence of Central America. Mexican independence was achieved at virtually the same time with the signing of the Treaty of Córdoba and the Declaration of Independence of the Mexican Empire, and the entire region was finally independent from Spanish authority by 28 September 1821. From its independence from Spain in 1821 until 1823, the former Captaincy General remained intact as part of the short-lived First Mexican Empire. When the Emperor of Mexico abdicated on 19 March 1823, Central America again became independent. On 1 July 1823, the Congress of Central America peacefully seceded from Mexico and declared absolute independence from all foreign nations, and the region formed the Federal Republic of Central America. The Federal Republic of Central America was a representative democracy with its capital at Guatemala City. This union consisted of the provinces of Costa Rica, El Salvador, Guatemala, Honduras, Los Altos, Mosquito Coast, and Nicaragua. The lowlands of southwest Chiapas, including Soconusco, initially belonged to the Republic until 1824, when Mexico annexed most of Chiapas and began its claims to Soconusco. The Republic lasted from 1823 to 1838, when it disintegrated as a result of civil wars. The territory that now makes up Belize was heavily contested in a dispute that continued for decades after Guatemala achieved independence (see History of Belize (1506–1862). Spain, and later Guatemala, considered this land a Guatemalan department. In 1862, Britain formally declared it a British colony and named it British Honduras. It became independent as Belize in 1981. Panama, situated in the southernmost part of Central America on the Isthmus of Panama, has for most of its history been culturally and politically linked to South America. Panama was part of the Province of Tierra Firme from 1510 until 1538 when it came under the jurisdiction of the newly formed "Audiencia Real de Panama". Beginning in 1543, Panama was administered as part of the Viceroyalty of Peru, along with all other Spanish possessions in South America. Panama remained as part of the Viceroyalty of Peru until 1739, when it was transferred to the Viceroyalty of New Granada, the capital of which was located at Santa Fé de Bogotá. Panama remained as part of the Viceroyalty of New Granada until the disestablishment of that viceroyalty in 1819. A series of military and political struggles took place from that time until 1822, the result of which produced the republic of Gran Colombia. After the dissolution of Gran Colombia in 1830, Panama became part of a successor state, the Republic of New Granada. From 1855 until 1886, Panama existed as Panama State, first within the Republic of New Granada, then within the Granadine Confederation, and finally within the United States of Colombia. The United States of Colombia was replaced by the Republic of Colombia in 1886. As part of the Republic of Colombia, Panama State was abolished and it became the Isthmus Department. Despite the many political reorganizations, Colombia was still deeply plagued by conflict, which eventually led to the secession of Panama on 3 November 1903. Only after that time did some begin to regard Panama as a North or Central American entity. By the 1930s the United Fruit Company owned of land in Central America and the Caribbean and was the single largest land owner in Guatemala. Such holdings gave it great power over the governments of small countries. That was one of the factors that led to the coining of the phrase banana republic. After more than two hundred years of social unrest, violent conflict, and revolution, Central America today remains in a period of political transformation. Poverty, social injustice, and violence are still widespread. Nicaragua is the second poorest country in the western hemisphere (only Haiti is poorer). Central America is the tapering isthmus of southern North America, with unique and varied geographic features. The Pacific Ocean lies to the southwest, the Caribbean Sea lies to the northeast, and the Gulf of Mexico lies to the north. Some physiographists define the Isthmus of Tehuantepec as the northern geographic border of Central America, while others use the northwestern borders of Belize and Guatemala. From there, the Central American land mass extends southeastward to the Atrato River, where it connects to the Pacific Lowlands in northwestern South America. Of the many mountain ranges within Central America, the longest are the Sierra Madre de Chiapas, the Cordillera Isabelia and the Cordillera de Talamanca. At, Volcán Tajumulco is the highest peak in Central America. Other high points of Central America are as listed in the table below: Between the mountain ranges lie fertile valleys that are suitable for the raising of livestock and for the production of coffee, tobacco, beans and other crops. Most of the population of Honduras, Costa Rica and Guatemala lives in valleys. Trade winds have a significant effect upon the climate of Central America. Temperatures in Central America are highest just prior to the summer wet season, and are lowest during the winter dry season, when trade winds contribute to a cooler climate. The highest temperatures occur in April, due to higher levels of sunlight, lower cloud cover and a decrease in trade winds. Central America is part of the Mesoamerican biodiversity hotspot, boasting 7% of the world's biodiversity. The Pacific Flyway is a major north–south flyway for migratory birds in the Americas, extending from Alaska to Tierra del Fuego. Due to the funnel-like shape of its land mass, migratory birds can be seen in very high concentrations in Central America, especially in the spring and autumn. As a bridge between North America and South America, Central America has many species from the Nearctic and the Neotropical realms. However the southern countries (Costa Rica and Panama) of the region have more biodiversity than the northern countries (Guatemala and Belize), meanwhile the central countries (Honduras, Nicaragua and El Salvador) have the least biodiversity. The table below shows recent statistics: Over 300 species of the region's flora and fauna are threatened, 107 of which are classified as critically endangered. The underlying problems are deforestation, which is estimated by FAO at 1.2% per year in Central America and Mexico combined, fragmentation of rainforests and the fact that 80% of the vegetation in Central America has already been converted to agriculture. Efforts to protect fauna and flora in the region are made by creating ecoregions and nature reserves. 36% of Belize's land territory falls under some form of official protected status, giving Belize one of the most extensive systems of terrestrial protected areas in the Americas. In addition, 13% of Belize's marine territory are also protected. A large coral reef extends from Mexico to Honduras: the Mesoamerican Barrier Reef System. The Belize Barrier Reef is part of this. The Belize Barrier Reef is home to a large diversity of plants and animals, and is one of the most diverse ecosystems of the world. It is home to 70 hard coral species, 36 soft coral species, 500 species of fish and hundreds of invertebrate species. So far only about 10% of the species in the Belize barrier reef have been discovered. From 2001 to 2010, of forest were lost in the region. In 2010 Belize had 63% of remaining forest cover, Costa Rica 46%, Panama 45%, Honduras 41%, Guatemala 37%, Nicaragua 29%, and El Salvador 21%. Most of the loss occurred in the moist forest biome, with. Woody vegetation loss was partially set off by a gain in the coniferous forest biome with, and a gain in the dry forest biome at. Mangroves and deserts contributed only 1% to the loss in forest vegetation. The bulk of the deforestation was located at the Caribbean slopes of Nicaragua with a loss of of forest in the period from 2001 to 2010. The most significant regrowth of of forest was seen in the coniferous woody vegetation of Honduras. The Central American pine-oak forests ecoregion, in the tropical and subtropical coniferous forests biome, is found in Central America and southern Mexico. The Central American pine-oak forests occupy an area of, extending along the mountainous spine of Central America, extending from the Sierra Madre de Chiapas in Mexico's Chiapas state through the highlands of Guatemala, El Salvador, and Honduras to central Nicaragua. The pine-oak forests lie between elevation, and are surrounded at lower elevations by tropical moist forests and tropical dry forests. Higher elevations above are usually covered with Central American montane forests. The Central American pine-oak forests are composed of many species characteristic of temperate North America including oak, pine, fir, and cypress. Laurel forest is the most common type of Central American temperate evergreen cloud forest, found in almost all Central American countries, normally more than above sea level. Tree species include evergreen oaks, members of the laurel family, and species of "Weinmannia", "Drimys", and "Magnolia". The cloud forest of Sierra de las Minas, Guatemala, is the largest in Central America. In some areas of southeastern Honduras there are cloud forests, the largest located near the border with Nicaragua. In Nicaragua, cloud forests are situated near the border with Honduras, but many were cleared to grow coffee. There are still some temperate evergreen hills in the north. The only cloud forest in the Pacific coastal zone of Central America is on the Mombacho volcano in Nicaragua. In Costa Rica, there are laurel forests in the Cordillera de Tilarán and Volcán Arenal, called Monteverde, also in the Cordillera de Talamanca. The Central American montane forests are an ecoregion of the tropical and subtropical moist broadleaf forests biome, as defined by the World Wildlife Fund. These forests are of the moist deciduous and the semi-evergreen seasonal subtype of tropical and subtropical moist broadleaf forests and receive high overall rainfall with a warm summer wet season and a cooler winter dry season. Central American montane forests consist of forest patches located at altitudes ranging from, on the summits and slopes of the highest mountains in Central America ranging from Southern Mexico, through Guatemala, El Salvador, and Honduras, to northern Nicaragua. The entire ecoregion covers an area of and has a temperate climate with relatively high precipitation levels. Ecoregions are not only established to protect the forests themselves but also because they are habitats for an incomparably rich and often endemic fauna. Almost half of the bird population of the Talamancan montane forests in Costa Rica and Panama are endemic to this region. Several birds are listed as threatened, most notably the resplendent quetzal (Pharomacrus mocinno), three-wattled bellbird (Procnias tricarunculata), bare-necked umbrellabird (Cephalopterus glabricollis), and black guan (Chamaepetes unicolor). Many of the amphibians are endemic and depend on the existence of forest. The golden toad that once inhabited a small region in the Monteverde Reserve, which is part of the Talamancan montane forests, has not been seen alive since 1989 and is listed as extinct by IUCN. The exact causes for its extinction are unknown. Global warming may have played a role, because the development of that frog is typical for this area may have been compromised. Seven small mammals are endemic to the Costa Rica-Chiriqui highlands within the Talamancan montane forest region. Jaguars, cougars, spider monkeys, as well as tapirs, and anteaters live in the woods of Central America. The Central American red brocket is a brocket deer found in Central America's tropical forest. Central America is geologically very active, with volcanic eruptions and earthquakes occurring frequently, and tsunamis occurring occasionally. Many thousands of people have died as a result of these natural disasters. Most of Central America rests atop the Caribbean Plate. This tectonic plate converges with the Cocos, Nazca, and North American plates to form the Middle America Trench, a major subduction zone. The Middle America Trench is situated some off the Pacific coast of Central America and runs roughly parallel to it. Many large earthquakes have occurred as a result of seismic activity at the Middle America Trench. For example, subduction of the Cocos Plate beneath the North American Plate at the Middle America Trench is believed to have caused the 1985 Mexico City earthquake that killed as many as 40,000 people. Seismic activity at the Middle America Trench is also responsible for earthquakes in 1902, 1942, 1956, 1982, 1992, 2001, 2007, 2012, 2014, and many other earthquakes throughout Central America. The Middle America Trench is not the only source of seismic activity in Central America. The Motagua Fault is an onshore continuation of the Cayman Trough which forms part of the tectonic boundary between the North American Plate and the Caribbean Plate. This transform fault cuts right across Guatemala and then continues offshore until it merges with the Middle America Trench along the Pacific coast of Mexico, near Acapulco. Seismic activity at the Motagua Fault has been responsible for earthquakes in 1717, 1773, 1902, 1976, 1980, and 2009. Another onshore continuation of the Cayman Trough is the Chixoy-Polochic Fault, which runs parallel to, and roughly to the north, of the Motagua Fault. Though less active than the Motagua Fault, seismic activity at the Chixoy-Polochic Fault is still thought to be capable of producing very large earthquakes, such as the 1816 earthquake of Guatemala. Managua, the capital of Nicaragua, was devastated by earthquakes in 1931 and 1972. Volcanic eruptions are also common in Central America. In 1968 the Arenal Volcano, in Costa Rica, erupted killing 87 people as the 3 villages of Tabacon, Pueblo Nuevo and San Luis were buried under pyroclastic flows and debris. Fertile soils from weathered volcanic lava have made it possible to sustain dense populations in the agriculturally productive highland areas. The population of Central America is estimated at 47,448,333 as of. With an area of, it has a population density of. Human Development Index values are from the estimates for 2017. The official language majority in all Central American countries is Spanish, except in Belize, where the official language is English. Mayan languages constitute a language family consisting of about 26 related languages. Guatemala formally recognized 21 of these in 1996. Xinca and Garifuna are also present in Central America. This region of the continent is very rich in terms of ethnic groups. The majority of the population is mestizo, with sizable Mayan and African descendent populations present, including Xinca and Garifuna minorities. The immigration of Arabs, Jews, Chinese, Europeans and others brought additional groups to the area. The predominant religion in Central America is Christianity (95.6%). Beginning with the Spanish colonization of Central America in the 16th century, Roman Catholicism became the most popular religion in the region until the first half of the 20th century. Since the 1960s, there has been an increase in other Christian groups, particularly Protestantism, as well as other religious organizations, and individuals identifying themselves as having no religion. Central America is currently undergoing a process of political, economic and cultural transformation that started in 1907 with the creation of the Central American Court of Justice. In 1951 the integration process continued with the signature of the San Salvador Treaty, which created the ODECA, the Organization of Central American States. However, the unity of the ODECA was limited by conflicts between several member states. In 1991, the integration agenda was further advanced by the creation of the Central American Integration System ("Sistema para la Integración Centroamericana", or SICA). SICA provides a clear legal basis to avoid disputes between the member states. SICA membership includes the 7 nations of Central America plus the Dominican Republic, a state that is traditionally considered part of the Caribbean. On 6 December 2008, SICA announced an agreement to pursue a common currency and common passport for the member nations. No timeline for implementation was discussed. Central America already has several supranational institutions such as the Central American Parliament, the Central American Bank for Economic Integration and the Central American Common Market. On 22 July 2011, President Mauricio Funes of El Salvador became the first president "pro tempore" to SICA. El Salvador also became the headquarters of SICA with the inauguration of a new building. Until recently, all Central American countries have maintained diplomatic relations with Taiwan instead of China. President Óscar Arias of Costa Rica, however, established diplomatic relations with China in 2007, severing formal diplomatic ties with Taiwan. After breaking off relations with the Republic of China in 2017, Panama established diplomatic relations with the People's Republic of China. In August 2018, El Salvador also severed ties with Taiwan to formally start recognizing the People's Republic of China as the sole China, a move many considered lacked transparency due to its abruptness and reports of the Chinese government's desires to invest in the department of La Union while also promising to fund the ruling party's reelection campaign. The Central American Parliament (also known as PARLACEN) is a political and parliamentary body of SICA. The parliament started around 1980, and its primary goal was to resolve conflicts in Nicaragua, Guatemala, and El Salvador. Although the group was disbanded in 1986, ideas of unity of Central Americans still remained, so a treaty was signed in 1987 to create the Central American Parliament and other political bodies. Its original members were Guatemala, El Salvador, Nicaragua and Honduras. The parliament is the political organ of Central America, and is part of SICA. New members have since then joined including Panama and the Dominican Republic. Costa Rica is not a member State of the Central American Parliament and its adhesion remains as a very unpopular topic at all levels of the Costa Rican society due to existing strong political criticism towards the regional parliament, since it is regarded by Costa Ricans as a menace to democratic accountability and effectiveness of integration efforts. Excessively high salaries for its members, legal immunity of jurisdiction from any member State, corruption, lack of a binding nature and effectiveness of the regional parliament's decisions, high operative costs and immediate membership of Central American Presidents once they leave their office and presidential terms, are the most common reasons invoked by Costa Ricans against the Central American Parliament. Signed in 2004, the Central American Free Trade Agreement (CAFTA) is an agreement between the United States, Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and the Dominican Republic. The treaty is aimed at promoting free trade among its members. Guatemala has the largest economy in the region. Its main exports are coffee, sugar, bananas, petroleum, clothing, and cardamom. Of its 10.29 billion dollar annual exports, 40.2% go to the United States, 11.1% to neighboring El Salvador, 8% to Honduras, 5.5% to Mexico, 4.7% to Nicaragua, and 4.3% to Costa Rica. The region is particularly attractive for companies (especially clothing companies) because of its geographical proximity to the[United States], very low wages and considerable tax advantages. In addition, the decline in the prices of coffee and other export products and the structural adjustment measures promoted by the international financial institutions have partly ruined agriculture, favouring the emergence of maquiladoras. This sector accounts for 42 per cent of total exports from El Salvador, 55 per cent from Guatemala, and 65 per cent from Honduras. However, its contribution to the economies of these countries is disputed; raw materials are imported, jobs are precarious and low-paid, and tax exemptions weaken public finances. They are also criticised for the working conditions of employees: insults and physical violence, abusive dismissals (especially of pregnant workers), working hours, non-payment of overtime. According to Lucrecia Bautista, coordinator of the"maquilas" sector of the audit firm Coverco,"labour law regulations are regularly violated in maquilas and there is no political will to enforce their application. In the case of infringements, the labour inspectorate shows remarkable leniency. It is a question of not discouraging investors. "Trade unionists are subject to pressure, and sometimes to kidnapping or murder. In some cases, business leaders have used the services of the maras. Finally, black lists containing the names of trade unionists or political activists are circulating in employers' circles. Economic growth in Central America is projected to slow slightly in 2014–15, as country-specific domestic factors offset the positive effects from stronger economic activity in the United States. Tourism in Belize has grown considerably in more recent times, and it is now the second largest industry in the nation. Belizean Prime Minister Dean Barrow has stated his intention to use tourism to combat poverty throughout the country. The growth in tourism has positively affected the agricultural, commercial, and finance industries, as well as the construction industry. The results for Belize's tourism-driven economy have been significant, with the nation welcoming almost one million tourists in a calendar year for the first time in its history in 2012. Belize is also the only country in Central America with English as its official language, making this country a comfortable destination for English-speaking tourists. Costa Rica is the most visited nation in Central America. Tourism in Costa Rica is one of the fastest growing economic sectors of the country, having become the largest source of foreign revenue by 1995. Since 1999, tourism has earned more foreign exchange than bananas, pineapples and coffee exports combined. The tourism boom began in 1987, with the number of visitors up from 329,000 in 1988, through 1.03 million in 1999, to a historical record of 2.43 million foreign visitors and $1.92-billion in revenue in 2013. In 2012 tourism contributed with 12.5% of the country's GDP and it was responsible for 11.7% of direct and indirect employment. Tourism in Nicaragua has grown considerably recently, and it is now the second largest industry in the nation. Nicaraguan President Daniel Ortega has stated his intention to use tourism to combat poverty throughout the country. The growth in tourism has positively affected the agricultural, commercial, and finance industries, as well as the construction industry. The results for Nicaragua's tourism-driven economy have been significant, with the nation welcoming one million tourists in a calendar year for the first time in its history in 2010. The Inter-American Highway is the Central American section of the Pan-American Highway, and spans between Nuevo Laredo, Mexico, and Panama City, Panama. Because of the break in the highway known as the Darién Gap, it is not possible to cross between Central America and South America in an automobile.

Central America (,, "Centroamérica" ) is a region in the southern tip of North America and is sometimes defined as a subregion of the Americas. This region is bordered by Mexico to the north, Colombia to the southeast, the Caribbean Sea to the east and the Pacific Ocean to the west and south. Central America consists of seven countries: El Salvador, Costa Rica, Belize, Guatemala, Honduras, Nicaragua and Panama. The combined population of Central America is estimated at 44.53 million (2016).

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summarize: The origin of the word Andorra is unknown, although several hypotheses have been formulated. The oldest derivation of the word Andorra is from the Greek historian Polybius ("The Histories" III, 35, 1) who describes the Andosins, an Iberian Pre-Roman tribe, as historically located in the valleys of Andorra and facing the Carthaginian army in its passage through the Pyrenees during the Punic Wars. The word Andosini or Andosins (Ἀνδοσίνοι) may derive from the Basque "handia" whose meaning is "big" or "giant". The Andorran toponymy shows evidence of Basque language in the area. Another theory suggests that the word La Balma de la Margineda, found by archaeologists at Sant Julià de Lòria, was settled in 9,500 BC as a passing place between the two sides of the Pyrenees. The seasonal camp was perfectly located for hunting and fishing by the groups of hunter-gatherers from Ariege and Segre. During the Neolithic Age, a group of people moved to the Valley of Madriu (nowadays Natural Parc located in Escaldes-Engordany declared UNESCO World Heritage Site) as a permanent camp in 6640 BC. The population of The inhabitants of the valleys were traditionally associated with the Iberians and historically located in Andorra as the Iberian tribe Andosins or Andosini (Ἀνδοσίνους) during the 7th and 2nd centuries BC. Influenced by Aquitanias, Basque and Iberian languages, the locals developed some current toponyms. Early writings and documents relating to this group of people goes back to the second century BC by the Greek writer Polybius in his "Histories" during the Punic Wars. Some After the fall of the Roman Empire, Andorra came under the influence of the Visigoths, not remotely from the Kingdom of Toledo, but locally from the Diocese of Urgell. The Visigoths remained in the valleys for 200 years, during which time Christianity spread. When the Muslim Empire and its conquest of most of the Iberian Peninsula replaced the ruling Visigoths, Andorra was sheltered from these invaders by the Franks. Tradition holds that Charles the Great (Charlemagne) granted a charter to the Andorran people for a contingent of five thousand soldiers under the command of Marc Almugaver, in return for fighting against the Moors near Porté-Puymorens Before 1095, Andorra did not have any type of military protection and the Bishop of Urgell, who knew that the count of Urgell wanted to reclaim the Andorran valleys, asked the lord of Caboet for help and protection. In 1095, the Lord of Caboet and the bishop of Urgell signed under oath a declaration of their co-sovereignty over Andorra. Arnalda, daughter of Arnau of Caboet, married the viscount of Castellbò. Their daughter, Ermessenda, married the count of Foix, Roger-Bernard II. Roger-Bernard II and Ermessenda shared ruled over Andorra with the bishop of In 1601 the Tribunal de Corts (High Court of Justice) was created as a result of Huguenot rebellions from France, Inquisition courts coming from Spain and indigenous witchcraft experienced in the country due to the Reformation and Counter-Reformation. With the passage of time, the co-title to Andorra passed to the kings of Navarre. After Henry III of Navarre became king of France, he issued an edict in 1607 that established the head of the French state and the bishop of Urgell as co-princes of Andorra. During 1617, communal councils form the sometent (popular militia or army) to deal with the rise of bandolerisme (brigandage) and the Consell de la Terra was defined and structured in terms of its composition, organization and competences current today. Andorra continued with the same economic system that it had during the 12th–14th centuries with a large production of metallurgy (fargues, a system similar to Farga catalana) and with the introduction of tobacco circa 1692 After the French Revolution in 1809, Napoleon I reestablished the Co-Principate and removed the French medieval title. In 1812–1813, the First French Empire annexed Catalonia during the Peninsular War () and divided the region into four départements, with Andorra as a part of the district of Puigcerdà. In 1814, an imperial decree reestablished the independence and economy of Andorra. During this period, Andorra's late medieval institutions and rural culture remained largely unchanged. In 1866, the syndic Guillem d'Areny-Plandolit led the reformist group in a Council General of 24 members elected by suffrage limited to heads of families. The Council General replaced the aristocratic oligarchy that previously ruled the state. The New Reform () began after ratification by both Co-Princes and established the basis of the constitution and symbols—such as the tricolor flag—of Andorra. A new service economy arose as a demand of the valley inhabitants and began to build infrastructure such as hotels, spa resorts, roads and telegraph lines. The authorities of the Co-Princes banned casinos and betting houses throughout the country. The Andorra declared war on Imperial Germany during World War I, but did not take part directly in the fighting. Some Andorrans volunteered to take part in the conflict as part of the French Legions. It remained in an official state of belligerency until 1958 as it was not included in the Treaty of Versailles. In 1933, France occupied Andorra following social unrest which occurred before elections due to the Revolution of 1933 and the FHASA strikes (Vagues de FHASA); the revolt led by Joves Andorrans (a labour union group related to the Spanish CNT and FAI) called for political reforms, the universal suffrage vote of all Andorrans and acted in defense of the rights of local and foreign workers during the construction of FHASA's hydroelectric power station in Encamp. The 5 April 1933 Joves Andorrans seized the Andorran Parliament. These actions were preceded by the arrival of Colonel René-Jules Baulard with 50 gendarmes and the mobilization of 200 local militias or sometent led by the Síndic Francesc Cairat. On 6 July 1934, adventurer and nobleman Boris Skossyreff, with his promise of freedoms and modernization of the country and wealth through the establishment of Andorra is a parliamentary co-principality with the president of France and the Catholic bishop of Urgell (Catalonia, Spain) as co-princes. This peculiarity makes the president of France, in his capacity as prince of Andorra, an elected monarch, although he is not elected by a popular vote of the Andorran people. The politics of Andorra take place in a framework of a parliamentary representative democracy, whereby the head of government is the chief executive, and of a pluriform multi-party system. The current head of government is Xavier Espot Zamora of the Democrats for Andorra (DA). Executive power is exercised by the government. Legislative power is vested in both government and parliament. The Parliament of Andorra is known as the General Council. The General Council consists of between 28 and 42 councillors. The councillors serve for four-year terms, and elections are held between the 30th and 40th days following the dissolution of the previous Council. Half are elected in equal numbers by each of the seven administrative parishes, and the other half of the councillors are elected in a single national constituency. Fifteen days after the election, the councillors hold their The judiciary is composed of the Magistrates Court, the Criminal Law Court, the High Court of Andorra, and the Constitutional Court. The High Court of Justice is composed of five judges: one appointed by the head of government, one each by the co-princes, one by the Syndic General, and one by the judges and magistrates. It is presided over by the member appointed by the Syndic General and the judges Andorra does not have its own armed forces, although there is a small ceremonial army. Responsibility for defending the nation rests primarily with France and Spain. However, in case of emergencies or natural disasters, the Sometent (an alarm) is called and all able-bodied men between 21 and 60 of Andorran nationality must serve. This is why all Andorrans, and especially the head of each house (usually the eldest able-bodied man of a house) should, by law, keep a rifle, even though the law also states that the police will offer a firearm in case of need. Andorra is a full member of the United Nations (UN), the Organization for Security and Co-operation in Europe (OSCE), and has a special agreement with the European Union (EU). Andorra has a small army, which has historically been raised or reconstituted at various dates, but has never in modern times amounted to a standing army. The basic principle of Andorran defence is that all able-bodied men are available to fight if called upon by the sounding of the Sometent. Being a landlocked country, Andorra has no navy. Before World War I, Andorra maintained an armed force of about 600 part-time militiamen under the supervision of a Captain (Capità or Cap de Sometent) and a Lieutenant (Desener or Lloctinent del Capità). This body was not liable for service outside the principality and was commanded by two officials (veguers) appointed by France and the Bishop of Urgell. Despite not being involved in any fighting during the First World War, Andorra was technically the longest combatant, as the country was left out of the Versailles Peace Conference, technically remaining at war with Germany from its original declaration of war in 1914 until 24 September 1958 when Andorra officially declared peace with Germany. In the modern era, the army has consisted of a very small body of volunteers willing to undertake ceremonial duties. Uniforms and Andorra maintains a small but modern and well-equipped internal police force, with around 240 police officers supported by civilian assistants. The principal services supplied by the corps are uniformed community policing, criminal detection, border control, and traffic policing. There are also small specialist units including police dogs, mountain rescue, and a bomb disposal team. The "Grup d'Intervenció Policia d'Andorra" (GIPA) is a small special forces unit trained in counter-terrorism, and hostage recovery tasks. Although it is the closest in style to an active military force, it is part of the Police Corps, and not the army. As terrorist and hostage situations are a rare threat to the country, the GIPA is commonly assigned to prisoner escort duties, and at other times to routine policing. The Andorran Fire Brigade, with headquarters at Santa Coloma, operates from four modern fire stations, and has a staff of around 120 firefighters. The service is equipped with 16 heavy appliances (fire tenders, turntable ladders, and specialist four-wheel drive vehicles), four light support vehicles (cars and vans) and four ambulances. Historically, the families of the six ancient parishes Andorra consists Due to its location in the eastern Pyrenees mountain range, Andorra consists predominantly of rugged mountains, the highest being the Coma Pedrosa at, and the average elevation of Andorra is. These are dissected by three narrow valleys in a Y Andorra has alpine, continental and oceanic climates, depending on altitude. Its higher elevation means there is, on average, more snow in winter and it is slightly cooler in summer. The diversity of landmarks, the different orientation of the valleys and the irregularity relief typical of the Mediterranean climates make the country have a great diversity of microclimates that hinder the general dominance of the high mountain climate. The great differences of altitude in Tourism, the mainstay of Andorra's tiny, well-to-do economy, accounts for roughly 80% of GDP. An estimated 10.2 million tourists visit annually, attracted by Andorra's duty-free status and by its summer and winter resorts. One of the main sources of income in Andorra is tourism from ski resorts which total over of ski ground. The sport brings in over 7 million visitors annually and an estimated 340 million euros per year, sustaining 2,000 direct and 10,000 indirect jobs at present since 2007. The banking sector, with its tax haven status, also contributes substantially to the economy (the financial and insurance sector accounts for approximately 19% of GDP). The financial system comprises five banking groups, one specialised credit entity, 8 investment undertaking management entities, 3 asset management companies and 29 insurance companies, 14 of which are branches of foreign insurance companies authorised to operate in the principality. Agricultural production is limited; only 5% of the land is arable, and most food has to be imported. Some tobacco is grown locally. The principal livestock activity is domestic sheep raising. Manufacturing output consists mainly of cigarettes, cigars, and furniture. Andorra's natural resources include hydroelectric power, mineral water, timber, iron ore, and The population of Andorra is estimated at (). The Andorrans are a Romance ethnic group of originally Catalan descent. The population has grown from 5,000 in 1900. The historic and official language is Catalan, a Romance language. The Andorran government encourages the use of Catalan. It funds a Commission for Catalan Toponymy in Andorra (Catalan: ), and provides free Catalan classes to assist immigrants. Andorran television and radio stations use Catalan. Because of immigration, historical links, and close geographic proximity, Spanish, The population of Andorra is predominantly (88.2%) Catholic. Their patron saint is Our Lady of Meritxell. Though it is not an official state religion, the constitution acknowledges a special relationship with the Catholic Church, offering some special Children between the ages of 6 and 16 are required by law to have full-time education. Education up to secondary level is provided free of charge by the government. There are three systems of school, Andorran, French and Spanish, which use The Universitat d'Andorra (UdA) is the state public university and is the only university in Andorra. It was established in 1997. The university provides first-level degrees in nursing, computer science, business administration, and educational sciences, in addition to higher professional education courses. The only two graduate schools in Andorra are the Nursing School and the School of Computer Science, the latter having a PhD programme. The geographical complexity of the country as well as the small number of students prevents the University of Andorra from developing a full academic programme, and it serves principally as a centre for virtual studies, connected to Spanish and French universities. The Virtual Studies Centre (Centre d'Estudis Virtuals) at the University runs approximately 20 different academic degrees at both undergraduate and postgraduate levels in fields including tourism, law, Catalan philology, humanities, psychology, political sciences, audiovisual communication, telecommunications engineering, and East Asia studies. The Centre also runs various postgraduate programmes and continuing-education courses for professionals. Until the 20th century, Andorra had very limited transport links to the outside world, and development of the country was affected by its physical isolation. Even now, the nearest major airports at Toulouse and Barcelona are both three hours' drive from Andorra. Andorra has a road network of, of which is unpaved. The two main roads out of Andorra la Vella are the CG-1 to the Spanish border near Sant Julia de Loria, and the CG-2 to the French border via the Envalira Tunnel near El Pas de la Casa. Bus services cover all metropolitan areas and many rural communities, with services on most major routes running half-hourly or more frequently during peak travel times. There are frequent long-distance bus services from Andorra to Barcelona and Toulouse, plus a daily tour from the former city. Bus services mostly are run by private companies, but some local ones are operated by the In Andorra, mobile and fixed telephone and internet services are operated exclusively by the Andorran national telecommunications company, SOM, also known as Andorra Telecom (STA). The same company also manages the technical infrastructure for national broadcasting of digital television and radio. In 2010 Andorra became the first country to provide a direct optical fiber link to all homes (FTTH) and businesses. The first commercial radio station to broadcast was Radio Andorra, which was active from 1939 to 1981. On 12 October 1989, the General Council established radio and television as essential public services creating and The official and historic language is Catalan. Thus the culture is Catalan, with its own specificity. Andorra is home to folk dances like the contrapàs and marratxa, which survive in Sant Julià de Lòria especially. Andorran folk music has similarities to the music of its neighbours, but is especially Catalan in character, especially in the presence of dances such as the sardana. Other Andorran folk dances include contrapàs in Andorra la Vella and Saint Anne's dance in Escaldes-Engordany. Andorra's national holiday is Our Lady of Meritxell Day, 8 September. Among the more important festivals and traditions are the Canólich Gathering in May, the Roser d'Ordino in July, the Meritxell Day (National Day of Andorra), the Andorra la Vella Fair, the Sant Jordi Day, the Santa Llúcia Fair, the Festivity from La Candelera to Canillo, the Carnival of Encamp, the sung of caramelles, the Festivity of Sant Esteve and the Festa del Poble. In popular folklore, the best-known Andorran legends are the legend of Charlemagne, according to which this Frankish King would have founded the country, the White Lady of Auvinyà, the Buner d'Ordino, the legend of Engolasters Lake and the legend of Our Lady of Meritxell. Andorran gastronomy is mainly Catalan, although it has also adopted other elements of French and Italian cuisines. The cuisine of the country has similar characteristics with the neighbors of the Cerdanya and the Alt Urgell, with whom it has a strong cultural ties. Andorra's cuisine is marked by its nature as mountain valleys. Typical dishes of the country are the quince all-i-oli, the duck with winter pear, the lamb in the oven with nuts, pork civet, the massegada cake, the escarole with pear trees, confited duck and mushrooms, escudella, spinach with raisins and pine nuts, jelly marmalade, stuffed murgues (mushrooms) with pork, dandelion salad and the Andorran trout of river. To drink, the mulled wine and beer are also popular. Some of the dishes are very common in the mountainous regions of Catalonia, such as trinxat, embotits, cooked snails, rice with mushrooms, mountain rice and mató. Pre-Romanesque and Romanesque art are one of the most important artistic manifestations and characteristics of the Principality. The Romanesque one allows to know the formation of the parochial communities, the relations of (social and political) power and the national culture. There are a total of forty Romanesque churches that stand out as being small austere ornamentation constructions, as well as bridges, fortresses and manor houses of the same period. Summer solstice fire festivals in the Pyrenees was included as UNESCO Intangible cultural heritage in 2015. Also the Madriu-Perafita-Claror Valley became Andorra's first, and to date its only, UNESCO World Heritage Site in 2004, with a small extension in 2006. Andorra is famous for the practice of winter sports. Andorra has the largest territory of ski slopes in the Pyrenees (3100 hectares and about 350 km of slopes) and two ski resorts. Grandvalira is the largest and most popular resort. Other popular sports played in Andorra include football, rugby union, basketball, and roller hockey. For roller hockey, Andorra usually plays in CERH Euro Cup and in FIRS Roller Hockey World Cup. In 2011, Andorra was the host country to the 2011 European League Final Eight. The country is represented in association football by the Andorra national football team. The team gained its first competitive win in a World Cup qualifier on 11 October 2019, in a European Championship qualifier against Moldova. Football is governed in Andorra by the Andorran Football Federation - founded in 1994, it organizes the national competitions of association football (Primera Divisió, Copa Constitució and Supercopa) and futsal. Andorra was admitted to UEFA and FIFA in the same year, 1996.

Andorra (, ; ), officially the Principality of Andorra (), is a sovereign landlocked microstate on the Iberian Peninsula, in the eastern Pyrenees, bordered by France to the north and Spain to the south. Believed to have been created by Charlemagne, Andorra was ruled by the count of Urgell until 988, when it was transferred to the Roman Catholic Diocese of Urgell. The present principality was formed by a charter in 1278. It is known as a principality as it is a diarchy headed by two princes: the Bishop of Urgell in Catalonia, Spain, and the President of the French Republic.

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summarize: The city-state of Athens is where western theatre originated. It was part of a broader culture of theatricality and performance in classical Greece that included festivals, religious rituals, politics, law, athletics and gymnastics, music, poetry, weddings, funerals, and "symposia". Participation in the city-state's many festivals—and mandatory attendance at the City Dionysia as an audience member (or even as a participant in the theatrical productions) in particular—was an important part of citizenship. Civic participation also involved the evaluation of the rhetoric of orators evidenced in performances in the law-court or political assembly, both of which were understood as analogous to the theatre and increasingly came to absorb its dramatic vocabulary. The Greeks also developed the concepts of dramatic criticism and theatre architecture. Actors were Western theatre developed and expanded considerably under the Romans. The Roman historian Livy wrote that the Romans first experienced theatre in the 4th century BCE, with a performance by Etruscan actors. Beacham argues that they had been familiar with "pre-theatrical practices" for some time before that recorded contact. The theatre of ancient Rome was a thriving and diverse art form, ranging from festival performances of street The earliest-surviving fragments of Sanskrit drama date from the 1st century CE. The wealth of archeological evidence from earlier periods offers no indication of the existence of a tradition of theatre. The ancient "Vedas" (hymns from between 1500 and 1000 BCE that are among the earliest examples of literature in the world) contain no hint of it (although a small number are composed in a form of dialogue) and the rituals of the Vedic period do not appear to have developed into theatre. The "Mahābhāṣya" by Patañjali contains the The Tang dynasty is sometimes known as "The Age of 1000 Entertainments". During this era, Ming Huang formed an acting school known as The Pear Garden to produce a form of drama that was primarily musical. That is why actors are commonly called "Children of the Pear Garden." During the dynasty of Empress Ling, shadow puppetry first emerged as a recognized form of theatre in China. There were two distinct forms of shadow puppetry, Pekingese (northern) and Cantonese (southern). The two styles were differentiated by the method of making the puppets and the positioning of the rods on the puppets, as opposed to the type of play performed by the puppets. Both styles generally performed plays depicting great adventure and fantasy, rarely was this very stylized form of theatre used for political propaganda. Cantonese shadow puppets were the larger of the two. They were built using thick leather which created more substantial shadows. Symbolic color was also very prevalent; a black face represented honesty, a red one bravery. The rods used to control Cantonese puppets were attached perpendicular to the puppets' heads. Thus, they were not seen by the audience when the shadow was created. Theatre took on many alternate forms in the West between the 15th and 19th centuries, including "commedia dell'arte" and melodrama. The general trend was away from the poetic drama of the Greeks and the Renaissance and toward a more naturalistic prose style of dialogue, especially following the Industrial Revolution. Theatre took a big pause during 1642 and 1660 in England because of the Puritan Interregnum. Viewing theatre as something sinful, the Puritans ordered the closure of London theatres in 1642. This stagnant period ended once Charles II came back to the throne in 1660 in the Restoration. Theatre (among other arts) exploded, with influence from French culture, since Charles had been exiled in France in the years previous to his reign. One of the big changes was the new theatre house. Instead of the type of the Elizabethan era, such as the Globe Theatre, round with The first form of Indian theatre was the Sanskrit theatre. It began after the development of Greek and Roman theatre and before the development of theatre in other parts of Asia. It emerged sometime between the 2nd century BCE and the 1st century CE and flourished between the 1st century CE and the 10th, which was a period of relative peace in the history Drama is the specific mode of fiction represented in performance. The term comes from a Greek word meaning "action", which is derived from the verb δράω, "dráō", "to do" or "to act". The enactment of drama in theatre, performed by actors on a stage before an audience, presupposes collaborative modes of production and a collective form of reception. The structure of dramatic texts, unlike other forms of literature, is directly influenced by this collaborative production and collective reception. The early modern tragedy "Hamlet" (1601) by Shakespeare and the classical Athenian tragedy "Oedipus Rex" (c. 429 BCE) by Sophocles are among the masterpieces of the art of drama. A modern example is "Long Day's Journey into Night" by Eugene O'Neill (1956). Music and theatre have had a close relationship since ancient times—Athenian tragedy, for example, was a form of dance-drama that employed a chorus whose parts were sung (to the accompaniment of an "aulos"—an instrument comparable to the modern clarinet), as were some of the actors' responses and their'solo songs' (monodies). Modern musical theatre is a form of theatre that also combines music, spoken dialogue, and dance. It emerged from comic opera (especially Gilbert and Sullivan), variety, vaudeville, and music hall genres of the late 19th and early 20th century. After Theatre productions that use humour as a vehicle to tell a story qualify as comedies. This may include a modern farce such as "Boeing Boeing" or a Aristotle's phrase "several kinds being found in separate parts of the play" is a reference to the structural origins of drama. In it the spoken parts were written in the Attic dialect whereas the choral (recited or sung) ones in the Doric dialect, these discrepancies reflecting the differing religious origins and poetic metres of the parts that were fused into a new entity, the theatrical "drama". Tragedy refers to a specific tradition of drama that has played a unique and important role historically in the self-definition of Western civilisation. That tradition has been multiple and discontinuous, yet the term has often been used to invoke a powerful effect of Improvisation has been a consistent feature of theatre, with the Commedia dell'arte in the sixteenth century being recognised as the first improvisation form. Popularized by Nobel Prize Winner Dario Fo and troupes such as the Upright Citizens Brigade improvisational theatre continues to evolve with many different streams and philosophies. Keith Johnstone and Viola Spolin are recognized as Having been an important part of human culture for more than 2,500 years, theatre has evolved a wide range of different theories and practices. Some are related to political or spiritual ideologies, while others are based purely on "artistic" concerns. Some processes focus on a story, some on theatre as event, and some on theatre as catalyst for social change. The classical Greek philosopher Aristotle, in his seminal treatise, "Poetics" (c. 335 BCE) is the earliest-surviving example and its arguments have influenced theories of theatre ever since. In it, he offers an account of what he calls "poetry" (a term which in Greek literally means "making" and in this context includes drama—comedy, tragedy, and the satyr play—as well as lyric poetry, epic poetry, and the dithyramb). He examines its "first principles" and identifies its genres and basic elements; his analysis of tragedy constitutes the core of the discussion. Aristotle argues that tragedy consists of six qualitative parts, which are (in order of importance) "mythos" or "plot", "ethos" or "character", "dianoia" or "thought", "lexis" or Theatre presupposes collaborative modes of production and a collective form of reception. The structure of dramatic texts, unlike other forms of literature, is directly influenced by this collaborative production and collective reception. The production of plays usually involves contributions from a playwright, director, a cast of actors, and a technical production team that includes a scenic or set designer, lighting designer, costume designer, sound designer, stage manager, production manager and technical director. Depending on the production, this team may also include a composer, dramaturg, video designer or fight director. Stagecraft is a generic term referring to the technical aspects of theatrical, film, and video production. It includes, but is not limited to, constructing and There are many modern theatre movements which go about producing theatre in a variety of ways. Theatrical enterprises vary enormously in sophistication and purpose. People who are involved vary from novices and hobbyists (in community theatre) to professionals (in Broadway and similar productions). Theatre can be performed with a shoestring budget or on a grand scale with multimillion-dollar budgets. This diversity manifests in the abundance of theatre sub-categories, which include: While most modern theatre companies rehearse one piece of theatre at a time, perform that piece for a set "run", retire the piece, and begin rehearsing a new show, repertory companies rehearse multiple shows at one time. These companies are able to perform these various pieces upon request and often perform works for years before retiring them. In order to put on a piece of theatre, both a theatre company and a theatre venue are needed. When a theatre company is the sole company in residence at a theatre venue, this theatre (and its corresponding theatre company) are called a resident theatre or a producing theatre, because the venue produces its own work. Other theatre companies, as well as dance companies, who do not have their own theatre venue, perform at rental theatres or at presenting theatres. Both rental and presenting theatres have no full-time resident companies. They do, however, sometimes There are many theatre unions including: Actors' Equity Association (for actors and stage managers), the Stage Directors and

Theatre or theater is a collaborative form of performing art that uses live performers, typically actors or actresses, to present the experience of a real or imagined event before a live audience in a specific place, often a stage. The performers may communicate this experience to the audience through combinations of gesture, speech, song, music, and dance. Elements of art, such as painted scenery and stagecraft such as lighting are used to enhance the physicality, presence and immediacy of the experience. The specific place of the performance is also named by the word "theatre" as derived from the Ancient Greek θέατρον (théatron, "a place for viewing"), itself from θεάομαι (theáomai, "to see", "to watch", "to observe").

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summarize: During his lifetime Lotto was a well-respected painter and certainly popular in Northern Italy; he is traditionally included in the Venetian School, but his independent career actually places him outside the Venetian art scene. He was certainly not as highly regarded in Venice as in the other towns where he worked, for he had a stylistic individuality, even an idiosyncratic style (although it fits within the parametres of High Renaissance painting), and, after his death, he gradually became neglected and then almost forgotten. This oblivion could be attributed to the fact that his works now remain in lesser known churches or in provincial museums. Born in Venice, he worked in Treviso (1503–1506); in the Marches (1506–1508); in Rome (1508–1510); in Bergamo (1513–1525); in Venice (1525–1549); in Ancona (1549) and finally, as a Franciscan lay brother, in Loreto (1549–1556). Little is known of his training. As a Venetian he was influenced by Giovanni Bellini as he had a good knowledge of contemporary Venetian painting. Though Bellini was doubtless not his teacher, the influence is clear in his early painting "Virgin and Child with St. Jerome" (1506; National Gallery of Scotland, Edinburgh). However, in his portraits and in his early painting "Allegory of Virtue and Vice" (1505; National Gallery of Art, Washington), he shows the influence of Giorgione's Naturalism. As he grew older his style changed, perhaps evolving, from a detached Giorgionesque classicism, to a more vibrant dramatic setpiece, more reminiscent of his contemporary from Parma, Correggio. Lotto soon left Venice, because there the competition for a young painter would have been too great, with established names such as Giorgione, Palma the Elder and certainly with Titian. Nevertheless, Giorgio Vasari mentions in the third part of his book "Vite" that Lotto was a friend of Palma the Elder. In Treviso, a prospering town within the domain of the republic of Venice, he came under the patronage of bishop Bernardo de' Rossi. The already mentioned painting "Allegory of Virtue and Vice" was intended as an allegorical cover of his portrait (1505) of the bishop (now in National Museum of Capodimonte in Naples), who had survived an assassination attempt. The painting "St. Jerome in the Desert" (1500 or 1506; Louvre, Paris) shows his youthful inexperience as a draughtsman, however the dramatic rocky landscape is accentuated by the red garment of the saint, while at the same time giving an early impression of his skill as a miniaturist. He painted his first altarpieces for the parish church San Cristina al Tiverone (1505) and the baptistery of the Cathedral of Asolo (1506), both still on display in those churches. In 1508 he began the Recanati Polyptych altarpiece for the church of San Domenico; this two-tiered and rather conventionally painted polyptych consists of six panels. His portrait "Young Man against a White Curtain" in the Kunsthistorisches Museum, Vienna (c. 1506) and "Adoration of the Child" (c. 1508) in the National Museum in Kraków with Catherine Cornaro, Queen of Cyprus portraited as Saint Catherine, are paintings from this period. As he became a respected painter, he came to the attention of Bramante, the papal architect, who was passing through Loreto (a pilgrimage site near Recanati). Lotto was invited to Rome to decorate the papal apartments, but nothing survives of this work, as it was destroyed a few years later. This was probably because he had imitated the style of Raphael, a rapidly rising star in the Papal court; indeed he had done it before, in the "Transfiguration" of the Recanati polyptych. In 1511 he was at work for the confraternity of the Buon Gesù in Jesi, painting an "Entombment" (Pinacoteca Civica, Jesi); soon after he was painting altarpieces in Recanati: a "Transfiguration" (c.1512, now in the Pinacoteca Comunale, Recanati and a fresco ("St Vincent Ferrer") for the church of San Domenico. His work in Bergamo, the westernmost town of the Venetian republic, was to prove his best and most productive artistic period, when he received many commissions from wealthy merchants, well educated professionals and local aristocrats. He had become a rich colourist and an experienced draughtsman, who also developed the concept of the psychological portrait that revealed the thoughts and emotions of his subjects. In this he was continuing the tradition begun by Antonello da Messina and a good example would be his "Portrait of a Young Man with a Book" (now in the Accademia, Venice). He began 1513 with a monumental altarpiece: the "Martinengo Altarpiece" in the Dominican church of the Santi Bartolomeo e Stefano in Bergamo. This altarpiece was commissioned by Count Alessandro Martinengo-Colleoni, grandson of the famous condottiere Bartolomeo Colleoni, which would be finished in 1516 and shows us the influence of Bramante and Giorgione. His next assignment was the decoration of the churches of S Bernardino and of Sant'Alessandro in Colonna, with frescoes and distemper paintings. He would finish five more altarpieces between 1521 and 1523. In 1523 he went for a brief stay in the Marches, obtaining there several commissions for altarpieces, which he would paint during his stay in Venice. His next works are mostly wall paintings: in 1524 he painted a series of frescoes with the lives of saints (such as Saint Barbara) in the Suardi Chapel in Trescore (near Bergamo). In the details he depicts scenes of each saint's life, such as in the fresco "Martyrdom of St. Claire". In the same fresco he portrays Christ with vines sprouting from his hands, illustrating the words of the New Testament: "I am the vine, you are the branches". In 1524 he also painted cartoons with Old Testament stories, as models for the intarsia panels for the choir stalls of Santa Maria Maggiore in Bergamo. More than 20 private paintings date from the same period; they are mostly of religious and pious subjects, such as "Madonnas" or a "Deposition", used for worship at home. Though he painted in the Classical tradition, Lotto adds a personal touch to the intense emotions. Using contrasting poses and opposing movement, he breaks the traditional symmetry of the Virgin surrounded by angels and saints. In Venice, Lotto first resided at the Dominican monastery of Santi Giovanni e Paolo, but he was forced to leave after a few months after a conflict with intarsia artist Fra Damiano da Bergamo. To cope with the many commissions he started to receive, he founded a workshop. He shipped five altarpieces for churches in the Marches and another one for the church Santa Maria Assunta in Celano (near Bergamo). Another altarpiece was for the Venetian church of Santa Maria dei Carmini, portraying "St. Nicholas of Bari in Glory". As Venice was a city of great wealth and as popularity increased, he received many orders for private paintings, including ten portraits, among them, "Portrait of a Young Man" (Gemäldegalerie, Berlin). His portrait of "Andrea Odoni" (Royal Art Collection, Hampton Court) (1527) would later influence the portrait of "Jacopo Strada" by Titian (1568) (Kunsthistorisches Museum, Vienna). But in Venice he was overshadowed by Titian, who dominated the artistic scene. In this last period of his life, Lorenzo Lotto would frequently move from town to town, searching for patrons and commissions. In 1532 he went to Treviso. Next he spent about seven years in the Marches (Ancona, Macerata and Jesi), before returning to Venice in 1540. He moved again to Treviso in 1542 and back to Venice in 1545. Finally he went back to Ancona in 1549. This was a productive period in his life, during which he painted several altarpieces and portraits. At the end of his life, Lotto found it difficult to earn a living. Furthermore, in 1550, when he was about 70, one of his works had an unsuccessful auction in Ancona. As recorded in his personal account book, this deeply disillusioned him. As he had always been a deeply religious man, in 1552 he joined the Holy Sanctuary at Loreto, becoming a lay brother. During that time he decorated the basilica of Santa Maria and painted a "Presentation in the Temple" for the Palazzo Apostolico in Loreto. He died in 1556 and was buried, at his request, in a Dominican habit. Giorgio Vasari included Lotto's biography in the third volume of his book "Vite". Lorenzo Lotto himself left many letters and a detailed notebook ("Libro di spese diverse", 1538–1556), giving insight to his life and work. His influence was felt by many painters, including probably Giovanni Busi, and Ercole Ramazzani, born in Arcevia and active near Jesi. Another pupil was Durante Nobili. Thanks to the work of the art historian Bernard Berenson, Lotto was rediscovered at the end of the 19th century. Since then, many monographs and several exhibitions have been dedicated to Lorenzo Lotto, such as the exhibition in Venice in 1953 and one in the National Gallery of Art, Washington, USA, in 1998.

Lorenzo Lotto (c. 1480 – 1556/57) was an Italian painter, draughtsman and illustrator, traditionally placed in the Venetian school, though much of his career was spent in other North Italian cities. He painted mainly altarpieces, religious subjects and portraits. He was active during the High Renaissance and the first half of the Mannerist period, but his work maintained a generally similar High Renaissance style throughout his career, although his nervous and eccentric posings and distortions represented a transitional stage to the Florentine and Roman Mannerists.

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summarize: Color, made up of hue, saturation, and value, dispersed over a surface is the essence of painting, just as pitch and rhythm are the essence of music. Color is highly subjective, but has observable psychological effects, although these can differ from one culture to the next. Black is associated with mourning in the West, but in the East, white is. Some painters, theoreticians, writers and scientists, including Goethe, Kandinsky, and Newton, have written their own color theory. Moreover, the use of language is only an abstraction for a color equivalent. The word "red", for example, can cover a wide range of variations from the pure red of the visible spectrum of light. Modern artists have extended the practice of painting considerably to include, as one example, collage, which began with Cubism and is not painting in the strict sense. Some modern painters incorporate different materials such as metal, plastic, sand, Jean Metzinger's mosaic-like Divisionist technique had its parallel in literature; a characteristic of the alliance between Symbolist writers and Neo-Impressionist artists: I ask of divided brushwork not the objective rendering of light, but iridescences and certain aspects of color still foreign to painting. I make a kind of chromatic versification and for syllables I use strokes which, variable in quantity, cannot differ in dimension without modifying the rhythm of a pictorial phraseology destined to translate the diverse emotions aroused by nature. (Jean Metzinger, circa 1907) Rhythm, for artists such as Piet Mondrian, is important in painting as it is in music. If one defines rhythm as "a pause incorporated into a sequence", then there can be rhythm in paintings. These pauses allow creative force to intervene and add new creations—form, melody, coloration. The distribution of form, or any kind of information is of crucial importance in the given work of art, and it directly affects The oldest known paintings are at the Grotte Chauvet in France, which some historians believe are about 32,000 years old. They are engraved and painted using red ochre and black pigment, and they show horses, rhinoceros, lions, buffalo, mammoth, abstract designs and what are possibly partial human figures. However, the earliest evidence of the act of painting has been discovered in two rock-shelters in Arnhem Land, in northern Australia. In the lowest layer of material at these sites, there are used pieces of ochre estimated to be 60,000 years old. Archaeologists have also found a fragment of rock painting preserved in a limestone rock-shelter in the Kimberley region of North-Western Australia, that is dated 40,000 years old. There are examples of cave paintings all over the world—in Italy, France, Spain, Portugal, China, Australia, Mexico, etc. In Western cultures, oil painting and watercolor painting have rich and complex traditions in style Aesthetics is the study of art and beauty; it was an important issue for 18th- and 19th-century philosophers such as Kant and Hegel. Classical philosophers like Plato and Aristotle also theorized about art and painting in particular. Plato disregarded painters (as well as sculptors) in his philosophical system; he maintained that painting cannot depict the truth—it is a copy of reality (a shadow of the world of ideas) and is nothing but a craft, similar to shoemaking or iron casting. By the time of Leonardo, painting had become a closer representation of the truth than painting was in Ancient Greece. Leonardo da Vinci, on the contrary, said that "" (""). Kant distinguished between Beauty and the Sublime, in terms that clearly gave priority to the former. Although he did not refer to painting in particular, this concept was taken up by painters such as J.M.W. Turner and Caspar David Friedrich. Hegel recognized the failure of attaining a universal concept of beauty and, in his aesthetic essay, wrote Different types of paint are usually identified by the medium that the pigment is suspended or embedded in, which determines the general working characteristics of the paint, such as viscosity, miscibility, solubility, drying time, etc. Oil painting is the process of painting with pigments that are bound with a medium of drying oil, such as linseed oil, which was widely used in early modern Europe. Often the oil was boiled with a resin such as pine resin Pastel is a painting medium in the form of a stick, consisting of pure powdered pigment and a binder. The pigments used in pastels are the same as those used to produce all colored art media, including oil paints; the binder is of a neutral hue and low saturation. The color effect of pastels is closer to the natural Acrylic paint is fast drying paint containing pigment suspension in acrylic polymer emulsion. Acrylic paints can be diluted with water, but become water-resistant when dry. Depending on how much the paint is diluted (with water) or modified with acrylic gels, media, or pastes, the finished acrylic painting can Watercolor is a painting method in which the paints are made of pigments suspended in a water-soluble vehicle. The traditional and most common support for watercolor paintings is paper; other supports include papyrus, bark papers, plastics, vellum or leather, fabric, wood and Ink paintings are done with a liquid that contains pigments and/or dyes and is used to color a surface to produce an image, text, or design. Ink is used for drawing with a pen, Encaustic painting, also known as hot wax painting, involves using heated beeswax to which colored pigments are added. The liquid/paste is then applied to a surface—usually prepared wood, though canvas and other materials are often used. The simplest encaustic mixture can be made from adding pigments to beeswax, but there are several other recipes that can be used—some containing other types of waxes, damar resin, linseed oil, Fresco is any of several related mural painting types, done on plaster on walls or ceilings. The word fresco comes from the Italian word "affresco", which derives from the Latin word for "fresh". Frescoes were often made during the Renaissance and other early time Gouache is a water-based paint consisting of pigment and other materials designed to be used in an opaque painting method. Gouache differs from watercolor in that the particles Enamels are made by painting a substrate, typically metal, with powdered glass; minerals called color oxides provide coloration. After firing at a temperature of 750–850 degrees Celsius (1380–1560 degrees Fahrenheit), the result is a fused lamination of glass and metal. Unlike most painted techniques, the surface can be handled and wetted Enamels have traditionally been Aerosol paint (also called spray paint) is a type of paint that comes in a sealed pressurized container and is released in a fine spray mist when depressing a valve button. A form of spray painting, aerosol paint leaves a smooth, evenly coated surface. Standard sized cans are portable, inexpensive and easy to store. Aerosol primer can be applied directly to bare metal and many Tempera, also known as egg tempera, is a permanent, fast-drying painting medium consisting of colored pigment mixed with a water-soluble binder medium (usually a glutinous material such as egg yolk or some other size). Tempera also refers to the paintings done in this medium. Water miscible oil paints (also called "water soluble" or "water-mixable") is a modern variety of oil paint engineered to be thinned and cleaned up with water, rather than having to use chemicals such as turpentine. It can be mixed and Digital painting is a method of creating an art object (painting) digitally and/or a technique for making digital art in the computer. As a method of creating an art object, it adapts traditional painting medium such as acrylic paint, oils, ink, watercolor, etc. and applies the pigment to traditional carriers, such as woven canvas cloth, paper, polyester etc. by means of computer software driving industrial robotic or office machinery "Style" is used in two senses: It can refer to the distinctive visual elements, techniques and methods that typify an "individual" artist's work. It can also refer to the movement or school that an artist is associated with. This can stem from an actual group that the artist was consciously involved with or it can be a category in which art historians have placed the painter. The word'style' in the latter sense has fallen out of favor in academic discussions about contemporary painting, though it continues to be used in popular contexts. Such movements or classifications include the following: Modernism describes both a set of cultural tendencies and an array of associated cultural movements, originally arising from wide-scale and far-reaching changes to Western society in the late 19th century and early 20th century. Modernism was a revolt against the conservative values of realism. The term encompasses the activities and output of those who felt the "traditional" forms of art, architecture, literature, religious faith, social organization and daily life were becoming outdated in the new economic, social and political conditions of an emerging fully industrialized world. A salient characteristic of modernism is self-consciousness. This often led to experiments with form, and work that draws attention to the processes and materials used (and to the further tendency of abstraction). Allegory is a figurative mode of representation conveying meaning other than the literal. Allegory communicates its message by means of symbolic figures, actions or symbolic representation. Allegory is generally treated as a figure of rhetoric, but In Spanish art, a bodegón is a still life painting depicting pantry items, such as victuals, game, and drink, often arranged on a simple stone slab, and also a painting with one or more figures, but significant still life elements, typically set in a kitchen or tavern. Starting in the Baroque period, such paintings became popular in Spain in the second quarter A figure painting is a work of art in any of the painting media with the primary subject being the human figure, whether clothed or nude. Figure painting may also refer to the Illustration paintings are those used as illustrations in books, magazines, and theater or movie posters and comic books. Today, there is a growing interest in collecting and admiring the original artwork. Various museum exhibitions, magazines and art galleries have devoted space to the Landscape painting is a term that covers the depiction of natural scenery such as mountains, valleys, trees, rivers, and forests, and especially art where the main subject is a wide view, with its elements arranged into a coherent composition. In other works landscape backgrounds for figures can still Portrait paintings are representations of a person, in which the face and its expression is predominant. The intent is to display the likeness, personality, and even the mood of the person. The art of the A still life is a work of art depicting mostly inanimate subject matter, typically commonplace objects—which may be either natural (food, flowers, plants, rocks, or shells) or man-made (drinking glasses, books, vases, jewelry, coins, pipes, and so on). With origins in the Middle Ages and Ancient Greek/Roman art, A veduta is a highly detailed, usually large-scale painting of a cityscape or some other vista. This genre of landscape originated in Flanders, where artists such as Paul Bril painted "vedute" as early as the 16th

Painting is the practice of applying paint, pigment, color or other medium to a solid surface (called the "matrix" or "support"). The medium is commonly applied to the base with a brush, but other implements, such as knives, sponges, and airbrushes, can be used. The final work is also called a painting.

en

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summarize: "Yen" derives from the Japanese word, which borrows its phonetic reading from Chinese yuan, similar to North Korean won and South Korean won. Originally, the Chinese had traded silver in mass called sycees and when Spanish and Mexican silver coins arrived, the Chinese called them "silver rounds" () for their circular shapes. The coins and the name also appeared in Japan. While the Chinese eventually replaced with, the Japanese continued to use the same word, which was given the shinjitai form in reforms at the end of World War II. The spelling and pronunciation "yen" is standard in English because when Japan was first encountered by Europeans around the 16th century, Japanese () and () both had been pronounced and Portuguese missionaries had spelled them "ye". By the middle of the 18th century, and came to be pronounced as in modern Japanese, although some regions retain the pronunciation. Walter Henry Medhurst, who had neither been to Japan nor met any Japanese, having consulted mainly a Japanese-Dutch dictionary, spelled some "e"s as "ye" in his "An English and Japanese, and Japanese and English Vocabulary" (1830). In the early Meiji era, James Curtis Hepburn, following Medhurst, spelled all "e"s as "ye" in his "A Japanese and English dictionary" (1867); in Japanese, "e" and "i" are slightly palatalized, somewhat as in Russian. That was the first full-scale Japanese-English/English-Japanese dictionary, which had a strong influence on Westerners in Japan and probably prompted the spelling "yen". Hepburn revised most "ye"s to "e" in the 3rd edition (1886) to mirror the contemporary pronunciation, except "yen". This was probably already fixed and has remained so ever since. In the 19th century, silver Spanish dollar coins were common throughout Southeast Asia, the China coast, and Japan. These coins had been introduced through Manila over a period of two hundred and fifty years, arriving on ships from Acapulco in Mexico. These ships were known as the Manila galleons. Until the 19th century, these silver dollar coins were actual Spanish dollars minted in the new world, mostly at Mexico City. But from the 1840s, they were increasingly replaced by silver dollars of the new Latin American republics. In the later half of the 19th century, some local coins in the region were made in the resemblance of the Mexican peso. The first of these local silver coins was the Hong Kong silver dollar coin that was minted in Hong Kong between the years 1866 and 1869. The Chinese were slow to accept unfamiliar coinage and preferred the familiar Mexican dollars, and so the Hong Kong government ceased minting these coins and sold the mint machinery to Japan. The Japanese then decided to adopt a silver dollar coinage under the name of 'yen', meaning 'a round object'. The yen was officially adopted by the Meiji government in an Act signed on June 27, 1871. The new currency was gradually introduced beginning from July of that year. The yen was therefore basically a dollar unit, like all dollars, descended from the Spanish Pieces of eight, and up until the year 1873, all the dollars in the world had more or less the same value. The yen replaced Tokugawa coinage, a complex monetary system of the Edo period based on the mon. The "New Currency Act" of 1871, stipulated the adoption of the decimal accounting system of "yen" (1, ),'(, ), and'(, ), with the coins being round and manufactured using Western machinery. The yen was legally defined as 0.78 troy ounces (24.26 g) of pure silver, or 1.5 grams of pure gold (as recommended by the European Congress of Economists in Paris in 1867; the 5-yen coin was equivalent to the Argentine 5 peso fuerte coin), hence putting it on a bimetallic standard. Following the silver devaluation of 1873, the yen devalued against the U.S. dollar and the Canadian dollar (since those two countries adhered to a gold standard), and by the year 1897, the yen was worth only about US$0.50. In that year, Japan adopted a gold exchange standard and hence froze the value of the yen at $0.50. This exchange rate remained in place until Japan left the gold standard in December 1931, after which the yen fell to $0.30 by July 1932 and to $0.20 by 1933. It remained steady at around $0.30 until the start of the Pacific War on December 7, 1941, at which time it fell to $0.23. The sen and the rin were eventually taken out of circulation at the end of 1953. No true exchange rate existed for the yen between December 7, 1941, and April 25, 1949; wartime inflation reduced the yen to a fraction of its pre-war value. After a period of instability, on April 25, 1949, the U.S. occupation government fixed the value of the yen at ¥360 per US$1 through a United States plan, which was part of the Bretton Woods System, to stabilize prices in the Japanese economy. That exchange rate was maintained until 1971, when the United States abandoned the gold standard, which had been a key element of the Bretton Woods System, and imposed a 10 percent surcharge on imports, setting in motion changes that eventually led to floating exchange rates in 1973. By 1971, the yen had become undervalued. Japanese exports were costing too little in international markets, and imports from abroad were costing the Japanese too much. This undervaluation was reflected in the current account balance, which had risen from the deficits of the early 1960s, to a then-large surplus of US$5.8 billion in 1971. The belief that the yen, and several other major currencies, were undervalued motivated the United States' actions in 1971. Following the United States' measures to devalue the dollar in the summer of 1971, the Japanese government agreed to a new, fixed exchange rate as part of the Smithsonian Agreement, signed at the end of the year. This agreement set the exchange rate at ¥308 per US$1. However, the new fixed rates of the Smithsonian Agreement were difficult to maintain in the face of supply and demand pressures in the foreign-exchange market. In early 1973, the rates were abandoned, and the major nations of the world allowed their currencies to float. In the 1970s, Japanese government and business people were very concerned that a rise in the value of the yen would hurt export growth by making Japanese products less competitive and would damage the industrial base. The government therefore continued to intervene heavily in foreign-exchange marketing (buying or selling dollars), even after the 1973 decision to allow the yen to float. Despite intervention, market pressures caused the yen to continue climbing in value, peaking temporarily at an average of ¥271 per US$1 in 1973, before the impact of the 1973 oil crisis was felt. The increased costs of imported oil caused the yen to depreciate to a range of ¥290 per US$1 to ¥300 per US$1 between 1974 and 1976. The re-emergence of trade surpluses drove the yen back up to ¥211 in 1978. This currency strengthening was again reversed by the second oil shock in 1979, with the yen dropping to ¥227 per US$1 by 1980. During the first half of the 1980s, the yen failed to rise in value even though current account surpluses returned and grew quickly. From ¥221 per US$1 in 1981, the average value of the yen actually dropped to ¥239 per US$1 in 1985. The rise in the current account surplus generated stronger demand for yen in foreign-exchange markets, but this trade-related demand for yen was offset by other factors. A wide differential in interest rates, with United States interest rates much higher than those in Japan, and the continuing moves to deregulate the international flow of capital, led to a large net outflow of capital from Japan. This capital flow increased the supply of yen in foreign-exchange markets, as Japanese investors changed their yen for other currencies (mainly dollars) to invest overseas. This kept the yen weak relative to the dollar and fostered the rapid rise in the Japanese trade surplus that took place in the 1980s. In 1985, a dramatic change began. Finance officials from major nations signed an agreement (the Plaza Accord) affirming that the dollar was overvalued (and, therefore, the yen undervalued). This agreement, and shifting supply and demand pressures in the markets, led to a rapid rise in the value of the yen. From its average of ¥239 per US$1 in 1985, the yen rose to a peak of ¥128 in 1988, virtually doubling its value relative to the dollar. After declining somewhat in 1989 and 1990, it reached a new high of ¥123 to US$1 in December 1992. In April 1995, the yen hit a peak of under 80 yen per dollar, temporarily making Japan's economy nearly the size of that of the US. The yen declined during the Japanese asset price bubble and continued to do so afterwards, reaching a low of ¥134 to US$1 in February 2002. The Bank of Japan's policy of zero interest rates has discouraged yen investments, with the carry trade of investors borrowing yen and investing in better-paying currencies (thus further pushing down the yen) estimated to be as large as $1 trillion. In February 2007, "The Economist" estimated that the yen was 15% undervalued against the dollar, and as much as 40% undervalued against the euro. However, this trend of depreciation reversed after the global economic crisis of 2008. Other major currencies, except the Swiss franc, have been declining relative to the yen. On April 4, 2013, the Bank of Japan announced that they would expand their Asset Purchase Program by $1.4 trillion in two years. The Bank of Japan hopes to bring Japan from deflation to inflation, aiming for 2% inflation. The amount of purchases is so large that it is expected to double the money supply. But this move has sparked concerns that the authorities in Japan are deliberately devaluing the yen in order to boost exports. However, the commercial sector in Japan worried that the devaluation would trigger an increase in import prices, especially for energy and raw materials. Coins were introduced in 1870. There were silver 5-, 10-, 20- and 50-sen and 1-yen, and gold 2-, 5-, 10- and 20-yen. Gold 1-yen were introduced in 1871, followed by copper 1-rin, -, 1- and 2-sen in 1873. Cupronickel 5-sen coins were introduced in 1889. In 1897, the silver 1-yen coin was demonetized and the sizes of the gold coins were reduced by 50%, with 5-, 10- and 20-yen coins issued. In 1920, cupro-nickel 10-sen coins were introduced. Production of silver coins ceased in 1938, after which a variety of base metals were used to produce 1-, 5- and 10-sen coins during the Second World War. Clay 5- and 10-sen coins were produced in 1945, but not issued for circulation. After the war, brass 50-sen, 1- and 5-yen were introduced between 1946 and 1948. In 1949, the current type of holed 5-yen was introduced, followed by bronze 10-yen (of the type still in circulation) in 1951. Coins in denominations of less than 1-yen became invalid on December 31, 1953, following enforcement of the. In 1955, the current type of aluminium 1-yen was introduced, along with unholed, nickel 50-yen. In 1957, silver 100-yen pieces were introduced, followed by the holed 50-yen coin in 1959. These were replaced in 1967 by the current cupro-nickel type, along with a smaller 50-yen coin. In 1982, the first 500-yen coins were introduced. The date (expressed as the year in the reign of the emperor at the time the coin was stamped) is on the reverse of all coins, and, in most cases, country name (through 1945, ; after 1945, and the value in kanji is on the obverse, except for the present 5-yen coin where the country name is on the reverse. Alongside with the 5-Swiss franc coin and the rarely used 5-Cuban convertible peso coin, the 500-yen coin is one of the highest-valued coin to be used regularly in the world, with value of US$4.5. Because of this high face value, the 500-yen coin has been a favorite target for counterfeiters; it was counterfeited to such an extent, that in 2000, a new series of coins was issued with various security features, but counterfeiting continued. The 1-yen coin is made out of 100% aluminium and can float on water if placed correctly. On various occasions, commemorative coins are minted, often in gold and silver with face values up to 100,000 yen. The first of these were silver ¥100 and ¥1000 Summer Olympic coins issued on the occasion of the 1964 games. Recently this practice is undertaken with the 500-yen coin, the first two types were issued in 1985, in commemoration of the science and technology exposition in Tsukuba and the 100th anniversary of the Governmental Cabinet system. The current commemorative 500- and 1000-yen coin series honouring the 47 prefectures of Japan commenced in 2008, with 47 unique designs planned for each denomination. Only one coin per customer is available from banks in each prefecture. 100,000 of each 1000-yen silver coin have been minted. Even though all commemorative coins can be spent like ordinary (non-commemorative) coins, they are not seen often in typical daily use and normally do not circulate. Instead of displaying the Gregorian calendar year of mintage like most nations' coins, yen coins instead display the year of the current emperor's reign. For example, a coin minted in 2009, would bear the date Heisei 21 (the 21st year of Emperor Akihito's reign). Due to the great differences in style, size, weight and the pattern present on the edge of the coin they are very easy for people with visual impairments to tell apart from one another. The issuance of the yen banknotes began in 1872, two years after the currency was introduced. Throughout its history, the denominations have ranged from 10 yen to 10,000 yen; since 1984, the lowest-valued banknote is the 1,000 yen note. Before and during World War II, various bodies issued banknotes in yen, such as the Ministry of Finance and the Imperial Japanese National Bank. The Allied forces also issued some notes shortly after the war. Since then, the Bank of Japan has been the exclusive note issuing authority. The bank has issued five series after World War II. Series E, the current series introduced in 2004, consists of ¥1000, ¥5000, and ¥10,000 notes. The EURion constellation pattern is present in the designs. Japan is generally considered a cash-based society, with 38% of payments in Japan made by cash in 2014. Possible explanations are that cash payments protect one's privacy, merchants do not have to wait for payment, and it does not carry any negative connotation like credit. On April 9, 2019, Finance Minister Tarō Asō announced new designs for the ¥1000, ¥5000, and ¥10,000 notes, for use beginning in 2024. The ¥1000 bill will feature Kitasato Shibasaburō and The Great Wave off Kanagawa, the ¥5000 bill will feature Tsuda Umeko and wisteria flowers, and the ¥10,000 bill will feature Shibusawa Eiichi and Tokyo Station. Beginning in December 1931, Japan gradually shifted from the gold standard system to the managed currency system. The relative value of the yen is determined in foreign exchange markets by the economic forces of supply and demand. The supply of the yen in the market is governed by the desire of yen holders to exchange their yen for other currencies to purchase goods, services, or assets. The demand for the yen is governed by the desire of foreigners to buy goods and services in Japan and by their interest in investing in Japan (buying yen-denominated real and financial assets). Since the 1990s, the Bank of Japan, the country's central bank, has kept interest rates low in order to spur economic growth. Short-term lending rates have responded to this monetary relaxation and fell from 3.7% to 1.3% between 1993 and 2008. Low interest rates combined with a ready liquidity for the yen prompted investors to borrow money in Japan and invest it in other countries (a practice known as carry trade). This has helped to keep the value of the yen low compared to other currencies. The special drawing rights (SDR) valuation is an IMF basket of currencies, including the Japanese yen. The SDR is linked to a basket of five different currencies, with 41.73% for the U.S. dollar, 30.93% for the Euro, 10.92% for the Chinese renminbi, 8.33% for the Japanese yen, and 8.09% for the pound sterling (as of 2016). The percentage for the yen has, however, declined from 18% in 2000. The exchange rate for the Japanese yen is expressed in terms of currency units per U.S. dollar; other rates are expressed as U.S. dollars per currency unit. The SDR currency value is calculated daily and the valuation basket is reviewed and adjusted every five years. The SDR was created in 1969, to support the fixed exchange system. Before the war commenced, the yen traded on an average of 3.6 yen to the dollar. During the war, because of overprinting and inflation as the Empire occupied more territory, the yen went as low as 600 yen to the USD. When McArthur and the US forces entered Japan in 1945, they decreed an official conversion rate of 15 yen to the USD. Within 1945-1946: the rate tanked to 50 yen to the USD because of the ongoing inflation. During the first half of 1946, the rate fluctuated to 66 yen to the USD and eventually plummeting to 600 yen to the dollar by 1947 because of the failure of the economic remedies. Eventually, the peg was officially moved to 270 yen to the dollar in 1948 before being adjusted again from 1949–1971 to 360 yen to the dollar. The table below shows the monthly average of the U.S. dollar–yen spot rate (JPY per USD) at 17:00 JST:

Zoology () is the branch of biology that studies the animal kingdom, including the structure, embryology, evolution, classification, habits, and distribution of all animals, both living and extinct, and how they interact with their ecosystems. The term is derived from Ancient Greek ζῷον, "zōion", i.e. "animal" and λόγος, "logos", i.e. "knowledge, study".

en

78

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summarize: The name "England" is derived from the Old English name "Englaland", which means "land of the Angles". The Angles were one of the Germanic tribes that settled in Great Britain during the Early Middle Ages. The Angles came from the Anglia peninsula in the Bay of Kiel area (present-day German state of Schleswig–Holstein) of the Baltic Sea. The earliest recorded use of the term, as "Engla londe", is in the late-ninth-century translation into Old English of Bede's "Ecclesiastical History of the English People". The term was then used in a different sense to the modern one, meaning "the land inhabited by the English", and it included English people in what is now south-east Scotland but was then part of the English kingdom of Northumbria. The "Anglo-Saxon Chronicle" recorded that the Domesday Book of 1086 covered the whole of England, meaning the English kingdom, but a few years later the "Chronicle" stated that The earliest known evidence of human presence in the area now known as England was that of "Homo antecessor", dating to approximately 780,000 years ago. The oldest proto-human bones discovered in England date from 500,000 years ago. Modern humans are known to have inhabited the area during the Upper Paleolithic period, though permanent settlements were only established within the last 6,000 years. After the last ice age only large mammals such as mammoths, bison and woolly rhinoceros remained. Roughly 11,000 years ago, when the ice sheets began to recede, humans repopulated the area; genetic research suggests they came from the northern part of the Iberian Peninsula. Roman military withdrawals left Britain open to invasion by pagan, seafaring warriors from north-western continental Europe, chiefly the Saxons, Angles, Jutes and Frisians who had long raided the coasts of the Roman province. These groups then began to settle in increasing numbers over the course of the fifth and sixth centuries, initially in the eastern part of the country. Their advance was contained for some decades after the Britons' victory at the Battle of Mount Badon, but subsequently resumed, over-running the fertile lowlands of Britain and reducing the area under Brittonic control to a series of separate enclaves in the more rugged country to the west by the end of the 6th century. Contemporary texts describing this period are extremely scarce, giving rise to its description as a Dark Age. The nature and During the Tudor period, the Renaissance reached England through Italian courtiers, who reintroduced artistic, educational and scholarly debate from classical antiquity. England began to develop naval skills, and exploration to the West intensified. Henry VIII broke from communion with the Catholic Church, over issues relating to his divorce, under the Acts of Supremacy in 1534 which proclaimed the monarch head of the Church of England. In contrast with much of European Protestantism, the roots of the split were more political than theological. He also legally incorporated his ancestral land Wales into the Kingdom of England with the 1535–1542 acts. There were internal religious conflicts during the reigns of Henry's daughters, Mary I and Elizabeth I. The former took the country back to Catholicism Under the newly formed Kingdom of Great Britain, output from the Royal Society and other English initiatives combined with the Scottish Enlightenment to create innovations in science and engineering, while the enormous growth in British overseas trade protected by the Royal Navy paved the way for the establishment of the British Empire. Domestically it drove the Industrial Revolution, a period of profound change in the socioeconomic and cultural conditions of England, resulting in industrialised agriculture, manufacture, engineering and mining, as well as new and pioneering road, rail and water networks to facilitate their expansion and development. The opening As part of the United Kingdom, the basic political system in England is a constitutional monarchy and parliamentary system. There has not been a government of England since 1707, when the Acts of Union 1707, putting into effect the terms of the Treaty of Union, joined England and Scotland to form the Kingdom of Great Britain. Before the union England was ruled by its monarch and the Parliament of England. Today England is governed directly by the Parliament of the United Kingdom, although other countries of the United Kingdom have devolved governments. In the House of Commons which is the lower house of the British Parliament based at the Palace of Westminster, there are 532 Members of Parliament (MPs) for constituencies in England, out of the 650 total. As of the 2019 United Kingdom general election, The English law legal system, developed over the centuries, is the basis of common law legal systems used in most Commonwealth countries and the United States (except Louisiana). Despite now being part of the United Kingdom, the legal system of the Courts of England and Wales continued, under the Treaty of Union, as a separate legal system from the one used in Scotland. The general essence of English law is that it is made by judges sitting in courts, applying their common sense and knowledge of legal precedent – "stare decisis" – to the facts before them. The subdivisions of England consist of up to four levels of subnational division controlled through a variety of types of administrative entities created for the purposes of local government. The highest tier of local government were the nine regions of England: North East, North West, Yorkshire and the Humber, East Midlands, West Midlands, East, South East, South West, and London. These were created in 1994 as Government Offices, used by the UK government to deliver a wide range of policies and programmes regionally, but there are no elected bodies at this level, except in London, and in 2011 the regional government offices were abolished. After devolution began to take place in other parts of the United Kingdom it was planned that referendums for the regions of England would take place for their own elected regional assemblies as a counterweight. London accepted in 1998: the London Assembly was created two years later. However, when the proposal was rejected by the 2004 North East England devolution referendum in the North East, further referendums were cancelled. The regional assemblies outside London were abolished in Geographically England includes the central and southern two-thirds of the island of Great Britain, plus such offshore islands as the Isle of Wight and the Isles of Scilly. It is bordered by two other countries of the United Kingdom: to the north by Scotland and to the west by Wales. England is closer than any other part of mainland Britain to the European continent. It is separated from France (Hauts-de-France) by a sea gap, though the two countries are connected by the Channel Tunnel near Folkestone. England also has shores on the Irish Sea, North Sea and Atlantic Ocean. The ports of London, Liverpool, and Newcastle lie on the tidal rivers Thames, Mersey and Tyne respectively. At, the Severn is the longest river flowing through England. It empties into the Bristol Channel and is notable for its Severn Bore (a tidal bore), which can reach in height. However, the longest river entirely in England is the Thames, which is in length. There are many lakes in England; the largest is Windermere, within the aptly named Lake District. Most of England's landscape England has a temperate maritime climate: it is mild with temperatures not much lower than in winter and not much higher than in summer. The weather is damp relatively frequently and is changeable. The coldest months are January and February, the latter particularly on the English coast, while July is normally the warmest month. Months with mild to warm weather are The Greater London Built-up Area is by far the largest urban area in England and one of the busiest cities in the world. It is considered a global city and has a population larger than other countries in the United Kingdom besides England itself. Other urban areas of considerable size and influence England's economy is one of the largest in the world, with an average GDP per capita of £28,100 or $36,000. Usually regarded as a mixed market economy, it has adopted many free market principles, yet maintains an advanced social welfare infrastructure. The official currency in England is the pound sterling, whose ISO 4217 code is GBP. Taxation in England is quite competitive when compared to much of the rest of Europe – the basic rate of personal tax is 20% on taxable income up to £31,865 above the personal tax-free allowance (normally £10,000), and 40% on any additional earnings above that amount. The economy of England is the largest part of the UK's economy, which has the 18th highest GDP PPP per capita in the world. England is a leader in the chemical and pharmaceutical sectors and in key technical industries, particularly aerospace, the arms industry, and the manufacturing side of the software industry. London, home to the London Stock Exchange, the United Kingdom's main stock exchange and the largest in Europe, is England's financial centre, with 100 of Europe's 500 largest corporations being based there. London is the largest financial centre in Europe, and is the second largest in the world. The Bank of England, founded in 1694 by Scottish banker William Paterson, is the United Kingdom's central bank. Originally established as private banker to the government of England, since 1946 it has been a state-owned institution. The bank has a monopoly on the issue of banknotes in England and Wales, although not in other parts of the United Kingdom. The government has devolved responsibility to the bank's Monetary Policy Committee for managing the monetary policy of the country and setting interest rates. England is highly industrialised, but since the 1970s there has been a decline in traditional heavy and manufacturing industries, and an increasing emphasis on a more service industry oriented economy. Tourism has become a significant industry, attracting millions of visitors to England each year. The export part of the economy is dominated by pharmaceuticals, cars (although many English marques are now foreign-owned, such as Land Rover, Lotus, Jaguar and Bentley), crude oil and petroleum from the English parts of North Sea oil along with Wytch Farm, aircraft engines and alcoholic beverages. Most of the UK's £30 billion aerospace industry is primarily based in England. The global market opportunity for UK aerospace manufacturers over the next two decades is estimated at £3.5 trillion. GKN Aerospace – an expert in metallic and composite aerostructures is involved in almost every civil and military fixed and rotary wing aircraft in production is based in Redditch. BAE Systems makes large sections of the Typhoon Eurofighter at its sub-assembly plant in Salmesbury and assembles the aircraft for the RAF at its Warton plant, near Preston. It is also a principal subcontractor on the F35 Joint Strike Fighter – the world's largest single defence project – for which it designs and manufactures a range of components including the aft fuselage, vertical and horizontal tail and wing tips and fuel system. It also manufactures the Hawk, the world's most successful jet training aircraft. Rolls-Royce PLC is the world's second-largest aero-engine manufacturer. Its engines power more than 30 types of commercial aircraft, and it has more 30,000 engines currently in service across both the civil and defence sectors. With a workforce of over 12,000 people, Derby has the largest concentration of Rolls-Royce employees in the UK. Rolls-Royce also produces low-emission power systems for ships; makes critical equipment and safety systems for the nuclear industry and powers offshore platforms and major pipelines for the oil and gas industry. Much of the UK's space industry is centred on EADS Astrium, based in Stevenage and Portsmouth. The company builds the buses – the underlying structure onto which the payload and propulsion systems are built – for most of the European Space Agency's spacecraft, as well as commercial satellites. The world leader in compact satellite systems, Surrey Satellite Technology, is also part of Astrium. Reaction Engines Limited, the company planning to build Skylon, a single-stage-to-orbit spaceplane using their SABRE rocket engine, a combined-cycle, air-breathing rocket propulsion system is based Culham. Agriculture is intensive and highly mechanised, producing 60% of food needs with only 2% of the labour force. Two-thirds of production is devoted to livestock, the other to arable crops. National Health England (NHS England) is the publicly funded healthcare system responsible for providing the majority of healthcare in the country. The NHS began on 5 July 1948, putting into effect the provisions of the National Health Service Act 1946. It was based on the findings of the Beveridge Report, prepared by economist and social reformer William Beveridge. The NHS is largely funded from general taxation including National Insurance payments, and it provides most of its services free at the point of use, although there are charges for some people for eye tests, dental care, prescriptions and aspects of personal care. The government department responsible for the With over 53 million inhabitants, England is by far the most populous country of the United Kingdom, accounting for 84% of the combined total. England taken as a unit and measured against international states has the fourth largest population in the European Union and would be the 25th largest country by population in the world. With a density of 424 people per square kilometre, it would be the second most densely populated country in the European Union after Malta. The English people are a British people. Some genetic evidence suggests that 75–95% descend in the paternal line from prehistoric settlers who originally came from the Iberian Peninsula, as well as a 5% contribution from Angles and Saxons, and a significant Scandinavian (Viking) element. However, other geneticists place the Germanic estimate up to half. Over time, various cultures have been influential: Prehistoric, Brythonic, Roman, Anglo-Saxon, Viking (North Germanic), Gaelic cultures, as well as a large influence from Normans. There is an English diaspora in former parts of the British Empire; especially As its name suggests, the English language, today spoken by hundreds of millions of people around the world, originated as the language of England, where it remains the principal tongue spoken by 98% of the population. It is an Indo-European language in the Anglo-Frisian branch of the Germanic family. After the Norman conquest, the Old English language was displaced and confined to the lower social classes as Norman French and Latin were used by the aristocracy. By the 15th century, English was back in fashion among all classes, though much changed; the Middle English form showed many signs of French influence, both in vocabulary and spelling. During the English Renaissance, many words were coined from Latin and Greek origins. Modern English has extended this custom of flexibility when it comes to incorporating words from different languages. Thanks in large part to the British Empire, the English language is the world's unofficial "lingua franca". English language learning and teaching is an important economic In the 2011 census, 59.4% of the population of England specified their religion as Christian, 24.7% answered that they had no religion, 5% specified that they were Muslim, while 3.7% of the population belongs to other religions and 7.2% did not give an answer. Christianity is the most widely practised religion in England, as it has been since the Early Middle Ages, although it was first introduced much earlier in Gaelic and Roman times. This Celtic Church was gradually joined to the Catholic hierarchy following the 6th-century Gregorian mission The Department for Education is the government department responsible for issues affecting people in England up to the age of 19, including education. State-run and state-funded schools are attended by approximately 93% of English schoolchildren. Of these, a minority are faith schools (primarily Church of England or Roman Catholic schools). Children who are between the ages of 3 and 5 attend nursery or an Early Years Foundation Stage reception unit within a primary school. Children between the ages of 5 and 11 attend primary school, and secondary school is attended by those aged between 11 and 16. After finishing compulsory education, students take GCSE examinations. Students may then opt to continue into further education for two years. Further education colleges (particularly sixth form colleges) often form part of a secondary school site. A-level examinations are sat by a large number of further education students, and often form the basis of an application to university. Although most English secondary schools are comprehensive, in some areas there are selective intake grammar schools, to which entrance is subject to passing the eleven-plus exam. Around 7.2% of English schoolchildren attend private schools, which are funded by private sources. Standards in state schools are monitored by Many ancient standing stone monuments were erected during the prehistoric period; amongst the best known are Stonehenge, Devil's Arrows, Rudston Monolith and Castlerigg. With the introduction of Ancient Roman architecture there was a development of basilicas, baths, amphitheaters, triumphal arches, villas, Roman temples, Roman roads, Roman forts, stockades and aqueducts. It was the Romans who founded the first cities and towns such as London, Bath, York, Chester and St Albans. Perhaps the best-known example is Hadrian's Wall stretching right across northern England. Another well-preserved example is the Roman Baths at Bath, Somerset. Early Medieval architecture's secular buildings were simple constructions mainly using timber with thatch for roofing. Ecclesiastical architecture ranged from a synthesis of Hiberno–Saxon monasticism, to Early Christian basilica and architecture characterised by pilaster-strips, blank arcading, baluster shafts and triangular headed openings. After the Norman conquest in 1066 various Castles in England English folklore developed over many centuries. Some of the characters and stories are present across England, but most belong to specific regions. Common folkloric beings include pixies, giants, elves, bogeymen, trolls, goblins and dwarves. While many legends and folk-customs are thought to be ancient, for instance the tales featuring Offa of Angel and Wayland the Smith, others date from after the Norman invasion; Robin Hood and his Merry Men of Sherwood and their battles with the Sheriff of Nottingham being, perhaps, the best known. During the High Middle Ages tales originating from Brythonic traditions entered English folklore and developed into the Arthurian myth. These were derived from Anglo-Norman, Welsh and French sources, featuring King Arthur, Camelot, Excalibur, Merlin and the Knights of the Round Table such as Lancelot. These stories are most centrally brought together within Geoffrey of Monmouth's "Historia Regum Britanniae" ("History of the Kings Since the early modern period the food of England has historically been characterised by its simplicity of approach and a reliance on the high quality of natural produce. During the Middle Ages and through the Renaissance period, English cuisine enjoyed an excellent reputation, though a decline began during the Industrial Revolution with the move away from the land and increasing urbanisation of the populace. The cuisine of England has, however, recently undergone a revival, which has been recognised by food critics with some good ratings in "Restaurant"s best restaurant in the world charts. An early book of English recipes is the "Forme of Cury" from the royal court of Richard II. Traditional examples of English food include the Sunday roast, featuring a roasted joint (usually beef, lamb, chicken or pork) served with assorted vegetables, Yorkshire pudding and The earliest known examples are the prehistoric rock and cave art pieces, most prominent in North Yorkshire, Northumberland and Cumbria, but also feature further south, for example at Creswell Crags. With the arrival of Roman culture in the 1st century, various forms of art such as statues, busts, glasswork and mosaics were the norm. There are numerous surviving artefacts, such as those at Lullingstone and Aldborough. During the Early Middle Ages the style favoured sculpted crosses and ivories, manuscript painting, gold and enamel jewellery, demonstrating a love of intricate, interwoven designs such as in the Staffordshire Hoard discovered in 2009. Some of these blended Gaelic and Anglian styles, such as the Lindisfarne Gospels and Vespasian Psalter. Later Gothic art was popular at Winchester and Canterbury, examples survive Early authors such as Bede and Alcuin wrote in Latin. The period of Old English literature provided the epic poem "Beowulf" and the secular prose of the "Anglo-Saxon Chronicle", along with Christian writings such as "Judith", Cædmon's "Hymn" and hagiographies. Following the Norman conquest Latin continued amongst the educated classes, as well as an Anglo-Norman literature. Middle English literature emerged with Geoffrey Chaucer, author of "The Canterbury Tales", along with Gower, the Pearl Poet and Langland. William of Ockham and Roger Bacon, who were Franciscans, were major philosophers of the Middle Ages. Julian of Norwich, who wrote "Revelations of Divine Love", was a prominent Christian mystic. With the English Renaissance literature in the Early Modern English style appeared. William Shakespeare, whose works include "Hamlet", "Romeo and Juliet", "Macbeth", and "A Midsummer Night's Dream", remains one of the most championed authors in English literature. Christopher Marlowe, Edmund Spenser, Philip Sydney, Thomas Kyd, John Donne, and Ben Jonson are other established authors of The traditional folk music of England is centuries old and has contributed to several genres prominently; mostly sea shanties, jigs, hornpipes and dance music. It has its own distinct variations and regional peculiarities. Wynkyn de Worde printed ballads of Robin Hood from the 16th century are an important artefact, as are John Playford's "The Dancing Master" and Robert Harley's "Roxburghe Ballads" collections. Some of the best-known songs are "Greensleeves", "Pastime with Good Company", "Maggie May" and "Spanish Ladies" amongst others. Many nursery rhymes are of English England (and the UK as a whole) has had a considerable influence on the history of the cinema, producing some of the greatest actors, directors and motion pictures of all time, including Alfred Hitchcock, Charlie Chaplin, David Lean, Laurence Olivier, Vivien Leigh, John Gielgud, Peter Sellers, Julie Andrews, Michael Caine, Gary Oldman, Helen Mirren, Kate Winslet and Daniel Day-Lewis. Hitchcock and Lean are among the most critically acclaimed filmmakers. Hitchcock's first thriller, "" (1926), helped shape the thriller genre in film, while his 1929 film, "Blackmail", is often regarded as the first British feature film. Major film studios in England include Pinewood, Elstree and Shepperton. Some of the most commercially successful films of all time have been produced in England, including two of the highest-grossing film franchises ("Harry Potter" and "James Bond"). Ealing Studios in London has a claim to being the oldest English Heritage is a governmental body with a broad remit of managing the historic sites, artefacts and environments of England. It is currently sponsored by the Department for Culture, Media and Sport. The charity National Trust for Places of Historic Interest or Natural Beauty holds a contrasting role. 17 of the 25 United Kingdom UNESCO World Heritage Sites fall within England. Some of the best-known of these are: Hadrian's Wall, Stonehenge, Avebury and Associated Sites, Tower of London, Jurassic Coast, Saltaire, Ironbridge Gorge, Studley Royal Park and various others. England has a strong sporting heritage, and during the 19th century codified many sports that are now played around the world. Sports originating in England include association football, cricket, rugby union, rugby league, tennis, boxing, badminton, squash, rounders, hockey, snooker, billiards, darts, table tennis, bowls, netball, thoroughbred horseracing, greyhound racing and fox hunting. It has helped the development of golf, sailing and Formula One. Football is the most popular of these sports. The England national football team, whose home venue is Wembley Stadium, played Scotland in the first ever international football match in 1872. Referred to as the "home of football" by FIFA, England hosted the 1966 FIFA World Cup, and won the tournament by defeating West Germany 4–2 in the final, with Geoff Hurst scoring a hat-trick. With a British television audience peak of 32.30 million viewers, the final is the most watched television event ever in the UK. At club level, England is recognised by FIFA as the birthplace of club football, due to Sheffield F.C. founded in 1857 being the world's oldest club. The Football Association is the oldest governing body in the sport, with the rules of football first drafted in 1863 by Ebenezer Cobb Morley. The FA Cup and The Football League were the first cup and league competitions respectively. In the modern day, the Premier League is the world's most-watched football league, most lucrative, and amongst the elite. As is the case throughout the UK, football in England is notable for the rivalries between clubs and the passion of the supporters, which includes a tradition of football chants. The European Cup (now UEFA Champions League) has been won by several English clubs. The most successful English football team in the European Cup/UEFA Champions League is Liverpool F.C. who have won the competition on six occasions. Other English success has come from Manchester United F.C., winning the competition on 3 occasions; Nottingham Forest F.C. on 2 occasions, Aston Villa F.C. and Chelsea F.C. have both won the trophy once. Cricket is generally thought to have been developed in the early medieval period among the farming and metalworking communities of the Weald. The England cricket team is a composite England and Wales, team. One of the game's top rivalries is The Ashes series between England and Australia, contested since 1882. The climax of the 2005 Ashes was viewed by 7.4 million as it was available on terrestrial television. England has hosted five Cricket World Cups (1975, 1979, 1983, 1999 and 2019), winning the 2019 edition in a final regarded as one of the greatest one day internationals ever played. They hosted the ICC World Twenty20 in 2009, winning this format in 2010 beating rivals Australia in the final. In the domestic competition, the County Championship, Yorkshire are by far the most successful club having won the competition 32 times outright and sharing it on 1 other occasion. Lord's Cricket Ground situated in London is sometimes referred to as the "Mecca of Cricket". William Penny Brookes was prominent in organising the format for the modern Olympic Games. In 1994, then President of the IOC, Juan Antonio Samaranch, laid a wreath on Brooke's grave, and said, "I came to pay homage and tribute to Dr Brookes, who really was the founder of the modern Olympic Games". London has hosted the Summer Olympic Games three times, in 1908, 1948, and 2012. England competes in the Commonwealth Games, held every four years. Sport England is the governing body responsible for distributing funds and providing strategic guidance for sporting activity in England. Rugby union originated in Rugby School, Warwickshire in the early 19th century. The England rugby union team won the 2003 Rugby World Cup, with Jonny Wilkinson The St George's Cross has been the national flag of England since the 13th century. Originally the flag was used by the maritime Republic of Genoa. The English monarch paid a tribute to the Doge of Genoa from 1190 onwards so that English ships could fly the flag as a means of protection when entering the Mediterranean. A red cross was a symbol for many Crusaders in the 12th and 13th centuries. It became associated with Saint George, along with countries and cities, which claimed him as their patron saint and used his cross as a banner. Since 1606 the St George's Cross has formed part of the design of the Union Flag, a Pan-British flag designed by King James I. During the English Civil War and Interregnum, the New Model Army's standards and the Commonwealth's Great Seal both incorporated the flag of Saint George. There are numerous other symbols and symbolic artefacts, both official and unofficial, including the Tudor rose, the nation's floral emblem, and the Three Lions featured on the Royal Arms of England. The Tudor rose was adopted as a national emblem of England around the time of the Wars of the Roses as a symbol of peace. It is a syncretic symbol in that it merged the white rose of the Yorkists and the red rose of the Lancastrians—cadet branches of the Plantagenets who went to war over control of the nation. It is also known as the "Rose of England". The oak tree is a symbol of England, representing strength and endurance. The Royal Oak symbol and Oak Apple Day commemorate the escape of King Charles II from the grasp of the parliamentarians after his father's execution: he hid in an oak tree to avoid detection before safely reaching exile. The Royal Arms of England, a national coat of arms featuring three lions, originated with its adoption by Richard the Lionheart in 1198. It is blazoned as "gules, three lions passant guardant or" and it provides one of the most prominent symbols of England; it is similar to the traditional arms of Normandy. England does not have an official designated national anthem, as the United Kingdom as a whole has "God Save the Queen". However, the following are often considered unofficial English national anthems: "Jerusalem", "Land of Hope and Glory" (used for England during the 2002 Commonwealth Games), and "I Vow to Thee, My Country". England's National Day is 23 April which is St George's Day: St George is the patron saint of England.

England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest of England and the Celtic Sea to the southwest. England is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain, which lies in the North Atlantic, and includes over 100 smaller islands, such as the Isles of Scilly and the Isle of Wight. It is the largest country of the British Isles.

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summarize: Most liquids freeze by crystallization, formation of crystalline solid from the uniform liquid. This is a first-order thermodynamic phase transition, which means that as long as solid and liquid coexist, the temperature of the whole system remains very nearly equal to the melting point due to slow removal of heat when in contact with air, which is a poor heat conductor. Because of the latent heat of fusion, the freezing is greatly slowed and the temperature will not drop any more once the freezing starts but will continue dropping once it finishes. Crystallization consists of two major events, nucleation and crystal growth. Nucleation is the step wherein the molecules start to gather into clusters, on the nanometer scale, arranging in a defined and periodic manner that defines the crystal structure. The crystal growth is the subsequent growth of the nuclei that succeed in achieving the critical cluster size. In spite of the second law of thermodynamics, crystallization of pure liquids usually begins at a lower temperature than the melting point, due to high activation energy of homogeneous nucleation. The creation of a nucleus implies the formation of an interface at the boundaries of the new phase. Some energy is expended to form this interface, based on the surface energy of each phase. If a hypothetical nucleus is too small, the energy that would be released by forming its volume is not enough to create its surface, and nucleation does not proceed. Freezing does not start until the temperature is low enough to provide enough energy to form stable nuclei. In presence of irregularities on the surface of the containing vessel, solid or gaseous impurities, pre-formed solid crystals, or other nucleators, heterogeneous nucleation may occur, where some energy is released by the partial destruction of the previous interface, raising the supercooling point to be near or equal to the melting point. The melting point of water at 1 atmosphere of pressure is very close to 0 °C (32 °F, 273.15 K), and in the presence of nucleating substances the freezing point of water is close to the melting point, but in the absence of nucleators water can supercool to −40 °C (−40 °F, 233 K) before freezing. Under high pressure (2,000 atmospheres) water will supercool to as low as −70 °C (−94 °F, 203 K) before freezing. Freezing is almost always an exothermic process, meaning that as liquid changes into solid, heat and pressure are released. This is often seen as counter-intuitive, since the temperature of the material does not rise during freezing, except if the liquid were supercooled. But this can be understood since heat must be continually removed from the freezing liquid or the freezing process will stop. The energy released upon freezing is a latent heat, and is known as the enthalpy of fusion and is exactly the same as the energy required to melt the same amount of the solid. Low-temperature helium is the only known exception to the general rule. Helium-3 has a negative enthalpy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative enthalpy of fusion below 0.8 K. This means that, at appropriate constant pressures, heat must be "added" to these substances in order to freeze them. Certain materials, such as glass and glycerol, may harden without crystallizing; these are called amorphous solids. Amorphous materials, as well as some polymers, do not have a freezing point, as there is no abrupt phase change at any specific temperature. Instead, there is a gradual change in their viscoelastic properties over a range of temperatures. Such materials are characterized by a glass transition that occurs at a glass transition temperature, which may be roughly defined as the "knee" point of the material's density vs. temperature graph. Because vitrification is a non-equilibrium process, it does not qualify as freezing, which requires an equilibrium between the crystalline and liquid state. Some substances, such as water and bismuth, expand when frozen. Many living organisms are able to tolerate prolonged periods of time at temperatures below the freezing point of water. Most living organisms accumulate cryoprotectants such as anti-nucleating proteins, polyols, and glucose to protect themselves against frost damage by sharp ice crystals. Most plants, in particular, can safely reach temperatures of −4 °C to −12 °C. Certain bacteria, notably "Pseudomonas syringae", produce specialized proteins that serve as potent ice nucleators, which they use to force ice formation on the surface of various fruits and plants at about −2 °C. The freezing causes injuries in the epithelia and makes the nutrients in the underlying plant tissues available to the bacteria. Three species of bacteria, "Carnobacterium pleistocenium", as well as "Chryseobacterium greenlandensis" and "Herminiimonas glaciei", have reportedly been revived after surviving for thousands of years frozen in ice. Many plants undergo a process called hardening, which allows them to survive temperatures below 0 °C for weeks to months. The nematode "Haemonchus contortus" can survive 44 weeks frozen at liquid nitrogen temperatures. Other nematodes that survive at temperatures below 0 °C include "Trichostrongylus colubriformis" and "Panagrolaimus davidi". Many species of reptiles and amphibians survive freezing. See cryobiology for a full discussion. Human gametes and 2-, 4- and 8-cell embryos can survive freezing and are viable for up to 10 years, a process known as cryopreservation. Experimental attempts to freeze human beings for later revival are known as cryonics. Freezing is a common method of food preservation that slows both food decay and the growth of micro-organisms. Besides the effect of lower temperatures on reaction rates, freezing makes water less available for bacteria growth.

Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liquid or the liquid content of a substance, usually due to cooling.

en

52

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summarize: "Nucleate boiling" is characterized by the growth of bubbles or pops on a heated surface, which rises from discrete points on a surface, whose temperature is only slightly above the temperature of the liquid. In general, the number of nucleation sites is increased by an increasing surface temperature. An irregular surface of the boiling vessel (i.e., increased surface roughness) or additives to the fluid (i.e., surfactants and/or nanoparticles) facilitate nucleate boiling over a broader temperature range, while an exceptionally smooth surface, such as plastic, lends itself to superheating. Under these conditions, a heated liquid may show boiling delay and the temperature may go somewhat above the boiling point without boiling. "Critical heat flux (CHF)" describes the thermal limit of a phenomenon where a phase change occurs during heating (such as bubbles forming on a metal surface used to heat water), which suddenly decreases the efficiency of heat transfer, thus causing localised overheating of the heating surface. As the boiling surface is heated above a critical temperature, a film of vapor forms on the surface. Since this vapor film is much less capable of carrying heat away from the surface, the temperature rises very rapidly beyond this point into the transition boiling regime. The point at which this occurs is dependent on the characteristics of boiling fluid and the heating surface in question. "Transition boiling" may be defined as the unstable boiling, which occurs at surface temperatures between the maximum attainable in nucleate and the minimum attainable in film boiling. The formation of bubbles in a heated liquid is a complex physical process which often involves cavitation and acoustic effects, such as the broad-spectrum hiss one hears in a kettle not yet heated to the point where bubbles boil to the surface. If a surface heating the liquid is significantly hotter than the liquid then film boiling will occur, where a thin layer of vapor, which has low thermal conductivity, insulates the surface. This condition of a vapor film insulating the surface from the liquid characterizes "film boiling". The boiling point of an element at a given pressure is a characteristic attribute of the element. This is also true for many simple compounds including water and simple alcohols. Once boiling has started and provided that boiling remains stable and the pressure is constant, the temperature of the boiling liquid remains constant. This attribute led to the adoption of boiling points as the definition of 100°C. Mixtures of volatile liquids have a boiling point specific to that mixture producing vapour with a constant mix of components - the constant boiling mixture. This attribute allows mixtures of liquids to be separated or partly separated by boiling and is best known as a means of separating ethanol from water. Most types of refrigeration and some type of air-conditioning work by compressing a gas so that it becomes liquid and then allowing it to boil. This adsorbs heat from the surroundings cooling the 'fridge or freezer or cooling the air entering a building. Typical liquids include propane, ammonia, carbon dioxide or nitrogen. As a method of disinfecting water, bringing it to its boiling point at, is the oldest and most effective way since it does not affect the taste, it is effective despite contaminants or particles present in it, and is a single step process which eliminates most microbes responsible for causing intestine related diseases. The boiling point of water is at sea level and at normal barometric pressure. In places having a proper water purification system, it is recommended only as an emergency treatment method or for obtaining potable water in the wilderness or in rural areas, as it cannot remove chemical toxins or impurities. The elimination of micro-organisms by boiling follows first-order kinetics—at high temperatures, it is achieved in less time and at lower temperatures, in more time. The heat sensitivity of micro-organisms varies, at, Giardia species (causes Giardiasis) can take ten minutes for complete inactivation, most intestine affecting microbes and "E. coli" (gastroenteritis) take less than a minute; at boiling point, "Vibrio cholerae" (cholera) takes ten seconds and hepatitis A virus (causes the symptom of jaundice), one minute. Boiling does not ensure the elimination of all micro-organisms; the bacterial spores Clostridium can survive at but are not water-borne or intestine affecting. Thus for human health, complete sterilization of water is not required. The traditional advice of boiling water for ten minutes is mainly for additional safety, since microbes start getting eliminated at temperatures greater than and bringing it to its boiling point is also a useful indication that can be seen without the help of a thermometer, and by this time, the water is disinfected. Though the boiling point decreases with increasing altitude, it is not enough to affect the disinfecting process. "Boiling" is the method of cooking food in boiling water or other water-based liquids such as stock or milk. Simmering is gentle boiling, while in poaching the cooking liquid moves but scarcely bubbles. The boiling point of water is typically considered to be. Pressure and a change in the composition of the liquid may alter the boiling point of the liquid. High elevation cooking generally takes longer since boiling point is a function of atmospheric pressure. At an elevations of about, water boils at approximately 95 °C or 203 °F. Depending on the type of food and the elevation, the boiling water may not be hot enough to cook the food properly. Similarly, increasing the pressure as in a pressure cooker raises the temperature of the contents above the open air boiling point. Also known as "boil-in-bag", this involves heating or cooking ready-made foods sealed in a thick plastic bag. The bag containing the food, often frozen, is submerged in boiling water for a prescribed time. The resulting dishes can be prepared with greater convenience as no pots or pans are dirtied in the process. Such meals are available for camping as well as home dining. At any given temperature, all the molecules in a liquid do not have the same kinetic energy. Some high energy particles on the liquid surface may have enough energy to escape the intermolecular forces of attraction of the liquid and become a gas. This is called evaporation. Evaporation only happens on the surface while boiling happens throughout the liquid. When a liquid reaches its boiling point bubbles of gas form in it which rise into the surface and burst into the air. This process is called boiling. If the boiling liquid is heated more strongly the temperature does not rise but the liquid boils more quickly. This distinction is exclusive to the liquid-to-gas transition; any transition directly from solid to gas is always referred to as sublimation regardless of whether it is at its boiling point or not.

Boiling is the rapid vaporization of a liquid, which occurs when a liquid is heated to its boiling point, the temperature at which the vapour pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding atmosphere. There are two main types of boiling: nucleate boiling where small bubbles of vapour form at discrete points, and critical heat flux boiling where the boiling surface is heated above a certain critical temperature and a film of vapor forms on the surface. Transition boiling is an intermediate, unstable form of boiling with elements of both types. The boiling point of water is 100 °C or 212 °F but is lower with the decreased atmospheric pressure found at higher altitudes.

en

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summarize: A "saturated liquid" contains as much thermal energy as it can without boiling (or conversely a "saturated vapor" contains as little thermal energy as it can without condensing). Saturation temperature means "boiling point". The saturation temperature is the temperature for a corresponding saturation pressure at which a liquid boils into its vapor phase. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition. If the pressure in a system remains constant (isobaric), a vapor at saturation temperature will begin to condense into its liquid phase as thermal energy (heat) is removed. Similarly, a liquid at saturation temperature and pressure will boil into its vapor phase as additional thermal energy is applied. The boiling point corresponds to the temperature at which the vapor pressure of the liquid equals the surrounding environmental pressure. Thus, the boiling point is dependent on the pressure. Boiling points may be published with respect to the NIST, USA standard pressure of 101.325 kPa (or 1 atm), or the IUPAC standard pressure of 100.000 kPa. At higher elevations, where the atmospheric pressure is much lower, the boiling point is also lower. The boiling point increases with increased pressure up to the critical point, where the gas and liquid properties become identical. The boiling point cannot be increased beyond the critical point. Likewise, the boiling point decreases with decreasing pressure until the triple point is reached. The boiling point cannot be reduced below the triple point. If the heat of vaporization and the vapor pressure of a liquid at a certain temperature are known, the boiling point can be calculated by using the Clausius–Clapeyron equation, thus: where: Saturation pressure is the pressure for a corresponding saturation temperature at which a liquid boils into its vapor phase. Saturation pressure and saturation temperature have a direct relationship: as saturation pressure is increased, so is saturation temperature. If the temperature in a system remains constant (an "isothermal" system), vapor at saturation pressure and temperature will begin to condense into its liquid phase as the system pressure is increased. Similarly, a liquid at saturation pressure and temperature will tend to flash into its vapor phase as system pressure is decreased. There are two conventions regarding the "standard boiling point of water": The "normal boiling point" is at a pressure of 1 atm (i.e., 101.325 kPa). The IUPAC recommended "standard boiling point of water" at a standard pressure of 100 kPa (1 bar) is. For comparison, on top of Mount Everest, at elevation, the pressure is about and the boiling point of water is. The Celsius temperature scale was defined until 1954 by two points: 0 °C being defined by the water freezing point and 100 °C being defined by the water boiling point at standard atmospheric pressure. The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point (i.e., the boiling point at atmospheric pressure) of the liquid. The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids. As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points. For example, at any given temperature, methyl chloride has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point (−24.2 °C), which is where the vapor pressure curve of methyl chloride (the blue line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure. The critical point of a liquid is the highest temperature (and pressure) it will actually boil at. See also Vapour pressure of water. The element with the lowest boiling point is helium. Both the boiling points of rhenium and tungsten exceed 5000 K at standard pressure; because it is difficult to measure extreme temperatures precisely without bias, both have been cited in the literature as having the higher boiling point. As can be seen from the above plot of the logarithm of the vapor pressure vs. the temperature for any given pure chemical compound, its normal boiling point can serve as an indication of that compound's overall volatility. A given pure compound has only one normal boiling point, if any, and a compound's normal boiling point and melting point can serve as characteristic physical properties for that compound, listed in reference books. The higher a compound's normal boiling point, the less volatile that compound is overall, and conversely, the lower a compound's normal boiling point, the more volatile that compound is overall. Some compounds decompose at higher temperatures before reaching their normal boiling point, or sometimes even their melting point. For a stable compound, the boiling point ranges from its triple point to its critical point, depending on the external pressure. Beyond its triple point, a compound's normal boiling point, if any, is higher than its melting point. Beyond the critical point, a compound's liquid and vapor phases merge into one phase, which may be called a superheated gas. At any given temperature, if a compound's normal boiling point is lower, then that compound will generally exist as a gas at atmospheric external pressure. If the compound's normal boiling point is higher, then that compound can exist as a liquid or solid at that given temperature at atmospheric external pressure, and will so exist in equilibrium with its vapor (if volatile) if its vapors are contained. If a compound's vapors are not contained, then some volatile compounds can eventually evaporate away in spite of their higher boiling points. In general, compounds with ionic bonds have high normal boiling points, if they do not decompose before reaching such high temperatures. Many metals have high boiling points, but not all. Very generally—with other factors being equal—in compounds with covalently bonded molecules, as the size of the molecule (or molecular mass) increases, the normal boiling point increases. When the molecular size becomes that of a macromolecule, polymer, or otherwise very large, the compound often decomposes at high temperature before the boiling point is reached. Another factor that affects the normal boiling point of a compound is the polarity of its molecules. As the polarity of a compound's molecules increases, its normal boiling point increases, other factors being equal. Closely related is the ability of a molecule to form hydrogen bonds (in the liquid state), which makes it harder for molecules to leave the liquid state and thus increases the normal boiling point of the compound. Simple carboxylic acids dimerize by forming hydrogen bonds between molecules. A minor factor affecting boiling points is the shape of a molecule. Making the shape of a molecule more compact tends to lower the normal boiling point slightly compared to an equivalent molecule with more surface area. Most volatile compounds (anywhere near ambient temperatures) go through an intermediate liquid phase while warming up from a solid phase to eventually transform to a vapor phase. By comparison to boiling, a sublimation is a physical transformation in which a solid turns directly into vapor, which happens in a few select cases such as with carbon dioxide at atmospheric pressure. For such compounds, a sublimation point is a temperature at which a solid turning directly into vapor has a vapor pressure equal to the external pressure. In the preceding section, boiling points of pure compounds were covered. Vapor pressures and boiling points of substances can be affected by the presence of dissolved impurities (solutes) or other miscible compounds, the degree of effect depending on the concentration of the impurities or other compounds. The presence of non-volatile impurities such as salts or compounds of a volatility far lower than the main component compound decreases its mole fraction and the solution's volatility, and thus raises the normal boiling point in proportion to the concentration of the solutes. This effect is called boiling point elevation. As a common example, salt water boils at a higher temperature than pure water. In other mixtures of miscible compounds (components), there may be two or more components of varying volatility, each having its own pure component boiling point at any given pressure. The presence of other volatile components in a mixture affects the vapor pressures and thus boiling points and dew points of all the components in the mixture. The dew point is a temperature at which a vapor condenses into a liquid. Furthermore, at any given temperature, the composition of the vapor is different from the composition of the liquid in most such cases. In order to illustrate these effects between the volatile components in a mixture, a boiling point diagram is commonly used. Distillation is a process of boiling and [usually] condensation which takes advantage of these differences in composition between liquid and vapor phases.

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

en

31

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summarize: Values are usually quoted in J/mol or kJ/mol (molar enthalpy of vaporization), although kJ/kg or J/g (specific heat of vaporization), and older units like kcal/mol, cal/g and Btu/lb are sometimes still used, among others. The enthalpy of condensation (or heat of condensation) is by definition equal to the enthalpy of vaporization with the opposite sign: enthalpy changes of vaporization are always positive (heat is absorbed by the substance), whereas enthalpy changes of condensation are always negative (heat is released by the substance). The enthalpy of vaporization can be written as It is equal to the increased internal energy of the vapor phase compared with the liquid phase, plus the work done against ambient pressure. The increase in the internal energy can be viewed as the energy required to overcome the intermolecular interactions in the liquid (or solid, in the case of sublimation). Hence helium has a particularly low enthalpy of vaporization, 0.0845 kJ/mol, as the van der Waals forces between helium atoms are particularly weak. On the other hand, the molecules in liquid water are held together by relatively strong hydrogen bonds, and its enthalpy of vaporization, 40.65 kJ/mol, is more than five times the energy required to heat the same quantity of water from 0 °C to 100 °C ("c" = 75.3 J Kmol). Care must be taken, however, when using enthalpies of vaporization to "measure" the strength of intermolecular forces, as these forces may persist to an extent in the gas phase (as is the case with hydrogen fluoride), and so the calculated value of the bond strength will be too low. This is particularly true of metals, which often form covalently bonded molecules in the gas phase: in these cases, the enthalpy of atomization must be used to obtain a true value of the bond energy. An alternative description is to view the enthalpy of condensation as the heat which must be released to the surroundings to compensate for the drop in entropy when a gas condenses to a liquid. As the liquid and gas are in equilibrium at the boiling point ("T"), Δ"G" = 0, which leads to: As neither entropy nor enthalpy vary greatly with temperature, it is normal to use the tabulated standard values without any correction for the difference in temperature from 298 K. A correction must be made if the pressure is different from 100 kPa, as the entropy of a gas is proportional to its pressure (or, more precisely, to its fugacity): the entropies of liquids vary little with pressure, as the compressibility of a liquid is small. These two definitions are equivalent: the boiling point is the temperature at which the increased entropy of the gas phase overcomes the intermolecular forces. As a given quantity of matter always has a higher entropy in the gas phase than in a condensed phase (formula_6 is always positive), and from the Gibbs free energy change falls with increasing temperature: gases are favored at higher temperatures, as is observed in practice. Estimation of the enthalpy of vaporization of electrolyte solutions can be simply carried out using equations based on the chemical thermodynamic models, such as Pitzer model or TCPC model. The vaporization of metals is a key step in metal vapor synthesis, which exploits the increased reactivity of metal atoms or small particles relative to the bulk elements. Enthalpies of vaporization of common substances, measured at their respective standard boiling points:

The enthalpy of vaporization, (symbol ) also known as the (latent) heat of vaporization or heat of evaporation, is the amount of energy (enthalpy) that must be added to a liquid substance, to transform a quantity of that substance into a gas. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

en

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summarize: Solid carbon dioxide (dry ice) sublimes everywhere along the line below the triple point (e.g., at the temperature of −78.5 °C (194.65 K, ) at atmospheric pressure, whereas its melting into liquid CO can occur only along the line at pressures and temperatures above the triple point (i.e., 5.2 atm, −56.4 °C). Snow and ice sublime, although more slowly, at temperatures below the freezing/melting point temperature line at 0 °C for most pressures; see line below triple point. In freeze-drying, the material to be dehydrated is frozen and its water is allowed to sublime under reduced pressure or vacuum. The loss of snow from a snowfield during a cold spell is often caused by sunshine acting directly on the upper layers of the snow. Ablation is a process that includes sublimation and erosive wear of glacier ice. Naphthalene, an organic compound commonly found in pesticides such as mothballs, sublimes easily because it is made of non-polar molecules that are held together only by van der Waals intermolecular forces. Naphthalene is a solid that sublimes at standard atmospheric temperature with the sublimation point at around 80°C or 176°F. At low temperature, its vapour pressure is high enough, 1mmHg at 53°C, to make the solid form of naphthalene evaporate into gas. On cool surfaces, the naphthalene vapours will solidify to form needle-like crystals. Iodine produces fumes on gentle heating. It is possible to obtain liquid iodine at atmospheric pressure by controlling the temperature at just above the melting point of iodine. In forensic science, iodine vapor can reveal latent fingerprints on paper. Arsenic can also sublime at high temperatures. Cadmium and zinc are not suitable materials for use in vacuum because they sublime much more than other common materials. Sublimation is a technique used by chemists to purify compounds. A solid is typically placed in a sublimation apparatus and heated under vacuum. Under this reduced pressure, the solid volatilizes and condenses as a purified compound on a cooled surface (cold finger), leaving a non-volatile residue of impurities behind. Once heating ceases and the vacuum is removed, the purified compound may be collected from the cooling surface. For even higher purification efficiencies, a temperature gradient is applied, which also allows for the separation of different fractions. Typical setups use an evacuated glass tube that is heated gradually in a controlled manner. The material flow is from the hot end, where the initial material is placed, to the cold end that is connected to a pump stand. By controlling temperatures along the length of the tube, the operator can control the zones of re-condensation, with very volatile compounds being pumped out of the system completely (or caught by a separate cold trap), moderately volatile compounds re-condensing along the tube according to their different volatilities, and non-volatile compounds remaining in the hot end. Vacuum sublimation of this type is also the method of choice for purification of organic compounds for use in the organic electronics industry, where very high purities (often > 99.99%) are needed to satisfy the standards for consumer electronics and other applications. In ancient alchemy, a protoscience that contributed to the development of modern chemistry and medicine, alchemists developed a structure of basic laboratory techniques, theory, terminology, and experimental methods. "Sublimation" was used to refer to the process in which a substance is heated to a vapor, then immediately collects as sediment on the upper portion and neck of the heating medium (typically a retort or alembic), but can also be used to describe other similar non-laboratory transitions. It was mentioned by alchemical authors such as Basil Valentine and George Ripley, and in the "Rosarium philosophorum", as a process necessary for the completion of the magnum opus. Here, the word "sublimation" was used to describe an exchange of "bodies" and "spirits" similar to laboratory phase transition between solids and gases. Valentine, in his "Le char triomphal de l'antimoine" (Triumphal Chariot of Antimony, published 1646) made a comparison to spagyrics in which a vegetable sublimation can be used to separate the spirits in wine and beer. Ripley used language more indicative of the mystical implications of sublimation, indicating that the process has a double aspect in the spiritualization of the body and the corporalizing of the spirit. He writes: <poem> And Sublimations we make for three causes, The first cause is to make the body spiritual. The second is that the spirit may be corporeal, And become fixed with it and consubstantial. The third cause is that from its filthy original. It may be cleansed, and its saltiness sulphurious May be diminished in it, which is infectious. </poem> The enthalpy of sublimation has commonly been predicted using the equipartition theorem. If the lattice energy is assumed to be approximately half the packing energy, then the following thermodynamic corrections can be applied to predict the enthalpy of sublimation. Assuming a 1 molar ideal gas gives a correction for the thermodynamic environment (pressure and volume) in which pV = RT, hence a correction of 1RT. Additional corrections for the vibrations, rotations and translation then need to be applied. From the equipartition theorem gaseous rotation and translation contribute 1.5RT each to the final state, therefore a +3RT correction. Crystalline vibrations and rotations contribute 3RT each to the initial state, hence −6RT. Summing the RT corrections; −6RT + 3RT + RT = −2RT. This leads to the following approximate sublimation enthalpy. A similar approximation can be found for the entropy term if rigid bodies are assumed. formula_1 Dye-sub printing is a digital printing technology using full color artwork that works with polyester and polymer-coated substrates. Also referred to as digital sublimation, the process is commonly used for decorating apparel, signs and banners, as well as novelty items such as cell phone covers, plaques, coffee mugs, and other items with sublimation-friendly surfaces. The process uses the science of sublimation, in which heat and pressure are applied to a solid, turning it into a gas through an endothermic reaction without passing through the liquid phase. In sublimation printing, unique sublimation dyes are transferred to sheets of “transfer” paper via liquid gel ink through a piezoelectric print head. The ink is deposited on these high-release inkjet papers, which are used for the next step of the sublimation printing process. After the digital design is printed onto sublimation transfer sheets, it is placed on a heat press along with the substrate to be sublimated. In order to transfer the image from the paper to the substrate, it requires a heat press process that is a combination of time, temperature and pressure. The heat press applies this special combination, which can change depending on the substrate, to “transfer” the sublimation dyes at the molecular level into the substrate. The most common dyes used for sublimation activate at 350 degrees Fahrenheit. However, a range of 380 to 420 degrees Fahrenheit is normally recommended for optimal color. The end result of the sublimation process is a nearly permanent, high resolution, full color print. Because the dyes are infused into the substrate at the molecular level, rather than applied at a topical level (such as with screen printing and direct to garment printing), the prints will not crack, fade or peel from the substrate under normal conditions.

Sublimation is the transition of a substance directly from the solid to the gas state, without passing through the liquid state. Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation is deposition or desublimation, in which a substance passes directly from a gas to a solid phase. Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition). While a transition from liquid to gas is described as evaporation if it occurs below the boiling point of the liquid, and as boiling if it occurs at the boiling point, there is no such distinction within the solid-to-gas transition, which is always described as sublimation.

en

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summarize: Sebastiano del Piombo was probably born in Venice, though there is no certainty as to his background. His birthdate is extrapolated from Vasari's statement that he was 62 at his death in 1547. That he was first known as a musician and singer may suggest an upper-middle-class background; the extent to which his playing on the lute and other instruments was professional is unclear. Like his contemporary Raphael, his career was marked by his ability to get on well with both other artists and patrons. He began to train as a painter at a relatively late age, probably 18 or 20, so around 1503–05, becoming a pupil of Giovanni Bellini and probably afterwards of Giorgione, both of whose influence is apparent in his works; Vasari's mention of their relationship is rather vague: ""si acconciò con Giorgione"". No signed or firmly documented works survive from his period painting in Venice, and many attributions are disputed. As with other artists, some of Sebastiano's works have long been confused with Giorgione's. Like Titian, he may have completed work left unfinished at Giorgione's death in 1510; Marcantonio Michiel says he finished "The Three Philosophers". The earliest significant work attributed to him is a portrait of a girl in Budapest, of about 1505. He is now usually assigned the unfinished and reworked "Judgement of Solomon" now at Kingston Lacy. This dramatic and imposing picture, "one of the masterpieces of Venetian narrative painting", was also long attributed to Giorgione; it may have been abandoned about 1508, though the estimated dates vary in the period 1505–1510. After extensive restoration in the 1980s, removing later overpainting, the painting is now left with traces of the three different compositions visible; still more can be seen with infra-red reflectography. Still over 2 × 3 metres, it seems originally to have been even larger, with some 40 cm lost along the left edge. There are two versions of the elaborate architectural background, which was a recurrent interest of Sebastiano's Venetian period. The last setting is in a basilica, which may reflect a "more learned" picture intended for a building holding courts of justice. The figure at the front of the executioner, left without clothes or the baby, is clearly drawn from classical sculpture. Four standing figures of saints in niches on the organ-shutters of San Bartolomeo, Venice, now in the Gallerie dell'Accademia in Venice, date from c. 1508–09, and are "very Giorgionesque", especially the pair on the insides. They were painted at the same time as Giorgione's frescos for the Fondaco dei Tedeschi (now lost) just by the church, which was the German's church in Venice, and at this time also held Albrecht Dürer's "Madonna of the Rose-Garlands" of 1506. The outside pair of shutters also show what Sebastiano had learnt from Bellini. Their technique has developed "from the earlier smooth surface to the application of paint in heavy brushstrokes", and the figure of Saint Sebastian shows awareness of classical sculpture. The main altarpiece for San Giovanni Crisostomo, Venice of 1510–11 shows the patron saint, Saint John Chrysostom reading aloud at a desk, a Mary Magdalene looking out at the viewer, and two other female and three male saints. The organ-shutters for the church were also painted. The style shows developments "towards a new fullness of form and breadth of movement" that may have been influenced by the Florentine painter Fra Bartolommeo, who was in Venice in 1508. Aspects of the composition were also innovative, and later copied by Venetian painters, including even Titian. In 1511 the Papal banker Agostino Chigi was the richest man in Rome, and a generous patron of the arts. Early in the year he was sent to Venice by Pope Julius II to buy Venetian support for the papacy in the War of the League of Cambrai. When he returned to Rome after a stay of some six months, he brought Sebastiano with him; Sebastiano was to remain based in Rome for the rest of his life. Sebastiano began by painting mythological subjects in lunettes in the "Sala di Galatea" in Chigi's Villa Farnesina, under a ceiling just done by Baldassarre Peruzzi. In these he already shows an adaption to Roman style, especially that of Michelangelo, whose Sistine Chapel ceiling had just been completed. Probably the next year, he added a large "Polyphemus". It is possible that Raphael's famous "Galatea" of 1514, which is in the next bay and now dominates the room, replaced a fresco by Sebastiano. A larger cycle on the lower walls was apparently intended, but abandoned, for reasons that are not clear. Sebastiano had also been producing easel paintings from soon after his arrival, showing the development of his new style. A "Death of Adonis" in the Uffizi dates to about 1512–13, and shows that he "had achieved a working dialectic of Roman and Venetian classical styles", in which he "enlarged the proportion of his figures into an almost bulking massiveness, ponderous and sensuously splendid: idealizations, but of sensuous existence". By about 1515, Sebastiano had befriended and allied himself with Michelangelo, who recruited him "as a kind of deputy for him in painting", he having returned to his backlog of promised projects in sculpture. Michelangelo's intention was for Sebastiano to "contest Raphael's first place" in painting in Rome, using at least in part ideas and designs supplied by Michelangelo, whose rivalry with Raphael had become intense. The intention may have been for a closer relationship than actually resulted, as in 1516 Michelangelo returned to Florence, only returning occasionally to Rome for several years after. The first result of this collaboration was one of Sebastiano's most important paintings, a "Pietà" in Viterbo. Here the composition is highly unusual for this common subject (which Michelangelo had famously sculpted in 1498–99), with Christ lying across the bottom of the picture space, at the feet of a Virgin looking up to Heaven, so that the two figures do not actually touch. Though no drawing survives, this was Michelangelo's conception, where "an idea of high tragic power is expressed with extreme simplicity in a structure of severe geometric rigour". The back of the panels have large sketches in charcoal that seem to be by both artists. In 1516 he painted a similar subject, the "Lamentation of Jesus" (now Hermitage Museum) using his own composition, and showing his awareness of Raphael's handling of groups of figures. These led a Florentine friend of Michelangelo, Pierfrancesco Borgherini, to commission Sebastiano to decorate a chapel in San Pietro in Montorio in Rome; he no doubt hoped to get significant input from Michelangelo. There is a Michelangelo drawing of 1516 for the "Flagellation of Jesus" in the British Museum, and other sketches; the final design survives only in a copy by Giulio Clovio after another Michelangelo drawing (Royal Collection). In the event there were a series of interruptions and Sebastiano did not complete the chapel until early 1524. The "Flagellation" is painted in oil on plaster. This was a method first practiced by Domenico Veneziano, and afterwards by other artists; but according to Vasari only Sebastiano succeeded in preventing the colours eventually blackening. The last major work of the period was the "Raising of Lazarus", now in the National Gallery, London, which was commissioned in 1516 by Cardinal Giulio de Medici, archbishop of Narbonne in southern France, and the future Pope Clement VII, in blatant competition, engineered by Michelangelo, with a painting of the same size by Raphael, the "Transfiguration". Both were supposed to hang in Narbonne Cathedral. Michelangelo supplied at least drawings for the figure of Lazarus and the two men supporting him (British Museum), but probably did not do any work on the painting itself, if only because he was only briefly in Rome during the time it was painted. When the two paintings were hung together in the Vatican, just after Raphael's death in 1520, both were praised, but the Raphael generally preferred, as has remained the case ever since. In the early 1520s Sebastiano completed the Borgherini Chapel with a "Transfiguration" in the semi-dome above his "Flagellation". The combination shows the influence of the "Apocalipsis Nova", a contemporary text that prophesied the coming of an "Angelic Pastor" who would bring a new age of peace. Michelangelo was among many reformist Catholics interested in the text. The "Flagellation" represents "the current, corrupted state of Christianity and the Transfiguration the glorious future to come". The death of Raphael in 1520, immediately before the exhibition of the two rival paintings intended for Narbonne, left Sebastiano clearly the leading painter operating in Rome. As his letters show, he immediately attempted to secure for himself the "Sala dei Pontefici", Raphael's next Vatican project, but was frustrated by Raphael's workshop, armed with the master's drawings, and his own inability to enlist Michelangelo's help, as the pope had told him to work exclusively on the long-promised Tomb of Pope Julius II. In the following years Sebastiano mostly avoided very large commissions for churches, and concentrated on portraits, where he had a considerable reputation, and religious easel paintings, such as his "Visitation" for France (1518–19, now Louvre), and his "Madonna of the Veil" (c. 1525), a very successful adaptation of Raphael's "Madonna di Loreto". To both of these types he brought his refined monumental classicism. His career in the decade was greatly impacted by outside events. In 1522 there was plague in Rome, and he may have left Rome for a long period; there is little evidence of his activity for over a year. In 1523 Giulio de Medici became Pope Clement VII, and thereafter Sebastiano seems to have been a part of Vatican court life. He painted a number of portraits of the pope, and other paintings for him. In 1527 he seems to have remained with the pope all through the horrors of the Sack of Rome and his nervous retreat to Orvieto, though he seems to have spent time in Venice in 1528 and perhaps 1529, his first known return there since 1511. This catastrophe brought to an end the High Renaissance epoch in Rome, scattering Raphael's workshop and the emerging Roman Mannerists, and largely destroying the confidence of patrons. In 1531 the death of the previous holder allowed Sebastiano to press Pope Clement for the lucrative office of the ""piombatore"", which he obtained after promising to pay a fixed sum of 300 scudi annually to the other main contender, Giovanni da Udine, who was also a painter, from Raphael's workshop. To hold the position he had to take vows as a friar, despite having a wife and two children. After this his paintings, which are more often signed than dated, carry signatures such as "F(rater) Sebastianus Ven(etus)". Sebastiano's artistic output reduced after taking the court role, though possibly not by as much as Vasari suggests. Large projects, even of a single painting, could take many years to complete, as with a "Pieta" for Spain. This was the last piece where Michelangelo helped him with a drawing. Vasari, probably much influenced by Michelangelo, places great emphasis on Sebastiano's turning away from art for a comfortable life as a well-paid courtier from this point, but may overstate the reality. His friendship with Michelangelo came to an end in 1534, after a disagreement over the latter's "Last Judgment" in the Sistine Chapel. Sebastiano encouraged the pope to insist that this picture should be executed in oil on plaster, the technique he had developed and used. The enormous wall was prepared with the smooth plaster needed for this, with Michelangelo apparently acquiescent. There may even have been the idea floated that Sebastiano might do the painting to Michelangelo's designs. Michelangelo may also have tried painting in oils on the smooth surface. It is clear that several months after the idea of using oils first appeared, Michelangelo finally and furiously rejected it, and insisted that the whole wall be re-plastered in the rough "arriccio" needed as a base for fresco. It was on this occasion that he famously said that oil painting was "an art for women and for leisurely and idle people like Fra Sebastiano". Two late projects for churches were never finished by Sebastiano. A large altarpiece of the "Birth of the Virgin", still in Santa Maria del Popolo, Rome, was begun in the late 1530s but had to be finished after his death by Francesco Salviati. Before his death in 1541, the executor of Agostino Chigi's estate commissioned a large "Visitation" as a memorial, in Santa Maria della Pace, Rome. It was still half-finished at Sebastiano's death in 1547, and was eventually removed in the 17th century. Fragments with some of the over life-size main figures are at Alnwick Castle, in a style of impressive simplicity, the end point of a "tendency to over-generalize appearances and pictorial structures so that they verged on an effect of geometrical abstraction" that had been increasing apparent in his work since his early years in Rome. Vasari records that he died after a short illness on 14 June 1547, at the age of 62. His will directed that he be buried very simply in Santa Maria del Popolo, with the savings from not having an elaborate burial given to the poor. After efforts by Daniele da Volterra his remains were moved in 1561 to the predecessor of the Rome Accademia di San Luca. Sebastiano was trained in the Venetian tradition of rich, subtly varying, colours in oil painting. In the "Raising of Lazarus" (1517–1519) he used a very wide range of pigments, often in complicated mixtures, and the painting can be seen as a display of Venetian skill for the Roman critics, attempting to achieve "the greatest and most subtly varied range of colours ever seen in a single painting". He became less interested in colour as his career progressed, and many later works are rather sombre, with touches of bright colour. His early works generally use the Venetian technique of freehand underdrawing on the surface to be painted, no doubt following a relatively approximate sketch, as was his technique for the Kingston Lacy "Judgement of Solomon". But after some years in Rome he began to use full-size cartoons for frescos, which were pricked along the lines and then soot "pounced" through, to give dotted lines on the surface for the artist to follow. This technique, normal in Florence and Rome, was used in the fresco "Transfiguration" of the Borgherini Chapel, for which some pricked sheets survive. However, this was his last work in fresco. From early on he was innovative and ready to experiment in compositional details as well as technique, with a special interest in painting in oils on new surfaces, whether plaster, stone, alabaster or slate. Though tending to be dark, several of his works with these unorthodox backings have survived well. Though he often covered the whole surface, leaving no indication of the support, some of his paintings on mineral sheets leave the background unpainted. This is the case with a small head of Clement VII in Naples, wearing the beard he always had as a penance after the Sack of Rome. He made excellent drawings, nearly all as compositional sketches. He continued to prefer to draw on light blue paper in black chalk with white highlights, a Venetian habit. Few if any early ones survive, and he may have changed his methods to use more precise sketches under the influence of Michelangelo and Raphael. Few survive for his portraits. A British Museum "curator's comment" on one of their late drawings notes: "As so often with Sebastiano's drawings, the first impression is one of unrhythmic dryness; but the suggestion of atmosphere, the sensitively drawn contemplative faces and the subtle use of reflected lights and tonal transitions leave no doubt that [this] is from his own hand. Sebastiano seems to have followed Michelangelo in painting with "no more than merely mechanical assistance" from a studio, and had no significant pupils formed in his style. Whether this was a cause or result of his avoidance of large compositions and his court office from the 1530s we cannot know. The main sources for his personality and habits are Vasari and surviving letters, mostly to and from Michelangelo. Vasari knew Sebastiano, but probably not very well; although he had been compiling material for some time, the first edition of his "Lives" did not appear until 1550, after Sebastiano's death, and it is not clear if he had specifically discussed the biography with Sebastiano. He knew Michelangelo rather better, and his description of Sebastiano is probably heavily influenced by the hostile attitude Michelangelo had towards Sebastiano after 1534. Vasari takes up much of his "Life" bemoaning Sebastiano's supposed indolence and neglect of his artistic talent for a comfortable and convivial life, at least after 1531. Vasari says that in later life he lived in a fine house near the Piazza del Popolo, keeping a very good table, and often entertaining regular friends as well as visitors. He says he was always cheerful and humorous, and very good company. He became red-faced and rather fat, as the bearded portrait in the "Lives" suggests. As described above, he had become close to Michelangelo by about 1515. Though they eventually fell out, few people were able to remain on good terms with Michelangelo for a period of nearly twenty years. In 1519 Michelangelo became godfather to Sebastiano's first son, Luciano, after which Sebastiano addressed his letters to "My dearest "compare"" ("godfather"). The relationship suffered a dip in 1520 when Sebastiano asked Michelangelo to write to Cardinal Bibbiena, a close friend of Pope Leo X, recommending Sebastiano for projects in the Vatican after Raphael's death. Michelangelo sent the letter a month or so later, which Sebastiano presented to the cardinal, without reading it. The letter was in very flippant terms, and Sebastianio complained that it became "practically the only topic of conversation at the Palace, and it makes everyone laugh". Nor did it work in getting Vatican commissions. In 1521 he acted as Michelangelo's agent in the installation of the "Risen Christ" or "Cristo della Minerva" in Rome, which was botched by the assistant Michelangelo had sent. From 1525 there is a draft for an emotional letter by Michelangelo passing on praise for Sebastiano by one "Captain Cuio", who he had dined with. In 1531 Sebastiano writes a despondent letter describing how "I still don't feel I am the same Bastiano that I was before the Sack; I still don't feel in my right mind." The relationship never recovered from the argument over the "Last Judgement" in 1534, described above.

Sebastiano del Piombo (; c. 1485 – 21 June 1547) was an Italian painter of the High Renaissance and early Mannerist periods famous as the only major artist of the period to combine the colouring of the Venetian school in which he was trained with the monumental forms of the Roman school. He belongs both to the painting school of his native city, Venice, where he made significant contributions before he left for Rome in 1511, and that of Rome, where he stayed for the rest of his life, and whose style he thoroughly adopted.

en

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summarize: Modern flambéing became popular in the 19th century. The English Christmas pudding was served flaming in Charles Dickens' 1843 novel, "A Christmas Carol": "the pudding... blazing in half of half-a-quarter of ignited brandy". The most common flambé dish appears to have been sweet omelette with rum or kirsch; for example, Alexis Soyer's 1846 cookbook, "The Gastronomic Regenerator", gives a recipe for "Omelette au Rhum": "...the moment of going to table pour three glasses of rum round and set it on fire". Ida Joscelyne's book, "The Marvellous Little Housekeepers" (1880), mentions both rum and kirsch; another recipe appears in A.G. Payne's English cookbook, "Choice Dishes at Small Cost", of 1882: "Make a sweet omelet, and heat a tablespoonful of kirsch, by holding a light under the spoon. As soon as the spirit catches fire pour it round the omelet, and serve flaming." Perhaps the most famous flambé dish, Crêpe Suzette, was supposedly invented in 1895 as an accident. Cognac, rum, or other flavorful liquors that are about 40% alcohol (80 USA proof) are considered ideal for flambé. Wines and beers have too little alcohol and will not flambé. High-alcohol liquors, such as Bacardi 151 or Everclear, are highly flammable and considered too dangerous by professional cooks. Cinnamon is sometimes added not only for flavor but for show, as the powder ignites when added. The alcoholic beverage must be heated before lighting it on fire. This is because at room temperature, the liquid is still below the flash point, and there are not enough alcoholic vapors to ignite. By heating it, the vapor pressure increases, releasing enough vapors to catch fire from the match. Flambéing reduces the alcohol content of the food modestly. In one experimental model, about 25% of the alcohol was boiled off. The effects of the flames are also modest: although the temperature within the flame may be quite high (over 500 °C), the temperature at the surface of the pan is lower than that required for a Maillard browning reaction or for caramelization. Whether or not there is a change in flavor as result of flambéing is unclear. Some claim that because the flame is above the food, and since hot gases rise, it cannot significantly affect the flavor. Indeed, experimental work shows that most people cannot tell the difference. That said, in an informal taste test conducted by the "Los Angeles Times" of two batches of caramelized apples (one flambéed and one simmered), one tester declared the "flambéed dish was for adults, the other for kids". Others, however, dispute this and quote celebrated French chefs who claim that flambéing is strictly a show-biz aspect of restaurant business that ruins food but is done to create an impressive visual presentation at a dramatic point in the preparation of a meal. For safety, it is recommended that alcohol not be added to a pan on a burner, and that the cook use a long fireplace match to ignite the pan. Examples of popular flambé dishes include:

Flambé (, ; also spelled flambe) is a cooking procedure in which alcohol is added to a hot pan to create a burst of flames. The word means "flamed" in French.

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summarize: While it is possible to safely preserve many kinds of foodstuffs, home canning can expose consumers to botulism and other kinds of food poisoning if done incorrectly. The most common source of food-borne botulism is home-canned foods prepared in an unsafe manner. Safety measures must be taken when performing home canning, since ingestion of toxin in food produced by "Clostridium botulinum" can cause death. Because of the high risk of illness or death associated with improper canning techniques, the United States Department of Agriculture (USDA) considers it critical that consumers who intend to can at home obtain proper and current information from a reliable source. At the basis of these recommendations is the balance between bringing the food to a high enough temperature for a long enough time that spoilage and disease-producing microorganisms are killed, while not heating the food so much that it loses nutritive value or palatability. In North America, home canning is usually done in Mason jars, which have thicker walls than single-use commercial glass jars. Unless the food being preserved has a high acid content (pH <4.6) or salt or sugar content resulting in water availability <0.85, such as pickles or jellies, the filled jars are also processed under pressure in a canner, a specialized type of pressure cooker. Ordinary pressure cookers are not recommended for canning as their smaller size and the reduced thickness of the cooker wall will not allow for the correct building up and reducing time of pressure, which is factored into the overall processing time and therefore will not destroy all the harmful microorganisms. The goal in using a pressure canner is to achieve a "botulinum cook" of 121 °C for 3 minutes, throughout the entire volume of canned product. Canners often incorporate racks to hold Mason jars, and pressure canners are capable of achieving the elevated temperatures needed to prevent spoilage. The most common configuration is a Mason jar with a flat lid and screw ring. The lid is generally made of plated or painted steel, with an elastomeric washer or gasket bonded to the underside of the rim. The lid also incorporates a slightly dimpled shape, which acts as an indicator of the vacuum (or lack thereof) inside a sealed jar. A newer reusable lid is now available that uses a flat plastic disk with a reusable rubber gasket. The ring threads onto the top of the jar over the lid to hold it in place while the jar cools after processing; the ring can be removed once a vacuum has been established in the jar. Jars are commonly in either pint or quart capacities, with two opening diameters, known as "standard" and "wide mouth". When a jar has cooled and is properly sealed, pressing the dimple on the lid will not make any sound. An improperly sealed jar will allow the dimple to move up and down, sometimes making a popping noise. Lack of this noise does not necessarily indicate that the food in the jar is properly preserved. Typically, during the cooling process, a properly sealed lid will pop once as the pressure inside the jar is reduced enough that atmospheric pressure pushes the lid inward. Older variations had a ceramic seal inside a one-piece zinc lid. Another method that is no longer recommended was the use of layer of hot paraffin wax poured directly over the top of the food (especially jams and jellies) to seal it from air, thus reducing growth of aerobic microorganisms like mold. In the United Kingdom home bottling is done with Kilner jars in a similar way to the Mason jars in the US, and although old-style Kilner jars have a glass lid without a "dimple" more recent varieties do. Most home bottling is done using the "open kettle method", with hot food ladled into hot jars and lids placed on jars, with no water bath sterilization processing of the product afterward. In Australia the most popular home canning system is Fowler's Vacola. This system uses glass jars, single use seals, metal lids, and a water bath canning sterilization process. During the canning process the lids are secured by metal tension clips which are removed once a vacuum seal has formed. Fowler's Vacola products are still produced and are available from some hardware stores. Used equipment is frequently sold on online auction sites and in opportunity shops. In Germany the most popular home canning system is Weck jar. This system uses glass jars (80ml-2.5l) and glass bottles (200ml-1l), reusable rubber seals, glass lids, and a water bath canning sterilization process. During the canning process the lids are secured by steel tension clips which can be removed once a vacuum seal has formed. During storage the vertical position of the rubber seal's external tongue indicates the status of the sealing. Weck products are still produced and are available from German hardware stores. Used equipment is frequently sold on online auction sites and in opportunity shops. They can be used for water bath canning and pressure canning. For water bath canning use two steel tension clips and for pressure canning use three steel tension clips. Remove them after vacuum has formed. United States: Metric:

Home canning or bottling, also known colloquially as putting up or processing, is the process of preserving foods, in particular, fruits, vegetables, and meats, by packing them into glass jars and then heating the jars to create a vacuum seal and kill the organisms that would create spoilage.

en

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summarize: The vacuum flask was designed and invented by Scottish scientist Sir James Dewar in 1892 as a result of his research in the field of cryogenics and is sometimes called a Dewar flask in his honour. While performing experiments in determining the specific heat of the element palladium, Dewar made a brass chamber that he enclosed in another chamber to keep the palladium at its desired temperature. He evacuated the air between the two chambers, creating a partial vacuum to keep the temperature of the contents stable. Through the need for this insulated container James Dewar created the vacuum flask, which became a significant tool for chemical experiments and also became a common household item. The flask was later developed using new materials such as glass and aluminum; however, Dewar refused to patent his invention. Dewar's design was quickly transformed into a commercial item in 1904 as two German glassblowers, Reinhold Burger and Albert Aschenbrenner, discovered that it could be used to keep cold drinks cold and warm drinks warm and invented a more robust flask design, which was suited for everyday use. The Dewar flask design had never been patented but the German men who discovered the commercial use for the product named it "Thermos", and subsequently claimed both the rights to the commercial product and the trademark to the name. In his subsequent attempt to claim the rights to the invention, Dewar instead lost a court case to the company. The manufacturing and performance of the Thermos bottle was significantly improved and refined by the Viennese inventor and merchant Gustav Robert Paalen, who designed various types for domestic use, which he also patented, and distributed widely, through the Thermos Bottle Companies in the United States, Canada and the UK, which bought licences for respective national markets. The American Thermos Bottle Company built up a mass production in Norwich, CT, which brought prices down and enabled the wide distribution of the product for at-home use. Over time, the company expanded the size, shapes and materials of these consumer products, primarily used for carrying coffee on the go and carrying liquids on camping trips to keep them either hot or cold. Eventually other manufacturers produced similar products for consumer use. The name later became a genericized trademark after the term "thermos" became the household name for such a vacuum-insulated container for liquids. The vacuum flask went on to be used for many different types of scientific experiments and the commercial "Thermos" was transformed into a common item. "Thermos" remains a registered trademark in some countries, but it was declared a genericized trademark by court action in the United States in 1963, since it had become colloquially synonymous with vacuum flasks in general. However, there are other vacuum flasks. The vacuum flask consists of two vessels, one placed within the other and joined at the neck. The gap between the two vessels is partially evacuated of air, creating a partial-vacuum which reduces heat conduction or convection. Heat transfer by thermal radiation may be minimized by silvering flask surfaces facing the gap but can become problematic if the flask's contents or surroundings are very hot; hence vacuum flasks usually hold contents below the boiling point of water. Most heat transfer occurs through the neck and opening of the flask, where there is no vacuum. Vacuum flasks are usually made of metal, borosilicate glass, foam or plastic and have their opening stoppered with cork or polyethylene plastic. Vacuum flasks are often used as insulated shipping containers. Extremely large or long vacuum flasks sometimes cannot fully support the inner flask from the neck alone, so additional support is provided by "spacers" between the interior and exterior shell. These spacers act as a thermal bridge and partially reduce the insulating properties of the flask around the area where the spacer contacts the interior surface. Several technological applications, such as NMR and MRI machines, rely on the use of double vacuum flasks. These flasks have two vacuum sections. The inner flask contains liquid helium and the outer flask contains liquid nitrogen, with one vacuum section in between. The loss of precious helium is limited in this way. Other improvements to the vacuum flask include the "vapour-cooled radiation shield" and the "vapour-cooled neck", both of which help to reduce evaporation from the flask. In laboratories and industry, vacuum flasks are often used to hold liquefied gases (often LN2) for flash freezing, sample preparation and other processes where maintaining an extreme low temperature is desired. Larger vacuum flasks store liquids that become gaseous at well below ambient temperature, such as oxygen and nitrogen; in this case the leakage of heat into the extremely cold interior of the bottle results in a slow boiling-off of the liquid so that a narrow unstoppered opening, or a stoppered opening protected by a pressure relief valve, is necessary to prevent pressure from building up and eventually shattering the flask. The insulation of the vacuum flask results in a very slow "boil" and thus the contents remain liquid for long periods without refrigeration equipment. Vacuum flasks have been used to house standard cells and ovenized Zener diodes, along with their printed circuit board, in precision voltage-regulating devices used as electrical standards. The flask helped with controlling the Zener temperature over a long time span and was used to reduce variations of the output voltage of the Zener standard owing to temperature fluctuation to within a few parts per million. One notable use was by Guildline Instruments, of Canada, in their Transvolt, model 9154B, saturated standard cell, which is an electrical voltage standard. Here a silvered vacuum flask was encased in foam insulation and, using a large glass vacuum plug, held the saturated cell. The output of the device was 1.018 volts and was held to within a few parts per million. The principle of the vacuum flask makes it ideal for storing certain types of rocket fuel, and NASA used it extensively in the propellant tanks of the Saturn launch vehicles in the 1960s and 1970s. The design and shape of the Dewar flask was used as a model for optical experiments based on the idea that the shape of the two compartments with the space in between is similar to the way the light hits the eye. The vacuum flask has also been part of experiments using it as the capacitor of different chemicals in order to keep them at a consistent temperature. The industrial Dewar flask is the base for a device used to passively insulate medical shipments. Most vaccines are sensitive to heat and require a cold chain system to keep them at stable, near freezing temperatures. The Arktek device uses eight one-litre ice blocks to hold vaccines at under 10 °C. Vacuum flasks are at risk of implosion hazard, and glass vessels under vacuum, in particular, may shatter unexpectedly. Chips, scratches or cracks can be a starting point for dangerous vessel failure, especially when the vessel temperature changes rapidly (when hot or cold liquid is added). Proper preparation of the Dewar vacuum flask by tempering prior to use is advised to maintain and optimize the functioning of the unit. Glass vacuum flasks are usually fitted into a metal base with the cylinder contained in or coated with mesh, aluminum or plastic to aid in handling, protect it from physical damage, and contain fragments should they break. In addition, cryogenic storage dewars are usually pressurized, and they may explode if pressure relief valves are not used. The rate of heat (energy) loss through a vacuum flask can be analyzed thermodynamically, starting from the second relation: Assuming constant pressure throughout the process, Rearranging the equation in terms of the temperature of the outside surface of the vacuum flask's inner wall, Where Now consider the general expression for heat loss due to radiation: In the case of the vacuum flask, Substituting our earlier expression for "T", Where Assuming that the outer surface of the inner wall and the inner surface of the outer wall of the vacuum flask are coated with polished silver to minimize heat loss due to radiation, we can say that the rate of heat absorption by the inner surface of the outer wall is equal to the absorptivity of polished silver times the heat radiated by the outer surface of the inner wall, In order for energy balance to be maintained, the heat lost through the outer surface of the outer wall must be equal to the heat absorbed by the inner surface of the outer wall, Since the absorptivity of polished silver is the same as its emissivity, we can write We must also consider the rate of heat loss through the lid of the vacuum flask (assuming it is made of polypropylene, a common plastic) where there is no vacuum inside the material. In this area, the three heat transfer modes of conduction, convection, and radiation are present. Therefore, the rate of heat loss through the lid is, Where Now we have an expression for the total rate of heat loss, which is the sum of the rate of heat loss through the walls of the vacuum flask and the rate of heat loss through the lid, where we substitute each of the expressions for each component into the equation. The rate of entropy generation of this process can also be calculated, starting from entropy balance: Written in rate form, Assuming a steady-state process, Since there is no heat added to the system,

A vacuum flask (also known as a Dewar flask, Dewar bottle or thermos) is an insulating storage vessel that greatly lengthens the time over which its contents remain hotter or cooler than the flask's surroundings. Invented by Sir James Dewar in 1892, the vacuum flask consists of two flasks, placed one within the other and joined at the neck. The gap between the two flasks is partially evacuated of air, creating a near-vacuum which significantly reduces heat transfer by conduction or convection.

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summarize: The term kinematic is the English version of A.M. Ampère's "cinématique", which he constructed from the Greek "kinema" ("movement, motion"), itself derived from "kinein" ("to move"). Kinematic and cinématique are related to the French word cinéma, but neither are directly derived from it. However, they do share a root word in common, as cinéma came from the shortened form of cinématographe, "motion picture projector and camera," once again from the Greek word for movement and from the Greek "grapho" ("to write"). Particle kinematics is the study of the trajectory of particles. The position of a particle is defined as the coordinate vector from the origin of a coordinate frame to the particle. For example, consider a tower 50 m south from your home, where the coordinate frame is centered at your home, such that east is in the direction of the x-axis and north is in the direction of the y-axis, then the coordinate vector to the base of the tower is r = (0, −50, 0). If the tower is 50 m high, and this height is measured along the z-axis, then the coordinate vector to the top of the tower is r = (0, −50, 50). In the most general case, a three-dimensional coordinate system is used to define the position of a particle. However, if the particle is constrained to move within a plane, a two-dimensional coordinate system is sufficient. All observations in physics are incomplete without being described with respect to a reference frame. The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin. In three dimensions, the position of point "P" can be expressed as where formula_2, formula_3, and formula_4 are the Cartesian coordinates and formula_5, formula_6 and formula_7 are the unit vectors along the formula_8, formula_9, and formula_10 coordinate axes, respectively. The magnitude of the position vector formula_11 gives the distance between the point formula_12 and the origin. The direction cosines of the position vector provide a quantitative measure of direction. It is important to note that the position vector of a particle isn't unique. The position vector of a given particle is different relative to different frames of reference. The "trajectory" of a particle is a vector function of time, formula_14, which defines the curve traced by the moving particle, given by where the coordinates "x", "y", and "z" are each functions of time. The velocity of a particle is a vector quantity that describes the magnitude as well as direction of motion of the particle. More mathematically, the rate of change of the position vector of a point, with respect to time is the velocity of the point. Consider the ratio formed by dividing the difference of two positions of a particle by the time interval. This ratio is called the average velocity over that time interval and is defined as Velocity=displacement/time taken where ΔP is the change in the position vector over the time interval Δ"t". In the limit as the time interval Δ"t" becomes smaller and smaller, the average velocity becomes the time derivative of the position vector, Thus, velocity is the time rate of change of position of a point, and the dot denotes the derivative of those functions x, y, and z with respect to time. Furthermore, the velocity is tangent to the trajectory of the particle at every position the particle occupies along its path. Note that in a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The speed of an object is the magnitude |V| of its velocity. It is a scalar quantity: where "s" is the arc-length measured along the trajectory of the particle. This arc-length traveled by a particle over time is a non-decreasing quantity. Hence, "ds"/"dt" is non-negative, which implies that speed is also non-negative. The velocity vector can change in magnitude and in direction or both at once. Hence, the acceleration accounts for both the rate of change of the magnitude of the velocity vector and the rate of change of direction of that vector. The same reasoning used with respect to the position of a particle to define velocity, can be applied to the velocity to define acceleration. The acceleration of a particle is the vector defined by the rate of change of the velocity vector. The average acceleration of a particle over a time interval is defined as the ratio. where ΔV is the difference in the velocity vector and Δ"t" is the time interval. The acceleration of the particle is the limit of the average acceleration as the time interval approaches zero, which is the time derivative, or Thus, acceleration is the first derivative of the velocity vector and the second derivative of the position vector of that particle. Note that in a non-rotating frame of reference, the derivatives of the coordinate directions are not considered as their directions and magnitudes are constants. The magnitude of the acceleration of an object is the magnitude |A| of its acceleration vector. It is a scalar quantity: A relative position vector is a vector that defines the position of one point relative to another. It is the difference in position of the two points. The position of one point "A" relative to another point "B" is simply the difference between their positions formula_23 which is the difference between the components of their position vectors. If point "A" has position components formula_24 If point "B" has position components formula_25 then the position of point "A" relative to point "B" is the difference between their components: formula_26 The velocity of one point relative to another is simply the difference between their velocities formula_27 which is the difference between the components of their velocities. If point "A" has velocity components formula_28 and point "B" has velocity components formula_29 then the velocity of point "A" relative to point "B" is the difference between their components: formula_30 Alternatively, this same result could be obtained by computing the time derivative of the relative position vector R. In the case where the velocity is close to the speed of light "c" (generally within 95%), another scheme of relative velocity called rapidity, that depends on the ratio of V to c, is used in special relativity. The acceleration of one point "C" relative to another point "B" is simply the difference between their accelerations. formula_31 which is the difference between the components of their accelerations. If point "C" has acceleration components formula_32 and point "B" has acceleration components formula_33 then the acceleration of point "C" relative to point "B" is the difference between their components: formula_34 Alternatively, this same result could be obtained by computing the second time derivative of the relative position vector P. Assuming that the initial conditions of the position, formula_35, and velocity formula_36 at time formula_37 are known, the first integration yields the velocity of the particle as a function of time. A second integration yields its path (trajectory), Additional relations between displacement, velocity, acceleration, and time can be derived. Since the acceleration is constant, A relationship between velocity, position and acceleration without explicit time dependence can be had by solving the average acceleration for time and substituting and simplifying where ∘ denotes the dot product, which is appropriate as the products are scalars rather than vectors. The dot can be replaced by the cosine of the angle formula_45 between the vectors and the vectors by their magnitudes, in which case: In the case of acceleration always in the direction of the motion and the direction of motion should be in positive or nagetive, the angle between the vectors (formula_45) is 0, so formula_48, and This can be simplified using the notation for the magnitudes of the vectors formula_50 where formula_51 can be any curvaceous path taken as the constant tangential acceleration is applied along that path, so This reduces the parametric equations of motion of the particle to a cartesian relationship of speed versus position. This relation is useful when time is unknown. We also know that formula_53 or formula_51 is the area under a v, t graph. We can take formula_51 by adding the top area and the bottom area. The bottom area is a rectangle, and the area of a rectangle is the formula_56 where formula_57 is the width and formula_58 is the height. In this case formula_59 and formula_60 (note that the formula_57 here is different from the acceleration formula_62). This means that the bottom area is formula_63. Now let's find the top area (a triangle). The area of a trangle is formula_64 where formula_58 is the base and formula_66 is the height. In this case, formula_67 & formula_68 or formula_69. Adding formula_63 and formula_71 results in the equation formula_72 results in the equation formula_73. This equation is very useful when the final velocity formula_74 is unknown. It is often convenient to formulate the trajectory of a particle P(t) = (X(t), Y(t) and Z(t)) using polar coordinates in the "X"–"Y" plane. In this case, its velocity and acceleration take a convenient form. Recall that the trajectory of a particle "P" is defined by its coordinate vector P measured in a fixed reference frame "F". As the particle moves, its coordinate vector P(t) traces its trajectory, which is a curve in space, given by: where "i", "j", and "k" are the unit vectors along the "X", "Y" and "Z" axes of the reference frame "F", respectively. Consider a particle "P" that moves only on the surface of a circular cylinder R(t)=constant, it is possible to align the "Z" axis of the fixed frame "F" with the axis of the cylinder. Then, the angle θ around this axis in the "X"–"Y" plane can be used to define the trajectory as, The cylindrical coordinates for P(t) can be simplified by introducing the radial and tangential unit vectors, and their time derivatives from elementary calculus: Using this notation, P(t) takes the form, where "R" is constant in the case of the particle moving only on the surface of a cylinder of radius "R". In general, the trajectory P(t) is not constrained to lie on a circular cylinder, so the radius "R" varies with time and the trajectory of the particle in cylindrical-polar coordinates becomes: Where R, theta, and Z might be continuously differentiable functions of time and the function notation is dropped for simplicity. The velocity vector V is the time derivative of the trajectory P(t), which yields: Similarly, the acceleration A, which is the time derivative of the velocity V, is given by: The term formula_86 acts toward the center of curvature of the path at that point on the path, is commonly called the centripetal acceleration. The term formula_87 is called the Coriolis acceleration. If the trajectory of the particle is constrained to lie on a cylinder, then the radius "R" is constant and the velocity and acceleration vectors simplify. The velocity of V is the time derivative of the trajectory P(t), The acceleration vector becomes: A special case of a particle trajectory on a circular cylinder occurs when there is no movement along the "Z" axis: where "R" and "Z" are constants. In this case, the velocity V is given by: where is the angular velocity of the unit vector around the "z" axis of the cylinder. The acceleration A of the particle "P" is now given by: The components are called, respectively, the "radial" and "tangential components" of acceleration. The notation for angular velocity and angular acceleration is often defined as so the radial and tangential acceleration components for circular trajectories are also written as The movement of components of a mechanical system are analyzed by attaching a reference frame to each part and determining how the various reference frames move relative to each other. If the structural stiffness of the parts are sufficient, then their deformation can be neglected and rigid transformations can be used to define this relative movement. This reduces the description of the motion of the various parts of a complicated mechanical system to a problem of describing the geometry of each part and geometric association of each part relative to other parts. Geometry is the study of the properties of figures that remain the same while the space is transformed in various ways—more technically, it is the study of invariants under a set of transformations. These transformations can cause the displacement of the triangle in the plane, while leaving the vertex angle and the distances between vertices unchanged. Kinematics is often described as applied geometry, where the movement of a mechanical system is described using the rigid transformations of Euclidean geometry. The coordinates of points in a plane are two-dimensional vectors in R (two dimensional space). Rigid transformations are those that preserve the distance between any two points. The set of rigid transformations in an "n"-dimensional space is called the special Euclidean group on R, and denoted "SE(n)." The position of one component of a mechanical system relative to another is defined by introducing a reference frame, say "M", on one that moves relative to a fixed frame, "F," on the other. The rigid transformation, or displacement, of "M" relative to "F" defines the relative position of the two components. A displacement consists of the combination of a rotation and a translation. The set of all displacements of "M" relative to "F" is called the configuration space of "M." A smooth curve from one position to another in this configuration space is a continuous set of displacements, called the motion of "M" relative to "F." The motion of a body consists of a continuous set of rotations and translations. The combination of a rotation and translation in the plane R can be represented by a certain type of 3x3 matrix known as a homogeneous transform. The 3x3 homogeneous transform is constructed from a 2x2 rotation matrix A(φ) and the 2x1 translation vector d=(d, d), as: These homogeneous transforms perform rigid transformations on the points in the plane z=1, that is on points with coordinates p=(x, y, 1). In particular, let p define the coordinates of points in a reference frame "M" coincident with a fixed frame "F." Then, when the origin of "M" is displaced by the translation vector d relative to the origin of "F" and rotated by the angle φ relative to the x-axis of "F", the new coordinates in "F" of points in "M" are given by: Homogeneous transforms represent affine transformations. This formulation is necessary because a translation is not a linear transformation of R. However, using projective geometry, so that R is considered a subset of R, translations become affine linear transformations. If a rigid body moves so that its reference frame "M" does not rotate (∅=0) relative to the fixed frame "F", the motion is called pure translation. In this case, the trajectory of every point in the body is an offset of the trajectory d(t) of the origin of "M," that is: Thus, for bodies in pure translation, the velocity and acceleration of every point "P" in the body are given by: where the dot denotes the derivative with respect to time and V and A are the velocity and acceleration, respectively, of the origin of the moving frame "M". Recall the coordinate vector p in "M" is constant, so its derivative is zero. Rotational or angular kinematics is the description of the rotation of an object. The description of rotation requires some method for describing orientation. Common descriptions include Euler angles and the kinematics of turns induced by algebraic products. In what follows, attention is restricted to simple rotation about an axis of fixed orientation. The "z"-axis has been chosen for convenience. The description of rotation then involves these three quantities: The equations of translational kinematics can easily be extended to planar rotational kinematics for constant angular acceleration with simple variable exchanges: Here "θ" and "θ" are, respectively, the initial and final angular positions, "ω" and "ω" are, respectively, the initial and final angular velocities, and "α" is the constant angular acceleration. Although position in space and velocity in space are both true vectors (in terms of their properties under rotation), as is angular velocity, angle itself is not a true vector. Important formulas in kinematics define the velocity and acceleration of points in a moving body as they trace trajectories in three-dimensional space. This is particularly important for the center of mass of a body, which is used to derive equations of motion using either Newton's second law or Lagrange's equations. In order to define these formulas, the movement of a component "B" of a mechanical system is defined by the set of rotations [A(t)] and translations d(t) assembled into the homogeneous transformation [T(t)]=[A(t), d(t)]. If p is the coordinates of a point "P" in "B" measured in the moving reference frame "M", then the trajectory of this point traced in "F" is given by: This notation does not distinguish between P = (X, Y, Z, 1), and P = (X, Y, Z), which is hopefully clear in context. This equation for the trajectory of "P" can be inverted to compute the coordinate vector p in "M" as: This expression uses the fact that the transpose of a rotation matrix is also its inverse, that is: The velocity of the point "P" along its trajectory P(t) is obtained as the time derivative of this position vector, The dot denotes the derivative with respect to time; because p is constant, its derivative is zero. This formula can be modified to obtain the velocity of "P" by operating on its trajectory P(t) measured in the fixed frame "F". Substituting the inverse transform for p into the velocity equation yields: The matrix [S] is given by: where is the angular velocity matrix. Multiplying by the operator [S], the formula for the velocity V takes the form: where the vector ω is the angular velocity vector obtained from the components of the matrix [Ω]; the vector is the position of "P" relative to the origin "O" of the moving frame "M"; and is the velocity of the origin "O". The acceleration of a point "P" in a moving body "B" is obtained as the time derivative of its velocity vector: This equation can be expanded firstly by computing and The formula for the acceleration A can now be obtained as: or where α is the angular acceleration vector obtained from the derivative of the angular velocity matrix; is the relative position vector (the position of "P" relative to the origin "O" of the moving frame "M"); and is the acceleration of the origin of the moving frame "M". Kinematic constraints are constraints on the movement of components of a mechanical system. Kinematic constraints can be considered to have two basic forms, (i) constraints that arise from hinges, sliders and cam joints that define the construction of the system, called holonomic constraints, and (ii) constraints imposed on the velocity of the system such as the knife-edge constraint of ice-skates on a flat plane, or rolling without slipping of a disc or sphere in contact with a plane, which are called non-holonomic constraints. The following are some common examples. A kinematic coupling exactly constrains all 6 degrees of freedom. An object that rolls against a surface without slipping obeys the condition that the velocity of its center of mass is equal to the cross product of its angular velocity with a vector from the point of contact to the center of mass: For the case of an object that does not tip or turn, this reduces to formula_135. This is the case where bodies are connected by an idealized cord that remains in tension and cannot change length. The constraint is that the sum of lengths of all segments of the cord is the total length, and accordingly the time derivative of this sum is zero. A dynamic problem of this type is the pendulum. Another example is a drum turned by the pull of gravity upon a falling weight attached to the rim by the inextensible cord. An "equilibrium" problem (i.e. not kinematic) of this type is the catenary. Reuleaux called the ideal connections between components that form a machine kinematic pairs. He distinguished between higher pairs which were said to have line contact between the two links and lower pairs that have area contact between the links. J. Phillips shows that there are many ways to construct pairs that do not fit this simple classification. A lower pair is an ideal joint, or holonomic constraint, that maintains contact between a point, line or plane in a moving solid (three-dimensional) body to a corresponding point line or plane in the fixed solid body. There are the following cases: Generally speaking, a higher pair is a constraint that requires a curve or surface in the moving body to maintain contact with a curve or surface in the fixed body. For example, the contact between a cam and its follower is a higher pair called a "cam joint". Similarly, the contact between the involute curves that form the meshing teeth of two gears are cam joints. Rigid bodies ("links") connected by kinematic pairs ("joints") are known as "kinematic chains." Mechanisms and robots are examples of kinematic chains. The degree of freedom of a kinematic chain is computed from the number of links and the number and type of joints using the mobility formula. This formula can also be used to enumerate the topologies of kinematic chains that have a given degree of freedom, which is known as "type synthesis" in machine design. The planar one degree-of-freedom linkages assembled from "N" links and "j" hinged or sliding joints are: For larger chains and their linkage topologies, see R. P. Sunkari and L. C. Schmidt, "Structural synthesis of planar kinematic chains by adapting a Mckay-type algorithm", "Mechanism and Machine Theory" #41, pp. 1021–1030 (2006).

Kinematics is a subfield of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a field of study, is often referred to as the "geometry of motion" and is occasionally seen as a branch of mathematics. A kinematics problem begins by describing the geometry of the system and declaring the initial conditions of any known values of position, velocity and/or acceleration of points within the system. Then, using arguments from geometry, the position, velocity and acceleration of any unknown parts of the system can be determined. The study of how forces act on bodies falls within kinetics, not kinematics. For further details, see analytical dynamics.

en

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summarize: The English expression "deep-fried" is attested from the early 20th century. Frying food in olive oil is attested in Classical Greece from about the 5th century BCE. The late Roman cookbook of "Apicius" (c. 400), appears to list the ancient Romans' first use of deep frying to prepare Pullum Frontonianum, a chicken dish. The practice of deep frying spread to other parts of Europe and Arabia in the following centuries. Deep-fried foods such as funnel cakes arrived in northern Europe by the 13th century, and deep-fried fish recipes have been found in cookbooks in Spain and Portugal at around the same time. Falafel arrived in the Middle East from population migrations from Egypt as soon as the 14th century. Evidence of potato frying can be found as early as the late 17th century in Europe. French fries, invented in the late 18th century, became popular in the early 19th century western Europe. In 1860 Joseph Malin combined deep fried fish with chips (french fries) to open the first fish and chip shop in London. Modern deep frying in the United States began in the 19th century with the growing popularity of cast iron, particularly around the American South which led to the development of many modern deep-fried dishes. Doughnuts were invented in the mid-19th century, with foods such as onion rings, deep-fried turkey, and corn dogs all being invented in the early 20th century. In recent years, the growth of fast food has expanded the reach of deep-fried foods, especially French fries. Deep frying food is defined as a process where food is completely submerged in hot oil at temperatures typically between and. One common method for preparing food for deep frying involves adding multiple layers of batter around the food, such as cornmeal, flour, or tempura; breadcrumbs may also be used. After the food is submerged in oil, the surface of it begins to dehydrate and it undergoes Maillard reactions which break down sugars and proteins, creating the golden brown exterior of the food. Once the surface is dehydrated, it forms a crust which prevents further oil absorption. The heat conducts throughout the food causing proteins to denature, starches to undergo starch gelatinization, and dietary fiber to soften. While most foods need batter coatings for protection, it is not as necessary for cooked noodles and potatoes because their high starch content enables them to hold more moisture and resist shrinking. Meats may be cooked before deep frying to ensure that they are done inside while keeping juiciness. When performed properly, deep frying does not make food excessively greasy, because the moisture in the food repels the oil. The hot oil heats the water within the food, steaming it; oil cannot go against the direction of this powerful flow because (due to its high temperature) the water vapor pushes the bubbles toward the surface. As long as the oil is hot enough and the food is not immersed in the oil for too long, oil penetration will be confined to the outer surface. Foods deep-fried at proper temperatures typically absorb "no more than a couple of tablespoons per cups of oil" used. This oil absorption rate is around the same as occurs with shallow frying, such as in a pan. However, if the food is cooked in the oil for too long, much of the water will be lost and the oil will begin to penetrate the food. The correct frying temperature depends on the thickness and type of food, but in most cases it lies between. An informal test for a temperature close to this range involves adding a tiny amount of flour into the oil and watching to see if it sizzles without immediately burning. A second test involves adding one piece of food to deep fry and watching it sink somewhat and rise back up. Sinking without resurfacing indicates that the oil is too cold; not sinking at all indicates that the oil is too hot. It is recommended that deep fryers be cleaned often to prevent contamination. The process of cooking with oil can also contaminate nearby surfaces as oil may splatter on adjacent areas. Oil vapors can also condense on more distant surfaces such as walls and ceilings. Supplies such as dish detergent and baking soda can effectively clean affected surfaces. Deep frying is done with a deep fryer, a pan such as a wok or chip pan, a Dutch oven, or a cast-iron pot. Additional tools include fry baskets, which are used to contain foods in a deep fryer and to strain foods when removed from the oil, and cooking thermometers, used to gauge oil temperature. Tongs, slotted spoons, wooden spoons, and sieves may be used to remove or separate foods from the hot oil. Japanese deep frying tools include long metal chopsticks; the "agemono-nabe" deep frying pot, which is heavy for retaining heat and deep for holding oil; the "ami-shakushi" net ladle used for scooping out batter debris; and the "abura-kiri" oil drying rack pan. Deep-fried foods are common in many countries, and have also been described as "a staple of almost all street cuisines on all continents". There are hundreds of dishes that are associated with deep frying as most foods can be deep-fried. Examples of food that can be deep-fried include meat, poultry, fish and vegetables. Fish and chips, for instance, combines deep-fried fish and deep-fried potatoes. French fries, doughnuts, onion rings, and hushpuppies are common deep-fried foods. Other common deep-fried foods include Chinese "You Bing" deep-fried pancakes, Southeast Asian Jin deui, and Japanese tempura. Less common deep-fried foods include maple leaves, peanut butter and jelly sandwiches, pizza, and Snickers bars. In the United States, the "Chicago Tribune" notes that "you can deep fry almost anything". The American South has been noted as a modern center of innovation in the area of deep-fried food. According to the owner of a deep frying restaurant in the South, "If something is edible, you can bet that someone south of the Mason-Dixon line has tried to cook it in oil". In Northern Africa, deep-fried dishes are a part of the cuisine. A common food in this region is the deep-fried fritter, also referred to as "sponges". In East Africa deep fried food is common, cooked in cast iron or earthenware pots. Frying in batter is common. A Ugandan speciality is a kind of doughnut called Mandazi. In areas of Southern Africa, street foods include deep-fried potato and cassava chips. Deep-fried foods in the country of South Africa include fish and chips, "vetkoek" and "koeksisters", among others. Japanese tempura is a popular deep-fried food that generally consists of battered and fried seafood and vegetables. Japanese deep-fried dishes, or Agemono, include other styles besides tempura, such as Karaage, Korokke, Kushikatsu, and Tonkatsu. In areas of Southeast Asia such as Thailand, insects are commonly deep-fried for human consumption. Western-style fast food items such as donuts, deep-fried chicken, and deep-fried potatoes are also becoming popular in Asia. Deep-fried fish, tofu, and'are commonly eaten in Vietnamese cuisine. Deep frying is also used to make several kinds of ', including'(fried rice ball),'(sesame ball),'(hollow doughnut),'(sweet potato pancake),'(banana fritter), Hồ Tây–style'(shrimp fritter), and "" (pillow cake). Deep-fried sticks of dough, known as youtiao in Chinese, are eaten in many East and Southeast Asian cuisines. In Hong Kong, is a popular food. In South Asia, popular deep fried snacks are samosa, jalebi, and pakora. Many countries in Europe use pure or hydrogenated rapeseed oil for deep-frying. The deep-fried Mars bar originated in Scotland, with The Carron Fish Bar in Stonehaven claiming to have invented it in the early 1990s. Fish and chips is a very popular deep-fried dish in England since it originated in London in the 19th century and became popular among the working class. Its popularity continues with 229 million portions of fish and chips being sold annually in England. There is an annual trade fair devoted to deep-fried foods called the International Symposium on Deep-Fat Frying which features discussions on deep fat frying as well as exhibitions by companies involved with the process. Belgian tradition requires French fries to be deep-fried in filtered fat of cattle, locally called "blanc de boeuf" or "ossewit". In the United States, soybean oil is often used for deep-frying. Beignets, originally a French dish, are a popular deep-fried pastry in the U.S. city of New Orleans. Deep-fried food has been a core part of the culture of the American South with many restaurants solely serving deep-fried foods. The owner of one such restaurant has said that the deep-fried food, "in the South it's a way of life". Fast food is one of the most common ways to consume deep-fried food in North America. Novelty deep-fried foods are popular today in American fairs, especially those in the American South. Hundreds of items are served at these fairs. Some of them include deep-fried beer, butter, and bubblegum. Additionally, deep frying can be used as a form of artwork by frying non-edible objects, such as electronics. Artists such as Henry Hargreaves have deep-fried replicas of electronic items such as iPads, Game Boys, and laptops. Deep-fried food contests are frequently held at fairs such as the Texas State Fair, where they hold an annual contest for the most creative deep-fried food. Notable past winners have included fried Coke and deep-fried butter, both invented by Abel Gonzales. Since 2013, an American reality competition show called "deep-fried Masters", produced by Discovery Networks, holds deep frying competitions at several state fairs across the country. Milk bars in Australia may purvey several types of deep-fried foods, along with other food types. The buñuelo, a fried dough ball popular in Central America and Greece, is a popular deep-fried snack and street food in South America. Picarone, a Peruvian dessert originated in the colonial period, are deep-fried cakes made with pumpkin and sweet potatoes, popular in Peru and Chile, especially during harvest festivals. Deep fat frying involves heating oil to temperatures in excess of 180 °C in the presence of moisture and air. These conditions can induce a series of complex chemical reactions which may impact the quality of both the food and the oil it is cooked in. Examples of different chemical reactions include the production of free radicals, oxidation, hydrolysis, isomerization and polymerization. The exact reactions are dependent upon factors such as the oil type, frying conditions, and food being cooked. When frying, water can attack the ester linkage of triacylglycerols, resulting in di- and monoglycerols, glycerol, and free fatty acids (a type of hydrolysis reaction). The aforementioned hydrolysis reaction is enhanced by the produced fatty acids and other low molecular weight acid compounds. Overheating or over-using the frying oil leads to formation of rancid-tasting products of oxidation, polymerization, and other deleterious, unintended or even toxic compounds such as acrylamide (from starchy foods). Recent research suggests fat deterioration may be worse when fat or oil is fried with food than when fat or oil is tested on its own in a laboratory. Deep-frying under vacuum helps to significantly reduce acrylamide formation, but this process is not widely used in the food industry due to the high investment cost involved. Some useful tests and indicators of excessive oil deterioration are the following: Instruments that indicate total polar compounds, currently the best single gauge of how deep-fried an object is, are available with sufficient accuracy for restaurant and industry use. Cooking oil is flammable, and fires may be caused by it igniting at too high a temperature. Further, attempts to extinguish an oil fire with water cause an extremely dangerous condition, a boilover, as they cause the water to flash into steam due to the high heat of the oil, in turn sending the burning oil in all directions and thus aggravating the fire. This is the leading cause of house fires in the United Kingdom. Instead, oil fires must be extinguished with a non-water fire extinguisher or by smothering. Other means of extinguishing an oil fire include application of dry powder (e.g., baking soda, salt) or fire fighting foam. Most commercial deep fryers are equipped with automatic fire suppression systems using foam. Spilled hot cooking oil can also cause severe third degree burns, In the worst-case scenario, severe burns can be fatal. The higher temperatures and tendency of oil to stick to the skin make spilled hot cooking oil far more dangerous than spilled hot water. Children can accidentally place their hands on top of the stove, playing with the materials while being cooked, or accidentally pull the pot down, which can cause significant injury. The utmost care should be used when deep frying when children are present, to protect their safety at all times. Deep frying produces large amounts of waste oil, which must be disposed of properly. Waste oil can contribute to the creation of fatbergs, overflow sewage systems, bind to the walls of sewage pipes, and interfere with sewage treatment. Waste oil from deep frying is increasingly being recycled and refined into biodiesel. Potatoes that are stored in artificially humidified warehouses contain more water, which makes the time required to deep fry them into chips longer. This increases the carbon dioxide footprint of commercially producing chips because more energy is required for frying over a longer time. According to one source, an average home appliance deep fryer draws 2,000 watts. The process of deep frying food is generally detrimental to its nutritional value. The oils that foods absorb in their batter typically contain large amounts of fats, especially saturated fats and trans fats. Consumption of large amounts of saturated and trans fats has been linked to a higher risk for some cancers including prostate cancer. Eating deep-fried foods has also been linked to higher cholesterol levels, obesity, heart attacks, and diabetes. Deep-fried foods cooked at certain temperatures can also contain acrylamide, a possible carcinogen. Additionally, fat degradation processes (lipid peroxidation) during deep frying results in the loss of nutritional value in deep-fried foods. Cooking oil that has been used for too long may in addition cause blood pressure elevation and vascular hypertrophy. Trans fats are used in shortenings for deep-frying in restaurants, as they can be used for longer than most conventional oils before becoming rancid. In the early 21st century, non-hydrogenated vegetable oils that have lifespans exceeding that of the frying shortenings became available. As fast-food chains routinely use different fats in different locations, trans fat levels in fast food can have large variations. Some studies have found that deep frying in olive and sunflower oils has been found to be less of a detriment to health and in some cases have positive effects on insulin levels. Oil can be reused a few times after original use after straining out solids. However, excessive use of the same oil can cause it to break down and release compounds into the food that may be carcinogenic, affect liver health, or influence the body's ability to absorb vitamins. Some European countries have set public health standards for the safety of frying oil.

Deep frying (also referred to as deep fat frying) is a cooking method in which food is submerged in hot fat, most commonly oil, as opposed to the shallow oil used in conventional frying done in a frying pan. Normally, a deep fryer or chip pan is used for this; industrially, a pressure fryer or vacuum fryer may be used. Deep frying may also be performed using oil that is heated in a pot. Deep frying is classified as hot-fat cooking method. Typically, deep frying foods cook quickly: all sides of a food are cooked simultaneously as oil has a high rate of heat conduction.

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summarize: In 1679, French physicist Denis Papin, better known for his studies on steam, invented the "steam digester" in an attempt to reduce the cooking time of food. His airtight cooker used steam pressure to raise the water's boiling point, thus cooking food more quickly. In 1681 Papin presented his invention to the Royal Society of London as a scientific study; he was later elected as a member. In 1864, Georg Gutbrod of Stuttgart began manufacturing pressure cookers made of tinned cast iron. In 1918, Spain granted a patent for the pressure cooker to José Alix Martínez from Zaragoza. Martínez named it the "olla exprés", literally "express cooking pot", under patent number 71143 in the "Boletín Oficial de la Propiedad Industrial". In 1924, the first pressure cooking pot recipe book was published, written by José Alix and titled "360 fórmulas de cocina Para guisar con la 'olla expres'", or "360 recipes for cooking with a pressure cooker". In 1938, Alfred Vischer presented his invention, the "Flex-Seal Speed Cooker", in New York City. Vischer's pressure cooker was the first designed for home use, and its success led to competition among American and European manufacturers. At the 1939 New York World's Fair, the National Pressure Cooker Company, later renamed National Presto Industries, introduced its own pressure cooker. Also known as "old type" pressure cookers, these operate with a weight-modified or "jiggler" valve, which releases pressure during operation. Some people consider them loud because the valve rattles as excess steam is released. Older pressure cookers typically offered only one pressure level, but from the 1960s onwards some allow the operator to change the weight of the valve, thus changing the pressure. Today, most pressure cookers are variations on the first-generation cookers, with the addition of new safety features such as a mechanism that prevents the cooker from being opened until it is entirely depressurized. These operate with a spring-loaded valve that is often hidden from view in a proprietary mechanism. This generation is characterized by two or more pressure settings. Some of these pressure cookers do not release any steam during operation (non-venting) and instead use a rising indicator with markings to show the pressure level. These only release steam when the pan is opened, or as a safety precaution if the heat source is not reduced enough when the pan reaches the required cooking pressure. Others use a dial that the operator can advance by a few clicks (which alters the spring tension) to change the pressure setting or release pressure; these release steam during operation (venting). After the stove-top pressure cookers, in 1991 came the electric pressure cookers, called the "third generation" pressure cookers. These include an electric heat source that is automatically regulated to maintain the operating pressure. They also include a spring-loaded valve (as described above). This type of pressure cooker cannot be opened with a cold water quick-release method and should be operated with caution when releasing vapour through the valve, especially while cooking foamy foods and liquids (lentils, beans, grains, milk, gravy, etc.) An electric pressure cooker integrates a timer. Depending on cooking control capability, there are three generations of electric pressure cookers: Some cookers are multifunctional (multicookers): pressure cooker, saute/browning, slow cooker, rice cooker, yogurt maker, steamer, sous vide and stockpot warmer that can also be used to keep cooked food warm. In an ordinary, non-pressurized cooking vessel, the boiling point of water is at standard pressure. Once the temperature in the vessel reaches the boiling point of water, excess heat causes the water to vaporize into steam. In a sealed pressure cooker, however, the boiling point of water increases with increasing pressure. As the temperature increases, so does the pressure, resulting in superheated water. When the pressure reaches 1 bar or above the existing atmospheric pressure, the water will have reached a temperature of. Pressure cookers employ a regulator to limit the pressure, thereby maintaining a precise temperature. Once the desired pressure and temperature are reached, the heat can be lowered somewhat to minimize excess release of steam, saving energy. Some recipes require browning to develop flavors during roasting or frying. Browning occurs via the Maillard reaction, under temperatures higher than the roughly 250 deg F achieved in pressure cooking. One may brown foods by searing them either in the open pressure cooker or another pan beforehand. A pressure cooker can be used to compensate for lower atmospheric pressure at high elevations. The boiling point of water drops by approximately 1°C per every 294 metres of altitude, causing the boiling point of water to be significantly below the at standard pressure. For example, on the summit of Everest (8,848m), the boiling point of water would be 30°C. Without the use of a pressure cooker, boiled foods may be undercooked, as described in Charles Darwin's "The Voyage of the Beagle" (chapter XV, March 20, 1835): At higher altitudes, the boiling point of liquid is somewhat lower than it would be at sea level. When pressure cooking at high altitudes, cooking times need to be increased by approximately 5% for every above elevation. Since the regulators work off the pressure differential between interior and ambient pressure, the absolute pressure in the interior of a pressure cooker will always be lower at higher altitudes. Weight is a concern with backpackers, so mountaineering pressure cookers are designed to operate at a lower differential pressure than stove-top units. This enables them to use thinner, and therefore lighter materials. Generally, the goal is to raise the cooking temperature enough to make cooking possible and to conserve fuel by reducing heat lost through boiling. Lightweight pressure cookers as small as weighing are available for mountain climbers. Sherpas often use pressure cookers in base camp. Some food toxins can be reduced by pressure cooking. A Korean study of aflatoxins in rice (associated with "Aspergillus" fungus) showed that pressure cooking was capable of reducing aflatoxin concentrations to 32 percent of the amount in the uncooked rice, compared to 77 percent from ordinary cooking. Some foods are not recommended for pressure cooking. Foods such as noodles, pasta, cranberries, cereals and oatmeal can expand too much, froth and sputter, potentially blocking the steam vent and creating an unsafe condition. Pressure cookers are available in different capacities for cooking larger or smaller amounts, with 6 litres' capacity being common. The maximum capacity of food is less than the advertised capacity because pressure cookers can only be filled up to 2/3 full, depending on ingredients and liquid (see Safety features section). Pressure cookers are typically made of aluminum (aluminium) or stainless steel. Aluminum pressure cookers may be stamped, polished, or anodized, but all are unsuitable for the dishwasher. They are cheaper, but the aluminum is reactive to acidic foods, whose flavors are changed in the reactions, and less durable than stainless steel pressure cookers. Higher-quality stainless steel pressure cookers are made with heavy, three-layer, or copper-clad bottoms (heat spreader) for uniform heating because stainless steel has lower thermal conductivity. Most modern stainless steel cookers are dishwasher safe, although some manufacturers may recommend washing by hand. Some pressure cookers have a non-stick interior. A gasket or sealing ring, made from either rubber or silicone, forms a gas-tight seal that does not allow air or steam to escape between the lid and pan. Normally, the only way steam can escape is through a regulator on the lid while the cooker is pressurized. If the regulator becomes blocked, a safety valve provides a backup escape route for steam. To seal the gasket there are several main methods used. Each determines the design of the pressure cooker: Because of the forces that pressure cookers must withstand, they are usually heavier than conventional pots of similar size. Early pressure cookers equipped with only a primary safety valve risked explosion from food blocking the release valve. On modern pressure cookers, food residues blocking the steam vent or the liquid boiling dry will trigger additional safety devices. Modern pressure cookers sold from reputable manufacturers have sufficient safety features to prevent the pressure cooker itself from exploding. When excess pressure is released by a safety mechanism, debris of food being cooked may also be ejected with the steam, which is loud and forceful. This can be avoided if the pressure cooker is regularly cleaned and maintained in accordance with the manufacturer's instructions and never overfilled with food and/or liquid. Modern pressure cookers typically have two or three redundant safety valves and additional safety features, such as an interlock lid that prevents the user from opening the lid when the internal pressure exceeds atmospheric pressure, preventing accidents from a sudden release of hot liquid, steam and food. If safety mechanisms are not correctly in place, the cooker will not pressurize the contents. Pressure cookers should be operated only after reading the instruction manual, to ensure correct usage. Pressure cooker failure is dangerous: a large quantity of scalding steam and water will be forcefully ejected and if the lid separates it may be propelled with considerable force. Some cookers with an internally fitted lid may be particularly dangerous upon failure as the lid fits tighter with increasing pressure, preventing the lid from deforming and venting around the edges. Due to these dangers pressure cookers are generally over-engineered in a safety regard and some countries even have regulations to prevent the sale of non-compliant cookers. For first generation pressure cookers with a weighted valve or "jiggler", the primary safety valve or regulator is usually a weighted stopper, commonly called "the rocker" or "vent weight". This weighted stopper is lifted by the steam pressure, allowing excess pressure to be released. There is a backup pressure release mechanism that releases pressure quickly if the primary pressure release mechanism fails (e.g., food jams the steam discharge path). One such method is a hole in the lid that is blocked by a low melting point alloy plug and another is a rubber grommet with a metal insert at the center. At a sufficiently high pressure, the grommet will distort and the insert will blow out of its mounting hole to release pressure. If the pressure continues to increase, the grommet itself will blow out to release pressure. These safety devices usually require replacement when activated by excess pressure. Newer pressure cookers may have a self-resettable spring device, fixed onto the lid, that releases excess pressure. On second generation pressure cookers, a common safety feature is the gasket, which expands to release excess pressure downward between the lid and the pot. This release of excess pressure is forceful and sufficient to extinguish the flame of a gas stove. Pressure cookers sold in the European Union (EU) must comply with the Pressure Equipment Directive. The recommended maximum fill levels of food/liquid avoids blockage of the steam valve or developing excess pressure: two-thirds full with solid food, half full for liquids and foods that foam and froth (e.g., rice, pasta); adding a tablespoon of cooking oil minimizes foaming., and no more than one-third full for pulses (e.g., lentils). Pressure cooking always requires liquid. Pressure cooking cannot be used for cooking methods that produce little steam such as roasting, pan frying, or deep frying. Thick sauces do not contain enough liquid to vaporize and create pressure, so they usually burn onto the interior base of the pressure cooker after prolonged heating. Sauces should be thickened after pressure cooking. The inner pot of a pressure cooker should never be filled more than halfway when cooking beans. Food is placed inside the pressure cooker with a small amount of water or other liquid such as stock. Food is either cooked in the liquid or above the liquid to be steamed; the latter method prevents the transfer of flavors from the liquid. The lid is closed, the pressure setting is chosen and the pressure cooker is placed on a stove on the highest heat (less than high for induction cooking to allow air to be vented). Once the cooker reaches full pressure, the heat is lowered to maintain pressure; timing the recipe begins at this point. Recipes for foods using raising agents such as steamed puddings call for gentle pre-steaming, without pressure, in order to activate the raising agents prior to cooking and achieve a light, fluffy texture. It takes several minutes for the pressure cooker to reach the selected pressure level. It can take around 10 minutes or longer depending on: the quantity of food, the temperature of the food (cold or frozen food delays pressurization), the amount of liquid, the power of the heat source and the size of the pressure cooker. A common mistake is for the user to start timing when a colored pop-up indicator rises, which happens when there is the slightest increase in pressure, instead of waiting for the cooker to reach its selected pressure level. The typical pop-up indicator only shows that the cooker has pressure inside, which does not reliably signal that the cooker has reached the selected pressure. This pop-up indicator often acts as an interlock, preventing the lid from being opened while there is internal pressure. Manufacturers may use their own terminology for it, such as calling it a ""locking indicator."" As the internal temperature rises, the pressure also rises until it reaches the design gauge pressure. Timing the recipe begins when the selected pressure is reached. With first generation designs, the pressure regulator weight begins levitating above its nozzle, allowing excess steam to escape. In second generation pressure cookers, either a relief valve subsequently opens, releasing steam to prevent the pressure from rising any further or a rod rises with markers to indicate the pressure level, without constantly venting steam. At this stage, the heat source is reduced to the lowest possible heat that still maintains pressure, as extra heat wastes energy and increases liquid loss. Before the pressure cooker lid is sealed airtight, the internal air has to be mostly replaced by steam. Steam has a much higher specific heat than air, and the presence of steam rather than air inside the pressure cooker is how it is able to transfer sufficient heat into the parts of the food that are not submerged in liquid, such as a pot roast. If the lid is sealed before enough air has been removed, not enough heat can be transferred to the food, and food may be undercooked; the presence of air would make the food cook more like it is in an oven than a pressure cooker. To remove the air, steam is vented for several minutes to replace the volume of air inside the cooker. This is why a pressure cooker takes about 10 minutes to reach pressure. For pressure cookers with a weight, the weight is placed over the steam vent pipe while steam is being emitted to ensure the air inside has escaped. The newer generation pressure cookers, which have no weights, automatically expel air from inside for several minutes before a coloured pop-up indicator pin rises to seal the lid airtight; pressure then builds in the now airtight cooker. If the pressure cooker is already hot or a stovetop pressure cooker is placed on a very strong heat source, such as induction on too high a setting, the lid can seal airtight too quickly before the air inside has been removed. In these situations, a slightly lower heat setting can be used to allow the water to boil slower in order to vent the air. Small containers such as plastic pudding containers can be used in a pressure cooker, if the containers (and any covering used) can withstand temperatures of and are not placed directly on the interior base. The containers can be used for cooking foods that are prone to burning on the base of the pressure cooker. A lid for the container may be used if the lid allows some steam to come into contact with the food and the lid is securely fitted; an example is foil or greaseproof paper, pleated in the center and tied securely with string. Containers that are cracked or have otherwise sustained damage are not suitable. Cooking time is longer when using covered containers because the food is not in direct contact with the steam. Since non-metal containers are poorer heat conductors, the type of container material stated in the recipe cannot be substituted without affecting the outcome. For example, if the recipe time is calculated using a stainless steel container and a plastic container is used instead, the recipe will be undercooked, unless the cooking time is increased. Containers with thicker sides, e.g., oven-proof glass or ceramic containers, which are slower to conduct heat, will add about 10 minutes to the cooking time. Liquid can be added inside the container when pressure cooking foods such as rice, which need to absorb liquid in order to cook properly. The flavor of some foods, such as meat and onions, can be improved by gently cooking with a little pre-heated cooking oil, butter or other fat in the open pressure cooker over medium heat for stove-top models (unless the manufacturer advises against this) before pressure cooking, while avoiding overheating the empty pressure cooker not heating the empty cooker with the lid and gasket in place to avoid damage. Electric pressure cookers usually have a "saute" or "brown" option for frying ingredients. The pressure cooker needs to cool briefly before adding liquid; otherwise some of the liquid will evaporate instantly, possibly leaving insufficient liquid for the entire pressure cooking time; if deglazing the pan, more liquid may need to be added. After cooking, there are three ways of releasing the pressure, either quickly or slowly, before the lid can be opened. Recipes for pressure cookers state which release method is required at the end of the cooking time for proper results. Failure to follow the recommendation may result in food that is under-cooked or over-cooked. To avoid opening the pressure cooker too often while cooking different vegetables with varying cooking times, the vegetables that take longer to cook can be cut into smaller pieces and vegetables that cook faster can be cut into thicker pieces. This method is sometimes called a "quick release," not to be confused with the cold water release (mentioned below). It involves the quick release of vapor by gradually lifting (or removing) the valve, pushing a button, or turning a dial. It is most suitable to interrupt cooking to add food that cooks faster than what is already in the cooker. For example, since meat takes longer to cook than vegetables, it is necessary to add vegetables to stew later so that it will cook only for the last few minutes. Unlike the cold water release method, this release method does not cool down the pressure cooker. Releasing the steam with care avoids the risk of being scalded by the rapid release of hot steam. This release method is not suitable for foods that foam and froth while cooking; the hot contents might spray outwards due to the pressure released from the steam vent. This release method takes about two minutes to release the pressure before the lid can be opened. The natural release method allows the pressure to drop slowly; this is achieved by removing the pressure cooker from the heat source and allowing the pressure to lower without action. It takes approximately 10 to 15 minutes (possibly longer) for the pressure to disappear before the lid can be opened. On many pressure cookers, a coloured indicator pin will drop when the pressure has gone. This natural release method is recommended for foods that foam and froth during cooking, such as rice, legumes, or recipes with raising agents such as steamed puddings. The texture and tenderness of meat cooked in a pressure cooker can be improved by using the natural release method. The natural release method finishes cooking foods or recipes that have longer cooking times because the inside of the pressure cooker stays hot. This method is not recommended for foods that require very short cooking times, otherwise the food overcooks. This method is the fastest way of releasing pressure with portable pressure cookers, but can be dangerous if performed incorrectly. It is therefore safer to release pressure by following the other methods. The manufacturer's instruction book may advise against the cold water release or require it to be performed differently. The cold water release method involves using slow running cold tap water, over the edge of the pressure cooker lid, being careful to avoid the steam vent or any other valves or outlets and never immersing the pressure cooker under water, otherwise steam can be ejected from under the lid, which could cause scalding injury to the user; also the pressure cooker lid can be permanently damaged by an internal vacuum if water gets sucked into the pressure cooker, since the incoming water blocks the inrush of air. The cold water release is most suitable for foods with short cooking times. It takes about 20 seconds for the cooker to cool down enough to lower the pressure so that it can be safely opened. This method is not suitable for electric pressure cookers, as they are not immersible. The cold water release method is not recommended when cooking pulses e.g. red kidney beans, as the sudden release of pressure can cause the bean to burst its skin. Most pressure cookers have a cooking (operating) pressure setting between 0.8–1 bar (11.6–15 psi) (gauge) so the pressure cooker operates at 1.8 to 2.0 bar (absolute). The standard cooking pressure of 15 psi gauge was determined by the United States Department of Agriculture in 1917. At this pressure, water boils at (described in vapour pressure of water article). The higher temperature causes food to cook faster; cooking times can typically be reduced to one-third of the time for conventional cooking methods. The actual cooking time also depends on the pressure release method used after timing "(see Pressure release methods for details)" and the thickness and density of the food, since thicker (and denser) foods take longer to cook. Meat joints and some other foods like sponge puddings and Christmas puddings are typically timed according to their weight. Frozen foods need extra cooking time to allow for thawing. When pressure cooking at 1 bar/15 psi (gauge), approximate cooking times are one minute for shredded cabbage, seven minutes for boiled potatoes (if cut small, not diced) and three minutes for fresh green beans. If the pressure is released naturally after timing "(see Pressure release methods for details)," cooking times are even shorter. Food cooks more quickly when cut into smaller pieces. Some recipes may require cooking at lower than 1 bar/15 psi (gauge) e.g. fresh vegetables, as these can easily overcook. Many pressure cookers have 2 or more selectable pressure settings or weights. Some pressure cookers have a lower or higher "maximum" pressure than 1 bar/15 psi (gauge) or can be adjusted to different pressures for some recipes; cooking times will increase or decrease accordingly. This is typically done by having different regulator weights or different pressure settings. If the recipe is devised for a higher pressure and the pressure cooker does not reach that pressure, the cooking time can be increased slightly to compensate. Electric pressure cookers operate at lower pressures than stovetop pressure cookers. Foods cook much faster with pressure cooking than with other methods (except for small quantities in microwave ovens). Food is cooked more quickly in a pressure cooker because at the higher pressure (1 bar/15 psi), the boiling point of water rises from 100 °C (212 °F) to 121 °C (250 °F). The hotter steam is able to transmit its thermal energy to the food at around 4 times the rate of conventional boiling. Pressure cooking requires much less water than conventional boiling, so food can be ready sooner. Less energy is required than that of boiling, steaming, or oven cooking. Since less water or liquid has to be heated, the food reaches its cooking temperature faster. Using more liquid than necessary wastes energy because it takes longer to heat up; the liquid quantity is stated in the recipe. Pressure cookers can use much less liquid than the amount required for boiling or steaming in an ordinary saucepan. It is not necessary to immerse food in water. The minimum quantity of water or liquid used in the recipe to keep the pressure cooker filled with steam is sufficient. With sealed pressure cookers, steam isn't continually escaping, thus evaporation losses are non existent once it has reached pressure. Overall, energy used by pressure cookers can be as much as 70% lower than used by cooking in a pan. Because of this, vitamins and minerals are not leached (dissolved) away by water, as they would be if food were boiled in large amounts of water. Due to the shorter cooking time, vitamins are preserved relatively well during pressure cooking. Several foods can be cooked together in the pressure cooker, either for the same amount of time or added later for different times. Manufacturers provide steamer baskets to allow more foods to be cooked together inside the pressure cooker. Not only is this steam energy transmitted quickly to food, it is also transmitted rapidly to any micro-organisms that are present, easily killing even the deadliest types that are able to survive at the boiling point. Because of this enhanced germ killing ability, a pressure cooker can be used as an effective sterilizer for jam pots, glass baby bottles, or for water while camping. In fact, the autoclave, used in hospitals to sterilize surgical instruments, is really just a more precise and technical version of the ordinary pressure cooker. The appliance has been adapted as a crude type of bomb, which has been used in terrorist attacks. An "autoclave" is a type of pressure cooker used by laboratories and hospitals to sterilize equipment. Large pressure cookers are often called "pressure canners" in the United States, because of their capacity to hold jars used in canning. Pressure canners are specifically designed for home canning, whereas ordinary pressure cookers are not recommended for canning due to the risk of botulism poisoning, because pressure canners hold heat and pressure for much longer than ordinary pressure cookers; these factors are a critical part of the total processing time required to destroy harmful microbes. "Pressure fryers" are used for deep fat frying under pressure, because ordinary pressure cookers are not suitable for pressure frying. A "pressure air fryer" (not to be confused with a "pressure fryer") is a recent combination of a pressure cooker and an air fryer, with two separate lids, one for pressure cooking and one for air frying. The air frying lid has a convection fan in it that allows it to air fry foods, similar to an air fryer oven. This innovation was popularized by the Ninja Foodi Pressure Cooker, marketed as the first pressure cooker that can crisp and air fry. A "pressure oven" is a recent combination of an oven and pressure cooker, usually as a countertop convection oven. They operate at low pressures,, compared to other pressure cookers. Their main function is as an enhanced oven or broiler for meat and poultry, avoiding drying. As such, they often include a rotisserie. Although having insufficient pressure for most conventional pressure cooking functions, they do also have non-pressure oven modes.

Pressure cooking is the process of cooking food at high pressure, employing water or a water-based cooking liquid, in a sealed vessel known as a "pressure cooker". High pressure limits boiling, and permits cooking temperatures well above to be reached.

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summarize: Generally speaking, researchers involved in dynamics study how a physical system might develop or alter over time and study the causes of those changes. In addition, Newton established the fundamental physical laws which govern dynamics in physics. By studying his system of mechanics, dynamics can be understood. In particular, dynamics is mostly related to Newton's second law of motion. However, all three laws of motion are taken into account because these are interrelated in any given observation or experiment. The study of dynamics falls under two categories: linear and rotational. Linear dynamics pertains to objects moving in a line and involves such quantities as force, mass/inertia, displacement (in units of distance), velocity (distance per unit time), acceleration (distance per unit of time squared) and momentum (mass times unit of velocity). Rotational dynamics pertains to objects that are rotating or moving in a curved path and involves such quantities as torque, moment of inertia/rotational inertia, angular displacement (in radians or less often, degrees), angular velocity (radians per unit time), angular acceleration (radians per unit of time squared) and angular momentum (moment of inertia times unit of angular velocity). Very often, objects exhibit linear and rotational motion. For classical electromagnetism, Maxwell's equations describe the kinematics. The dynamics of classical systems involving both mechanics and electromagnetism are described by the combination of Newton's laws, Maxwell's equations, and the Lorentz force. From Newton, force can be defined as an exertion or pressure which can cause an object to accelerate. The concept of force is used to describe an influence which causes a free body (object) to accelerate. It can be a push or a pull, which causes an object to change direction, have new velocity, or to deform temporarily or permanently. Generally speaking, force causes an object's state of motion to change. Newton described force as the ability to cause a mass to accelerate. His three laws can be summarized as follows: Newton's Laws of Motion are valid only in an inertial frame of reference.

Dynamics is the branch of classical mechanics concerned with the study of forces and their effects on motion. Isaac Newton defined the fundamental physical laws which govern dynamics in physics, especially his second law of motion.

en

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summarize: Mammal classification has been through several iterations since Carl Linnaeus initially defined the class. No classification system is universally accepted; McKenna & Bell (1997) and Wilson & Reader (2005) provide useful recent compendiums. George Gaylord Simpson's "Principles of Classification and a Classification of Mammals" (AMNH "Bulletin" v. 85, 1945) provides systematics of mammal origins and relationships that were universally taught until the end of the 20th century. Since Simpson's classification, the paleontological record has been recalibrated, and the intervening years have seen much debate and progress concerning the theoretical underpinnings of systematization itself, partly through the new concept of cladistics. Though field work gradually made Simpson's classification outdated, it remains the closest thing to an official classification of mammals. Most mammals, including the six most species-rich orders, belong to the placental group. The three largest orders in numbers of species are Rodentia: mice, rats, porcupines, beavers, capybaras and other gnawing mammals; Chiroptera: bats; and Soricomorpha: shrews, moles and solenodons. The next three biggest orders, depending on the biological classification scheme used, are the Primates including the apes, monkeys and lemurs; the Cetartiodactyla including whales and even-toed ungulates; and the Carnivora which includes cats, dogs, weasels, bears, seals and allies. According to "Mammal Species of the World", 5,416 species were identified in 2006. These were grouped into 1,229 genera, 153 families and 29 orders. In 2008, the International Union for Conservation of Nature (IUCN) completed a five-year Global Mammal Assessment for its IUCN Red List, which counted 5,488 species. According to research published in the "Journal of Mammalogy" in 2018, the number of recognized mammal species is 6,495 including 96 recently extinct. The word "mammal" is modern, from the scientific name "Mammalia" coined by Carl Linnaeus in 1758, derived from the Latin "mamma" ("teat, pap"). In an influential 1988 paper, Timothy Rowe defined Mammalia phylogenetically as the crown group of mammals, the clade consisting of the most recent common ancestor of living monotremes (echidnas and platypuses) and therian mammals (marsupials and placentals) and all descendants of that ancestor. Since this ancestor lived in the Jurassic period, Rowe's definition excludes all animals from the earlier Triassic, despite the fact that Triassic fossils in the Haramiyida have been referred to the Mammalia since the mid-19th century. In 1997, the mammals were comprehensively revised by Malcolm C. McKenna and Susan K. Bell, which has resulted in the McKenna/Bell classification. Their 1997 book, "Classification of Mammals above the Species Level", is a comprehensive work on the systematics, relationships and occurrences of all mammal taxa, living and extinct, down As of the early 21st century, molecular studies based on DNA analysis have suggested new relationships among mammal families. Most of these findings have been independently validated by retrotransposon presence/absence data. Classification systems based on molecular studies reveal three major groups or lineages of placental mammals—Afrotheria, Xenarthra and Boreoeutheria—which diverged in the Cretaceous. The relationships between these three lineages is contentious, and all three Synapsida, a clade that contains mammals and their extinct relatives, originated during the Pennsylvanian subperiod (~323 million to ~300 million The first fully terrestrial vertebrates were amniotes. Like their amphibious tetrapod predecessors, they had lungs and limbs. Amniotic eggs, however, have internal membranes that allow the developing embryo to breathe but keep water in. Hence, amniotes can lay eggs on dry land, while amphibians generally need to lay their eggs in water. The first amniotes apparently arose in the Pennsylvanian subperiod of the Carboniferous. They descended from earlier reptiliomorph amphibious tetrapods, which lived on land that was already inhabited by insects and other invertebrates as well as ferns, mosses and other plants. Within a few million years, two important amniote lineages became distinct: the The Permian–Triassic extinction event about 252 million years ago, which was a prolonged event due to the accumulation of several extinction pulses, ended the dominance of carnivorous therapsids. In the early Triassic, most medium to large land carnivore niches were taken over by archosaurs which, over an extended period (35 million years), came to include the crocodylomorphs, the pterosaurs and the dinosaurs; however, large cynodonts like "Trucidocynodon" and traversodontids still occupied large sized carnivorous and herbivorous niches respectively. By the Jurassic, the dinosaurs had come to dominate the large terrestrial herbivore niches as well. The first mammals (in Kemp's sense) appeared in the Late Triassic epoch (about 225 million years ago), 40 million years after the first therapsids. They expanded out of their nocturnal insectivore niche from the mid-Jurassic onwards; The Jurassic "Castorocauda", for example, was a close relative of true mammals that had adaptations for swimming, digging and catching fish. Most, if not all, are thought to have remained nocturnal (the nocturnal bottleneck), accounting for much of the typical mammalian traits. The majority of the mammal species that existed in the Mesozoic Era were multituberculates, eutriconodonts and spalacotheriids. The "Hadrocodium", whose fossils date from approximately 195 million years ago, in the early Jurassic, provides the first clear evidence of a jaw joint formed solely by the squamosal and dentary bones; there is no space in the jaw for the articular, a bone involved in the jaws of all early synapsids. The earliest clear evidence of hair or fur is in fossils of "Castorocauda" and "Megaconus", from 164 million years ago in the mid-Jurassic. In the 1950s, it was suggested that the foramina (passages) in the maxillae and premaxillae (bones in the front of the upper jaw) of cynodonts were channels which supplied blood vessels and nerves to vibrissae (whiskers) and so were evidence of hair or fur; it was soon pointed out, however, that foramina do not necessarily show that an animal had vibrissae, as the modern lizard "Tupinambis" has foramina that are almost identical to those found in the nonmammalian cynodont "Thrinaxodon". Therian mammals took over the medium- to large-sized ecological niches in the Cenozoic, after the Cretaceous–Paleogene extinction event approximately 66 million years ago emptied ecological space once filled by non-avian dinosaurs and other groups of reptiles, as well as various other mammal groups, and underwent an exponential increase in body size (megafauna). Then mammals diversified very quickly; both birds and mammals show an exponential rise in diversity. For example, the earliest known bat dates from about 50 million years ago, only 16 million years after the extinction of the non-avian dinosaurs. Molecular phylogenetic studies Living mammal species can be identified by the presence of sweat glands, including those that are specialized to produce milk to nourish their young. In classifying fossils, however, other features must be used, since soft tissue The majority of mammals have seven cervical vertebrae (bones in the neck), including bats, giraffes, whales and humans. The exceptions are the manatee and the two-toed sloth, which have just six, and the three-toed sloth which has nine cervical vertebrae. All mammalian brains possess a neocortex, a brain region unique to mammals. Placental mammals have a corpus callosum, unlike monotremes and marsupials. The lungs of mammals are spongy and honeycombed. Breathing is mainly achieved with the diaphragm, which divides the thorax from the abdominal cavity, forming a dome convex to the thorax. Contraction of the diaphragm flattens the dome, increasing the volume of the lung cavity. Air enters through the oral and nasal cavities, and travels through the larynx, trachea and bronchi, and expands the alveoli. Relaxing the diaphragm has the opposite effect, decreasing the volume of the lung cavity, causing air to be pushed out of the lungs. During exercise, the abdominal wall contracts, increasing pressure on the diaphragm, which forces air out quicker and more forcefully. The rib As in all other tetrapods, mammals have a larynx that can quickly open and close to produce sounds, and a supralaryngeal vocal tract which filters this sound. The lungs and surrounding musculature provide the air stream and pressure required to phonate. The larynx controls the pitch and volume of sound, but the strength the lungs exert to exhale also contributes to volume. More primitive mammals, such as the echidna, can only hiss, as sound is achieved solely through exhaling through a partially closed larynx. Other mammals phonate using vocal folds, as opposed to the vocal cords seen in birds and reptiles. The movement or tenseness of the vocal folds can result in many sounds such as purring and screaming. Mammals can change the position of the larynx, allowing them to breathe through the nose while swallowing through the mouth, and to form both oral and nasal sounds; nasal sounds, such as a dog whine, are generally soft sounds, and oral sounds, such as a dog bark, are generally loud. Some mammals have a large larynx and thus a low-pitched voice, namely the hammer-headed The primary function of the fur of mammals is thermoregulation. Others include protection, sensory purposes, waterproofing, and camouflage. Different types of fur serve different purposes: Hair length is not a factor in thermoregulation: for example, some tropical mammals such as sloths have the same length of fur length as some arctic mammals but with less insulation; and, conversely, other tropical mammals with short hair have the same insulating value as arctic mammals. The denseness of fur can increase an animal's insulation value, and Mammalian coats are colored for a variety of reasons, the major selective pressures including camouflage, sexual selection, communication, and thermoregulation. Coloration in both the hair and skin of mammals is mainly determined by the type and amount of melanin; eumelanins for brown and black colors and pheomelanin for a range of yellow to reddish-brown colors, giving mammals an earth tone. Some mammals, like the mandrill, have more vibrant colors due to structural coloration. Many sloths appear green because their fur hosts green algae; this may be a symbiotic relation that affords camouflage to the sloths. Camouflage is a powerful influence in a large number of mammals, as it helps to conceal individuals from predators or prey. In arctic and subarctic mammals such as the arctic fox ("Alopex lagopus"), collared lemming ("Dicrostonyx groenlandicus"), stoat In male placentals, the penis is used both for urination and copulation. Depending on the species, an erection may be fueled by blood flow into vascular, spongy tissue or by muscular action. A penis may be contained in a prepuce when not erect, and some placentals also have a penis bone (baculum). Marsupials typically have forked penises, while the echidna penis generally has four heads with only two functioning. The testes of most mammals descend into the scrotum which is typically posterior to the penis but is often anterior in marsupials. Female mammals generally have a clitoris, labia majora and Nearly all mammals are endothermic ("warm-blooded"). Most mammals also have hair to help keep them warm. Like birds, mammals can forage or hunt in weather and climates too cold for ectothermic ("cold-blooded") reptiles and insects. Endothermy Among mammals, species maximum lifespan varies significantly (for example the shrew has a lifespan of two years, whereas the oldest bowhead whale is recorded to be 211 years). Although the underlying basis for these lifespan differences is still uncertain, numerous studies indicate that the ability to repair DNA damage is an important determinant of mammalian lifespan. In a 1974 study by Hart and Setlow, it was found that DNA excision repair Most vertebrates—the amphibians, the reptiles and some mammals such as humans and bears—are plantigrade, walking on the whole of the underside of the foot. Many mammals, such as cats and dogs, are digitigrade, walking on their toes, the greater stride length allowing more speed. Digitigrade mammals are also often adept at quiet movement. Some animals such as horses are unguligrade, walking on the tips of their toes. This even further increases their stride length and thus their speed. A few mammals, namely the great apes, are also known to walk on their knuckles, at least for their front legs. Giant anteaters and platypuses are also knuckle-walkers. Some mammals are bipeds, using only two limbs for locomotion, which can be seen in, for example, humans and the great apes. Bipedal species have a larger field of vision than quadrupeds, Arboreal animals frequently have elongated limbs that help them cross gaps, reach fruit or other resources, test the firmness of support ahead and, in some cases, to brachiate (swing between trees). Many arboreal species, such as tree porcupines, silky anteaters, spider monkeys, and possums, use prehensile tails to grasp branches. In the spider monkey, the tip of the tail has either a bare patch or adhesive pad, which provides increased friction. Claws can be used to interact with rough substrates and reorient the direction of forces the animal applies. This is what allows squirrels to climb tree trunks that are so large to be essentially flat from the perspective of such a small animal. However, claws can interfere with an animal's ability to grasp very small branches, as they may wrap too Bats are the only mammals that can truly fly. They fly through the air at a constant speed by moving their wings up and down (usually with some fore-aft movement as well). Because the animal is in motion, there is some airflow relative to its body which, combined with the velocity of the wings, generates a faster airflow moving over the wing. This generates a lift force vector pointing forwards and upwards, and a drag force vector pointing rearwards and upwards. The upwards components of these counteract gravity, keeping the body in the air, while the forward component provides thrust to counteract both the drag A fossorial (from Latin "fossor", meaning "digger") is an animal adapted to digging which lives primarily, but not solely, underground. Some examples are badgers, and naked mole-rats. Many rodent species are also considered fossorial because they live in burrows for most but not all of the day. Species that live exclusively underground are subterranean, and those with limited adaptations to a fossorial lifestyle sub-fossorial. Some organisms are fossorial to aid in temperature regulation while others use the underground habitat for protection from predators or for food storage. Fossorial mammals have a fusiform body, thickest at the shoulders and tapering off at the tail and Fully aquatic mammals, the cetaceans and sirenians, have lost their legs and have a tail fin to propel themselves through the water. Flipper movement is continuous. Whales swim by moving their tail fin and lower body up and down, propelling themselves through vertical movement, while their flippers are mainly used for steering. Their skeletal anatomy allows them to be fast swimmers. Most species have a dorsal fin to prevent themselves from turning upside-down in the water. The flukes of sirenians are raised up and down in long strokes to move the animal forward, and can be twisted to turn. The forelimbs are paddle-like flippers which aid in turning and slowing. Semi-aquatic mammals, like pinnipeds, have two Many mammals communicate by vocalizing. Vocal communication serves many purposes, including in mating rituals, as warning calls, to indicate food sources, and for social purposes. Males often call during mating rituals to ward off other males and to attract females, as in the roaring of lions and red deer. The songs of the humpback whale may be signals to females; they have different dialects in different regions of the ocean. Social vocalizations include the territorial calls of gibbons, and the use of frequency in greater spear-nosed bats to distinguish between groups. The vervet monkey gives a distinct alarm call for each of at least four different predators, and the reactions of other monkeys vary according to the call. For To maintain a high constant body temperature is energy expensive—mammals therefore need a nutritious and plentiful diet. While the earliest mammals were probably predators, different species have since adapted to meet their dietary requirements in a variety of ways. Some eat other animals—this is a carnivorous diet (and includes insectivorous diets). Other mammals, called herbivores, eat plants, which contain complex carbohydrates such as cellulose. An herbivorous diet includes subtypes such as granivory (seed eating), folivory (leaf eating), frugivory (fruit eating), nectarivory (nectar eating), gummivory (gum eating) and mycophagy (fungus eating). The digestive tract of an herbivore is host to bacteria that ferment these complex substances, and make them available for digestion, which are either In intelligent mammals, such as primates, the cerebrum is larger relative to the rest of the brain. Intelligence itself is not easy to define, but indications of intelligence include the ability to learn, matched with behavioral flexibility. Rats, for example, are considered to be highly intelligent, as they can learn and perform new tasks, an ability that may be important when they first colonize a fresh habitat. In some mammals, food gathering appears to be related to intelligence: a deer feeding on plants has a brain smaller than a cat, which must think to outwit its prey. Tool use by animals may indicate different levels of learning and cognition. The sea otter uses rocks as essential and regular parts of its foraging behaviour (smashing abalone from rocks or breaking open shells), with some populations spending 21% of their time making tools. Other tool use, such as chimpanzees using twigs to "fish" for termites, may be developed by watching Eusociality is the highest level of social organization. These societies have an overlap of adult generations, the division of reproductive labor and cooperative caring of young. Usually insects, such as bees, ants and termites, have eusocial behavior, but it is demonstrated in two rodent species: the naked mole-rat and the Damaraland mole-rat. Presociality is when animals exhibit more than just sexual interactions with members of the same species, but fall short of qualifying as eusocial. That is, presocial animals can display communal living, cooperative care of young, or primitive division of reproductive labor, but they do not display all of the three essential traits of eusocial animals. Humans and some species of Callitrichidae (marmosets and tamarins) are unique among primates in their degree Non-human mammals play a wide variety of roles in human culture. They are the most popular of pets, with tens of millions of dogs, cats and other animals including rabbits and mice kept by families around the world. Mammals such as mammoths, horses and deer are among the earliest subjects of art, being found in Upper Paleolithic cave paintings such as at Lascaux. Domestic mammals form a large part of the livestock raised for meat across the world. They include (2009) around 1.4 billion cattle, 1 billion sheep, 1 billion domestic pigs, and (1985) over 700 million rabbits. Working domestic animals including cattle and horses have been used for work and transport from the origins of agriculture, their numbers declining with the arrival of mechanised transport and agricultural machinery. In 2004 they still provided some 80% of the power for the mainly small farms in the third world, and some 20% of the world's transport, again mainly in rural areas. In mountainous regions unsuitable for wheeled vehicles, pack animals continue to transport goods. Mammal skins provide leather for shoes, clothing and upholstery. Wool from mammals including sheep, Hybrids are offspring resulting from the breeding of two genetically distinct individuals, which usually will result in a high degree of heterozygosity, though hybrid and heterozygous are not synonymous. The deliberate or accidental hybridizing of two or more species of closely related animals through captive breeding is a human activity which has been in existence for millennia and has grown for economic purposes. Hybrids between different subspecies within a species (such as between the Bengal tiger and Siberian tiger) are known as intra-specific hybrids. Hybrids between different species within the same genus (such as between lions and tigers) are known as interspecific hybrids or crosses. Hybrids between different genera (such as between sheep and goats) are known as intergeneric hybrids. Natural hybrids will occur in hybrid zones, where two populations of species within the same genera or species living in the same or adjacent areas will interbreed with each other. Some hybrids have been recognized The loss of species from ecological communities, defaunation, is primarily driven by human activity. This has resulted in empty forests, ecological communities depleted of large vertebrates. In the Quaternary extinction event, the mass die-off of megafaunal variety coincided with the appearance of humans, suggesting a human influence. One hypothesis is that humans hunted large mammals, such as the woolly mammoth, into extinction. The 2019 "Global Assessment Report on Biodiversity and Ecosystem Services" by IPBES states that the total biomass of wild mammals has declined by 82 percent since the beginning of human civilization. Various species are predicted to become extinct in the near future, among them the rhinoceros, primates, pangolins, and giraffes. Hunting alone threatens hundreds of mammalian species around the world. Scientists claim that the growing demand for meat is contributing to biodiversity loss as this is a significant driver of deforestation and habitat destruction; species-rich habitats, such as significant portions of the Amazon rainforest, are being converted to agricultural land for meat production. According to the World Wildlife

Mammals (from Latin "mamma" "breast") are vertebrate animals constituting the class Mammalia (), and characterized by the presence of mammary glands which in females (and sometimes males) produce milk for feeding (nursing) their young, a neocortex (a region of the brain), fur or hair, and three middle ear bones. These characteristics distinguish them from reptiles and birds, from which they diverged in the late Carboniferous, approximately 300 million years ago. Around 6,400 extant species of mammals have been described. The largest orders are the rodents, bats and Eulipotyphla (hedgehogs, moles, shrews, and others). The next three are the Primates (apes including humans, monkeys, and others), the Cetartiodactyla (cetaceans and even-toed ungulates), and the Carnivora (cats, dogs, seals, and others).

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summarize: Energy is a scalar quantity and the mechanical energy of a system is the sum of the potential energy (which is measured by the position of the parts of the system) and the kinetic energy (which is also called the energy of motion): The potential energy, "U", depends on the position of an object subjected to a conservative force. It is defined as the object's ability to do work and is increased as the object is moved in the opposite direction of the direction of the force. If "F" represents the conservative force and "x" the position, the potential energy of the force between the two positions "x" and "x" is defined as the negative integral of "F" from "x" to "x": The kinetic energy, "K", depends on the speed of an object and is the ability of a moving object to do work on other objects when it collides with them. It is defined as one half the product of the object's mass with the square of its speed, and the total kinetic energy of a system of objects is the sum of the kinetic energies of the respective objects: The principle of conservation of mechanical energy states that if a body or system is subjected only to conservative forces, the mechanical energy of that body or system remains constant. The difference between a conservative and a non-conservative force is that when a conservative force moves an object from one point to another, the work done by the conservative force is independent of the path. On the contrary, when a non-conservative force acts upon an object, the work done by the non-conservative force is dependent of the path. According to the principle of conservation of mechanical energy, the mechanical energy of an isolated system remains constant in time, as long as the system is free of friction and other non-conservative forces. In any real situation, frictional forces and other non-conservative forces are present, but in many cases their effects on the system are so small that the principle of conservation of mechanical energy can be used as a fair approximation. Though energy cannot be created or destroyed in an isolated system, it can be converted to another form of energy. In a mechanical system like a swinging pendulum subjected to the conservative gravitational force where frictional forces like air drag and friction at the pivot are negligible, energy passes back and forth between kinetic and potential energy but never leaves the system. The pendulum reaches greatest kinetic energy and least potential energy when in the vertical position, because it will have the greatest speed and be nearest the Earth at this point. On the other hand, it will have its least kinetic energy and greatest potential energy at the extreme positions of its swing, because it has zero speed and is farthest from Earth at these points. However, when taking the frictional forces into account, the system loses mechanical energy with each swing because of the negative work done on the pendulum by these non-conservative forces. That the loss of mechanical energy in a system always resulted in an increase of the system's temperature has been known for a long time, but it was the amateur physicist James Prescott Joule who first experimentally demonstrated how a certain amount of work done against friction resulted in a definite quantity of heat which should be conceived as the random motions of the particles that comprise matter. This equivalence between mechanical energy and heat is especially important when considering colliding objects. In an elastic collision, mechanical energy is conserved – the sum of the mechanical energies of the colliding objects is the same before and after the collision. After an inelastic collision, however, the mechanical energy of the system will have changed. Usually, the mechanical energy before the collision is greater than the mechanical energy after the collision. In inelastic collisions, some of the mechanical energy of the colliding objects is transformed into kinetic energy of the constituent particles. This increase in kinetic energy of the constituent particles is perceived as an increase in temperature. The collision can be described by saying some of the mechanical energy of the colliding objects has been converted into an equal amount of heat. Thus, the total energy of the system remains unchanged though the mechanical energy of the system has reduced. A satellite of mass formula_4 at a distance formula_5 from the centre of Earth possesses both kinetic energy, formula_6, (by virtue of its motion) and gravitational potential energy, formula_7, (by virtue of its position within the Earth's gravitational field; Earth's mass is formula_8). Hence, mechanical energy formula_9 of the satellite-Earth system is given by If the satellite is in circular orbit, the energy conservation equation can be further simplified into since in circular motion, Newton's 2nd Law of motion can be taken to be Today, many technological devices convert mechanical energy into other forms of energy or vice versa. These devices can be placed in these categories: The classification of energy into different types often follows the boundaries of the fields of study in the natural sciences. Notes Citations Bibliography

In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. It is the macroscopic energy associated with a system. The principle of conservation of mechanical energy states that in an isolated system that is only subject to conservative forces, the mechanical energy is constant. If an object moves in the opposite direction of a conservative net force, the potential energy will increase; and if the speed (not the velocity) of the object changes, the kinetic energy of the object also changes. In all real systems, however, nonconservative forces, such as frictional forces, will be present, but if they are of negligible magnitude, the mechanical energy changes little and its conservation is a useful approximation. In elastic collisions, the mechanical energy is conserved, but in inelastic collisions some mechanical energy is converted into thermal energy. The equivalence between lost mechanical energy (dissipation) and an increase in temperature was discovered by James Prescott Joule.

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summarize: The idea of a simple machine originated with the Greek philosopher Archimedes around the 3rd century BC, who studied the Archimedean simple machines: lever, pulley, and screw. He discovered the principle of mechanical advantage in the lever. Archimedes' famous remark with regard to the lever: "Give me a place to stand on, and I will move the Earth," () expresses his realization that there was no limit to the amount of force amplification that could be achieved by using mechanical advantage. Later Greek philosophers defined the classic five simple machines (excluding the inclined plane) and were able to calculate their (ideal) mechanical advantage. For example, Heron of Alexandria (c. 10–75 AD) in his work "Mechanics" lists five mechanisms that can "set a load in motion"; lever, windlass, pulley, wedge, and screw, and describes their fabrication and uses. However the Greeks' understanding was limited to the statics of simple machines (the balance of forces), and did not include dynamics, the tradeoff between force and distance, or the concept of work. During the Renaissance the dynamics of the "Mechanical Powers", as the simple machines were called, began to be studied from the standpoint of how far they could lift a load, in addition to the force they could apply, leading eventually to the new concept of mechanical work. In 1586 Flemish engineer Simon Stevin derived the mechanical advantage of the inclined plane, and it was included with the other simple machines. The complete dynamic theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in "Le Meccaniche" ("On Mechanics"), in which he showed the underlying mathematical similarity of the machines as force amplifiers. He was the first to explain that simple machines do not create energy, only transform it. The classic rules of sliding friction in machines were discovered by Leonardo da Vinci (1452–1519), but were unpublished and merely documented in his notebooks, and were based on pre-Newtonian science such as believing friction was an ethereal fluid. They were rediscovered by Guillaume Amontons (1699) and were further developed by Charles-Augustin de Coulomb (1785). If a simple machine does not dissipate energy through friction, wear or deformation, then energy is conserved and it is called an ideal simple machine. In this case, the power into the machine equals the power out, and the mechanical advantage can be calculated from its geometric dimensions. Although each machine works differently mechanically, the way they function is similar mathematically. In each machine, a force formula_1 is applied to the device at one point, and it does work moving a load, formula_2 at another point. Although some machines only change the direction of the force, such as a stationary pulley, most machines multiply the magnitude of the force by a factor, the mechanical advantage that can be calculated from the machine's geometry and friction. Simple machines do not contain a source of energy, so they cannot do more work than they receive from the input force. A simple machine with no friction or elasticity is called an "ideal machine". Due to conservation of energy, in an ideal simple machine, the power output (rate of energy output) at any time formula_4 is equal to the power input formula_5 The power output equals the velocity of the load formula_7 multiplied by the load force formula_8. Similarly the power input from the applied force is equal to the velocity of the input point formula_9 multiplied by the applied force formula_10. Therefore, So the mechanical advantage of an ideal machine formula_12 is equal to the "velocity ratio", the ratio of input velocity to output velocity The "velocity ratio" is also equal to the ratio of the distances covered in any given period of time Therefore the mechanical advantage of an ideal machine is also equal to the "distance ratio", the ratio of input distance moved to output distance moved This can be calculated from the geometry of the machine. For example, the mechanical advantage and distance ratio of the lever is equal to the ratio of its lever arms. The mechanical advantage can be greater or less than one: In the screw, which uses rotational motion, the input force should be replaced by the torque, and the velocity by the angular velocity the shaft is turned. All real machines have friction, which causes some of the input power to be dissipated as heat. If formula_19 is the power lost to friction, from conservation of energy The mechanical efficiency formula_21 of a machine (where formula_22) is defined as the ratio of power out to the power in, and is a measure of the frictional energy losses As above, the power is equal to the product of force and velocity, so Therefore, So in non-ideal machines, the mechanical advantage is always less than the velocity ratio by the product with the efficiency "η". So a machine that includes friction will not be able to move as large a load as a corresponding ideal machine using the same input force. A "compound machine" is a machine formed from a set of simple machines connected in series with the output force of one providing the input force to the next. For example, a bench vise consists of a lever (the vise's handle) in series with a screw, and a simple gear train consists of a number of gears (wheels and axles) connected in series. The mechanical advantage of a compound machine is the ratio of the output force exerted by the last machine in the series divided by the input force applied to the first machine, that is Because the output force of each machine is the input of the next, formula_27, this mechanical advantage is also given by Thus, the mechanical advantage of the compound machine is equal to the product of the mechanical advantages of the series of simple machines that form it Similarly, the efficiency of a compound machine is also the product of the efficiencies of the series of simple machines that form it In many simple machines, if the load force "F" on the machine is high enough in relation to the input force "F", the machine will move backwards, with the load force doing work on the input force. So these machines can be used in either direction, with the driving force applied to either input point. For example, if the load force on a lever is high enough, the lever will move backwards, moving the input arm backwards against the input force. These are called ""reversible"", ""non-locking"" or ""overhauling"" machines, and the backward motion is called ""overhauling"". However, in some machines, if the frictional forces are high enough, no amount of load force can move it backwards, even if the input force is zero. This is called a ""self-locking"", ""nonreversible"", or ""non-overhauling"" machine. These machines can only be set in motion by a force at the input, and when the input force is removed will remain motionless, "locked" by friction at whatever position they were left. Self-locking occurs mainly in those machines with large areas of sliding contact between moving parts: the screw, inclined plane, and wedge: A machine will be self-locking if and only if its efficiency "η" is below 50%: Whether a machine is self-locking depends on both the friction forces (coefficient of static friction) between its parts, and the distance ratio "d/d" (ideal mechanical advantage). If both the friction and ideal mechanical advantage are high enough, it will self-lock. When a machine moves in the forward direction from point 1 to point 2, with the input force doing work on a load force, from conservation of energy the input work formula_32 is equal to the sum of the work done on the load force formula_33 and the work lost to friction formula_34 If the efficiency is below 50% formula_35 From When the machine moves backward from point 2 to point 1 with the load force doing work on the input force, the work lost to friction formula_34 is the same So the output work is Thus the machine self-locks, because the work dissipated in friction is greater than the work done by the load force moving it backwards even with no input force Machines are studied as mechanical systems consisting of actuators and mechanisms that transmit forces and movement, monitored by sensors and controllers. The components of actuators and mechanisms consist of links and joints that form kinematic chains. Simple machines are elementary examples of kinematic chains that are used to model mechanical systems ranging from the steam engine to robot manipulators. The bearings that form the fulcrum of a lever and that allow the wheel and axle and pulleys to rotate are examples of a kinematic pair called a hinged joint. Similarly, the flat surface of an inclined plane and wedge are examples of the kinematic pair called a sliding joint. The screw is usually identified as its own kinematic pair called a helical joint. Two levers, or cranks, are combined into a planar four-bar linkage by attaching a link that connects the output of one crank to the input of another. Additional links can be attached to form a six-bar linkage or in series to form a robot. The identification of simple machines arises from a desire for a systematic method to invent new machines. Therefore, an important concern is how simple machines are combined to make more complex machines. One approach is to attach simple machines in series to obtain compound machines. However, a more successful strategy was identified by Franz Reuleaux, who collected and studied over 800 elementary machines. He realized that a lever, pulley, and wheel and axle are in essence the same device: a body rotating about a hinge. Similarly, an inclined plane, wedge, and screw are a block sliding on a flat surface. This realization shows that it is the joints, or the connections that provide movement, that are the primary elements of a machine. Starting with four types of joints, the revolute joint, sliding joint, cam joint and gear joint, and related connections such as cables and belts, it is possible to understand a machine as an assembly of solid parts that connect these joints. The design of mechanisms to perform required movement and force transmission is known as kinematic synthesis. This is a collection of geometric techniques for the mechanical design of linkages, cam and follower mechanisms and gears and gear trains.

A simple machine is a mechanical device that changes the direction or magnitude of a force. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. Usually the term refers to the six classical simple machines that were defined by Renaissance scientists:

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summarize: Before the invention of the refrigerator, icehouses were used to provide cool storage for most of the year. Placed near freshwater lakes or packed with snow and ice during the winter, they were once very common. Natural means are still used to cool foods today. On mountainsides, runoff from melting snow is a convenient way to cool drinks, and during the winter one can keep milk fresh much longer just by keeping it outdoors. The word "refrigeratory" was used at least as early as the 17th century The history of artificial refrigeration began when Scottish professor William Cullen designed a small refrigerating machine in 1755. Cullen used a pump to create a partial vacuum over a container of diethyl ether, which then boiled, absorbing heat from the surrounding air. The experiment even created a small amount of ice, but had no practical application at that time. In 1805, American inventor Oliver Evans described a closed vapor-compression refrigeration cycle for the production of ice by ether under vacuum. In 1820, the British scientist Michael Faraday liquefied ammonia and other gases by using high pressures and low temperatures, and in 1834, an American expatriate in Great Britain, Jacob Perkins, built the first working vapor-compression refrigeration system. It was a closed-cycle device that could operate continuously. A similar attempt was made in 1842, by American physician, John Gorrie, who built a working prototype, but it was a commercial failure. American engineer Alexander Twining took out a British patent in 1850 for a vapor compression system that used ether. The first practical vapor compression refrigeration system was built by James Harrison, a Scottish Australian. His 1856 patent was for a vapor compression system using ether, alcohol or ammonia. He built a mechanical ice-making machine in 1851 on the banks of the Barwon River at Rocky Point in Geelong, Victoria, and his first commercial ice-making machine followed in 1854. Harrison also introduced commercial vapor-compression refrigeration to breweries and meat packing houses, and by 1861, a dozen of his systems were in operation. The first gas absorption refrigeration system using gaseous ammonia dissolved in water (referred to as "aqua ammonia") was developed by Ferdinand Carré of France in 1859 and patented in 1860. Carl von Linde, an engineering professor at the Technological University Munich in Germany, patented an improved method of liquefying gases in 1876. His new process made possible the use of gases such as ammonia (NH), sulfur dioxide (SO) and methyl chloride (CHCl) as refrigerants and they were widely used for that purpose until the late 1920s. Commercial refrigerator and freezer units, which go by many other names, were in use for almost 40 years prior to the common home models. They used gas systems such as ammonia (R-717) or sulfur dioxide (R-764), which occasionally leaked, making them unsafe for home use. Practical household refrigerators were introduced in 1915 and gained wider acceptance in the United States in the 1930s as prices fell and non-toxic, non-flammable synthetic refrigerants such as Freon-12 (R-12) were introduced. However, R-12 damaged the ozone layer, causing governments to issue a ban on its use in new refrigerators and air-conditioning systems in 1994. The less harmful replacement for R-12, R-134a (tetrafluoroethane), has been in common use since 1990, but R-12 is still found in many old systems today. A common commercial refrigerator is the glass fronted beverage cooler. These type of appliances are typically designed for specific re-load conditions meaning that they generally have a larger cooling system. This ensures that they are able to cope with a large throughput of drinks and frequent door opening. As a result, it is common for these types of commercial refrigerators to have energy consumption of >4 kWh/day. In 1913, refrigerators for home and domestic use were invented by Fred W. Wolf of Fort Wayne, Indiana, with models consisting of a unit that was mounted on top of an ice box. In 1914, engineer Nathaniel B. Wales of Detroit, Michigan, introduced an idea for a practical electric refrigeration unit, which later became the basis for the Kelvinator. A self-contained refrigerator, with a compressor on the bottom of the cabinet was invented by Alfred Mellowes in 1916. Mellowes produced this refrigerator commercially but was bought out by William C. Durant in 1918, who started the Frigidaire company to mass-produce refrigerators. In 1918, Kelvinator company introduced the first refrigerator with any type of automatic control. The absorption refrigerator was invented by Baltzar von Platen and Carl Munters from Sweden in 1922, while they were still students at the Royal Institute of Technology in Stockholm. It became a worldwide success and was commercialized by Electrolux. Other pioneers included Charles Tellier, David Boyle, and Raoul Pictet. Carl von Linde was the first to patent and make a practical and compact refrigerator. These home units usually required the installation of the mechanical parts, motor and compressor, in the basement or an adjacent room while the cold box was located in the kitchen. There was a 1922 model that consisted of a wooden cold box, water-cooled compressor, an ice cube tray and a compartment, and cost $714. (A 1922 Model-T Ford cost about $450.) By 1923, Kelvinator held 80 percent of the market for electric refrigerators. Also in 1923 Frigidaire introduced the first self-contained unit. About this same time porcelain-covered metal cabinets began to appear. Ice cube trays were introduced more and more during the 1920s; up to this time freezing was not an auxiliary function of the modern refrigerator. The first refrigerator to see widespread use was the General Electric "Monitor-Top" refrigerator introduced in 1927, so-called, by the public, because of its resemblance to the gun turret on the ironclad warship USS "Monitor" of the 1860s. The compressor assembly, which emitted a great deal of heat, was placed above the cabinet, and enclosed by a decorative ring. Over a million units were produced. As the refrigerating medium, these refrigerators used either sulfur dioxide, which is corrosive to the eyes and may cause loss of vision, painful skin burns and lesions, or methyl formate, which is highly flammable, harmful to the eyes, and toxic if inhaled or ingested. The introduction of Freon in the 1920s expanded the refrigerator market during the 1930s and provided a safer, low-toxicity alternative to previously used refrigerants. Separate freezers became common during the 1940s; the popular term at the time for the unit was a "deep freeze". These devices, or "appliances", did not go into mass production for use in the home until after World War II. The 1950s and 1960s saw technical advances like automatic defrosting and automatic ice making. More efficient refrigerators were developed in the 1970s and 1980s, even though environmental issues led to the banning of very effective (Freon) refrigerants. Early refrigerator models (from 1916) had a cold compartment for ice cube trays. From the late 1920s fresh vegetables were successfully processed through freezing by the Postum Company (the forerunner of General Foods), which had acquired the technology when it bought the rights to Clarence Birdseye's successful fresh freezing methods. In the early 1950s most refrigerators were white, but from the mid-1950s through present day designers and manufacturers put color onto refrigerators. In the late-1950s/early-1960s, pastel colors like turquoise and pink became popular, and brushed chrome-plating (similar to stainless finish) was available on some models. In the late 1960s and throughout the 1970s, earth tone colors were popular, including Harvest Gold, Avocado Green and almond. In the 1980s, black became fashionable. In the late 1990s stainless steel came into vogue, and in 2009, one manufacturer introduced multi-color designs. Since 1961 the Color Marketing Group has attempted to coordinate the colors of appliances and other consumer goods. Freezer units are used in households and in industry and commerce. Food stored at or below is safe indefinitely. Most household freezers maintain temperatures from, although some freezer-only units can achieve and lower. Refrigerator freezers generally do not achieve lower than, since the same coolant loop serves both compartments: Lowering the freezer compartment temperature excessively causes difficulties in maintaining above-freezing temperature in the refrigerator compartment. Domestic freezers can be included as a separate compartment in a refrigerator, or can be a separate appliance. Domestic freezers may be either upright units resembling a refrigerator, or chests (with the lid or door on top, sacrificing convenience for efficiency and partial immunity to power outages). Many modern upright freezers come with an ice dispenser built into their door. Some upscale models include thermostat displays and controls, and sometimes flat screen televisions as well. Home freezers as separate compartments (larger than necessary just for ice cubes), or as separate units, were introduced in the United States in 1940. Frozen foods, previously a luxury item, became commonplace. The following table shows worldwide production of household refrigerator units as of 2005. A vapor compression cycle is used in most household refrigerators, refrigerator–freezers and freezers. In this cycle, a circulating refrigerant such as R134a enters a compressor as low-pressure vapor at or slightly below the temperature of the refrigerator interior. The vapor is compressed and exits the compressor as high-pressure superheated vapor. The superheated vapor travels under pressure through coils or tubes that make up the "condenser"; the coils or tubes are passively cooled by exposure to air in the room. The condenser cools the vapor, which liquefies. As the refrigerant leaves the condenser, it is still under pressure but is now only slightly above room temperature. This liquid refrigerant is forced through a metering or throttling device, also known as an expansion valve (essentially a pin-hole sized constriction in the tubing) to an area of much lower pressure. The sudden decrease in pressure results in explosive-like flash evaporation of a portion (typically about half) of the liquid. The latent heat absorbed by this flash evaporation is drawn mostly from adjacent still-liquid refrigerant, a phenomenon known as "auto-refrigeration". This cold and partially vaporized refrigerant continues through the coils or tubes of the evaporator unit. A fan blows air from the compartment ("box air") across these coils or tubes and the refrigerant completely vaporizes, drawing further latent heat from the box air. This cooled air is returned to the refrigerator or freezer compartment, and so keeps the box air cold. Note that the cool air in the refrigerator or freezer is still warmer than the refrigerant in the evaporator. Refrigerant leaves the evaporator, now fully vaporized and slightly heated, and returns to the compressor inlet to continue the cycle. Modern domestic refrigerators are extremely reliable because motor and compressor are integrated within a welded container, "sealed unit", with greatly reduced likelihood of leakage or contamination. By comparison, externally-coupled refrigeration compressors, such as those in automobile air conditioning, inevitably leak fluid and lubricant past the shaft seals. This leads to a requirement for periodic recharging and, if ignored, possible compressor failure. Refrigerators with two compartments need special design to control the cooling of refrigerator or freezer compartments. Typically, the compressors and condenser coils are mounted at the top of the cabinet, with a single fan to cool them both. This arrangement has a few downsides: each compartment cannot be controlled independently and the more humid refrigerator air is mixed with the dry freezer air. A few manufacturers offer dual compressor models. These models have separate freezer and refrigerator compartments that operate independently of each other, sometimes mounted within a single cabinet. Each has its own separate compressor, condenser and evaporator coils, insulation, thermostat, and door. A hybrid between the two designs is using a separate fan for each compartment, the Dual Fan approach. Doing so allows for separate control and airflow on a single compressor system. An absorption refrigerator works differently from a compressor refrigerator, using a source of heat, such as combustion of liquefied petroleum gas, solar thermal energy or an electric heating element. These heat sources are much quieter than the compressor motor in a typical refrigerator. A fan or pump might be the only mechanical moving parts; reliance on convection is considered impractical. Other uses of an absorption refrigerator (or "chiller") include large systems used in office buildings or complexes such as hospitals and universities. These large systems are used to chill a brine solution that is circulated through the building. The Peltier effect uses electricity to pump heat directly; refrigerators employing this system are sometimes used for camping, or in situations where noise is not acceptable. They can be totally silent (if a fan for air circulation is not fitted) but are less energy-efficient than other methods. "Ultra-cold" or "ultra-low temperature (ULT)" (typically −80C) freezers, as used for storing biological samples, also generally employ two stages of cooling, but in cascade. The lower temperature stage uses methane, or a similar gas, as a refrigerant, with its condenser kept at around −40C by a second stage which uses a more conventional refrigerant. Well known brands include Forma and Revco (both now Thermo Scientific) and Thermoline. For much lower temperatures (around −196C), laboratories usually purchase liquid nitrogen, kept in a Dewar flask, into which the samples are suspended. Alternatives to the vapor-compression cycle not in current mass production include: Many modern refrigerator/freezers have the freezer on top and the refrigerator on the bottom. Most refrigerator-freezers—except for manual defrost models or cheaper units—use what appears to be two thermostats. Only the refrigerator compartment is properly temperature controlled. When the refrigerator gets too warm, the thermostat starts the cooling process and a fan circulates the air around the freezer. During this time, the refrigerator also gets colder. The freezer control knob only controls the amount of air that flows into the refrigerator via a damper system. Changing the refrigerator temperature will inadvertently change the freezer temperature in the opposite direction. Changing the freezer temperature will have no effect on the refrigerator temperature. The freezer control may also be adjusted to compensate for any refrigerator adjustment. This means the refrigerator may become too warm. However, because only enough air is diverted to the refrigerator compartment, the freezer usually re-acquires the set temperature quickly, unless the door is opened. When a door is opened, either in the refrigerator or the freezer, the fan in some units stops immediately to prevent excessive frost build up on the freezer's evaporator coil, because this coil is cooling two areas. When the freezer reaches temperature, the unit cycles off, no matter what the refrigerator temperature is. Modern computerized refrigerators do not use the damper system. The computer manages fan speed for both compartments, although air is still blown from the freezer. Newer refrigerators may include: These older freezer compartments were the main cooling body of the refrigerator, and only maintained a temperature of around, which is suitable for keeping food for a week. Later advances included automatic ice units and self compartmentalized freezing units. Domestic refrigerators and freezers for food storage are made in a range of sizes. Among the smallest is a 4 L Peltier refrigerator advertised as being able to hold 6 cans of beer. A large domestic refrigerator stands as tall as a person and may be about 1 m wide with a capacity of 600 L. Some models for small households fit under kitchen work surfaces, usually about 86 cm high. Refrigerators may be combined with freezers, either stacked with refrigerator or freezer above, below, or side by side. A refrigerator without a frozen food storage compartment may have a small section just to make ice cubes. Freezers may have drawers to store food in, or they may have no divisions (chest freezers). Refrigerators and freezers may be free-standing, or built into a kitchen. Three distinct classes of refrigerator are common: Other specialized cooling mechanisms may be used for cooling, but have not been applied to domestic or commercial refrigerators. In a house without air-conditioning (space heating and/or cooling) refrigerators consumed more energy than any other home device. In the early 1990s a competition was held among the major manufacturers to encourage energy efficiency. Current US models that are Energy Star qualified use 50% less energy than the average models made in 1974. The most energy-efficient unit made in the US consumes about half a kilowatt-hour per day (equivalent to 20 W continuously). But even ordinary units are quite efficient; some smaller units use less than 0.2 kWh per day (equivalent to 8 W continuously). Larger units, especially those with large freezers and icemakers, may use as much as 4 kW·h per day (equivalent to 170 W continuously). The European Union uses a letter-based mandatory energy efficiency rating label instead of the Energy Star; thus EU refrigerators at the point of sale are labelled according to how energy-efficient they are. For US refrigerators, the Consortium on Energy Efficiency (CEE) further differentiates between Energy Star qualified refrigerators. Tier 1 refrigerators are those that are 20% to 24.9% more efficient than the Federal minimum standards set by the National Appliance Energy Conservation Act (NAECA). Tier 2 are those that are 25% to 29.9% more efficient. Tier 3 is the highest qualification, for those refrigerators that are at least 30% more efficient than Federal standards. About 82% of the Energy Star qualified refrigerators are Tier 1, with 13% qualifying as Tier 2, and just 5% at Tier 3. Besides the standard style of compressor refrigeration used in normal household refrigerators and freezers, there are technologies such as absorption refrigeration and magnetic refrigeration. Although these designs generally use a much larger amount of energy compared to compressor refrigeration, other qualities such as silent operation or the ability to use gas can favor these refrigeration units in small enclosures, a mobile environment or in environments where unit failure would lead to devastating consequences. Many refrigerators made in the 1930s and 1940s were far more efficient than most that were made later. This is partly attributable to the addition of new features, such as auto-defrost, that reduced efficiency. Additionally, after World War 2, refrigerator style became more important than efficiency. This was especially true in the US in the 1970s, when side-by-side models (known as American fridgefreezers outside of the US) with ice dispensers and water chillers became popular. However, the reduction in efficiency also arose partly from reduction in the amount of insulation to cut costs. Because of the introduction of new energy efficiency standards, refrigerators made today are much more efficient than those made in the 1930s; they consume the same amount of energy while being three times as large. The efficiency of older refrigerators can be improved by defrosting (if the unit is manual defrost) and cleaning them regularly, replacing old and worn door seals with new ones, adjusting the thermostat to accommodate the actual contents (a refrigerator needn't be colder than to store drinks and non-perishable items) and also replacing insulation, where applicable. Some sites recommend cleaning condenser coils every month or so on units with coils on the rear, to add life to the coils and not suffer an unnoticeable deterioration in efficiency over an extended period, the unit should be able to ventilate or "breathe" with adequate spaces around the front, back, sides and above the unit. If the refrigerator uses a fan to keep the condenser cool, then this must be cleaned or serviced, at per individual manufactures recommendations. Frost-free refrigerators or freezers use electric fans to cool the appropriate compartment. This could be called a "fan forced" refrigerator, whereas manual defrost units rely on colder air lying at the bottom, versus the warm air at the top to achieve adequate cooling. The air is drawn in through an inlet duct and passed through the evaporator where it is cooled, the air is then circulated throughout the cabinet via a series of ducts and vents. Because the air passing the evaporator is supposedly warm and moist, frost begins to form on the evaporator (especially on a freezer's evaporator). In cheaper and/or older models, a defrost cycle is controlled via a mechanical timer. This timer is set to shut off the compressor and fan and energize a heating element located near or around the evaporator for about 15 to 30 minutes at every 6 to 12 hours. This melts any frost or ice build up and allows the refrigerator to work normally once more. It is believed that frost free units have a lower tolerance for frost, due to their air-conditioner like evaporator coils. Therefore, if a door is left open accidentally (especially the freezer), the defrost system may not remove all frost, in this case, the freezer (or refrigerator) must be defrosted. If the defrosting system melts all the ice before the timed defrosting period ends, then a small device (called a defrost limiter) acts like a thermostat and shuts off the heating element to prevent too large a temperature fluctuation, it also prevents hot blasts of air when the system starts again, should it finish defrosting early. On some early frost-free models, the defrost limiter also sends a signal to the defrost timer to start the compressor and fan as soon as it shuts off the heating element before the timed defrost cycle ends. When the defrost cycle is completed, the compressor and fan are allowed to cycle back on. Frost-free refrigerators, including some early frost free refrigerator/freezers that used a cold plate in their refrigerator section instead of airflow from the freezer section, generally don't shut off their refrigerator fans during defrosting. This allows consumers to leave food in the main refrigerator compartment uncovered, and also helps keep vegetables moist. This method also helps reduce energy consumption, because the refrigerator is above freeze point and can pass the warmer-than-freezing air through the evaporator or cold plate to aid the defrosting cycle. With the advent of digital inverter compressors, the energy consumption is even further reduced than a single-speed induction motor compressor, and thus contributes far less in the way of greenhouse gases. The energy consumption of a refrigerator is also dependent on the type of refrigeration being done. For instance, Inverter Refrigerators consume comparatively less energy than a typical non-inverter refrigerator. In an inverter refrigerator, the compressor is used conditionally on requirement basis. For instance, an inverter refrigerator might use less energy during the winters than it does during the summers. This is because the compressor works for a shorter time than it does during the summers. The phycial design of refrigerators also plays a large part in its energy efficiency. The most efficient is the chest-style freezer, as its top-opening design minimizes convection when opening the doors, reducing the amount of warm moist air entering the freezer. On the other hand, in-door ice dispensers cause more heat leakage, contributing to an increase in energy consumption. The refrigerator allows the modern family to keep food fresh for longer than before. The most notable improvement is for meat and other highly perishable wares, which needed to be refined to gain anything resembling shelf life. (On the other hand, refrigerators and freezers can also be stocked with processed, quick-cook foods that are less healthy.) Refrigeration in transit makes it possible to enjoy food from distant places. Dairy products, meats, fish, poultry and vegetables can be kept refrigerated in the same space within the kitchen (although raw meat should be kept separate from other food for reasons of hygiene). Freezers allow people to buy food in bulk and eat it at leisure, and bulk purchases save money. Ice cream, a popular commodity of the 20th century, could previously only be obtained by traveling to where the product was made and eating it on the spot. Now it is a common food item. Ice on demand not only adds to the enjoyment of cold drinks, but is useful for first-aid, and for cold packs that can be kept frozen for picnics or in case of emergency. The capacity of a refrigerator is measured in either liters or cubic feet. Typically the volume of a combined refrigerator-freezer is split with 1/3rds to 1/4th of the volume allocated to the freezer although these values are highly variable. Temperature settings for refrigerator and freezer compartments are often given arbitrary numbers by manufacturers (for example, 1 through 9, warmest to coldest), but generally is ideal for the refrigerator compartment and for the freezer. Some refrigerators must be within certain external temperature parameters to run properly. This can be an issue when placing units in an unfinished area, such as a garage. Some refrigerators are now divided into four zones to store different types of food: European freezers, and refrigerators with a freezer compartment, have a four star rating system to grade freezers. Although both the three and four star ratings specify the same storage times and same minimum temperature of, only a four star freezer is intended for freezing fresh food, and may include a "fast freeze" function (runs the compressor continually, down to as low as ) to facilitate this. Three (or fewer) stars are used for frozen food compartments that are only suitable for storing frozen food; introducing fresh food into such a compartment is likely to result in unacceptable temperature rises. This difference in categorization is shown in the design of the 4-star logo, where the "standard" three stars are displayed in a box using "positive" colours, denoting the same normal operation as a 3-star freezer, and the fourth star showing the additional fresh food/fast freeze function is prefixed to the box in "negative" colours or with other distinct formatting. Most European refrigerators include a moist cold refrigerator section (which does require (automatic) defrosting at irregular intervals) and a (rarely frost free) freezer section. An increasingly important environmental concern is the disposal of old refrigerators—initially because freon coolant damages the ozone layer—but as older generation refrigerators wear out, the destruction of CFC-bearing insulation also causes concern. Modern refrigerators usually use a refrigerant called HFC-134a (1,1,1,2-Tetrafluoroethane), which does not deplete the ozone layer, instead of Freon. A R-134a is now becoming very uncommon in Europe. Newer refrigerants are being used instead. The main refrigerant now used is R-600a, or isobutane which has a smaller effect on the atmosphere if released. There have been reports of refrigerators exploding if the refrigerant leaks isobutane in the presence of a spark. If the coolant leaks into the fridge, at times when the door is not being opened (such as overnight) the concentration of coolant in the air within the fridge can build up to form an explosive mixture that can be ignited either by a spark from the thermostat or when the light comes on as the door is opened, resulting in documented cases of serious property damage and injury or even death from the resulting explosion. Disposal of discarded refrigerators is regulated, often mandating the removal of doors for safety reasons. Children playing hide-and-seek have been asphyxiated while hiding inside discarded refrigerators, particularly older models with latching doors, in a phenomenon called refrigerator death. Since 2 August 1956, under U.S. federal law, refrigerator doors are no longer permitted to latch so they cannot be opened from the inside. Modern units use a magnetic door gasket that holds the door sealed but allows it to be pushed open from the inside. This gasket was invented, developed and manufactured by Max Baermann (1903–1984) of Bergisch Gladbach/Germany. Regarding total life-cycle costs, many governments offer incentives to encourage recycling of old refrigerators. One example is the Phoenix refrigerator program launched in Australia. This government incentive picked up old refrigerators, paying their owners for "donating" the refrigerator. The refrigerator was then refurbished, with new door seals, a thorough cleaning and the removal of items, such as the cover that is strapped to the back of many older units. The resulting refrigerators, now over 10% more efficient, were then distributed to low income families.

A refrigerator (colloquially fridge) consists of a thermally insulated compartment and a heat pump (mechanical, electronic or chemical) that transfers heat from the inside of the fridge to its external environment so that the inside of the fridge is cooled to a temperature below the room temperature. Refrigeration is an essential food storage technique in developed countries. The lower temperature lowers the reproduction rate of bacteria, so the refrigerator reduces the rate of spoilage. A refrigerator maintains a temperature a few degrees above the freezing point of water. Optimum temperature range for perishable food storage is. A similar device that maintains a temperature below the freezing point of water is called a freezer. The refrigerator replaced the icebox, which had been a common household appliance for almost a century and a half.

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summarize: The order Carnivora belongs to a group of mammals known as Laurasiatheria, which also includes other groups such as bats and ungulates. Within this group the carnivorans are placed in the clade Ferae. Ferae includes the closest extant relative of carnivorans, the pangolins, as well as several extinct groups of mostly Paleogene carnivorous placentals such as the creodonts, the arctocyonians, and mesonychians. The creodonts were originally thought of as the sister taxon to the carnivorans, perhaps even ancestral to, based on the presence of the carnassial teeth. but the nature of the carnassial teeth is different between the two groups. In carnivorans the carnassials are positioned near the front of the molar row, while in the creodonts they are positioned near the back of the molar row. and this suggests a separate evolutionary history and an order-level distinction. In addition recent phylogenetic analysis suggests that creodonts are more closely related to pangolins while mesonychians might be the sister group to carnivorans and their stem-relatives. The closest stem-carnivorans are the miacoids. The miacoids include the families Viverravidae and Miacidae, and together the Carnivora and Miacoidea form the stem-clade Carnivoramorpha. The miacoids were small, gennet-like carnivoramorphs that occupy a variety of niches such as terrestrial and arboreal habitats. Recent studies have shown a supporting amount of evidence that Miacoidea is an evolutionary grade of canivoramorphs that, while viverravids are monophyletic basal group, the miacids are paraphyletic in respect to Carnivora (as shown in the phylogeny below). Carnivoramorpha as a whole first appeared in the Paleocene of North America about 60 million years ago. Crowned carnivorans first appeared around 42 million years ago in the Middle Eocene. Their molecular phylogeny shows the extant Carnivora are a monophyletic group, the crown group of the Carnivoramorpha. From there carnivorans have split into two clades based on the composition of the bony structures that surround the middle ear of the skull, the cat-like feliforms and the dog-like caniforms. In feliforms, the auditory bullae are double-chambered, composed of two bones joined by a septum. Caniforms have single-chambered or partially divided auditory bullae, composed of a single bone. Initially the early representatives of carnivorans were small as the creodonts dominated the niches as top apex predators, but by the Miocene most of the extant carnivoran families have diversified and successfully out-competed the creodonts. The phylogenetic relationships of the carnivorans are shown in the following cladogram: In 1758 the Swedish botanist Carl Linnaeus placed all the carnivorans that was known at the time in the group Ferae (not to be confused with the modern concept of Ferae which also include pangolins) in the tenth edition of his book "Systema Naturae". He recognized six genera: "Canis" (canids and hyaenids), "Phoca" (pinnipeds), "Felis" (felids), "Viverra" (viverrids, herpestids, and mephitids), "Mustela" (non-badger mustelids), "Ursus" (ursids, large species of mustelids, and procyonids). It wasn't until in 1821 when the English writer and traveler Thomas Edward Bowdich gave the group its modern and accepted name. Initially the modern concept of Carnivora was divided into two suborders: the terrestrial Fissipedia and the marine Pinnipedia. Below is the classification of how the extant families were related to each other after American paleontologist George Gaylord Simpson in 1945: Since then, however, the methods in which mammalogists use to assess the phylogenetic relationships among the carnivoran families has been improved with using more complicated and intensive incorporation of genetics, morphology and the fossil record. Research into Carnivora phylogeny since 1945 has found Fisspedia to be paraphlyetic in respect to Pinnipedia, with pinnipeds being either more closely related to bears or to weasels. The small carnivoran families Viverridae, Procyonidae, and Mustelidae have found to be polyphyletic: Below is a table chart of the extant carnivoran families and number of extant species recognized by various authors of the first and fourth volumes of "Handbook of the Mammals of the World" published in 2009 and 2014 respectively: The canine teeth are usually large and conical. The canines are thick and incredibly stress resistant. All of the terrestrial species of carnivorans have three incisors on the top and bottom row of the dentition (the exception being is the sea otter ("Enhydra lutris") which only has two lower incisor teeth). The third molar has been lost. The carnassial pair is made up by the fourth upper premolar and the first lower molar teeth. Like most mammals the dentition is heterodont in nature, though in some species like the aardwolf ("Proteles cristata") the teeth have been greatly reduced and the cheek teeth are specialised for eating insects. In pinnipeds the teeth are homodont as they have evolved to grasp or to catch fish, and the cheek teeth are often lost. In bears and raccoons the carnassial pair is secondarily reduced. The skulls are heavily built with a strong zygomatic arch. Often a sagittal crest is present, sometimes more evident in sexual dimorphic species like sea lions and fur seals, though it has also been greatly reduced seen in some small carnivorans. The braincase is enlarged and the frontoparietal is position at the front of it. In most species the eyes are position at the front of the face. In caniforms the rostrum is usually longer with many teeth, where in comparison with felifoms the rostrum is shorter and have fewer teeth. The carnassial teeth in feliforms, however is more sectional. The turbinates are large and complex in comparison to other mammals, providing a large surface area for olfactory receptors. Aside from an accumulation of characteristics in the dental and cranial features, not much of their overall anatomy unites them as a group. All species of carnivorans have quadrupedal limbs with usually five digits at the front feet and four digits at the back feet. In terrestrial carnivorans the feet have soft pads. The feet can either be digitigrade seen in cats, hyenas and dogs or plantigrade seen in bears, skunks, raccoons, weasels, civets and mongooses. In pinnipeds the limbs have been modified into flippers. Unlike other marine mammals, such as cetaceans and sirenians which have fully functional tails to help them swim, pinnipeds use their limbs underwater for locomotion. In earless seals they use their back flippers; sea lions and fur seals use their front flippers, and the walrus use all of their limbs. This resulted in pinnipeds having significantly shorter tails. Aside from the pinnipeds, dogs, bears, hyenas, and cats have distinct and recognizable appearances. Dogs are usually cursorial mammals and are gracile in appearance, often relying on their teeth to hold to prey; bears are much larger and rely on their physical strength to forage for food. Cats in comparison to dogs and bears have much longer and stronger frontlimbs armed with retractable claws to hold on to prey. Hyenas are dog-like feliforms that have sloping backs due to their front legs being longer than their hindlegs. The raccoon family as well as the red panda are small, bear-like carnivorans with long tails. The other small carnivoran families Nandiniidae, Prionodontidae, Viverridae, Herpestidae, Eupleridae, Mephitidae and Mustelidae have through convergent evolution maintained the small, ancestral appearance of the miacoids, though there is some variation seen such as the robust and stout physicality of badgers and the wolverine ("Gulo gulo"). Male carnivorans usually have bacula, though they are absent in hyenas and binturongs. Depending on the environment the species is, the length and density of their fur varies. In warm climate species the fur is often short in length and lighter. In comparison to cold climate species the fur is either dense or long, often with an oily substance to keep them warm. The pelage coloration comes in many colors, often including black, white, orange, yellow, red, and many shades of gray and brown. There can be colored patterns too, such striped, spotted, blotched, banded, or otherwise boldly patterned. There seems to be a correlation between habitat and color pattern as for example spotted or banded species tend to be found in heavily forested environments. Some species like the grey wolf is a polymorphic species with different individual variation in colors. The arctic fox ("Vulpes lagopus") and the stoat ("Mustela erminea") the fur goes from white and dense in the winter to brown and sparse in the summer. In pinnipeds, polar bears, and sea otters have a thick insulating layer of blubber to help maintain their body temperature.

Carnivora is an order of placental mammals that have specialized in primarily eating flesh. Its members are formally referred to as carnivorans, though some species are omnivorous, like raccoons and bears, and quite a few species like pandas are specialized herbivores. The word 'carnivore' is derived from Latin "carō" (stem "carn-") "flesh" and "vorāre" "to devour", it refers to any meat-eating organism. The order Carnivora is the fifth largest order of mammals and one of the more successful members of the group; it comprises at least 279 species living on every major landmass and in a variety of habitats, ranging the cold polar regions to the hyper-arid region of the Sahara Desert to the open seas. They come in a huge array of different body plans in contrasting shapes and sizes. The smallest carnivoran is the least weasel ("Mustela nivalis") with a body length of about and a weight of about. The largest is the southern elephant seal ("Mirounga leonina"), with adult males weighing up to and measuring up to. All species of carnivorans are descended from a group of mammals which were related to today's pangolins, having appeared in North America 6 million years after the Cretaceous–Paleogene extinction event. These early ancestors of carnivorans would have resembled small weasel or genet-like mammals, occupying a nocturnal shift on the forest floor or in the trees, as other groups of mammals like the mesonychians and creodonts were occupying the top faunivorous niche. However, by the time Miocene epoch appeared, most if not all of the major lineages and families of carnivorans had diversified and took over this niche.

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summarize: The study of fluid mechanics goes back at least to the days of ancient Greece, when Archimedes investigated fluid statics and buoyancy and formulated his famous law known now as the Archimedes' principle, which was published in his work "On Floating Bodies"—generally considered to be the first major work on fluid mechanics. Rapid advancement in fluid mechanics began with Leonardo da Vinci (observations and experiments), Evangelista Torricelli (invented the barometer), Isaac Newton (investigated viscosity) and Blaise Pascal (researched hydrostatics, formulated Pascal's law), and was continued by Daniel Bernoulli with the introduction of mathematical fluid dynamics in "Hydrodynamica" (1739). Inviscid flow was further analyzed by various mathematicians (Jean le Rond d'Alembert, Joseph Louis Lagrange, Pierre-Simon Laplace, Siméon Denis Poisson) and viscous flow was explored by a multitude of engineers including Jean Léonard Marie Poiseuille and Gotthilf Hagen. Further mathematical justification was provided by Claude-Louis Navier and George Gabriel Stokes in the Navier–Stokes equations, and boundary layers were investigated (Ludwig Prandtl, Theodore von Kármán), while various scientists such as Osborne Reynolds, Andrey Kolmogorov, and Geoffrey Ingram Taylor advanced the understanding of fluid viscosity and turbulence. Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at rest. It embraces the study of the conditions under which fluids are at rest in stable equilibrium; and is contrasted with fluid dynamics, the study of fluids in motion. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressure changes with altitude, why wood and oil float on water, and why the surface of water is always level whatever the shape of its container. Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to some aspects of geophysics and astrophysics (for example, in understanding plate tectonics and anomalies in the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow—the science of liquids and gases in motion. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as velocity, pressure, density, and temperature, as functions of space and time. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and movements on aircraft, determining the mass flow rate of petroleum through pipelines, predicting evolving weather patterns, understanding nebulae in interstellar space and modeling explosions. Some fluid-dynamical principles are used in traffic engineering and crowd dynamics. Fluid mechanics is a subdiscipline of continuum mechanics, as illustrated in the following table. In a mechanical view, a fluid is a substance that does not support shear stress; that is why a fluid at rest has the shape of its containing vessel. A fluid at rest has no shear stress. The assumptions inherent to a fluid mechanical treatment of a physical system can be expressed in terms of mathematical equations. Fundamentally, every fluid mechanical system is assumed to obey: For example, the assumption that mass is conserved means that for any fixed control volume (for example, a spherical volume)—enclosed by a control surface—the rate of change of the mass contained in that volume is equal to the rate at which mass is passing through the surface from "outside" to "inside", minus the rate at which mass is passing from "inside" to "outside". This can be expressed as an equation in integral form over the control volume. The is an idealization of continuum mechanics under which fluids can be treated as continuous, even though, on a microscopic scale, they are composed of molecules. Under the continuum assumption, macroscopic (observed/measurable) properties such as density, pressure, temperature, and bulk velocity are taken to be well-defined at "infinitesimal" volume elements—small in comparison to the characteristic length scale of the system, but large in comparison to molecular length scale. Fluid properties can vary continuously from one volume element to another and are average values of the molecular properties. The continuum hypothesis can lead to inaccurate results in applications like supersonic speed flows, or molecular flows on nano scale. Those problems for which the continuum hypothesis fails can be solved using statistical mechanics. To determine whether or not the continuum hypothesis applies, the Knudsen number, defined as the ratio of the molecular mean free path to the characteristic length scale, is evaluated. Problems with Knudsen numbers below 0.1 can be evaluated using the continuum hypothesis, but molecular approach (statistical mechanics) can be applied for all ranges of Knudsen numbers. The Navier–Stokes equations (named after Claude-Louis Navier and George Gabriel Stokes) are differential equations that describe the force balance at a given point within a fluid. For an incompressible fluid with vector velocity field formula_1, the Navier–Stokes equations are These differential equations are the analogues for deformable materials to Newton's equations of motion for particles – the Navier–Stokes equations describe changes in momentum (force) in response to pressure formula_3 and viscosity, parameterized by the kinematic viscosity formula_4 here. Occasionally, body forces, such as the gravitational force or Lorentz force are added to the equations. Solutions of the Navier–Stokes equations for a given physical problem must be sought with the help of calculus. In practical terms, only the simplest cases can be solved exactly in this way. These cases generally involve non-turbulent, steady flow in which the Reynolds number is small. For more complex cases, especially those involving turbulence, such as global weather systems, aerodynamics, hydrodynamics and many more, solutions of the Navier–Stokes equations can currently only be found with the help of computers. This branch of science is called computational fluid dynamics. An inviscid fluid has no viscosity, formula_5. In practice, an inviscid flow is an idealization, one that facilitates mathematical treatment. In fact, purely inviscid flows are only known to be realized in the case of superfluidity. Otherwise, fluids are generally viscous, a property that is often most important within a boundary layer near a solid surface, where the flow must match onto the no-slip condition at the solid. In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then matching its solution onto that for a thin laminar boundary layer. For fluid flow over a porous boundary, the fluid velocity can be discontinuous between the free fluid and the fluid in the porous media (this is related to the Beavers and Joseph condition). Further, it is useful at low subsonic speeds to assume that gas is incompressible—that is, the density of the gas does not change even though the speed and static pressure change. A Newtonian fluid (named after Isaac Newton) is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. This definition means regardless of the forces acting on a fluid, it "continues to flow". For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. (Compare friction). Important fluids, like water as well as most gases, behave—to good approximation—as a Newtonian fluid under normal conditions on Earth. By contrast, stirring a non-Newtonian fluid can leave a "hole" behind. This will gradually fill up over time—this behavior is seen in materials such as pudding, oobleck, or sand (although sand isn't strictly a fluid). Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" (this is seen in non-drip paints). There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property—for example, most fluids with long molecular chains can react in a non-Newtonian manner. The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation to describe incompressible Newtonian fluid behavior is where For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure, not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress (in Cartesian coordinates) is where If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is where formula_19 is the second viscosity coefficient (or bulk viscosity). If a fluid does not obey this relation, it is termed a non-Newtonian fluid, of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic. In some applications, another rough broad division among fluids is made: ideal and non-ideal fluids. An ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force. An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. One example of this is the flow far from solid surfaces. In many cases, the viscous effects are concentrated near the solid boundaries (such as in boundary layers) while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid (ideal flow). When the viscosity is neglected, the term containing the viscous stress tensor formula_20 in the Navier–Stokes equation vanishes. The equation reduced in this form is called the Euler equation.

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. It has applications in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology.

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summarize: A "solid" is a material that can support a substantial amount of shearing force over a given time scale during a natural or industrial process or action. This is what distinctly distinguishes solids from fluids, because fluids also support "normal forces" which are those forces that are directed perpendicular to the material plane across from which they act and "normal stress" is the normal force per unit area of that material plane. "Shearing forces" in contrast with "normal forces", act parallel rather than perpendicular to the material plane and the shearing force per unit area is called "shear stress". Therefore, solid mechanics examines the shear stress, deformation and the failure of solid materials and structures. The most common topics covered in solid mechanics include: As shown in the following table, solid mechanics inhabits a central place within continuum mechanics. The field of rheology presents an overlap between solid and fluid mechanics. A material has a rest shape and its shape departs away from the rest shape due to stress. The amount of departure from rest shape is called deformation, the proportion of deformation to original size is called strain. If the applied stress is sufficiently low (or the imposed strain is small enough), almost all solid materials behave in such a way that the strain is directly proportional to the stress; the coefficient of the proportion is called the modulus of elasticity. This region of deformation is known as the linearly elastic region. It is most common for analysts in solid mechanics to use linear material models, due to ease of computation. However, real materials often exhibit non-linear behavior. As new materials are used and old ones are pushed to their limits, non-linear material models are becoming more common. These are basic models that describe how a solid responds to an applied stress:

Solid mechanics, also known as mechanics of solids, is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation under the action of forces, temperature changes, phase changes, and other external or internal agents.

en

48

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summarize: The name "Belarus" is closely related with the term "Belaya Rus", i.e., "White Rus'". There are several claims to the origin of the name "White Rus'." An ethno-religious theory suggests that the name used to describe the part of old Ruthenian lands within the Grand Duchy of Lithuania that had been populated mostly by Slavs who had been Christianized early, as opposed to Black Ruthenia, which was predominantly inhabited by pagan Balts. An alternate explanation for the name comments on the white clothing worn by the local Slavic population. A third theory suggests that the old Rus' lands that were not conquered by the Tatars (i.e., Polotsk, Vitebsk and Mogilev) had been referred to as "White Rus'". The name "Rus" is often conflated with its Latin forms "Russia" and "Ruthenia", thus Belarus is often referred to as "White Russia" or "White Ruthenia". The name first appeared in German and Latin medieval literature; the chronicles of Jan of Czarnków mention the imprisonment of Lithuanian grand duke Jogaila and his mother at "" in 1381. In some languages, including German, Afrikaans and Dutch, the country is generally called "White Russia" to this day (' and'respectively). The Latin term "Alba Russia" was used again by Pope Pius VI in 1783 to recognize the Society of Jesus there, exclaiming "." The first known use of "White Russia" to refer to Belarus was in the late-16th century by Englishman Sir Jerome Horsey, who was known for his close contacts with the Russian Royal Court. During the 17th century, the Russian tsars used "White Rus" to describe the lands added From 5000 to 2000 BC, Bandkeramik cultures predominated. In addition, remains from the Dnieper-Donets culture were found in Belarus and parts of Ukraine. Cimmerians and other pastoralists roamed through the area by 1,000 BC, and by 500 AD, Slavs had taken up residence, which was circumscribed by the Scythians who roamed its outskirts. Invaders from Asia, among whom were the Huns and Avars, swept through c. 400–600 AD, but were unable to dislodge the Slavic presence. The region that is now Belarus was first settled by Baltic tribes in the 3rd century. Around the 5th century, the area was taken over by Slavic tribes. The takeover was partially due to the lack of military coordination of the Balts but the gradual assimilation of the Balts into Slavic culture was peaceful in nature. In the 9th century the territory of On 2 February 1386, the Grand Duchy of Lithuania and the Kingdom of Poland were joined in a personal union through a marriage of their rulers. This union set in motion the developments that eventually resulted in the formation of the Polish–Lithuanian Commonwealth, created in 1569 by the Union of Lublin. The Lithuanian nobles were forced to go for rapprochement because of the threat coming from Muscovy. To strengthen the independence in the format of the union, three editions of the Statutes of Lithuania were issued in the 16th century. The third Article of the Statute establishes that all lands of Grand Duchy of Lithuania will be eternally in Grand Duchy of Lithuania and never enter as The union between Poland and Lithuania ended in 1795 with the Third Partition of Poland by Imperial Russia, Prussia, and Austria. The Belarusian territories acquired by the Russian Empire under the reign of Catherine II were included into the Belarusian Governorate () in 1796 and held until their occupation by the German Empire during World War I. Under Nicholas I and Alexander III the national cultures were repressed. Policies of Polonization changed by Russification, which included the return to Orthodox Christianity of Belorusian Uniates. Belarusian language was banned in schools while in neighboring Samogitia primary school education with Samogitian literacy was allowed. The Belarusian People's Republic was the first attempt to create an independent Belarusian state under name "Belarus". Despite significant efforts the state ceased to exist, primarily because the territory was continually dominated by the German Imperial Army and the Imperial Russian Army in The Republic of Central Lithuania was a short-lived political entity, which was the last attempt to restore Lithuania in the historical confederacy state (it was also supposed to create Lithuania Upper and Lithuania Lower). The republic was created in 1920 following the staged rebellion of soldiers of the 1st Lithuanian–Belarusian Division of the Polish Army under Lucjan Żeligowski. Centered on the historical capital of the Grand Duchy of Lithuania, Vilna A part of Belarus under Russian rule emerged as the Byelorussian Soviet Socialist Republic (Byelorussian SSR) in 1919. Soon thereafter it merged to form the Lithuanian-Byelorussian SSR. The contested lands were divided between Poland and the Soviet Union after the war ended in 1921, and the Byelorussian SSR became a founding member of the Union of Soviet Socialist Republics in 1922. The western part of modern Belarus remained part of Poland. In the 1920s and 1930s, Soviet agricultural and economic policies, including collectivization and five-year plans for the national economy, led to In March 1990, elections for seats in the Supreme Soviet of the Byelorussian SSR took place. Though the pro-independence Belarusian Popular Front took only 10% of the seats, the populace was content with the selection of the delegates. Belarus declared itself sovereign on 1990 by issuing the Declaration of State Sovereignty of the Belarusian Soviet Socialist Republic. Two-round elections for the presidency on ( 1994 and 1994) catapulted the formerly unknown Alexander Lukashenko into national prominence. He garnered 45% of the vote in the first round and 80% in the second, defeating Vyacheslav Kebich who received 14% of the vote. Lukashenko was re-elected in 2001, in 2006, in 2010 and again in 2015. Western governments, Amnesty International, and Human Rights Watch have criticized Lukashenko's authoritarian style of government. Since 2014, following years of embrace of Russian influence in the country, Lukashenko has pressed a revival of Belarusian identity, following the Russian annexation of Crimea and military intervention in Eastern Ukraine. Belarus lies between latitudes 51° and 57° N, and longitudes 23° and 33° E. Its extension from north to south is, from west to east is. It is landlocked, relatively flat, and contains large tracts of marshy land. About 40% of Belarus is covered by forests. Many streams and 11,000 lakes are found in Belarus. Three major rivers run through the country: the Neman, the Pripyat, and the Dnieper. The Neman flows westward towards the Baltic sea and the Pripyat flows eastward to the Dnieper; the Dnieper flows southward towards the Black Sea. The highest point is Dzyarzhynskaya Hara (Dzyarzhynsk Hill) at, and the lowest point is on the Neman River at. The average elevation of Belarus is above sea level. The climate features mild to cold winters, with Belarus is a presidential republic, governed by a president and the National Assembly. The term for each presidency is five years. Under the 1994 constitution, the president could serve for only two terms as president, but a change in the constitution in 2004 eliminated term limits. Alexander Lukashenko has been the president of Belarus since 1994. In 1996, Lukashenko called for a controversial vote to extend the presidential term from five to seven years, and as a result the election that was supposed to occur in 1999 was pushed back to 2001. The referendum on the extension was denounced as a "fantastic" fake by the chief electoral officer, Viktar Hanchar, who was removed from the office for official matters only during the campaign. The National Assembly is a bicameral parliament comprising the 110-member House of Representatives (the lower house) and the 64-member Council of the Republic (the upper house). The House of Representatives has the power to appoint the prime minister, make constitutional amendments, call for a vote of confidence on the prime minister, and make suggestions on foreign and domestic policy. The Council of the Republic has the power to select various government officials, conduct an impeachment trial of the president, and accept or reject the bills passed by the House of Representatives. Each chamber has the ability to veto any law passed by local officials if it is contrary to the constitution. The government includes a Council of Ministers, headed by the prime minister and five deputy prime ministers. The members of this council need not be members of the legislature and are appointed by the president. The judiciary comprises the Supreme Court and specialized courts such as the Constitutional Court, which deals with specific issues related to constitutional and business law. The judges of national courts are appointed by the president and confirmed by the Council of the Republic. For criminal cases, the highest court of appeal is the Supreme Court. The Belarusian Constitution forbids the use of special extrajudicial courts. In the 2012 parliamentary election, 105 of the 110 members elected to the House of Representatives were not affiliated with any political party. The Communist Party of Belarus won 3 seats, and the Agrarian Party and Republican Party of Labour and Justice, one each. Most non-partisans represent a wide scope of social organizations such as workers' collectives, public associations, and civil society organizations, similar to the composition of the Soviet legislature. In 2014 the share of manufacturing in GDP was 37%, more than two thirds of this amount falls on manufacturing industries. The number of people employed in industry is 32.7% of the working population. The growth rate is much lower than for the economy as a whole – about 1.9% in 2014. At the time of the dissolution of the Soviet Union in 1991, Belarus was one of the world's most industrially developed states by percentage of GDP as well as the richest CIS member-state. In 2015, 39.3% of Belarusians were employed by state-controlled companies, 57.2% were employed by private companies (in which the government has a 21.1% stake) and 3.5% were employed by foreign companies. The country relies According to the National Statistical Committee,, the population is 9.49 million. Ethnic Belarusians constitute 83.7% of Belarus's total population. The next largest ethnic groups are: Russians (8.3%), Poles (3.1%), and Ukrainians (1.7%). Belarus has a population density of about 50 people per square kilometer (127 per sq mi); 70% of its total population is concentrated in urban areas. Minsk, the nation's capital and largest city, was home to 1,937,900 residents. Gomel, with a population of 481,000, is the second-largest city and serves as the capital of the Homiel Voblast. Other large cities are Mogilev (365,100), Vitebsk (342,400), Hrodna (314,800) and Brest (298,300). Like many other eastern European countries, Belarus has a negative population growth rate and a negative natural growth rate. In 2007, Belarus's population declined by 0.41% and its fertility rate was 1.22, well below the replacement rate. Its net migration rate is +0.38 per 1,000, indicating that Belarus experiences slightly more immigration than emigration., 69.9% of Belarus's population is aged 14 to 64; 15.5% is under 14, and 14.6% is 65 or older. Its population is also aging; the median age of 30–34 is estimated to rise to between 60 and 64 in 2050. There are about 0.87 males per female in Belarus. The average life expectancy is 72.15 (66.53 years for men and 78.1 years for women). Over 99% of Belarusians aged 15 and older are literate. Belarus's two official languages are Russian and Belarusian; Russian is the most common language used at home, used by 70% of the population, while Belarusian, the official first According to the census of, 58.9% of all Belarusians adhere to some kind of religion; out of those, Eastern Orthodoxy (Belarusian Exarchate of the Russian Orthodox Church) makes up about 82%. Roman Catholicism is practiced mostly in the western regions, and there are also different denominations of Protestantism. Minorities also practice Greek Catholicism, Judaism, Islam and Neopaganism. Overall, 48.3% of the population is Orthodox Christian, 41.1% is not religious, 7.1% is Catholic and 3.3% follows other religions. Belarus's Catholic minority is concentrated in the western part of the country, The Belarusian government sponsors annual cultural festivals such as the Slavianski Bazaar in Vitebsk, which showcases Belarusian performers, artists, writers, musicians, and actors. Several state holidays, such as Independence Day and Victory Day, draw big crowds and often include displays such as fireworks and military parades, especially in Vitebsk and Minsk. The government's Ministry of Culture finances events promoting Belarusian arts and culture both inside and outside the country. Belarusian literature began with 11th- to 13th-century religious scripture, such as the 12th-century poetry of Cyril of Turaw. By the 16th century, Polotsk resident Francysk Skaryna translated the Bible into Belarusian. It was published in Prague and Vilnius sometime between 1517 and 1525, making it the first book printed in Belarus or anywhere in Eastern Europe. The modern era of Belarusian literature began in the late 19th century; one prominent writer was Yanka Kupala. Many Belarusian writers of the time, such as Uładzimir Žyłka, Kazimir Svayak, Yakub Kolas, Źmitrok Biadula, and Maksim Haretski, wrote for "Nasha Niva", a Belarusian-language paper published that was previously published in Vilnius but now is published in Minsk. After Belarus was incorporated into the Soviet Union, the Soviet government took control of the Republic's cultural affairs. At first, a policy of "Belarusianization" was followed in the newly formed Byelorussian SSR. This policy was reversed in the 1930s, and the majority of prominent Belarusian intellectuals and nationalist advocates were either exiled or killed in Stalinist purges. The free development of literature occurred only The traditional Belarusian dress originates from the Kievan Rus' period. Due to the cool climate, clothes were designed to preserve body heat and were usually made from flax or wool. They were Belarusian cuisine consists mainly of vegetables, meat (particularly pork), and bread. Foods are usually either slowly cooked or stewed. Typically, Belarusians eat a light breakfast and two hearty meals Belarus has competed in the Olympic Games since the 1994 Winter Olympics. Its National Olympic Committee has been headed by President Lukashenko since 1997. Receiving heavy sponsorship from the government, ice hockey is the nation's second most popular sport after football. The national football team has never qualified for a major tournament; however, BATE Borisov has played in the Champions League. The national hockey team finished fourth at the 2002 Salt Lake City Olympics following a memorable upset win over Sweden in the quarterfinals, and regularly competes in the World Championships, often making the quarterfinals. Numerous Belarusian players are present in the Kontinental Hockey League in Eurasia, particularly for Belarusian club HC Dinamo Minsk, and several have also played in the National The state telecom monopoly, Beltelecom, holds the exclusive interconnection with Internet providers outside of Belarus. Beltelecom owns all the backbone Belarus has four UNESCO-designated World Heritage Sites: the Mir Castle Complex, the In May 2020 it was reported that the country had one of Europe's highest per capita infection rates in the COVID-19 pandemic. President Lukashenko, campaigning for the August presidential election, had repeatedly

Belarus (;, ), officially the Republic of Belarus (, ), formerly known by its Russian name Byelorussia or Belorussia (), is a landlocked country in Eastern Europe. It is bordered by Russia to the northeast, Ukraine to the south, Poland to the west, and Lithuania and Latvia to the northwest. Its capital and most populous city is Minsk. Over 40% of its is forested. Its major economic sectors are service industries and manufacturing. Until the 20th century, different states at various times controlled the lands of modern-day Belarus, including the Principality of Polotsk (11th to 14th centuries), the Grand Duchy of Lithuania, the Polish–Lithuanian Commonwealth, and the Russian Empire.

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summarize: Many physical processes are Temperature scales differ in two ways: the point chosen as zero degrees, and the magnitudes of incremental units or degrees on the scale. The Celsius scale (°C) is used for common temperature measurements in most of the world. It is an empirical scale that was developed by a historical progress, which led to its zero point being defined by the freezing point of water, and additional degrees defined so that was the boiling point of water, both at sea-level atmospheric pressure. Because At the absolute zero of temperature, no more energy can be removed from matter as heat, a fact expressed in the third law of thermodynamics. At this temperature, matter contains no macroscopic thermal energy, but still has quantum-mechanical zero-point energy as predicted by the uncertainty principle. Referring to the Boltzmann constant, to the Maxwell–Boltzmann distribution, and to the Boltzmann statistical mechanical definition of entropy, as distinct from the Gibbs definition, for independently moving microscopic particles, disregarding interparticle potential energy, by international agreement, a temperature scale is defined and said to be absolute because it is independent of the characteristics of particular thermometric substances and thermometer mechanisms. Apart from the absolute zero, it does not have a reference temperature. It is known as the Kelvin scale, widely used in science and technology. The kelvin (the word is spelled with a lower-case Many scientific measurements use the Kelvin temperature scale (unit symbol: K), named in honor of the physicist who first defined it. It is an absolute scale. Its numerical zero point,, is at the absolute zero of temperature. Since May, Since May 2019, the magnitude of the kelvin is defined in relation to microscopic phenomena, characterized in terms of statistical mechanics. Previously, since 1954, the International System of Units defined a scale and unit for the kelvin as a thermodynamic temperature, by There is a variety of kinds of temperature scale. It may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century. Empirically based temperature scales rely directly on measurements of simple macroscopic physical properties of materials. For example, the length of a column of mercury, confined in a glass-walled capillary tube, is dependent largely on temperature, and is the basis of the very useful mercury-in-glass thermometer. Such scales are valid only within convenient ranges of temperature. For example, above the boiling point of mercury, a mercury-in-glass thermometer is impracticable. Most materials expand with temperature increase, but some materials, such Theoretically based temperature scales are based directly on theoretical arguments, especially those of kinetic theory and thermodynamics. They are more or less ideally realised in practically feasible physical devices and materials. Theoretically based temperature scales are used to provide calibrating standards for practical empirically based thermometers. In physics, the internationally agreed conventional temperature scale is called the Kelvin scale. It is calibrated through the internationally agreed and prescribed value of the Boltzmann constant, referring to motions of microscopic particles, such as atoms, molecules, and electrons, constituent in the body whose temperature is to be measured. In contrast with the thermodynamic temperature scale invented by Kelvin, the presently conventional Kelvin temperature is not defined through comparison with the temperature of a reference state of a standard body, nor in terms of macroscopic thermodynamics. Apart from the absolute zero Historically, till May 2019, the definition of the Kelvin scale was that invented by Kelvin, based on a ratio of quantities of energy in processes in an ideal Carnot engine, entirely in terms of macroscopic thermodynamics. That Carnot engine was to work between two temperatures, that of the body A material on which a macroscopically defined temperature scale may be based is the ideal gas. The pressure exerted by a fixed volume and mass of an ideal gas is directly proportional to its temperature. Some natural gases show so nearly ideal properties over suitable temperature ranges that they can be used for thermometry; this was important during the development of thermodynamics and is still of practical importance today. The ideal gas thermometer is, however, not theoretically perfect for thermodynamics. This is because the entropy of an ideal gas at its absolute zero of temperature is not a positive semi-definite quantity, which puts the gas in violation of the third law of thermodynamics. In contrast to real materials, the ideal gas does not liquefy or solidify, no matter how cold it is. Alternatively thinking, the ideal gas law, refers to the limit of infinitely high temperature and zero pressure; these conditions guarantee non-interactive motions of the constituent molecules. The magnitude of the kelvin is now defined in terms of kinetic theory, derived from the value of Boltzmann's constant. Kinetic theory provides a microscopic account of temperature for some bodies of material, especially gases, based on macroscopic systems' being composed of many microscopic particles, such as molecules and ions of various species, the particles of a species being all alike. It explains macroscopic phenomena through the classical mechanics of the microscopic particles. The equipartition theorem of kinetic theory asserts that each classical degree of freedom of a freely moving particle has an average kinetic energy of where denotes Boltzmann's constant. The translational motion of the particle has three degrees of freedom, so that, except at very low temperatures where quantum effects predominate, the average translational kinetic energy of a freely moving particle in a system with temperature will be. Molecules, such as oxygen (O), have more degrees of freedom than Temperature is one of the principal quantities in the study of thermodynamics. Formerly, the magnitude of the kelvin was defined in thermodynamic terms, but nowadays, as mentioned above, it is defined in terms of kinetic theory. The thermodynamic temperature is said to be absolute for two reasons. One is that its formal character is independent of the properties of particular materials. The other reason is that its zero is, in a sense, absolute, in that it indicates absence of microscopic classical motion of the constituent particles of matter, so that they have a limiting specific heat of zero for zero temperature, according to the third law of thermodynamics. Nevertheless, a thermodynamic temperature does in fact have a definite numerical value that has been arbitrarily chosen by tradition and is dependent on the property of a particular materials; it is simply less arbitrary than relative "degrees" scales such as Celsius and Fahrenheit. Being an absolute scale with one fixed point (zero), there is only one degree of freedom left to arbitrary choice, rather than two as in relative scales. For the Kelvin scale since May 2019, by international convention, the choice has been made to use knowledge of modes of operation of various thermometric devices, relying on microscopic kinetic theories about molecular motion. The numerical scale is settled by a conventional definition of the value of the Boltzmann constant, which relates macroscopic temperature to average microscopic kinetic energy of particles such as molecules. Its numerical value is arbitrary, and an alternate, less widely used absolute temperature scale exists called the Rankine scale, made to be aligned with the Fahrenheit scale as Kelvin is with Celsius. The thermodynamic definition of temperature is due to Kelvin. It is framed in terms of an idealized device called a Carnot engine, imagined to run in a fictive continuous cycle of successive processes that traverse a cycle of states of its working body. The engine takes in a quantity of heat from a hot reservoir and passes out a lesser quantity of heat to a cold reservoir. The difference in energy is passed, as thermodynamic work, to a work reservoir, and is considered to be the output of the engine. The cycle is imagined to run so slowly that at each point of the cycle the working body is in a state of thermodynamic equilibrium. The successive processes the cycle are thus imagined to run reversibly with no entropy production. Then the quantity of entropy taken in from the hot reservoir when the working body is heated is equal to that passed to the cold reservoir when the working body is cooled. Then the absolute or thermodynamic temperatures, and, of the reservoirs are defined so that to be such that The zeroth law of thermodynamics allows this definition to be used to measure the absolute or thermodynamic temperature of an arbitrary body of interest, by making the other heat reservoir have the same temperature as the body of interest. Kelvin's original work postulating absolute temperature was published in 1848. It was based on the work of Carnot, before the formulation of the first law of thermodynamics. Carnot had no sound understanding of heat, and no specific concept of entropy. He wrote of 'caloric', and said that all the caloric that passed from the hot reservoir was passed into the cold reservoir. Kelvin wrote in his 1848 paper that his scale was absolute in the sense that it was defined "independently of the properties of any particular kind of matter". His definitive publication, which sets out the definition just stated, was printed in 1853, a paper read in 1851. Numerical details were formerly settled by making one of the heat reservoirs a cell at the triple point of water, which was defined to have an absolute temperature of 273.16 K. Nowadays, the numerical value is instead obtained from measurement through the microscopic statistical mechanical international definition, as above. Temperature is a measure of a quality of a state of a material. The quality may be regarded as a more abstract entity than any particular temperature scale that measures it, and is called "hotness" by some writers. The quality of hotness refers to the state of material only in a particular locality, and in general, apart from bodies held in a steady state of thermodynamic equilibrium, hotness varies from place to place. It is not necessarily the case that a material in a particular place is in a state that is steady and nearly homogeneous enough to allow it to have a well-defined hotness or temperature. Hotness may be represented abstractly as a one-dimensional manifold. Every valid temperature scale has its own one-to-one map into the hotness manifold. When two systems in thermal contact are at the same temperature no heat transfers between them. When a temperature difference does exist heat flows spontaneously from the warmer system to the colder system until they are in thermal equilibrium. Such heat transfer occurs by conduction or by thermal radiation. Experimental physicists, for example Galileo and Newton, found that there are indefinitely many empirical temperature scales. Nevertheless, the zeroth law of thermodynamics says that they all measure the same quality. This means that for a body in its own state of internal thermodynamic equilibrium, every correctly calibrated thermometer, of whatever kind, that measures the temperature of the body, records one and the same temperature. For a body that is not in its own state of internal thermodynamic equilibrium, different thermometers can record different temperatures, depending respectively on the mechanisms of operation of the thermometers. For experimental physics, hotness means that, when comparing any two given bodies in their respective separate thermodynamic equilibria, any two suitably given empirical thermometers with numerical scale readings will agree as to which is the hotter of the two given bodies, or that they have the same temperature. This does not require the two thermometers to have a linear relation between their numerical scale readings, but it does require that the relation between their numerical readings shall be strictly monotonic. A definite sense of greater hotness can be had, independently of calorimetry, of thermodynamics, and of properties of particular materials, from Wien's displacement law of thermal radiation: the temperature of a bath of thermal While for bodies in their own thermodynamic equilibrium states, the notion of temperature requires that all empirical thermometers must agree as to which of two bodies is the hotter or that they are at the same temperature, this requirement is not safe for bodies that are in steady states though When a body is not in a steady state, then the notion of temperature becomes even For axiomatic treatment of thermodynamic equilibrium, since the 1930s, it has become customary to refer to a zeroth law of thermodynamics. The customarily stated minimalist version of such a law postulates only that all bodies, which when thermally connected would be in thermal equilibrium, should be said to have the same temperature by definition, but by itself does not establish temperature as a quantity expressed as a real number on a scale. A more physically informative version of such a law views empirical temperature as a chart When an energy transfer to or from a body is only as heat, the state of the body changes. Depending on the surroundings and the walls separating them from the body, various changes are possible in the body. They include chemical reactions, increase of pressure, increase of temperature, and phase change. For each kind of change under specified conditions, the heat capacity is the ratio of the quantity of heat transferred to the magnitude of Temperature measurement using modern scientific thermometers and temperature scales goes back at least as far as the early 18th century, when Gabriel Fahrenheit adapted a thermometer (switching to mercury) and a scale both developed by Ole Christensen Rømer. Fahrenheit's scale is still in use in the United States for non-scientific applications. Temperature is measured with thermometers that may be calibrated to a variety of temperature scales. In most of the world (except for Belize, Myanmar, Liberia and the United States), the Celsius scale is used for most temperature measuring purposes. Most scientists measure temperature using the Celsius scale and thermodynamic temperature using the Kelvin scale, which is the Celsius scale offset so that its null point is =, or absolute zero. Many engineering fields in the US, notably high-tech and US federal specifications (civil and military), also use the Kelvin and Celsius scales. Other engineering fields in the US also rely upon the Rankine scale (a shifted Fahrenheit scale) when working in thermodynamic-related disciplines such as combustion. The basic unit of temperature in the International System of Units (SI) is the Kelvin. It has the symbol K. For everyday applications, it is often convenient to use the Celsius scale, in which corresponds very closely to the freezing point of water and is its boiling point at sea level. Because liquid droplets commonly exist in clouds at sub-zero temperatures, is better defined as the melting point of ice. In this scale a temperature difference of 1 degree Celsius is the same as a increment, but the scale is offset by the temperature at which ice melts (). By international agreement, until May 2019, the Kelvin and Celsius scales were defined by two fixing points: absolute zero and the triple point of Vienna Standard Mean Ocean Water, which is water specially prepared with a specified blend of The following table shows the temperature The field of plasma physics deals with phenomena of electromagnetic nature that involve very high temperatures. It is customary to express temperature as energy in units of electronvolts (eV) or kiloelectronvolts (keV). The energy, which has a different dimension from temperature, is then calculated as the product of the Boltzmann constant and temperature, formula_2. Then, 1eV corresponds to. In the study of QCD matter one routinely encounters temperatures of the order of a few hundred MeV, equivalent to about. Historically, there are several scientific approaches to the explanation of temperature: the classical thermodynamic description based on macroscopic empirical variables that can be measured in a laboratory; the kinetic theory of gases which relates the macroscopic description to the probability distribution of the energy of motion of gas particles; and a microscopic explanation based on statistical physics and quantum mechanics. In addition, rigorous and purely mathematical treatments have provided an axiomatic approach to classical thermodynamics and temperature. Statistical physics provides a deeper understanding by describing the atomic behavior of matter, and derives macroscopic properties from statistical averages of microscopic states, including both classical and quantum states. In the fundamental physical description, using natural units, temperature may be measured directly in units of energy. However, in the practical systems of measurement for science, technology, and commerce, such as the modern metric system of units, the macroscopic and the microscopic descriptions are interrelated by the Boltzmann constant, a proportionality factor that scales temperature to the microscopic mean kinetic energy. The microscopic description in statistical mechanics is based on a model that analyzes a system into its fundamental particles of matter or into a set of classical or quantum-mechanical oscillators and considers the system as a statistical ensemble of microstates. As a collection of classical material particles, temperature is a measure of the mean energy of motion, called kinetic energy, of the particles, whether in solids, liquids, gases, or plasmas. The kinetic energy, a concept of classical mechanics, is half the mass of a particle times its speed squared. In this mechanical interpretation of thermal motion, the kinetic energies of material particles may reside in the velocity of the particles of their translational or vibrational motion or in the inertia of their rotational modes. In monatomic perfect gases and, approximately, in most gases, temperature is a measure of the mean particle kinetic energy. It also determines the probability distribution function of the energy. In condensed matter, and particularly in solids, this purely mechanical description is often less useful and the oscillator model provides a better description to account for quantum mechanical phenomena. Temperature determines the statistical occupation of the microstates of the ensemble. The microscopic definition of temperature is only meaningful in the thermodynamic limit, meaning for large ensembles of states or particles, to fulfill the requirements of the statistical model. The kinetic energy is also considered as a component of thermal energy. The thermal energy may be partitioned into independent components attributed to the degrees of freedom of the particles or to the modes of oscillators in a thermodynamic system. In general, the number of these degrees of freedom that are available for the equipartitioning of energy depends on the temperature, i.e. the energy region of the interactions under consideration. For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas, the kinetic energy is found exclusively in the purely translational motions of the particles. In other systems, vibrational and rotational motions also contribute degrees of freedom. Maxwell and Boltzmann developed a kinetic theory that yields a fundamental understanding of temperature in gases. This theory also explains the ideal gas law and the observed heat capacity of monatomic (or 'noble') gases. The ideal gas law is based on observed empirical relationships between pressure ("p"), volume ("V"), and temperature ("T"), and was recognized long before the kinetic theory of gases was developed (see Boyle's and Charles's laws). The ideal gas law states: where "n" is the number of moles of gas and is the gas constant. This relationship gives us our first hint that there is an absolute zero on the temperature scale, because it only holds if the temperature is measured on an absolute scale such as Kelvin's. The ideal gas law allows one to measure temperature on this absolute scale using the gas thermometer. The temperature in kelvins can be defined as the pressure in pascals of one mole of gas in a container When two otherwise isolated bodies are connected together by a rigid physical path impermeable to matter, there is spontaneous transfer of energy as heat from the hotter to the colder of them. Eventually, they reach a state of mutual thermal equilibrium, in which heat transfer has ceased, and the bodies' respective state variables have settled to become unchanging. One statement of the zeroth law of thermodynamics is that if two systems are each in thermal equilibrium with a third system, then they are also in thermal equilibrium with each other. This statement As an alternative to considering or defining the zeroth law of thermodynamics, it was the historical development in thermodynamics to define temperature in terms of the second law of thermodynamics which deals with entropy. The second law states that any process will result in either no change or a net increase in the entropy of the universe. This can be understood in terms of probability. For example, in a series of coin tosses, a perfectly ordered system would be one in which either every toss comes up heads or every toss comes up tails. This means the outcome is always 100% the same result. In contrast, many mixed ("disordered") outcomes are possible, and their number increases with each toss. Eventually, the combinations of ~50% heads and ~50% tails dominate and obtaining an outcome significantly different from 50/50 becomes increasingly unlikely. Thus the system naturally progresses to a state of maximum disorder or entropy. As temperature governs the transfer of heat between two systems and the universe tends to progress toward a maximum of entropy, it is expected that there is some relationship between temperature and entropy. A heat engine is a device for converting thermal energy into mechanical energy, resulting in the performance of work. and analysis of the Carnot heat engine provides the necessary relationships. The work from a heat engine corresponds to the difference between the heat put into the system at high temperature, "q" and the heat extracted at the Statistical mechanics defines temperature based on a system's fundamental degrees of freedom. Eq.(10) It is possible to extend the definition of temperature even to systems of few particles, like in a quantum dot. The generalized temperature is obtained by considering time ensembles instead of configuration-space ensembles given in statistical mechanics in the case of thermal and particle exchange between On the empirical temperature scales that are not referenced to absolute zero, a negative temperature is one below the zero-point of the scale used. For example, dry ice has a sublimation temperature of which is equivalent to. On the absolute kelvin scale this temperature is. No body can be brought to exactly (the temperature of the ideally coldest possible body) by any finite practicable process; this is a consequence of the third law of thermodynamics. The international kinetic theory temperature of a body cannot take negative values. The thermodynamic temperature scale, however, is not so constrained. For a body of matter, there can sometimes be conceptually defined, in terms of microscopic degrees of freedom, namely particle spins, a subsystem, with a temperature other than that of the whole body. When the body is in its own state of internal thermodynamic equilibrium, the temperatures of the whole body and of the subsystem must be

Temperature is a physical property of matter that quantitatively expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, when a body is in contact with another that is colder.

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summarize: The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles (objects with negligible size). The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it. Each of these parameters is discussed in turn. In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of "very" small particles, such as the electron, is more accurately described by quantum mechanics.) Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom, e.g., a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made of a large number of collectively acting point particles. The center of mass of a composite object behaves like a point particle. Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as location in space and speed. Non-relativistic mechanics also assumes that forces act instantaneously (see also Action at a distance). The "position" of a point particle is defined in relation to a coordinate system centered on an arbitrary fixed reference point in space called the origin "O". A simple coordinate system might describe the position of a particle "P" with a vector notated by an arrow labeled r that points from the origin "O" to point "P". In general, the point particle does not need to be stationary relative to "O". In cases where "P" is moving relative to "O", r is defined as a function of "t", time. In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval that is observed to elapse between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space. The "velocity", or the rate of change of position with time, is defined as the derivative of the position with respect to time: In classical mechanics, velocities are directly additive and subtractive. For example, if one car travels east at 60 km/h and passes another car traveling in the same direction at 50 km/h, the slower car perceives the faster car as traveling east at. However, from the perspective of the faster car, the slower car is moving 10 km/h to the west, often denoted as -10 km/h where the sign implies opposite direction. Velocities are directly additive as ; they must be dealt with using vector analysis. Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector and the velocity of the second object by the vector, where "u" is the speed of the first object, "v" is the speed of the second object, and d and e are unit vectors in the directions of motion of each object respectively, then the velocity of the first object as seen by the second object is Similarly, the first object sees the velocity of the second object as When both objects are moving in the same direction, this equation can be simplified to Or, by ignoring direction, the difference can be given in terms of speed only: The "acceleration", or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time): Acceleration represents the velocity's change over time. Velocity can change in either magnitude or direction, or both. Occasionally, a decrease in the magnitude of velocity ""v"" is referred to as "deceleration", but generally any change in the velocity over time, including deceleration, is simply referred to as acceleration. While the position, velocity and acceleration of a particle can be described with respect to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames. An inertial frame is an idealized frame of reference within which an object has no external force acting upon it. Because there is no external force acting upon it, the object has a constant velocity; that is, it is either at rest or moving uniformly in a straight line. A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that do not accelerate with respect to distant stars (an extremely distant point) are regarded as good approximations to inertial frames. Non-inertial reference frames accelerate in relation to an existing inertial frame. They form the basis for Einstein's relativity. Due to the relative motion, particles in the non-inertial frame appear to move in ways not explained by forces from existing fields in the reference frame. Hence, it appears that there are other forces that enter the equations of motion solely as a result of the relative acceleration. These forces are referred to as fictitious forces, inertia forces, or pseudo-forces. Consider two reference frames "S" and S'. For observers in each of the reference frames an event has space-time coordinates of ("x","y","z","t") in frame "S" and (x',y',z',t') in frame S'. Assuming time is measured the same in all reference frames, and if we require when, then the relation between the space-time coordinates of the same event observed from the reference frames S' and "S", which are moving at a relative velocity of "u" in the "x" direction is: This set of formulas defines a group transformation known as the Galilean transformation (informally, the "Galilean transform"). This group is a limiting case of the Poincaré group used in special relativity. The limiting case applies when the velocity "u" is very small compared to "c", the speed of light. The transformations have the following consequences: For some problems, it is convenient to use rotating coordinates (reference frames). Thereby one can either keep a mapping to a convenient inertial frame, or introduce additionally a fictitious centrifugal force and Coriolis force. A force in physics is any action which causes an object's velocity to change; that is, to accelerate. A force originates from within a field, such as an electro-static field (caused by static electrical charges), electro-magnetic field (caused by moving charges), or gravitational field (caused by mass), among others. Newton was the first to mathematically express the relationship between force and momentum. Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law": The quantity "m"v is called the (canonical) momentum. The net force on a particle is thus equal to the rate of change of the momentum of the particle with time. Since the definition of acceleration is, the second law can be written in the simplified and more familiar form: So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the "equation of motion". As an example, assume that friction is the only force acting on the particle, and that it may be modeled as a function of the velocity of the particle, for example: where "λ" is a positive constant, the negative sign states that the force is opposite the sense of the velocity. Then the equation of motion is This can be integrated to obtain where v is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. In this case, an equivalent viewpoint is that the kinetic energy of the particle is absorbed by friction (which converts it to heat energy in accordance with the conservation of energy), and the particle is slowing down. This expression can be further integrated to obtain the position r of the particle as a function of time. Important forces include the gravitational force and the Lorentz force for electromagnetism. In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle "A" exerts a force F on another particle "B", it follows that "B" must exert an equal and opposite "reaction force", −F, on "A". The strong form of Newton's third law requires that F and −F act along the line connecting "A" and "B", while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces. If a constant force F is applied to a particle that makes a displacement Δr, the "work done" by the force is defined as the scalar product of the force and displacement vectors: More generally, if the force varies as a function of position as the particle moves from r to r along a path "C", the work done on the particle is given by the line integral If the work done in moving the particle from r to r is the same no matter what path is taken, the force is said to be conservative. Gravity is a conservative force, as is the force due to an idealized spring, as given by Hooke's law. The force due to friction is non-conservative. The kinetic energy "E" of a particle of mass "m" travelling at speed "v" is given by For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles. The work–energy theorem states that for a particle of constant mass "m", the total work "W" done on the particle as it moves from position r to r is equal to the change in kinetic energy "E" of the particle: Conservative forces can be expressed as the gradient of a scalar function, known as the potential energy and denoted "E": If all the forces acting on a particle are conservative, and "E" is the total potential energy (which is defined as a work of involved forces to rearrange mutual positions of bodies), obtained by summing the potential energies corresponding to each force The decrease in the potential energy is equal to the increase in the kinetic energy This result is known as "conservation of energy" and states that the total energy, is constant in time. It is often useful, because many commonly encountered forces are conservative. Classical mechanics also describes the more complex motions of extended non-pointlike objects. Euler's laws provide extensions to Newton's laws in this area. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. The rocket equation extends the notion of rate of change of an object's momentum to include the effects of an object "losing mass". There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics. These, and other modern formulations, usually bypass the concept of "force", instead referring to other physical quantities, such as energy, speed and momentum, for describing mechanical systems in generalized coordinates. The expressions given above for momentum and kinetic energy are only valid when there is no significant electromagnetic contribution. In electromagnetism, Newton's second law for current-carrying wires breaks down unless one includes the electromagnetic field contribution to the momentum of the system as expressed by the Poynting vector divided by "c", where "c" is the speed of light in free space. Many branches of classical mechanics are simplifications or approximations of more accurate forms; two of the most accurate being general relativity and relativistic statistical mechanics. Geometric optics is an approximation to the quantum theory of light, and does not have a superior "classical" form. When both quantum mechanics and classical mechanics cannot apply, such as at the quantum level with many degrees of freedom, quantum field theory (QFT) is of use. QFT deals with small distances and large speeds with many degrees of freedom as well as the possibility of any change in the number of particles throughout the interaction. When treating large degrees of freedom at the macroscopic level, statistical mechanics becomes useful. Statistical mechanics describes the behavior of large (but countable) numbers of particles and their interactions as a whole at the macroscopic level. Statistical mechanics is mainly used in thermodynamics for systems that lie outside the bounds of the assumptions of classical thermodynamics. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. In case that objects become extremely heavy (i.e. their Schwarzschild radius is not negligibly small for a given application), deviations from Newtonian mechanics become apparent and can be quantified by using the Parameterized post-Newtonian formalism. In that case, General relativity (GR) becomes applicable. However, until now there is no theory of Quantum gravity unifying GR and QFT in the sense that it could be used when objects become extremely small and heavy.[4] [5] In special relativity, the momentum of a particle is given by where "m" is the particle's rest mass, v its velocity, "v" is the modulus of v, and "c" is the speed of light. If "v" is very small compared to "c", "v"/"c" is approximately zero, and so Thus the Newtonian equation is an approximation of the relativistic equation for bodies moving with low speeds compared to the speed of light. For example, the relativistic cyclotron frequency of a cyclotron, gyrotron, or high voltage magnetron is given by where "f" is the classical frequency of an electron (or other charged particle) with kinetic energy "T" and (rest) mass "m" circling in a magnetic field. The (rest) mass of an electron is 511 keV. So the frequency correction is 1% for a magnetic vacuum tube with a 5.11 kV direct current accelerating voltage. The ray approximation of classical mechanics breaks down when the de Broglie wavelength is not much smaller than other dimensions of the system. For non-relativistic particles, this wavelength is where "h" is Planck's constant and "p" is the momentum. Again, this happens with electrons before it happens with heavier particles. For example, the electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 V, had a wavelength of 0.167 nm, which was long enough to exhibit a single diffraction side lobe when reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With a larger vacuum chamber, it would seem relatively easy to increase the angular resolution from around a radian to a milliradian and see quantum diffraction from the periodic patterns of integrated circuit computer memory. More practical examples of the failure of classical mechanics on an engineering scale are conduction by quantum tunneling in tunnel diodes and very narrow transistor gates in integrated circuits. Classical mechanics is the same extreme high frequency approximation as geometric optics. It is more often accurate because it describes particles and bodies with rest mass. These have more momentum and therefore shorter De Broglie wavelengths than massless particles, such as light, with the same kinetic energies. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology, Some Greek philosophers of antiquity, among them Aristotle, founder of Aristotelian physics, may have been the first to maintain the idea that "everything happens for a reason" and that theoretical principles can assist in the understanding of nature. While to a modern reader, many of these preserved ideas come forth as eminently reasonable, there is a conspicuous lack of both mathematical theory and controlled experiment, as we know it. These later became decisive factors in forming modern science, and their early application came to be known as classical mechanics. In his "Elementa super demonstrationem ponderum", medieval mathematician Jordanus de Nemore introduced the concept of "positional gravity" and the use of component forces. The first published causal explanation of the motions of planets was Johannes Kepler's "Astronomia nova," published in 1609. He concluded, based on Tycho Brahe's observations on the orbit of Mars, that the planet's orbits were ellipses. This break with ancient thought was happening around the same time that Galileo was proposing abstract mathematical laws for the motion of objects. He may (or may not) have performed the famous experiment of dropping two cannonballs of different weights from the tower of Pisa, showing that they both hit the ground at the same time. The reality of that particular experiment is disputed, but he did carry out quantitative experiments by rolling balls on an inclined plane. His theory of accelerated motion was derived from the results of such experiments and forms a cornerstone of classical mechanics. Newton founded his principles of natural philosophy on three proposed laws of motion: the law of inertia, his second law of acceleration (mentioned above), and the law of action and reaction; and hence laid the foundations for classical mechanics. Both Newton's second and third laws were given the proper scientific and mathematical treatment in Newton's "Philosophiæ Naturalis Principia Mathematica." Here they are distinguished from earlier attempts at explaining similar phenomena, which were either incomplete, incorrect, or given little accurate mathematical expression. Newton also enunciated the principles of conservation of momentum and angular momentum. In mechanics, Newton was also the first to provide the first correct scientific and mathematical formulation of gravity in Newton's law of universal gravitation. The combination of Newton's laws of motion and gravitation provide the fullest and most accurate description of classical mechanics. He demonstrated that these laws apply to everyday objects as well as to celestial objects. In particular, he obtained a theoretical explanation of Kepler's laws of motion of the planets. Newton had previously invented the calculus, of mathematics, and used it to perform the mathematical calculations. For acceptability, his book, the "Principia", was formulated entirely in terms of the long-established geometric methods, which were soon eclipsed by his calculus. However, it was Leibniz who developed the notation of the derivative and integral preferred today. Newton, and most of his contemporaries, with the notable exception of Huygens, worked on the assumption that classical mechanics would be able to explain all phenomena, including light, in the form of geometric optics. Even when discovering the so-called Newton's rings (a wave interference phenomenon) he maintained his own corpuscular theory of light. After Newton, classical mechanics became a principal field of study in mathematics as well as physics. Several re-formulations progressively allowed finding solutions to a far greater number of problems. The first notable re-formulation was in 1788 by Joseph Louis Lagrange. Lagrangian mechanics was in turn re-formulated in 1833 by William Rowan Hamilton. Some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. Some of these difficulties related to compatibility with electromagnetic theory, and the famous Michelson–Morley experiment. The resolution of these problems led to the special theory of relativity, often still considered a part of classical mechanics. A second set of difficulties were related to thermodynamics. When combined with thermodynamics, classical mechanics leads to the Gibbs paradox of classical statistical mechanics, in which entropy is not a well-defined quantity. Black-body radiation was not explained without the introduction of quanta. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the energy levels and sizes of atoms and the photo-electric effect. The effort at resolving these problems led to the development of quantum mechanics. Since the end of the 20th century, classical mechanics in physics has no longer been an independent theory. Instead, classical mechanics is now considered an approximate theory to the more general quantum mechanics. Emphasis has shifted to understanding the fundamental forces of nature as in the Standard model and its more modern extensions into a unified theory of everything. Classical mechanics is a theory useful for the study of the motion of non-quantum mechanical, low-energy particles in weak gravitational fields. Also, it has been extended into the complex domain where complex classical mechanics exhibits behaviors very similar to quantum mechanics. Classical mechanics was traditionally divided into three main branches: Another division is based on the choice of mathematical formalism: Alternatively, a division can be made by region of application:

Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.

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summarize: The Greeks, including Aristotle, Vitruvius, and Pliny the Elder, were interested in the cause and mitigation of friction. They were aware of differences between static and kinetic friction with Themistius stating in 350 that "it is easier to further the motion of a moving body than to move a body at rest". The classic laws of sliding friction were discovered by Leonardo da Vinci in 1493, a pioneer in tribology, but the laws documented in his notebooks, were not published and remained unknown. These laws were rediscovered by Guillaume Amontons in 1699 and became known as Amonton's three laws of dry friction "(below)". Amontons presented the nature of friction in terms of surface irregularities and the force required to raise the weight pressing the surfaces together. This view was further elaborated by Bernard Forest de Bélidor and Leonhard Euler (1750), who derived the angle of repose of a weight on an inclined plane and first distinguished between static and kinetic friction. John Theophilus Desaguliers (1734) first recognized the role of adhesion in friction. Microscopic forces cause surfaces to stick together; he proposed that friction was the force necessary to tear the adhering surfaces apart. The understanding of friction was further developed by Charles-Augustin de Coulomb (1785). Coulomb investigated the influence of four main factors on friction: the nature of the materials in contact and their surface coatings; the extent of the surface area; the normal pressure (or load); and the length of time that the surfaces remained in contact (time of repose). Coulomb further considered the influence of sliding velocity, temperature and humidity, in order to decide between the different explanations on the nature of friction that had been proposed. The distinction between static and dynamic friction is made in Coulomb's friction law (see below), although this distinction was already drawn by Johann Andreas von Segner in 1758. The effect of the time of repose was explained by Pieter van Musschenbroek (1762) by considering the surfaces of fibrous materials, with fibers meshing together, which takes a finite time in which the friction increases. John Leslie (1766–1832) noted a weakness in the views of Amontons and Coulomb: If friction arises from a weight being drawn up the inclined plane of successive asperities, why then isn't it balanced through descending the opposite slope? Leslie was equally skeptical about the role of adhesion proposed by Desaguliers, which should on the whole have the same tendency to accelerate as to retard the motion. In Leslie's view, friction should be seen as a time-dependent process of flattening, pressing down asperities, which creates new obstacles in what were cavities before. Arthur Jules Morin (1833) developed the concept of sliding versus rolling friction. Osborne Reynolds (1866) derived the equation of viscous flow. This completed the classic empirical model of friction (static, kinetic, and fluid) commonly used today in engineering. In 1877, Fleeming Jenkin and J. A. Ewing investigated the continuity between static and kinetic friction. The focus of research during the 20th century has been to understand the physical mechanisms behind friction. Frank Philip Bowden and David Tabor (1950) showed that, at a microscopic level, the actual area of contact between surfaces is a very small fraction of the apparent area. This actual area of contact, caused by asperities increases with pressure. The development of the atomic force microscope (ca. 1986) enabled scientists to study friction at the atomic scale, showing that, on that scale, dry friction is the product of the inter-surface shear stress and the contact area. These two discoveries explain Amonton's first law "(below)"; the macroscopic proportionality between normal force and static frictional force between dry surfaces. L.A. Sosnovskiy, S.S. Sherbakov and V.V. Komissarov showed that the friction force is proportional to both the contact and the volumetric (tensile-compression, bending, torsion, etc.) load, if the volumetric load causes cyclic stresses (±σ) in the contact area. The elementary property of sliding (kinetic) friction were discovered by experiment in the 15th to 18th centuries and were expressed as three empirical laws: Dry friction resists relative lateral motion of two solid surfaces in contact. The two regimes of dry friction are'static friction' ("stiction") between non-moving surfaces, and "kinetic friction" (sometimes called sliding friction or dynamic friction) between moving surfaces. Coulomb friction, named after Charles-Augustin de Coulomb, is an approximate model used to calculate the force of dry friction. It is governed by the model: where The Coulomb friction formula_2 may take any value from zero up to formula_6, and the direction of the frictional force against a surface is opposite to the motion that surface would experience in the absence of friction. Thus, in the static case, the frictional force is exactly what it must be in order to prevent motion between the surfaces; it balances the net force tending to cause such motion. In this case, rather than providing an estimate of the actual frictional force, the Coulomb approximation provides a threshold value for this force, above which motion would commence. This maximum force is known as traction. The force of friction is always exerted in a direction that opposes movement (for kinetic friction) or potential movement (for static friction) between the two surfaces. For example, a curling stone sliding along the ice experiences a kinetic force slowing it down. For an example of potential movement, the drive wheels of an accelerating car experience a frictional force pointing forward; if they did not, the wheels would spin, and the rubber would slide backwards along the pavement. Note that it is not the direction of movement of the vehicle they oppose, it is the direction of (potential) sliding between tire and road. The normal force is defined as the net force compressing two parallel surfaces together, and its direction is perpendicular to the surfaces. In the simple case of a mass resting on a horizontal surface, the only component of the normal force is the force due to gravity, where formula_7. In this case, the magnitude of the friction force is the product of the mass of the object, the acceleration due to gravity, and the coefficient of friction. However, the coefficient of friction is not a function of mass or volume; it depends only on the material. For instance, a large aluminum block has the same coefficient of friction as a small aluminum block. However, the magnitude of the friction force itself depends on the normal force, and hence on the mass of the block. If an object is on a level surface and the force tending to cause it to slide is horizontal, the normal force formula_8 between the object and the surface is just its weight, which is equal to its mass multiplied by the acceleration due to earth's gravity, "g". If the object is on a tilted surface such as an inclined plane, the normal force is less, because less of the force of gravity is perpendicular to the face of the plane. Therefore, the normal force, and ultimately the frictional force, is determined using vector analysis, usually via a free body diagram. Depending on the situation, the calculation of the normal force may include forces other than gravity. The coefficient of friction (COF), often symbolized by the Greek letter μ, is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together. The coefficient of friction depends on the materials used; for example, ice on steel has a low coefficient of friction, while rubber on pavement has a high coefficient of friction. Coefficients of friction range from near zero to greater than one. It is an axiom of the nature of friction between metal surfaces that it is greater between two surfaces of similar metals than between two surfaces of different metals— hence, brass will have a higher coefficient of friction when moved against brass, but less if moved against steel or aluminum. For surfaces at rest relative to each other formula_9, where formula_10 is the "coefficient of static friction". This is usually larger than its kinetic counterpart. The coefficient of static friction exhibited by a pair of contacting surfaces depends upon the combined effects of material deformation characteristics and surface roughness, both of which have their origins in the chemical bonding between atoms in each of the bulk materials and between the material surfaces and any adsorbed material. The fractality of surfaces, a parameter describing the scaling behavior of surface asperities, is known to play an important role in determining the magnitude of the static friction. For surfaces in relative motion formula_11, where formula_12 is the "coefficient of kinetic friction". The Coulomb friction is equal to formula_2, and the frictional force on each surface is exerted in the direction opposite to its motion relative to the other surface. Arthur Morin introduced the term and demonstrated the utility of the coefficient of friction. The coefficient of friction is an empirical measurement – it has to be measured experimentally, and cannot be found through calculations. Rougher surfaces tend to have higher effective values. Both static and kinetic coefficients of friction depend on the pair of surfaces in contact; for a given pair of surfaces, the coefficient of static friction is "usually" larger than that of kinetic friction; in some sets the two coefficients are equal, such as teflon-on-teflon. Most dry materials in combination have friction coefficient values between 0.3 and 0.6. Values outside this range are rarer, but teflon, for example, can have a coefficient as low as 0.04. A value of zero would mean no friction at all, an elusive property. Rubber in contact with other surfaces can yield friction coefficients from 1 to 2. Occasionally it is maintained that μ is always < 1, but this is not true. While in most relevant applications μ < 1, a value above 1 merely implies that the force required to slide an object along the surface is greater than the normal force of the surface on the object. For example, silicone rubber or acrylic rubber-coated surfaces have a coefficient of friction that can be substantially larger than 1. While it is often stated that the COF is a "material property," it is better categorized as a "system property." Unlike true material properties (such as conductivity, dielectric constant, yield strength), the COF for any two materials depends on system variables like temperature, velocity, atmosphere and also what are now popularly described as aging and deaging times; as well as on geometric properties of the interface between the materials, namely surface structure. For example, a copper pin sliding against a thick copper plate can have a COF that varies from 0.6 at low speeds (metal sliding against metal) to below 0.2 at high speeds when the copper surface begins to melt due to frictional heating. The latter speed, of course, does not determine the COF uniquely; if the pin diameter is increased so that the frictional heating is removed rapidly, the temperature drops, the pin remains solid and the COF rises to that of a 'low speed' test. Under certain conditions some materials have very low friction coefficients. An example is (highly ordered pyrolytic) graphite which can have a friction coefficient below 0.01. This ultralow-friction regime is called superlubricity. Static friction is friction between two or more solid objects that are not moving relative to each other. For example, static friction can prevent an object from sliding down a sloped surface. The coefficient of static friction, typically denoted as "μ", is usually higher than the coefficient of kinetic friction. Static friction is considered to arise as the result of surface roughness features across multiple length-scales at solid surfaces. These features, known as asperities are present down to nano-scale dimensions and result in true solid to solid contact existing only at a limited number of points accounting for only a fraction of the apparent or nominal contact area. The linearity between applied load and true contact area, arising from asperity deformation, gives rise to the linearity between static frictional force and normal force, found for typical Amonton-Coulomb type friction. The static friction force must be overcome by an applied force before an object can move. The maximum possible friction force between two surfaces before sliding begins is the product of the coefficient of static friction and the normal force: formula_14. When there is no sliding occurring, the friction force can have any value from zero up to formula_15. Any force smaller than formula_15 attempting to slide one surface over the other is opposed by a frictional force of equal magnitude and opposite direction. Any force larger than formula_15 overcomes the force of static friction and causes sliding to occur. The instant sliding occurs, static friction is no longer applicable—the friction between the two surfaces is then called kinetic friction. An example of static friction is the force that prevents a car wheel from slipping as it rolls on the ground. Even though the wheel is in motion, the patch of the tire in contact with the ground is stationary relative to the ground, so it is static rather than kinetic friction. The maximum value of static friction, when motion is impending, is sometimes referred to as limiting friction, although this term is not used universally. Kinetic friction, also known as dynamic friction or sliding friction, occurs when two objects are moving relative to each other and rub together (like a sled on the ground). The coefficient of kinetic friction is typically denoted as "μ", and is usually less than the coefficient of static friction for the same materials. However, Richard Feynman comments that "with dry metals it is very hard to show any difference." The friction force between two surfaces after sliding begins is the product of the coefficient of kinetic friction and the normal force: formula_18. New models are beginning to show how kinetic friction can be greater than static friction. Kinetic friction is now understood, in many cases, to be primarily caused by chemical bonding between the surfaces, rather than interlocking asperities; however, in many other cases roughness effects are dominant, for example in rubber to road friction. Surface roughness and contact area affect kinetic friction for micro- and nano-scale objects where surface area forces dominate inertial forces. The origin of kinetic friction at nanoscale can be explained by thermodynamics. Upon sliding, new surface forms at the back of a sliding true contact, and existing surface disappears at the front of it. Since all surfaces involve the thermodynamic surface energy, work must be spent in creating the new surface, and energy is released as heat in removing the surface. Thus, a force is required to move the back of the contact, and frictional heat is released at the front. For certain applications, it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the "angle of friction" or "friction angle". It is defined as: where "θ" is the angle from horizontal and "μ" is the static coefficient of friction between the objects. This formula can also be used to calculate "μ" from empirical measurements of the friction angle. Determining the forces required to move atoms past each other is a challenge in designing nanomachines. In 2008 scientists for the first time were able to move a single atom across a surface, and measure the forces required. Using ultrahigh vacuum and nearly zero temperature (5o K), a modified atomic force microscope was used to drag a cobalt atom, and a carbon monoxide molecule, across surfaces of copper and platinum. The Coulomb approximation follows from the assumptions that: surfaces are in atomically close contact only over a small fraction of their overall area; that this contact area is proportional to the normal force (until saturation, which takes place when all area is in atomic contact); and that the frictional force is proportional to the applied normal force, independently of the contact area. The Coulomb approximation is fundamentally an empirical construct. It is a rule-of-thumb describing the approximate outcome of an extremely complicated physical interaction. The strength of the approximation is its simplicity and versatility. Though the relationship between normal force and frictional force is not exactly linear (and so the frictional force is not entirely independent of the contact area of the surfaces), the Coulomb approximation is an adequate representation of friction for the analysis of many physical systems. When the surfaces are conjoined, Coulomb friction becomes a very poor approximation (for example, adhesive tape resists sliding even when there is no normal force, or a negative normal force). In this case, the frictional force may depend strongly on the area of contact. Some drag racing tires are adhesive for this reason. However, despite the complexity of the fundamental physics behind friction, the relationships are accurate enough to be useful in many applications. , a single study has demonstrated the potential for an "effectively negative coefficient of friction in the low-load regime", meaning that a decrease in normal force leads to an increase in friction. This contradicts everyday experience in which an increase in normal force leads to an increase in friction. This was reported in the journal "Nature" in October 2012 and involved the friction encountered by an atomic force microscope stylus when dragged across a graphene sheet in the presence of graphene-adsorbed oxygen. Despite being a simplified model of friction, the Coulomb model is useful in many numerical simulation applications such as multibody systems and granular material. Even its most simple expression encapsulates the fundamental effects of sticking and sliding which are required in many applied cases, although specific algorithms have to be designed in order to efficiently numerically integrate mechanical systems with Coulomb friction and bilateral or unilateral contact. Some quite nonlinear effects, such as the so-called Painlevé paradoxes, may be encountered with Coulomb friction. Dry friction can induce several types of instabilities in mechanical systems which display a stable behaviour in the absence of friction. These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding, by material expansion due to heat generation during friction (the thermo-elastic instabilities), or by pure dynamic effects of sliding of two elastic materials (the Adams-Martins instabilities). The latter were originally discovered in 1995 by George G. Adams and João Arménio Correia Martins for smooth surfaces and were later found in periodic rough surfaces. In particular, friction-related dynamical instabilities are thought to be responsible for brake squeal and the'song' of a glass harp, phenomena which involve stick and slip, modelled as a drop of friction coefficient with velocity. A practically important case is the self-oscillation of the strings of bowed instruments such as the violin, cello, hurdy-gurdy, erhu, etc. A connection between dry friction and flutter instability in a simple mechanical system has been discovered, watch the movie for more details. Frictional instabilities can lead to the formation of new self-organized patterns (or "secondary structures") at the sliding interface, such as in-situ formed tribofilms which are utilized for the reduction of friction and wear in so-called self-lubricating materials. Fluid friction occurs between fluid layers that are moving relative to each other. This internal resistance to flow is named "viscosity". In everyday terms, the viscosity of a fluid is described as its "thickness". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. The less viscous the fluid, the greater its ease of deformation or movement. All real fluids (except superfluids) offer some resistance to shearing and therefore are viscous. For teaching and explanatory purposes it is helpful to use the concept of an inviscid fluid or an ideal fluid which offers no resistance to shearing and so is not viscous. Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. Lubrication is a technique employed to reduce wear of one or both surfaces in close proximity moving relative to each another by interposing a substance called a lubricant between the surfaces. In most cases the applied load is carried by pressure generated within the fluid due to the frictional viscous resistance to motion of the lubricating fluid between the surfaces. Adequate lubrication allows smooth continuous operation of equipment, with only mild wear, and without excessive stresses or seizures at bearings. When lubrication breaks down, metal or other components can rub destructively over each other, causing heat and possibly damage or failure. Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the area of the surface of the body that is in contact with the fluid. Skin friction follows the drag equation and rises with the square of the velocity. Skin friction is caused by viscous drag in the boundary layer around the object. There are two ways to decrease skin friction: the first is to shape the moving body so that smooth flow is possible, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as is practicable. Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation. Plastic deformation in solids is an irreversible change in the internal molecular structure of an object. This change may be due to either (or both) an applied force or a change in temperature. The change of an object's shape is called strain. The force causing it is called stress. Elastic deformation in solids is reversible change in the internal molecular structure of an object. Stress does not necessarily cause permanent change. As deformation occurs, internal forces oppose the applied force. If the applied stress is not too large these opposing forces may completely resist the applied force, allowing the object to assume a new equilibrium state and to return to its original shape when the force is removed. This is known as elastic deformation or elasticity. As a consequence of light pressure, Einstein in 1909 predicted the existence of "radiation friction" which would oppose the movement of matter. He wrote, “radiation will exert pressure on both sides of the plate. The forces of pressure exerted on the two sides are equal if the plate is at rest. However, if it is in motion, more radiation will be reflected on the surface that is ahead during the motion (front surface) than on the back surface. The backwardacting force of pressure exerted on the front surface is thus larger than the force of pressure acting on the back. Hence, as the resultant of the two forces, there remains a force that counteracts the motion of the plate and that increases with the velocity of the plate. We will call this resultant 'radiation friction' in brief.” Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. Typical values for the coefficient of rolling resistance are 0.001. One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products. Any wheel equipped with a brake is capable of generating a large retarding force, usually for the purpose of slowing and stopping a vehicle or piece of rotating machinery. Braking friction differs from rolling friction because the coefficient of friction for rolling friction is small whereas the coefficient of friction for braking friction is designed to be large by choice of materials for brake pads. Rubbing dissimilar materials against one another can cause a build-up of electrostatic charge, which can be hazardous if flammable gases or vapours are present. When the static build-up discharges, explosions can be caused by ignition of the flammable mixture. Belt friction is a physical property observed from the forces acting on a belt wrapped around a pulley, when one end is being pulled. The resulting tension, which acts on both ends of the belt, can be modeled by the belt friction equation. In practice, the theoretical tension acting on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a designer of such a rig to know how many times the belt or rope must be wrapped around the pulley to prevent it from slipping. Mountain climbers and sailing crews demonstrate a standard knowledge of belt friction when accomplishing basic tasks. Devices such as wheels, ball bearings, roller bearings, and air cushion or other types of fluid bearings can change sliding friction into a much smaller type of rolling friction. Many thermoplastic materials such as nylon, HDPE and PTFE are commonly used in low friction bearings. They are especially useful because the coefficient of friction falls with increasing imposed load. For improved wear resistance, very high molecular weight grades are usually specified for heavy duty or critical bearings. A common way to reduce friction is by using a lubricant, such as oil, water, or grease, which is placed between the two surfaces, often dramatically lessening the coefficient of friction. The science of friction and lubrication is called tribology. Lubricant technology is when lubricants are mixed with the application of science, especially to industrial or commercial objectives. Superlubricity, a recently discovered effect, has been observed in graphite: it is the substantial decrease of friction between two sliding objects, approaching zero levels. A very small amount of frictional energy would still be dissipated. Lubricants to overcome friction need not always be thin, turbulent fluids or powdery solids such as graphite and talc; acoustic lubrication actually uses sound as a lubricant. Another way to reduce friction between two parts is to superimpose micro-scale vibration to one of the parts. This can be sinusoidal vibration as used in ultrasound-assisted cutting or vibration noise, known as dither. According to the law of conservation of energy, no energy is destroyed due to friction, though it may be lost to the system of concern. Energy is transformed from other forms into thermal energy. A sliding hockey puck comes to rest because friction converts its kinetic energy into heat which raises the thermal energy of the puck and the ice surface. Since heat quickly dissipates, many early philosophers, including Aristotle, wrongly concluded that moving objects lose energy without a driving force. When an object is pushed along a surface along a path C, the energy converted to heat is given by a line integral, in accordance with the definition of work where Energy lost to a system as a result of friction is a classic example of thermodynamic irreversibility. In the reference frame of the interface between two surfaces, static friction does "no" work, because there is never displacement between the surfaces. In the same reference frame, kinetic friction is always in the direction opposite the motion, and does "negative" work. However, friction can do "positive" work in certain frames of reference. One can see this by placing a heavy box on a rug, then pulling on the rug quickly. In this case, the box slides backwards relative to the rug, but moves forward relative to the frame of reference in which the floor is stationary. Thus, the kinetic friction between the box and rug accelerates the box in the same direction that the box moves, doing "positive" work. The work done by friction can translate into deformation, wear, and heat that can affect the contact surface properties (even the coefficient of friction between the surfaces). This can be beneficial as in polishing. The work of friction is used to mix and join materials such as in the process of friction welding. Excessive erosion or wear of mating sliding surfaces occurs when work due to frictional forces rise to unacceptable levels. Harder corrosion particles caught between mating surfaces in relative motion (fretting) exacerbates wear of frictional forces. As surfaces are worn by work due to friction, fit and surface finish of an object may degrade until it no longer functions properly. For example, bearing seizure or failure may result from excessive wear due to work of friction. Friction is an important factor in many engineering disciplines.

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:

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summarize: Gastronomy involves discovering, tasting, experiencing, researching, understanding and writing about food preparation and the sensory qualities of human nutrition as a whole. It also studies how nutrition interfaces with the broader culture. The biological and chemical basis of cooking has become known as molecular gastronomy, while gastronomy covers a much broader, interdisciplinary ground. The culinary term appears for the first time in a title in a poem by Joseph Berchoux in 1801 entitled "Gastronomie" Pascal Ory, a French historian, defines gastronomy as the establishment of rules of eating and drinking, an "art of the table," and distinguishes it from good cooking (bonne cuisine) or fine cooking (haute cuisine). Ory traces the origins of gastronomy back to the French reign of Louis XIV when people took interest in developing rules to discriminate between good and bad style and extended their thinking to define good culinary taste. The lavish and sophisticated cuisine and practices of the French court became the culinary model for the French. Alexandre Grimod de La Reyniere wrote the first gastronomic work "Almanach des gourmands (1803)" elevating the status of food discourse to a disciplined level based on his views of French tradition and morals. Grimod aimed to reestablish order lost after the revolution and institute gastronomy as a serious subject in France. Grimod expanded gastronomic literature to the three forms of the genre: the guidebook, the gastronomic treatise, and the gourmet periodical. The invention of gastronomic literature coincided with important cultural transformations in France that increased the relevance of the subject. The end of nobility in France changed how people consumed food; fewer wealthy households employed cooks and the new bourgeoisie class wanted to assert their status by consuming elitist food. The emergence of the restaurant satisfied these social needs and provided good food available for popular consumption. The center of culinary excellence in France shifted from Versailles to Paris, a city with a competitive and innovative culinary culture. The culinary commentary of Grimod and other gastronomes influenced the tastes and expectations of consumers in an unprecedented manner as a third party to the consumer-chef interaction. The French origins of gastronomy explain the widespread use of French terminology in gastronomic literature. Gastronomic literature, Pascal Ory criticizes, is conceptually vague relying heavily on anecdotal evidence and using confusing, poorly defined terminology. Despite Ory’s criticism, gastronomy has grown from a marginalized subject in France to a serious and popular interest worldwide. The derivative "gourmet" has come into use since the publication of the book by Brillat-Savarin, "The Physiology of Taste". According to Brillat-Savarin, "Gastronomy is the knowledge and understanding of all that relates to man as he eats. Its purpose is to ensure the conservation of men, using the best food possible." Many writings on gastronomy throughout the world capture the thoughts and esthetics of a culture's cuisine during a period in their history. Some works continue to define or influence the contemporary gastronomic thought and cuisine of their respective cultures as listed below:

Gastronomy is the study of the relationship between food and culture, the art of preparing and serving rich or delicate and appetizing food, the cooking styles of particular regions, and the science of good eating. One who is well versed in gastronomy is called a gastronome, while a gastronomist is one who unites theory and practice in the study of gastronomy. Practical gastronomy is associated with the practice and study of the preparation, production, and service of the various foods and beverages, from countries around the world. Theoretical gastronomy supports practical gastronomy. It is related with a system and process approach, focused on recipes, techniques and cookery books. Food gastronomy is connected with food and beverages and their genesis. Technical gastronomy underpins practical gastronomy, introducing a rigorous approach to evaluation of gastronomic topics.

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summarize: The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in "Cartesian frame of reference". Sometimes the state of motion is emphasized, as in "rotating frame of reference". Sometimes the way it transforms to frames considered as related is emphasized as in "Galilean frame of reference". Sometimes frames are distinguished by the scale of their observations, as in "macroscopic" and "microscopic frames of reference". In this article, the term "observational frame of reference" is used when emphasis is upon the "state of motion" rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a "coordinate system" may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs "generalized coordinates", "normal modes" or "eigenvectors", which are only indirectly related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below: Here is a quotation applicable to moving observational frames formula_1 and various associated Euclidean three-space coordinate systems ["R", "R′", "etc."]: and this on the utility of separating the notions of formula_1 and ["R", "R′", "etc."]: and this, also on the distinction between formula_1 and ["R", "R′", "etc."]: and from J. D. Norton: The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani. Extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, and quantum gravity. Although the term "coordinate system" is often used (particularly by physicists) in a nontechnical sense, the term "coordinate system" does have a precise meaning in mathematics, and sometimes that is what the physicist means as well. A coordinate system in mathematics is a facet of geometry or of algebra, in particular, a property of manifolds (for example, in physics, configuration spaces or phase spaces). The coordinates of a point r in an "n"-dimensional space are simply an ordered set of "n" numbers: In a general Banach space, these numbers could be (for example) coefficients in a functional expansion like a Fourier series. In a physical problem, they could be spacetime coordinates or normal mode amplitudes. In a robot design, they could be angles of relative rotations, linear displacements, or deformations of joints. Here we will suppose these coordinates can be related to a Cartesian coordinate system by a set of functions: where "x", "y", "z", "etc." are the "n" Cartesian coordinates of the point. Given these functions, coordinate surfaces are defined by the relations: The intersection of these surfaces define coordinate lines. At any selected point, tangents to the intersecting coordinate lines at that point define a set of basis vectors {e, e,..., e} at that point. That is: which can be normalized to be of unit length. For more detail see curvilinear coordinates. Coordinate surfaces, coordinate lines, and basis vectors are components of a coordinate system. If the basis vectors are orthogonal at every point, the coordinate system is an orthogonal coordinate system. An important aspect of a coordinate system is its metric tensor "g", which determines the arc length "ds" in the coordinate system in terms of its coordinates: where repeated indices are summed over. As is apparent from these remarks, a coordinate system is a mathematical construct, part of an axiomatic system. There is no necessary connection between coordinate systems and physical motion (or any other aspect of reality). However, coordinate systems can include time as a coordinate, and can be used to describe motion. Thus, Lorentz transformations and Galilean transformations may be viewed as coordinate transformations. General and specific topics of coordinate systems can be pursued following the See also links below. An observational frame of reference, often referred to as a "physical frame of reference", a "frame of reference", or simply a "frame", is a physical concept related to an observer and the observer's state of motion. Here we adopt the view expressed by Kumar and Barve: an observational frame of reference is characterized "only by its state of motion". However, there is lack of unanimity on this point. In special relativity, the distinction is sometimes made between an "observer" and a "frame". According to this view, a "frame" is an "observer" plus a coordinate lattice constructed to be an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector. See Doran. This restricted view is not used here, and is not universally adopted even in discussions of relativity. In general relativity the use of general coordinate systems is common (see, for example, the Schwarzschild solution for the gravitational field outside an isolated sphere). There are two types of observational reference frame: inertial and non-inertial. An inertial frame of reference is defined as one in which all laws of physics take on their simplest form. In special relativity these frames are related by Lorentz transformations, which are parametrized by rapidity. In Newtonian mechanics, a more restricted definition requires only that Newton's first law holds true; that is, a Newtonian inertial frame is one in which a free particle travels in a straight line at constant speed, or is at rest. These frames are related by Galilean transformations. These relativistic and Newtonian transformations are expressed in spaces of general dimension in terms of representations of the Poincaré group and of the Galilean group. In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations. An example is an observational frame of reference centered at a point on the Earth's surface. This frame of reference orbits around the center of the Earth, which introduces the fictitious forces known as the Coriolis force, centrifugal force, and gravitational force. (All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall.) A further aspect of a frame of reference is the role of the measurement apparatus (for example, clocks and rods) attached to the frame (see Norton quote above). This question is not addressed in this article, and is of particular interest in quantum mechanics, where the relation between observer and measurement is still under discussion (see measurement problem). In physics experiments, the frame of reference in which the laboratory measurement devices are at rest is usually referred to as the laboratory frame or simply "lab frame." An example would be the frame in which the detectors for a particle accelerator are at rest. The lab frame in some experiments is an inertial frame, but it is not required to be (for example the laboratory on the surface of the Earth in many physics experiments is not inertial). In particle physics experiments, it is often useful to transform energies and momenta of particles from the lab frame where they are measured, to the center of momentum frame "COM frame" in which calculations are sometimes simplified, since potentially all kinetic energy still present in the COM frame may be used for making new particles. In this connection it may be noted that the clocks and rods often used to describe observers' measurement equipment in thought, in practice are replaced by a much more complicated and indirect metrology that is connected to the nature of the vacuum, and uses atomic clocks that operate according to the standard model and that must be corrected for gravitational time dilation. (See second, meter and kilogram). In fact, Einstein felt that clocks and rods were merely expedient measuring devices and they should be replaced by more fundamental entities based upon, for example, atoms and molecules. Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities. See Figure 1. At some particular moment, they are separated by 200 metres. The car in front is travelling at 22 metres per second and the car behind is travelling at 30 metres per second. If we want to find out how long it will take the second car to catch up with the first, there are three obvious "frames of reference" that we could choose. First, we could observe the two cars from the side of the road. We define our "frame of reference" "S" as follows. We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance apart. Since neither of the cars is accelerating, we can determine their positions by the following formulas, where formula_9 is the position in meters of car one after time "t" in seconds and formula_10 is the position of car two after time "t". Notice that these formulas predict at "t" = 0 s the first car is 200 m down the road and the second car is right beside us, as expected. We want to find the time at which formula_12. Therefore, we set formula_12 and solve for formula_14, that is: Alternatively, we could choose a frame of reference "S′" situated in the first car. In this case, the first car is stationary and the second car is approaching from behind at a speed of. In order to catch up to the first car, it will take a time of, that is, 25 seconds, as before. Note how much easier the problem becomes by choosing a suitable frame of reference. The third possible frame of reference would be attached to the second car. That example resembles the case just discussed, except the second car is stationary and the first car moves backward towards it at. It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily. It is also necessary to note that one is able to convert measurements made in one coordinate system to another. For example, suppose that your watch is running five minutes fast compared to the local standard time. If you know that this is the case, when somebody asks you what time it is, you are able to deduct five minutes from the time displayed on your watch in order to obtain the correct time. The measurements that an observer makes about a system depend therefore on the observer's frame of reference (you might say that the bus arrived at 5 past three, when in fact it arrived at three). For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving towards the right. However, for the person facing west, the car was moving toward the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system. For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the -axis and the direction in front of him as the positive -axis. To him, the car moves along the axis with some velocity in the positive -direction. Alfred's frame of reference is considered an inertial frame of reference because he is not accelerating (ignoring effects such as Earth's rotation and gravity). Now consider Betsy, the person driving the car. Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive -axis, and the direction in front of her as the positive -axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving – for instance, as she drives past Alfred, she observes him moving with velocity in the negative -direction. If she is driving north, then north is the positive -direction; if she turns east, east becomes the positive -direction. Finally, as an example of non-inertial observers, assume Candace is accelerating her car. As she passes by him, Alfred measures her acceleration and finds it to be in the negative -direction. Assuming Candace's acceleration is constant, what acceleration does Betsy measure? If Betsy's velocity is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same as Alfred in her frame of reference, in the negative -direction. However, if she is accelerating at rate in the negative -direction (in other words, slowing down), she will find Candace's acceleration to be in the negative -direction—a smaller value than Alfred has measured. Similarly, if she is accelerating at rate "A" in the positive -direction (speeding up), she will observe Candace's acceleration as in the negative -direction—a larger value than Alfred's measurement. Frames of reference are especially important in special relativity, because when a frame of reference is moving at some significant fraction of the speed of light, then the flow of time in that frame does not necessarily apply in another frame. The speed of light is considered to be the only true constant between moving frames of reference. It is important to note some assumptions made above about the various inertial frames of reference. Newton, for instance, employed universal time, as explained by the following example. Suppose that you own two clocks, which both tick at exactly the same rate. You synchronize them so that they both display exactly the same time. The two clocks are now separated and one clock is on a fast moving train, traveling at constant velocity towards the other. According to Newton, these two clocks will still tick at the same rate and will both show the same time. Newton says that the rate of time as measured in one frame of reference should be the same as the rate of time in another. That is, there exists a "universal" time and all other times in all other frames of reference will run at the same rate as this universal time irrespective of their position and velocity. This concept of time and simultaneity was later generalized by Einstein in his special theory of relativity (1905) where he developed transformations between inertial frames of reference based upon the universal nature of physical laws and their economy of expression (Lorentz transformations). The definition of inertial reference frame can also be extended beyond three-dimensional Euclidean space. Newton's assumed a Euclidean space, but general relativity uses a more general geometry. As an example of why this is important, consider the geometry of an ellipsoid. In this geometry, a "free" particle is defined as one at rest or traveling at constant speed on a geodesic path. Two free particles may begin at the same point on the surface, traveling with the same constant speed in different directions. After a length of time, the two particles collide at the opposite side of the ellipsoid. Both "free" particles traveled with a constant speed, satisfying the definition that no forces were acting. No acceleration occurred and so Newton's first law held true. This means that the particles were in inertial frames of reference. Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again. In a similar way, it is now common to describe that we exist in a four-dimensional geometry known as spacetime. In this picture, the curvature of this 4D space is responsible for the way in which two bodies with mass are drawn together even if no forces are acting. This curvature of spacetime replaces the force known as gravity in Newtonian mechanics and special relativity. Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below. An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g. "x′", "y′", "a′". The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R. Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called r, and the vector from the accelerated origin to the point is called r′. From the geometry of the situation, we get Taking the first and second derivatives of this with respect to time, we obtain where V and A are the velocity and acceleration of the accelerated system with respect to the inertial system and v and a are the velocity and acceleration of the point of interest with respect to the inertial frame. These equations allow transformations between the two coordinate systems; for example, we can now write Newton's second law as When there is accelerated motion due to a force being exerted there is manifestation of inertia. If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia. However, the manifestation of inertia does not prevent acceleration (or deceleration), for manifestation of inertia occurs in response to change in velocity due to a force. Seen from the perspective of a rotating frame of reference the manifestation of inertia appears to exert a force (either in centrifugal direction, or in a direction orthogonal to an object's motion, the Coriolis effect). A common sort of accelerated reference frame is a frame that is both rotating and translating (an example is a frame of reference attached to a CD which is playing while the player is carried). This arrangement leads to the equation (see Fictitious force for a derivation): or, to solve for the acceleration in the accelerated frame, Multiplying through by the mass "m" gives where

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements within that frame.

en

43

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summarize: The adjective "Cartesian" refers to the French mathematician and philosopher René Descartes, who published this idea in 1637. It was independently discovered by Pierre de Fermat, who also worked in three dimensions, although Fermat did not publish the discovery. The French cleric Nicole Oresme used constructions similar to Cartesian coordinates well before the time of Descartes and Fermat. Both Descartes and Fermat used a single axis in their treatments and have a variable length measured in reference to this axis. The concept of using a pair of axes was introduced later, after Descartes' "La Géométrie" was translated into Latin in 1649 by Frans van Schooten and his students. These commentators introduced several concepts while trying to clarify the ideas contained in Descartes' work. The development of the Cartesian coordinate system would play a fundamental role in the development of the calculus by Isaac Newton and Gottfried Wilhelm Leibniz. The two-coordinate description of the plane was later generalized into the concept of vector spaces. Many other coordinate systems have been developed since Descartes, such as the polar coordinates for the plane, and the spherical and cylindrical coordinates for three-dimensional space. Choosing a Cartesian coordinate system for a one-dimensional space—that is, for a straight line—involves choosing a point "O" of the line (the origin), a unit of length, and an orientation for the line. An orientation chooses which of the two half-lines determined by "O" is the positive, and which is negative; we then say that the line "is oriented" (or "points") from the negative half towards the positive half. Then each point "P" of the line can be specified by its distance from "O", taken with a + or − sign depending on which half-line contains "P". A line with a chosen Cartesian system is called a number line. Every real number has a unique location on the line. Conversely, every point on the line can be interpreted as a number in an ordered continuum such as the real numbers. A Cartesian coordinate system in two dimensions (also called a rectangular coordinate system or an orthogonal coordinate system) is defined by an ordered pair of perpendicular lines (axes), a single unit of length for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning each axis into a number line. For any point "P", a line is drawn through "P" perpendicular to each axis, and the position where it meets the axis is interpreted as a number. The two numbers, in that chosen order, are the "Cartesian coordinates" of "P". The reverse construction allows one to determine the point "P" given its coordinates. The first and second coordinates are called the "abscissa" and the "ordinate" of "P", respectively; and the point where the axes meet is called the "origin" of the coordinate system. The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in. Thus the origin has coordinates, and the points on the positive half-axes, one unit away from the origin, have coordinates and. In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards. (However, in some computer graphics contexts, the ordinate axis may be oriented downwards.) The origin is often labeled "O", and the two coordinates are often denoted by the letters "X" and "Y", or "x" and "y". The axes may then be referred to as the "X"-axis and "Y"-axis. The choices of letters come from the original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values. A Euclidean plane with a chosen Cartesian coordinate system is called a "Cartesian plane". In a Cartesian plane one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at and ), the unit hyperbola, and so on. The two axes divide the plane into four right angles, called "quadrants". The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the "first quadrant". If the coordinates of a point are, then its distances from the "X"-axis and from the "Y"-axis are |"y"| and |"x"|, respectively; where |...| denotes the absolute value of a number. A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines (the "axes") that go through a common point (the "origin"), and are pair-wise perpendicular; an orientation for each axis; and a single unit of length for all three axes. As in the two-dimensional case, each axis becomes a number line. For any point "P" of space, one considers a hyperplane through "P" perpendicular to each coordinate axis, and interprets the point where that hyperplane cuts the axis as a number. The Cartesian coordinates of "P" are those three numbers, in the chosen order. The reverse construction determines the point "P" given its three coordinates. Alternatively, each coordinate of a point "P" can be taken as the distance from "P" to the hyperplane defined by the other two axes, with the sign determined by the orientation of the corresponding axis. Each pair of axes defines a "coordinate hyperplane". These hyperplanes divide space into eight trihedra, called "octants". The octants are: | (+x,+y,+z) | (-x,+y,+z) | (+x,+y,-z) | (-x,+y,-z) | (+x,-y,+z) | (-x,-y,+z) | (+x,-y,-z) | (-x,-y,-z) | The coordinates are usually written as three numbers (or algebraic formulas) surrounded by parentheses and separated by commas, as in or. Thus, the origin has coordinates, and the unit points on the three axes are,, and. There are no standard names for the coordinates in the three axes (however, the terms "abscissa", "ordinate" and "applicate" are sometimes used). The coordinates are often denoted by the letters "X", "Y", and "Z", or "x", "y", and "z". The axes may then be referred to as the "X"-axis, "Y"-axis, and "Z"-axis, respectively. Then the coordinate hyperplanes can be referred to as the "XY"-plane, "YZ"-plane, and "XZ"-plane. In mathematics, physics, and engineering contexts, the first two axes are often defined or depicted as horizontal, with the third axis pointing up. In that case the third coordinate may be called "height" or "altitude". The orientation is usually chosen so that the 90 degree angle from the first axis to the second axis looks counter-clockwise when seen from the point ; a convention that is commonly called "the right hand rule". Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with pairs of real numbers; that is with the Cartesian product formula_1, where formula_2 is the set of all real numbers. In the same way, the points in any Euclidean space of dimension "n" be identified with the tuples (lists) of "n" real numbers, that is, with the Cartesian product formula_3. The concept of Cartesian coordinates generalizes to allow axes that are not perpendicular to each other, and/or different units along each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in general, to the hyperplane defined by all the other axes). In such an oblique coordinate system the computations of distances and angles must be modified from that in standard Cartesian systems, and many standard formulas (such as the Pythagorean formula for the distance) do not hold (see affine plane). The Cartesian coordinates of a point are usually written in parentheses and separated by commas, as in or. The origin is often labelled with the capital letter "O". In analytic geometry, unknown or generic coordinates are often denoted by the letters ("x", "y") in the plane, and ("x", "y", "z") in three-dimensional space. This custom comes from a convention of algebra, which uses letters near the end of the alphabet for unknown values (such as the coordinates of points in many geometric problems), and letters near the beginning for given quantities. These conventional names are often used in other domains, such as physics and engineering, although other letters may be used. For example, in a graph showing how a pressure varies with time, the graph coordinates may be denoted "p" and "t". Each axis is usually named after the coordinate which is measured along it; so one says the "x-axis", the "y-axis", the "t-axis", etc. Another common convention for coordinate naming is to use subscripts, as ("x", "x",..., "x") for the "n" coordinates in an "n"-dimensional space, especially when "n" is greater than 3 or unspecified. Some authors prefer the numbering ("x", "x",..., "x"). These notations are especially advantageous in computer programming: by storing the coordinates of a point as an array, instead of a record, the subscript can serve to index the coordinates. In mathematical illustrations of two-dimensional Cartesian systems, the first coordinate (traditionally called the abscissa) is measured along a horizontal axis, oriented from left to right. The second coordinate (the ordinate) is then measured along a vertical axis, usually oriented from bottom to top. Young children learning the Cartesian system, commonly learn the order to read the values before cementing the "x"-, "y"-, and "z"-axis concepts, by starting with 2D mnemonics (e.g. 'Walk along the hall then up the stairs' akin to straight across the "x"-axis then up vertically along the "y"-axis). Computer graphics and image processing, however, often use a coordinate system with the "y"-axis oriented downwards on the computer display. This convention developed in the 1960s (or earlier) from the way that images were originally stored in display buffers. For three-dimensional systems, a convention is to portray the "xy"-plane horizontally, with the "z"-axis added to represent height (positive up). Furthermore, there is a convention to orient the "x"-axis toward the viewer, biased either to the right or left. If a diagram (3D projection or 2D perspective drawing) shows the "x"- and "y"-axis horizontally and vertically, respectively, then the "z"-axis should be shown pointing "out of the page" towards the viewer or camera. In such a 2D diagram of a 3D coordinate system, the "z"-axis would appear as a line or ray pointing down and to the left or down and to the right, depending on the presumed viewer or camera perspective. In any diagram or display, the orientation of the three axes, as a whole, is arbitrary. However, the orientation of the axes relative to each other should always comply with the right-hand rule, unless specifically stated otherwise. All laws of physics and math assume this right-handedness, which ensures consistency. For 3D diagrams, the names "abscissa" and "ordinate" are rarely used for "x" and "y", respectively. When they are, the "z"-coordinate is sometimes called the applicate. The words "abscissa", "ordinate" and "applicate" are sometimes used to refer to coordinate axes rather than the coordinate values. The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called quadrants, each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by Roman numerals: I (where the signs of the two coordinates are I (+,+), II (−,+), III (−,−), and IV (+,−). When the axes are drawn according to the mathematical custom, the numbering goes counter-clockwise starting from the upper right ("north-east") quadrant. Similarly, a three-dimensional Cartesian system defines a division of space into eight regions or octants, according to the signs of the coordinates of the points. The convention used for naming a specific octant is to list its signs, e.g. or. The generalization of the quadrant and octant to an arbitrary number of dimensions is the orthant, and a similar naming system applies. The Euclidean distance between two points of the plane with Cartesian coordinates formula_4 and formula_5 is This is the Cartesian version of Pythagoras's theorem. In three-dimensional space, the distance between points formula_7 and formula_8 is which can be obtained by two consecutive applications of Pythagoras' theorem. The Euclidean transformations or Euclidean motions are the (bijective) mappings of points of the Euclidean plane to themselves which preserve distances between points. There are four types of these mappings (also called isometries): translations, rotations, reflections and glide reflections. Translating a set of points of the plane, preserving the distances and directions between them, is equivalent to adding a fixed pair of numbers to the Cartesian coordinates of every point in the set. That is, if the original coordinates of a point are, after the translation they will be To rotate a figure counterclockwise around the origin by some angle formula_11 is equivalent to replacing every point with coordinates ("x","y") by the point with coordinates ("x<nowiki>'</nowiki>","y<nowiki>'</nowiki>"), where Thus: formula_14 If are the Cartesian coordinates of a point, then are the coordinates of its reflection across the second coordinate axis (the y-axis), as if that line were a mirror. Likewise, are the coordinates of its reflection across the first coordinate axis (the x-axis). In more generality, reflection across a line through the origin making an angle formula_11 with the x-axis, is equivalent to replacing every point with coordinates by the point with coordinates, where Thus: formula_18 A glide reflection is the composition of a reflection across a line followed by a translation in the direction of that line. It can be seen that the order of these operations does not matter (the translation can come first, followed by the reflection). These Euclidean transformations of the plane can all be described in a uniform way by using matrices. The result formula_19 of applying a Euclidean transformation to a point formula_20 is given by the formula where "A" is a 2×2 orthogonal matrix and is an arbitrary ordered pair of numbers; that is, where To be "orthogonal", the matrix "A" must have orthogonal rows with same Euclidean length of one, that is, and This is equivalent to saying that "A" times its transpose must be the identity matrix. If these conditions do not hold, the formula describes a more general affine transformation of the plane provided that the determinant of "A" is not zero. The formula defines a translation if and only if "A" is the identity matrix. The transformation is a rotation around some point if and only if "A" is a rotation matrix, meaning that A reflection or glide reflection is obtained when, Assuming that translation is not used transformations can be combined by simply multiplying the associated transformation matrices. Another way to represent coordinate transformations in Cartesian coordinates is through affine transformations. In affine transformations an extra dimension is added and all points are given a value of 1 for this extra dimension. The advantage of doing this is that point translations can be specified in the final column of matrix "A". In this way, all of the euclidean transformations become transactable as matrix point multiplications. The affine transformation is given by: Using affine transformations multiple different euclidean transformations including translation can be combined by simply multiplying the corresponding matrices. An example of an affine transformation which is not a Euclidean motion is given by scaling. To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number "m". If are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates If "m" is greater than 1, the figure becomes larger; if "m" is between 0 and 1, it becomes smaller. A shearing transformation will push the top of a square sideways to form a parallelogram. Horizontal shearing is defined by: Shearing can also be applied vertically: Fixing or choosing the "x"-axis determines the "y"-axis up to direction. Namely, the "y"-axis is necessarily the perpendicular to the "x"-axis through the point marked 0 on the "x"-axis. But there is a choice of which of the two half lines on the perpendicular to designate as positive and which as negative. Each of these two choices determines a different orientation (also called "handedness") of the Cartesian plane. The usual way of orienting the plane, with the positive "x"-axis pointing right and the positive "y"-axis pointing up (and the "x"-axis being the "first" and the "y"-axis the "second" axis), is considered the "positive" or "standard" orientation, also called the "right-handed" orientation. A commonly used mnemonic for defining the positive orientation is the "right-hand rule". Placing a somewhat closed right hand on the plane with the thumb pointing up, the fingers point from the "x"-axis to the "y"-axis, in a positively oriented coordinate system. The other way of orienting the plane is following the "left hand rule", placing the left hand on the plane with the thumb pointing up. When pointing the thumb away from the origin along an axis towards positive, the curvature of the fingers indicates a positive rotation along that axis. Regardless of the rule used to orient the plane, rotating the coordinate system will preserve the orientation. Switching any two axes will reverse the orientation, but switching both will leave the orientation unchanged. Once the "x"- and "y"-axes are specified, they determine the line along which the "z"-axis should lie, but there are two possible orientation for this line. The two possible coordinate systems which result are called 'right-handed' and 'left-handed'. The standard orientation, where the "xy"-plane is horizontal and the "z"-axis points up (and the "x"- and the "y"-axis form a positively oriented two-dimensional coordinate system in the "xy"-plane if observed from "above" the "xy"-plane) is called right-handed or positive. The name derives from the right-hand rule. If the index finger of the right hand is pointed forward, the middle finger bent inward at a right angle to it, and the thumb placed at a right angle to both, the three fingers indicate the relative orientation of the "x"-, "y"-, and "z"-axes in a "right-handed" system. The thumb indicates the "x"-axis, the index finger the "y"-axis and the middle finger the "z"-axis. Conversely, if the same is done with the left hand, a left-handed system results. Figure 7 depicts a left and a right-handed coordinate system. Because a three-dimensional object is represented on the two-dimensional screen, distortion and ambiguity result. The axis pointing downward (and to the right) is also meant to point "towards" the observer, whereas the "middle"-axis is meant to point "away" from the observer. The red circle is "parallel" to the horizontal "xy"-plane and indicates rotation from the "x"-axis to the "y"-axis (in both cases). Hence the red arrow passes "in front of" the "z"-axis. Figure 8 is another attempt at depicting a right-handed coordinate system. Again, there is an ambiguity caused by projecting the three-dimensional coordinate system into the plane. Many observers see Figure 8 as "flipping in and out" between a convex cube and a concave "corner". This corresponds to the two possible orientations of the space. Seeing the figure as convex gives a left-handed coordinate system. Thus the "correct" way to view Figure 8 is to imagine the "x"-axis as pointing "towards" the observer and thus seeing a concave corner. A point in space in a Cartesian coordinate system may also be represented by a position vector, which can be thought of as an arrow pointing from the origin of the coordinate system to the point. If the coordinates represent spatial positions (displacements), it is common to represent the vector from the origin to the point of interest as formula_33. In two dimensions, the vector from the origin to the point with Cartesian coordinates (x, y) can be written as: where formula_35, and formula_36 are unit vectors in the direction of the "x"-axis and "y"-axis respectively, generally referred to as the "standard basis" (in some application areas these may also be referred to as versors). Similarly, in three dimensions, the vector from the origin to the point with Cartesian coordinates formula_37 can be written as: where formula_39 is the unit vector in the direction of the z-axis. There is no "natural" interpretation of multiplying vectors to obtain another vector that works in all dimensions, however there is a way to use complex numbers to provide such a multiplication. In a two dimensional cartesian plane, identify the point with coordinates with the complex number. Here, i is the imaginary unit and is identified with the point with coordinates, so it is not the unit vector in the direction of the "x"-axis. Since the complex numbers can be multiplied giving another complex number, this identification provides a means to "multiply" vectors. In a three dimensional cartesian space a similar identification can be made with a subset of the quaternions. Cartesian coordinates are an abstraction that have a multitude of possible applications in the real world. However, three constructive steps are involved in superimposing coordinates on a problem application. 1) Units of distance must be decided defining the spatial size represented by the numbers used as coordinates. 2) An origin must be assigned to a specific spatial location or landmark, and 3) the orientation of the axes must be defined using available directional cues for all but one axis. Consider as an example superimposing 3D Cartesian coordinates over all points on the Earth (i.e. geospatial 3D). What units make sense? Kilometers are a good choice, since the original definition of the kilometer was geospatial—10 000 km equaling the surface distance from the Equator to the North Pole. Where to place the origin? Based on symmetry, the gravitational center of the Earth suggests a natural landmark (which can be sensed via satellite orbits). Finally, how to orient X-, Y- and Z-axis? The axis of Earth's spin provides a natural orientation strongly associated with "up vs. down", so positive Z can adopt the direction from geocenter to North Pole. A location on the Equator is needed to define the X-axis, and the prime meridian stands out as a reference orientation, so the X-axis takes the orientation from geocenter out to 0 degrees longitude, 0 degrees latitude. Note that with three dimensions, and two perpendicular axes orientations pinned down for X and Z, the Y-axis is determined by the first two choices. In order to obey the right-hand rule, the Y-axis must point out from the geocenter to 90 degrees longitude, 0 degrees latitude. So what are the geocentric coordinates of the Empire State Building in New York City? From a longitude of −73.985656 degrees, a latitude 40.748433 degrees, and Earth radius of 40,000/2π km, and transforming from spherical to Cartesian coordinates, you can estimate the geocentric coordinates of the Empire State Building, ("x", "y", "z") = (1330.53 km, –4635.75 km, 4155.46 km). GPS navigation relies on such geocentric coordinates. In engineering projects, agreement on the definition of coordinates is a crucial foundation. One cannot assume that coordinates come predefined for a novel application, so knowledge of how to erect a coordinate system where there is none is essential to applying René Descartes' thinking. While spatial applications employ identical units along all axes, in business and scientific applications, each axis may have different units of measurement associated with it (such as kilograms, seconds, pounds, etc.). Although four- and higher-dimensional spaces are difficult to visualize, the algebra of Cartesian coordinates can be extended relatively easily to four or more variables, so that certain calculations involving many variables can be done. (This sort of algebraic extension is what is used to define the geometry of higher-dimensional spaces.) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables. The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, "f", the set of all points, where is the graph of the function "f". For a function "g" of two variables, the set of all points, where is the graph of the function "g". A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.

A Cartesian coordinate system (, ) is a coordinate system that specifies each point uniquely in a plane by a set of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length. Each reference line is called a "coordinate axis" or just "axis" (plural "axes") of the system, and the point where they meet is its "origin", at ordered pair. The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

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summarize: In the simplest case of circular motion at radius formula_2, with position given by the angular displacement formula_3 from the x-axis, the orbital angular velocity is the rate of change of angle with respect to time: formula_4. If formula_5 is measured in radians, the arc-length from the positive x-axis around the circle to the particle is formula_6, and the linear velocity is formula_7, so that formula_8. In the general case of a particle moving in the plane, the orbital angular velocity is the rate at which the position vector relative to a chosen origin "sweeps out" angle. The diagram shows the position vector formula_9 from the origin formula_10 to a particle formula_11, with its polar coordinates formula_12. (All variables are functions of time formula_13.) The particle has linear velocity splitting as formula_14, with the radial component formula_15 parallel to the radius, and the cross-radial (or tangential) component formula_16 perpendicular to the radius. When there is no radial component, the particle moves around the origin in a circle; but when there is no cross-radial component, it moves in a straight line from the origin. Since radial motion leaves the angle unchanged, only the cross-radial component of linear velocity contributes to angular velocity. The angular velocity "ω" is the rate of change of angular position with respect to time, which can be computed from the cross-radial velocity as: Here the cross-radial speed formula_18 is the signed magnitude of formula_16, positive for counter-clockwise motion, negative for clockwise. Taking polar coordinates for the linear velocity formula_20 gives magnitude formula_21 (linear speed) and angle formula_22 relative to the radius vector; in these terms, formula_23, so that These formulas may be derived from formula_25, formula_26 and formula_27, together with the projection formula formula_28, where formula_29. In two dimensions, angular velocity is a number with plus or minus sign indicating orientation, but not pointing in a direction. The sign is conventionally taken to be positive if the radius vector turns counter-clockwise, and negative if clockwise. Angular velocity then may be termed a pseudoscalar, a numerical quantity which changes sign under a parity inversion, such as inverting one axis or switching the two axes. In three-dimensional space, we again have the position vector r of a moving particle. Here, orbital angular velocity is a pseudovector whose magnitude is the rate at which r sweeps out angle, and whose direction is perpendicular to the instantaneous plane in which r sweeps out angle (i.e. the plane spanned by r and v). However, as there are "two" directions perpendicular to any plane, an additional condition is necessary to uniquely specify the direction of the angular velocity; conventionally, the right-hand rule is used. Let the pseudovector formula_30 be the unit vector perpendicular to the plane spanned by r and v, so that the right-hand rule is satisfied (i.e. the instantaneous direction of angular displacement is counter-clockwise looking from the top of formula_30). Taking polar coordinates formula_32 in this plane, as in the two-dimensional case above, one may define the orbital angular velocity vector as: where "θ" is the angle between r and v. In terms of the cross product, this is: From the above equation, one can recover the tangential velocity as: If a point rotates with orbital angular velocity formula_36 about its center of rotation in a coordinate frame formula_37 which itself rotates with a spin angular velocity formula_38 with respect to an external frame formula_39, we can define formula_40 to be the composite orbital angular velocity vector of the point about its center of rotation with respect to formula_39. This operation coincides with usual addition of vectors, and it gives angular velocity the algebraic structure of a true vector, rather than just a pseudo-vector. The only non-obvious property of the above addition is commutativity. This can be proven from the fact that the velocity tensor "W" (see below) is skew-symmetric, so that formula_42 is a rotation matrix which can be expanded as formula_43. The composition of rotations is not commutative, but formula_44 is commutative to first order, and therefore formula_45. Notice that this also defines the subtraction as the addition of a negative vector. Given a rotating frame of three unit coordinate vectors, all the three must have the same angular speed at each instant. In such a frame, each vector may be considered as a moving particle with constant scalar radius. The rotating frame appears in the context of rigid bodies, and special tools have been developed for it: the spin angular velocity may be described as a vector or equivalently as a tensor. Consistent with the general definition, the spin angular velocity of a frame is defined as the orbital angular velocity of any of the three vectors (same for all) with respect to its own centre of rotation. The addition of angular velocity vectors for frames is also defined by the usual vector addition (composition of linear movements), and can be useful to decompose the rotation as in a gimbal. All components of the vector can be calculated as derivatives of the parameters defining the moving frames (Euler angles or rotation matrices). As in the general case, addition is commutative: formula_45. By Euler's rotation theorem, any rotating frame possesses an instantaneous axis of rotation, which is the direction of the angular velocity vector, and the magnitude of the angular velocity is consistent with the two-dimensional case. Considering a coordinate vector of the frame as a particle, formula_47 with formula_48, we obtain the orbital angular velocity vector: Here formula_50 are the columns of the matrix of the frame, and formula_51 their time derivatives. The components of the spin angular velocity pseudovector were first calculated by Leonhard Euler using his Euler angles and the use of an intermediate frame: Euler proved that the projections of the angular velocity pseudovector on each of these three axes is the derivative of its associated angle (which is equivalent to decomposing the instantaneous rotation into three instantaneous Euler rotations). Therefore: This basis is not orthonormal and it is difficult to use, but now the velocity vector can be changed to the fixed frame or to the moving frame with just a change of bases. For example, changing to the mobile frame: where formula_54 are unit vectors for the frame fixed in the moving body. This example has been made using the Z-X-Z convention for Euler angles. The angular velocity vector formula_55 defined above may be equivalently expressed as an angular velocity tensor, the matrix (or linear mapping) "W" = "W"("t") defined by: This is an infinitesimal rotation matrix. The linear mapping "W" acts as formula_57: A vector formula_59 undergoing uniform circular motion around an axis satisfies: Given the orientation matrix "A"("t") of a frame, whose columns are the moving orthonormal coordinate vectors formula_61, we can obtain its angular velocity tensor "W"("t") as follows. Angular velocity must be the same for the three vectors formula_62, so arranging the three vector equations into columns of a matrix, we have: (This holds even if "A"("t") does not rotate uniformly.) Therefore the angular velocity tensor is: since the inverse of the orthogonal matrix formula_65 is its transpose formula_66. In general, the angular velocity in an "n"-dimensional space is the time derivative of the angular displacement tensor, which is a second rank skew-symmetric tensor. This tensor "W" will have independent components, which is the dimension of the Lie algebra of the Lie group of rotations of an "n"-dimensional inner product space. In three dimensions, angular velocity can be represented by a pseudovector because second rank tensors are dual to pseudovectors in three dimensions. Since the angular velocity tensor "W" = "W"("t") is a skew-symmetric matrix: its Hodge dual is a vector, which is precisely the previous angular velocity vector formula_68. If we know an initial frame "A"(0) and we are given a "constant" angular velocity tensor "W", we can obtain "A"("t") for any given "t". Recall the matrix differential equation: This equation can be integrated to give: which shows a connection with the Lie group of rotations. We prove that angular velocity tensor is skew symmetric, i.e. formula_71 satisfies formula_72. A rotation matrix "A" is orthogonal, inverse to its transpose, so we have formula_73. For formula_74 a frame matrix, taking the time derivative of the equation gives: Applying the formula formula_76, Thus, "W" is the negative of its transpose, which implies it is skew symmetric. At any instant formula_13, the angular velocity tensor represents a linear map between the position vector formula_79 and the velocity vectors formula_80 of a point on a rigid body rotating around the origin: The relation between this linear map and the angular velocity pseudovector formula_82 is the following. Because "W" is the derivative of an orthogonal transformation, the bilinear form is skew-symmetric. Thus we can apply the fact of exterior algebra that there is a unique linear form formula_84 on formula_85 that where formula_87 is the exterior product of formula_9 and formula_89. Taking the sharp "L" of "L" we get Introducing formula_91, as the Hodge dual of "L", and applying the definition of the Hodge dual twice supposing that the preferred unit 3-vector is formula_92 where by definition. Because formula_89 is an arbitrary vector, from nondegeneracy of scalar product follows Since the spin angular velocity tensor of a rigid body (in its rest frame) is a linear transformation that maps positions to velocities (within the rigid body), it can be regarded as a constant vector field. In particular, the spin angular velocity is a Killing vector field belonging to an element of the Lie algebra SO(3) of the 3-dimensional rotation group SO(3). Also, it can be shown that the spin angular velocity vector field is exactly half of the curl of the linear velocity vector field v(r) of the rigid body. In symbols, The same equations for the angular speed can be obtained reasoning over a rotating rigid body. Here is not assumed that the rigid body rotates around the origin. Instead, it can be supposed rotating around an arbitrary point that is moving with a linear velocity "V"("t") in each instant. To obtain the equations, it is convenient to imagine a rigid body attached to the frames and consider a coordinate system that is fixed with respect to the rigid body. Then we will study the coordinate transformations between this coordinate and the fixed "laboratory" system. As shown in the figure on the right, the lab system's origin is at point "O", the rigid body system origin is at and the vector from "O" to is R. A particle ("i") in the rigid body is located at point P and the vector position of this particle is R in the lab frame, and at position r in the body frame. It is seen that the position of the particle can be written: The defining characteristic of a rigid body is that the distance between any two points in a rigid body is unchanging in time. This means that the length of the vector formula_99 is unchanging. By Euler's rotation theorem, we may replace the vector formula_99 with formula_101 where formula_102 is a 3×3 rotation matrix and formula_103 is the position of the particle at some fixed point in time, say. This replacement is useful, because now it is only the rotation matrix formula_102 that is changing in time and not the reference vector formula_103, as the rigid body rotates about point. Also, since the three columns of the rotation matrix represent the three versors of a reference frame rotating together with the rigid body, any rotation about any axis becomes now visible, while the vector formula_99 would not rotate if the rotation axis were parallel to it, and hence it would only describe a rotation about an axis perpendicular to it (i.e., it would not see the component of the angular velocity pseudovector parallel to it, and would only allow the computation of the component perpendicular to it). The position of the particle is now written as: Taking the time derivative yields the velocity of the particle: where V is the velocity of the particle (in the lab frame) and V is the velocity of (the origin of the rigid body frame). Since formula_102 is a rotation matrix its inverse is its transpose. So we substitute formula_110: or where formula_115 is the previous angular velocity tensor. It can be proved that this is a skew symmetric matrix, so we can take its dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector formula_116: Substituting "ω" for "W" into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the orbital angular velocity of the particle with respect to the reference point. This angular velocity is what physicists call the "spin angular velocity" of the rigid body, as opposed to the "orbital" angular velocity of the reference point about the origin "O". We have supposed that the rigid body rotates around an arbitrary point. We should prove that the spin angular velocity previously defined is independent of the choice of origin, which means that the spin angular velocity is an intrinsic property of the spinning rigid body. (Note the marked contrast of this with the "orbital" angular velocity of a point particle, which certainly "does" depend on the choice of origin.) See the graph to the right: The origin of lab frame is "O", while "O" and "O" are two fixed points on the rigid body, whose velocity is formula_119 and formula_120 respectively. Suppose the angular velocity with respect to "O" and O is formula_121 and formula_122 respectively. Since point "P" and "O" have only one velocity, The above two yields that Since the point "P" (and thus formula_126) is arbitrary, it follows that If the reference point is the instantaneous axis of rotation the expression of the velocity of a point in the rigid body will have just the angular velocity term. This is because the velocity of the instantaneous axis of rotation is zero. An example of the instantaneous axis of rotation is the hinge of a door. Another example is the point of contact of a purely rolling spherical (or, more generally, convex) rigid body.

In physics, angular velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time. There are two types of angular velocity: orbital angular velocity and spin angular velocity. Spin angular velocity refers to how fast a rigid body rotates with respect to its centre of rotation. Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. Spin angular velocity is independent of the choice of origin, in contrast to orbital angular velocity which depends on the choice of origin.

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summarize: The simplest example of a coordinate system is the identification of points on a line with real numbers using the "number line". In this system, an arbitrary point "O" (the "origin") is chosen on a given line. The coordinate of a point "P" is defined as the signed distance from "O" to "P", where the signed distance is the distance taken as positive or negative depending on which side of the line "P" lies. Each point is given a unique coordinate and each real number is the coordinate of a unique point. The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes. This can be generalized to create "n" coordinates for any point in "n"-dimensional Euclidean space. Depending on the direction and order of the coordinate axes, the three-dimensional system may be a right-handed or a left-handed system. This is one of many coordinate systems. Another common coordinate system for the plane is the "polar coordinate system". A point is chosen as the "pole" and a ray from this point is taken as the "polar axis". For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line). Then there is a unique point on this line whose signed distance from the origin is "r" for given number "r". For a given pair of coordinates ("r", θ) there is a single point, but any point is represented by many pairs of coordinates. For example, ("r", θ), ("r", θ+2π) and (−"r", θ+π) are all polar coordinates for the same point. The pole is represented by (0, θ) for any value of θ. There are two common methods for extending the polar coordinate system to three dimensions. In the cylindrical coordinate system, a "z"-coordinate with the same meaning as in Cartesian coordinates is added to the "r" and "θ" polar coordinates giving a triple ("r", "θ", "z"). Spherical coordinates take this a step further by converting the pair of cylindrical coordinates ("r", "z") to polar coordinates ("ρ", "φ") giving a triple ("ρ", "θ", "φ"). A point in the plane may be represented in "homogeneous coordinates" by a triple ("x", "y", "z") where "x"/"z" and "y"/"z" are the Cartesian coordinates of the point. This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the use of infinity. In general, a homogeneous coordinate system is one where only the ratios of the coordinates are significant and not the actual values. Some other common coordinate systems are the following: There are ways of describing curves without coordinates, using intrinsic equations that use invariant quantities such as curvature and arc length. These include: Coordinates systems are often used to specify the position of a point, but they may also be used to specify the position of more complex figures such as lines, planes, circles or spheres. For example, Plücker coordinates are used to determine the position of a line in space. When there is a need, the type of figure being described is used to distinguish the type of coordinate system, for example the term "line coordinates" is used for any coordinate system that specifies the position of a line. It may occur that systems of coordinates for two different sets of geometric figures are equivalent in terms of their analysis. An example of this is the systems of homogeneous coordinates for points and lines in the projective plane. The two systems in a case like this are said to be "dualistic". Dualistic systems have the property that results from one system can be carried over to the other since these results are only different interpretations of the same analytical result; this is known as the "principle of duality". Because there are often many different possible coordinate systems for describing geometrical figures, it is important to understand how they are related. Such relations are described by "coordinate transformations" which give formulas for the coordinates in one system in terms of the coordinates in another system. For example, in the plane, if Cartesian coordinates ("x", "y") and polar coordinates ("r", "θ") have the same origin, and the polar axis is the positive "x" axis, then the coordinate transformation from polar to Cartesian coordinates is given by "x" = "r" cos"θ" and "y" = "r" sin"θ". With every bijection from the space to itself two coordinate transformations can be associated: For example, in 1D, if the mapping is a translation of 3 to the right, the first moves the origin from 0 to 3, so that the coordinate of each point becomes 3 less, while the second moves the origin from 0 to −3, so that the coordinate of each point becomes 3 more. In two dimensions, if one of the coordinates in a point coordinate system is held constant and the other coordinate is allowed to vary, then the resulting curve is called a coordinate curve. In the Cartesian coordinate system the coordinate curves are, in fact, straight lines, thus coordinate lines. Specifically, they are the lines parallel to one of the coordinate axes. For other coordinate systems the coordinates curves may be general curves. For example, the coordinate curves in polar coordinates obtained by holding "r" constant are the circles with center at the origin. A coordinate system for which some coordinate curves are not lines is called a curvilinear coordinate system. This procedure does not always make sense, for example there are no coordinate curves in a homogeneous coordinate system. In three-dimensional space, if one coordinate is held constant and the other two are allowed to vary, then the resulting surface is called a coordinate surface. For example, the coordinate surfaces obtained by holding ρ constant in the spherical coordinate system are the spheres with center at the origin. In three-dimensional space the intersection of two coordinate surfaces is a coordinate curve. In the Cartesian coordinate system we may speak of coordinate planes. Similarly, coordinate hypersurfaces are the -dimensional spaces resulting from fixing a single coordinate of an "n"-dimensional coordinate system. The concept of a "coordinate map", or "coordinate chart" is central to the theory of manifolds. A coordinate map is essentially a coordinate system for a subset of a given space with the property that each point has exactly one set of coordinates. More precisely, a coordinate map is a homeomorphism from an open subset of a space "X" to an open subset of R. It is often not possible to provide one consistent coordinate system for an entire space. In this case, a collection of coordinate maps are put together to form an atlas covering the space. A space equipped with such an atlas is called a "manifold" and additional structure can be defined on a manifold if the structure is consistent where the coordinate maps overlap. For example, a differentiable manifold is a manifold where the change of coordinates from one coordinate map to another is always a differentiable function. In geometry and kinematics, coordinate systems are used to describe the (linear) position of points and the angular position of axes, planes, and rigid bodies. In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as "global" or "world" coordinate system). For instance, the orientation of a rigid body can be represented by an orientation matrix, which includes, in its three columns, the Cartesian coordinates of three points. These points are used to define the orientation of the axes of the local system; they are the tips of three unit vectors aligned with those axes.

In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the "x"-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and "vice versa"; this is the basis of analytic geometry.

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summarize: In its most simple and basic form, a moment is the product of the distance to some point, raised to some power, and some physical quantity such as the force, charge, etc. at that point: where formula_2 is the physical quantity such as a force applied at a point, or a point charge, or a point mass, etc. If the quantity is not concentrated solely at a single point, the moment is the integral of that quantity's density over space: where formula_4 is the distribution of the density of charge, mass, or whatever quantity is being considered. More complex forms take into account the angular relationships between the distance and the physical quantity, but the above equations capture the essential feature of a moment, namely the existence of an underlying formula_5 or equivalent term. This implies that there are multiple moments (one for each value of "n") and that the moment generally depends on the reference point from which the distance formula_6 is measured, although for certain moments (technically, the lowest non-zero moment) this dependence vanishes and the moment becomes independent of the reference point. Each value of "n" corresponds to a different moment: the 1st moment corresponds to "n" = 1; the 2nd moment to "n" = 2, etc. The 0th moment ("n" = 0) is sometimes called the "monopole moment"; the 1st moment ("n" = 1) is sometimes called the "dipole moment", and the 2nd moment ("n" = 2) is sometimes called the "quadrupole moment", especially in the context of electric charge distributions. Moments of mass: Assuming a density function that is finite and localized to a particular region, outside that region a 1/"r" potential may be expressed as a series of spherical harmonics: The coefficients formula_21 are known as "multipole moments", and take the form: where formula_23 expressed in spherical coordinates formula_24 is a variable of integration. A more complete treatment may be found in pages describing multipole expansion or spherical multipole moments. (Note: the convention in the above equations was taken from Jackson. The conventions used in the referenced pages may be slightly different.) When formula_4 represents an electric charge density, the formula_26 are, in a sense, projections of the moments of electric charge: formula_27 is the monopole moment; the formula_28 are projections of the dipole moment, the formula_29 are projections of the quadrupole moment, etc. The multipole expansion applies to 1/"r" scalar potentials, examples of which include the electric potential and the gravitational potential. For these potentials, the expression can be used to approximate the strength of a field produced by a localized distribution of charges (or mass) by calculating the first few moments. For sufficiently large "r", a reasonable approximation can be obtained from just the monopole and dipole moments. Higher fidelity can be achieved by calculating higher order moments. Extensions of the technique can be used to calculate interaction energies and intermolecular forces. The technique can also be used to determine the properties of an unknown distribution formula_4. Measurements pertaining to multipole moments may be taken and used to infer properties of the underlying distribution. This technique applies to small objects such as molecules, but has also been applied to the universe itself, being for example the technique employed by the WMAP and Planck experiments to analyze the cosmic microwave background radiation. The concept of moment in physics is derived from the mathematical concept of moments. The principle of moments is derived from Archimedes' discovery of the operating principle of the lever. In the lever one applies a force, in his day most often human muscle, to an arm, a beam of some sort. Archimedes noted that the amount of force applied to the object, the moment of force, is defined as M = rF, where F is the applied force, and r is the distance from the applied force to object. However, historical evolution of the term'moment' and its use in different branches of science, such as mathematics, physics and engineering, is unclear. Federico Commandino, in 1565, translated into Latin from Archimedes: This was apparently the first use of the word "moment" (Latin, "momentorum") in the sense which we now know it: a moment about a center of rotation.

In physics, a moment is an expression involving the product of a distance and another physical quantity, and in this way it accounts for how the physical quantity is located or arranged.

en

35

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summarize: In physics, uniform circular motion describes the motion of a body traversing a circular path at constant speed. Since the body describes circular motion, its distance from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: velocity, a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, produced by a centripetal force which is also constant in magnitude and directed towards the axis of rotation. In the case of rotation around a fixed axis of a rigid body that is not negligibly small compared to the radius of the path, each particle of the body describes a uniform circular motion with the same angular velocity, but with velocity and acceleration varying with the position with respect to the axis. For motion in a circle of radius "r", the circumference of the circle is "C" = 2"r". If the period for one rotation is "T", the angular rate of rotation, also known as angular velocity, ω is: The speed of the object travelling the circle is: The angle θ swept out in a time "t" is: The angular acceleration, "α", of the particle is: In the case of uniform circular motion, α will be zero. The acceleration due to change in the direction is: The centripetal and centrifugal force can also be found out using acceleration: The vector relationships are shown in Figure 1. The axis of rotation is shown as a vector ω perpendicular to the plane of the orbit and with a magnitude ω = "d"θ / "dt". The direction of ω is chosen using the right-hand rule. With this convention for depicting rotation, the velocity is given by a vector cross product as which is a vector perpendicular to both ω and r("t"), tangential to the orbit, and of magnitude ω "r". Likewise, the acceleration is given by which is a vector perpendicular to both ω and v("t") of magnitude ω |v| = ω "r" and directed exactly opposite to r("t"). In the simplest case the speed, mass and radius are constant. Consider a body of one kilogram, moving in a circle of radius one metre, with an angular velocity of one radian per second. During circular motion the body moves on a curve that can be described in polar coordinate system as a fixed distance "R" from the center of the orbit taken as origin, oriented at an angle θ("t") from some reference direction. See Figure 4. The displacement "vector" formula_9 is the radial vector from the origin to the particle location: where formula_11 is the unit vector parallel to the radius vector at time "t" and pointing away from the origin. It is convenient to introduce the unit vector orthogonal to formula_11 as well, namely formula_13. It is customary to orient formula_13 to point in the direction of travel along the orbit. The velocity is the time derivative of the displacement: Because the radius of the circle is constant, the radial component of the velocity is zero. The unit vector formula_11 has a time-invariant magnitude of unity, so as time varies its tip always lies on a circle of unit radius, with an angle θ the same as the angle of formula_17. If the particle displacement rotates through an angle "d"θ in time "dt", so does formula_11, describing an arc on the unit circle of magnitude "d"θ. See the unit circle at the left of Figure 4. Hence: where the direction of the change must be perpendicular to formula_11 (or, in other words, along formula_13) because any change formula_22 in the direction of formula_11 would change the size of formula_11. The sign is positive, because an increase in "d"θ implies the object and formula_11 have moved in the direction of formula_13. Hence the velocity becomes: The acceleration of the body can also be broken into radial and tangential components. The acceleration is the time derivative of the velocity: The time derivative of formula_13 is found the same way as for formula_11. Again, formula_13 is a unit vector and its tip traces a unit circle with an angle that is /2 + θ. Hence, an increase in angle "d"θ by formula_17 implies formula_13 traces an arc of magnitude "d"θ, and as formula_13 is orthogonal to formula_11, we have: where a negative sign is necessary to keep formula_13 orthogonal to formula_11. (Otherwise, the angle between formula_13 and formula_11 would "decrease" with increase in "d"θ.) See the unit circle at the left of Figure 4. Consequently, the acceleration is: The centripetal acceleration is the radial component, which is directed radially inward: while the tangential component changes the magnitude of the velocity: Circular motion can be described using complex numbers. Let the axis be the real axis and the formula_44 axis be the imaginary axis. The position of the body can then be given as formula_45, a complex "vector": where is the imaginary unit, and formula_47 is the argument of the complex number as a function of time, "t". Since the radius is constant: where a "dot" indicates differentiation in respect of time. With this notation the velocity becomes: and the acceleration becomes: The first term is opposite in direction to the displacement vector and the second is perpendicular to it, just like the earlier results shown before. Figure 1 illustrates velocity and acceleration vectors for uniform motion at four different points in the orbit. Because the velocity v is tangent to the circular path, no two velocities point in the same direction. Although the object has a constant "speed", its "direction" is always changing. This change in velocity is caused by an acceleration a, whose magnitude is (like that of the velocity) held constant, but whose direction also is always changing. The acceleration points radially inwards (centripetally) and is perpendicular to the velocity. This acceleration is known as centripetal acceleration. For a path of radius "r", when an angle θ is swept out, the distance travelled on the periphery of the orbit is "s" = "r"θ. Therefore, the speed of travel around the orbit is where the angular rate of rotation is ω. (By rearrangement, ω = "v"/"r".) Thus, "v" is a constant, and the velocity vector v also rotates with constant magnitude "v", at the same angular rate ω. In this case the three-acceleration vector is perpendicular to the three-velocity vector, and the square of proper acceleration, expressed as a scalar invariant, the same in all reference frames, becomes the expression for circular motion, or, taking the positive square root and using the three-acceleration, we arrive at the proper acceleration for circular motion: The left-hand circle in Figure 2 is the orbit showing the velocity vectors at two adjacent times. On the right, these two velocities are moved so their tails coincide. Because speed is constant, the velocity vectors on the right sweep out a circle as time advances. For a swept angle "d"θ = ω "dt" the change in v is a vector at right angles to v and of magnitude "v" "d"θ, which in turn means that the magnitude of the acceleration is given by In non-uniform circular motion an object is moving in a circular path with a varying speed. Since the speed is changing, there is tangential acceleration in addition to normal acceleration. In non-uniform circular motion the net acceleration (a) is along direction of Δv which is directed inside circle but does not pass through its center (see figure). The net acceleration may be resolved into two components: tangential acceleration and normal acceleration also known as the centripetal or radial acceleration. Unlike tangential acceleration, centripetal acceleration is present in both uniform and non-uniform circular motion. In non-uniform circular motion, normal force does not always point in the opposite direction of weight. Here is an example with an object traveling in a straight path then loops a loop back into a straight path again. This diagram shows the normal force pointing in other directions rather than opposite to the weight force. The normal force is actually the sum of the radial and tangential forces. The component of weight force is responsible for the tangential force here (We have neglected frictional force). The radial force (centripetal force) is due the change in direction of velocity as discussed earlier. In non-uniform circular motion, normal force and weight may point in the same direction. Both forces can point down, yet the object will remain in a circular path without falling straight down. First let's see why normal force can point down in the first place. In the first diagram, let's say the object is a person sitting inside a plane, the two forces point down only when it reaches the top of the circle. The reason for this is that the normal force is the sum of the tangential force and centripetal force. The tangential force is zero at the top (as no work is performed when the motion is perpendicular to the direction of force applied. Here weight force is perpendicular to the direction of motion of the object at the top of the circle) and centripetal force points down, thus normal force will point down as well. From a logical standpoint, a person who is travelling in the plane will be upside down at the top of the circle. At that moment, the person's seat is actually pushing down on the person, which is the normal force. The reason why the object does not fall down when subjected to only downward forces is a simple one. Think about what keeps an object up after it is thrown. Once an object is thrown into the air, there is only the downward force of earth's gravity that acts on the object. That does not mean that once an object is thrown in the air, it will fall instantly. What keeps that object up in the air is its velocity. The first of Newton's laws of motion states that an object's inertia keeps it in motion, and since the object in the air has a velocity, it will tend to keep moving in that direction. A varying angular speed for an object moving in a circular path can also be achieved if the rotating body does not have an homogeneous mass distribution. For inhomogeneous objects, it is necessary to approach the problem as in. Solving applications dealing with non-uniform circular motion involves force analysis. With uniform circular motion, the only force acting upon an object traveling in a circle is the centripetal force. In non-uniform circular motion, there are additional forces acting on the object due to a non-zero tangential acceleration. Although there are additional forces acting upon the object, the sum of all the forces acting on the object will have to equal to the centripetal force. Radial acceleration is used when calculating the total force. Tangential acceleration is not used in calculating total force because it is not responsible for keeping the object in a circular path. The only acceleration responsible for keeping an object moving in a circle is the radial acceleration. Since the sum of all forces is the centripetal force, drawing centripetal force into a free body diagram is not necessary and usually not recommended. Using formula_58, we can draw free body diagrams to list all the forces acting on an object then set it equal to formula_59. Afterwards, we can solve for what ever is unknown (this can be mass, velocity, radius of curvature, coefficient of friction, normal force, etc.). For example, the visual above showing an object at the top of a semicircle would be expressed as formula_60. In uniform circular motion, total acceleration of an object in a circular path is equal to the radial acceleration. Due to the presence of tangential acceleration in non uniform circular motion, that does not hold true any more. To find the total acceleration of an object in non uniform circular, find the vector sum of the tangential acceleration and the radial acceleration. Radial acceleration is still equal to formula_62. Tangential acceleration is simply the derivative of the velocity at any given point: formula_63. This root sum of squares of separate radial and tangential accelerations is only correct for circular motion; for general motion within a plane with polar coordinates formula_64, the Coriolis term formula_65 should be added to formula_66, whereas radial acceleration then becomes formula_67.

In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body.

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summarize: The order is divided into three suborders, Tyranni (suboscines), Passeri (oscines), and the basal Acanthisitti. Oscines have the best control of their syrinx muscles among birds, producing a wide range of songs and other vocalizations (though some of them, such as the crows, do not sound musical to human beings); some such as the lyrebird are accomplished imitators. The acanthisittids or New Zealand wrens are tiny birds restricted to New Zealand, at least in modern times; they were long placed in Passeri. Most passerines are smaller than typical members of other avian orders. The heaviest and altogether largest passerines are the thick-billed raven and the larger races of common raven, each exceeding and. The superb lyrebird and some birds-of-paradise, due to very long tails or tail coverts, are longer overall. The smallest passerine is the short-tailed pygmy tyrant, at and. The foot of a passerine has three toes directed forward and one toe directed backward, called anisodactyl arrangement, and the hind toe (hallux) joins the leg at approximately the same level as the front toes. This arrangement enables passerine birds to easily perch upright on branches. The toes have no webbing or joining, but in some cotingas, the second and third toes are united at their basal third. The leg of passerine birds contains an additional special adaptation for perching. A tendon in the rear of the leg running from the underside of the toes to the muscle behind the tibiotarsus will automatically be pulled and tighten when the leg bends, causing the foot to curl and become stiff when the bird lands on a branch. This enables passerines to sleep while perching without falling off. Most passerine birds have 12 tail feathers but the superb lyrebird has 16, and several spinetails in the family Furnariidae have 10, 8, or even 6, as is the case of Des Murs's wiretail. Species adapted to tree trunk climbing such as woodcreeper and treecreepers have stiff tail feathers that are used as props during climbing. Extremely long tails used as sexual ornaments are shown by species in different families. A well-known example is the long-tailed widowbird. The chicks of passerines are altricial: blind, featherless, and helpless when hatched from their eggs. Hence, the chicks require extensive parental care. Most passerines lay coloured eggs, in contrast with nonpasserines, most of whose eggs are white except in some ground-nesting groups such as Charadriiformes and nightjars, where camouflage is necessary, and in some parasitic cuckoos, which match the passerine host's egg. Vinous-throated parrotbill has two egg colours, white and blue. This can prevent the brood parasitic Common cuckoo. Clutches vary considerably in size: some larger passerines of Australia such as lyrebirds and scrub-robins lay only a single egg, most smaller passerines in warmer climates lay between two and five, while in the higher latitudes of the Northern Hemisphere, hole-nesting species like tits can lay up to a dozen and other species around five or six. The family Viduidae do not build their own nests, instead, they lay eggs in other birds' nests. The evolutionary history of the passerine families and the relationships among them remained rather mysterious until the late 20th century. In many cases, passerine families were grouped together on the basis of morphological similarities that, it is now believed, are the result of convergent evolution, not a close genetic relationship. For example, the wrens of the Americas and Eurasia; those of Australia; and those of New Zealand look superficially similar and behave in similar ways, and yet belong to three far-flung branches of the passerine family tree; they are as unrelated as it is possible to be while remaining Passeriformes. Much research remains to be done, but advances in molecular biology and improved paleobiogeographical data gradually are revealing a clearer picture of passerine origins and evolution that reconciles molecular affinities, the constraints of morphology and the specifics of the fossil record. The first passerines are now thought to have evolved in the Southern Hemisphere in the late Paleocene or early Eocene, around 50 million years ago. The initial split was between the New Zealand wrens (Acanthisittidae) and all other passerines, and the second split involved the Tyranni (suboscines) and the Passeri (oscines or songbirds). The latter experienced a great radiation of forms out of the Australian continent. A major branch of the Passeri, parvorder Passerida, expanded deep into Eurasia and Africa, where a further explosive radiation of new lineages occurred. This eventually led to three major Passerida lineages comprising about 4,000 species, which in addition to the Corvida and numerous minor lineages make up songbird diversity today. Extensive biogeographical mixing happens, with northern forms returning to the south, southern forms moving north, and so on. Perching bird osteology, especially of the limb bones, is rather diagnostic. However, the early fossil record is poor because the first Passeriformes were apparently on the small side of the present size range, and their delicate bones did not preserve well. Queensland Museum specimens F20688 (carpometacarpus) and F24685 (tibiotarsus) from Murgon, Queensland, are fossil bone fragments initially assigned to Passeriformes. However, the material is too fragmentary and their affinities have been questioned. Several more recent fossils from the Oligocene of Europe, such as "Wieslochia", "Jamna", and "Resoviaornis", are more complete and definitely represent early passeriforms, although their exact position in the evolutionary tree is not known. From the Bathans Formation at the Manuherikia River in Otago, New Zealand, MNZ S42815 (a distal right tarsometatarsus of a tui-sized bird) and several bones of at least one species of saddleback-sized bird have recently been described. These date from the Early to Middle Miocene (Awamoan to Lillburnian, 19–16 mya). In Europe, perching birds are not too uncommon in the fossil record from the Oligocene onward, but most are too fragmentary for a more definite placement: That suboscines expanded much beyond their region of origin is proven by several fossil from Germany such as a broadbill (Eurylaimidae) humerus fragment from the Early Miocene (roughly 20 mya) of, Germany, the Late Oligocene carpometacarpus from France listed above, and "Wieslochia", among others. Extant Passeri super-families were quite distinct by that time and are known since about 12–13 mya when modern genera were present in the corvoidean and basal songbirds. The modern diversity of Passerida genera is known mostly from the Late Miocene onwards and into the Pliocene (about 10–2 mya). Pleistocene and early Holocene lagerstätten (<1.8 mya) yield numerous extant species, and many yield almost nothing but extant species or their chronospecies and paleosubspecies. In the Americas, the fossil record is more scant before the Pleistocene, from which several still-existing suboscine families are documented. Apart from the indeterminable MACN-SC-1411 (Pinturas Early/Middle Miocene of Santa Cruz Province, Argentina), an extinct lineage of perching birds has been described from the Late Miocene of California, United States: the Palaeoscinidae with the single genus "Palaeoscinis". ""Palaeostruthus" eurius" (Pliocene of Florida) probably belongs to an extant family, most likely passeroidean. The Passeriformes is currently divided into three suborders: Acanthisitti (New Zealand wrens), Tyranni (suboscines) and Passeri (oscines). The Passeri has been traditionally subdivided into two major groups recognized now as Corvida and Passerida respectively containing the large superfamilies Corvoidea and Meliphagoidea, as well as minor lineages, and the superfamilies Sylvioidea, Muscicapoidea, and Passeroidea but this arrangement has been found to be oversimplified. Since the mid-2000s, literally, dozens of studies have investigated the phylogeny of the Passeriformes and found that many families from Australasia traditionally included in the Corvoidea actually represent more basal lineages within oscines. Likewise, the traditional three-superfamily arrangement within the Passeri has turned out to be far more complex and will require changes in classification. Major "wastebin" families such as the Old World warblers and Old World babblers have turned out to be paraphyletic and are being rearranged. Several taxa turned out to represent highly distinct lineages, so new families had to be established, some of them – like the stitchbird of New Zealand and the Eurasian bearded reedling – monotypic with only one living species. In the Passeri alone, a number of minor lineages will eventually be recognized as distinct superfamilies. For example, the kinglets constitute a single genus with less than 10 species today but seem to have been among the first perching bird lineages to diverge as the group spread across Eurasia. No particularly close relatives of them have been found among comprehensive studies of the living Passeri, though they might be fairly close to some little-studied tropical Asian groups. Nuthatches, wrens, and their closest relatives as currently grouped in a distinct super-family Certhioidea. This list is in taxonomic order, placing related families next to one another. The families listed are those recognised by the International Ornithologists' Union (IOC). The order and the division into infraorders, parvorders and superfamilies follows the phylogenetic analysis published by Carl Oliveros and colleagues in 2019. The relationships between the families in the suborder Tyranni (suboscines) were all well determined but some of the nodes in Passeri (oscines) were unclear owing to the rapid splitting of the lineages. Living Passeriformes based on the "Taxonomy in Flux family phylogenetic tree" by John Boyd.

A passerine is any bird of the order Passeriformes, which includes more than half of all bird species. Sometimes known as perching birds or songbirds, passerines are distinguished from other orders of birds by the arrangement of their toes (three pointing forward and one back), which facilitates perching, amongst other features specific to their evolutionary history in Australaves.

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summarize: The word 'jaguar' is thought to derive from the Tupian word "yaguara", meaning "beast of prey". The word entered English presumably via the Amazonian trade language Tupinambá, via Portuguese "jaguar". The specific word for jaguar is "yaguareté", with the suffix -"eté" meaning "real" or "true". The word 'panther' derives from classical Latin "panthēra", itself from the ancient Greek "pánthēr" (πάνθηρ). In Mexican Spanish, its nickname is "el tigre": 16th century Spaniards had no native word in their language for the jaguar, which is smaller than a lion, but bigger than a leopard, nor had ever encountered it in the Old World, and so named it after the tiger, since its ferocity would have been known to them through Roman writings and popular literature during the Renaissance. "Onca" is the Portuguese "onça", with the cedilla dropped for typographical reasons, found in English as "ounce" for the snow leopard, "Panthera uncia". It derives from the Latin "lyncea" lynx, with the letter L confused with the definite article (Italian "lonza", Old French "l'once)". In 1758, Carl Linnaeus described the jaguar in his work "Systema Naturae" and gave it the scientific name "Felis onca". In the 19th and 20th centuries, several jaguar type specimens formed the basis for descriptions of subspecies. In 1939, Reginald Innes Pocock recognized eight subspecies based on geographic origins and skull morphology of these specimens. Pocock did not have access to sufficient zoological specimens to critically evaluate their subspecific status, but expressed doubt about the status of several. Later consideration of his work suggested only three subspecies should be recognized. The description of "P. o. palustris" was based on a fossil skull. The author of "Mammal Species of the World" listed nine subspecies and both "P. o. palustris" or "P. o. paraguensis" separately. Results of morphologic and genetic research indicate a clinal north–south variation between populations, but no evidence for subspecific differentiation. A subsequent, more detailed study confirmed the predicted population structure within jaguar populations in Colombia. IUCN Red List assessors for the species and members of the Cat Specialist Group do not recognize any jaguar subspecies as valid. The following table is based on the former classification of the species provided in "Mammal Species of the World". The genus "Panthera" probably evolved in Asia between six and ten million years ago. The jaguar is thought to have diverged from a common ancestor of the "Panthera" at least 1.5 million years ago and to have entered the American continent in the Early Pleistocene via Beringia, the land bridge that once spanned the Bering Strait. Results of jaguar mitochondrial DNA analysis indicate that the species' lineage evolved between 280,000 and 510,000 years ago. Its immediate ancestor was "Panthera onca augusta", which was larger than the contemporary jaguar. Phylogenetic studies generally have shown the clouded leopard ("Neofelis nebulosa") is basal to this group. Fossils of extinct "Panthera" species, such as the European jaguar ("P. gombaszoegensis") and the American lion ("P. atrox"), show characteristics of both the jaguar and the lion ("P. leo"). Based on morphological evidence, the British zoologist Reginald Innes Pocock concluded that the jaguar is most closely related to the leopard ("P. pardus"). However, DNA-based evidence is inconclusive, and the position of the jaguar relative to the other species varies between studies. The jaguar is a compact and well-muscled animal. It is the largest cat native to the Americas and the third largest in the world, exceeded in size by the tiger and the lion. Its coat is generally a tawny yellow, but ranges to reddish-brown, for most of the body. The ventral areas are white. The fur is covered with rosettes for camouflage in the dappled light of its forest habitat. The spots and their shapes vary between individual jaguars: rosettes may include one or several dots. The spots on the head and neck are generally solid, as are those on the tail, where they may merge to form a band. Forest jaguars are frequently darker and considerably smaller than those in open areas, possibly due to the smaller numbers of large, herbivorous prey in forest areas. While the jaguar closely resembles the leopard, it is generally more robust, with a stockier limbs and a squarer head. The rosettes on a jaguar's coat are larger, darker, fewer in number and have thicker lines with a small spot in the middle. Its size and weight vary considerably: weights are normally in the range of. Exceptionally big males have been recorded to weigh as much as. The smallest females weigh about. Females are typically 10–20 percent smaller than males. The length, from the nose to the base of the tail, varies from. The tail is the shortest of any big cat, at in length. Legs are also short, but thick and powerful, considerably shorter when compared to a small tiger or lion in a similar weight range. The jaguar stands tall at the shoulders. Further variations in size have been observed across regions and habitats, with size tending to increase from north to south. Jaguars in the Chamela-Cuixmala Biosphere Reserve on the Pacific coast weighed around, about the size of a female cougar. South American jaguars in Venezuela or Brazil are much larger with average weights of about in males and of about in females. A short and stocky limb structure makes the jaguar adept at climbing, crawling, and swimming. The head is robust and the jaw extremely powerful, it has the third highest bite force of all felids, after the tiger and the lion. A jaguar can bite with a force of with the canine teeth and at the carnassial notch. This allows it to pierce the shells of armored reptiles and turtles. A comparative study of bite force adjusted for body size ranked it as the top felid, alongside the clouded leopard and ahead of the tiger and lion. It has been reported that an individual jaguar can drag an bull in its jaws and pulverize the heaviest bones. Melanistic jaguars are informally known as black panthers, but as with all forms of polymorphism they do not form a separate species. The black morph is less common than the spotted morph, estimated at occurring in about 6% of the South American jaguar population. In Mexico's Sierra Madre Occidental, the first black jaguar was recorded in 2004. Some evidence indicates that the melanistic allele is dominant, and being supported by natural selection. The black form may be an example of heterozygote advantage; breeding in captivity is not yet conclusive on this. Melanistic jaguars (or "black" jaguars) occur primarily in parts of South America, and are virtually unknown in wild populations residing in the subtropical and temperate regions of North America; they have rarely been documented north of Mexico's Isthmus of Tehuantepec. Extremely rare albino individuals, sometimes called white panthers, also occur among jaguars, as with the other big cats. As usual with albinos in the wild, selection keeps the frequency close to the rate of mutation. At present, the jaguar's range extends from Mexico through Central America to South America, including much of Amazonian Brazil. The countries included in this range are Argentina, Belize, Bolivia, Colombia, Costa Rica (particularly on the Osa Peninsula), Ecuador, French Guiana, Guatemala, Guyana, Honduras, Nicaragua, Panama, Paraguay, Peru, Suriname, the United States and Venezuela. It is now locally extinct in El Salvador and Uruguay. The inclusion of the United States in the list is based on occasional sightings in the southwest, particularly in Arizona, New Mexico and Texas. There are rock drawings made by the Hopi, Anasazi, and Pueblo all over the desert and chaparral regions of the American Southwest of an explicitly spotted cat: the only other feline that could even come close to such a profile would be the ocelot, but the pictographs distinctly display a much larger beast more than twice as large as any known ocelot. There are records of the beast being sold for its pelt in the vicinity of San Antonio, Texas for $18 apiece in the mid 19th century and there are records from well before California was a state that fit the description of this cat perfectly, mostly written down in Spanish. The historic range of the species included much of the southern half of the United States, and in the south extended much farther to cover most of the South American continent. In total, its northern range has receded southward and its southern range northward. Ice age fossils of the jaguar, dated between 40,000 and 11,500 years ago, have been discovered in the United States, including some at an important site as far north as Missouri. Fossil evidence shows jaguars of up to, much larger than the contemporary average for the animal. The habitat of the cat typically includes the rain forests and cloud forests of South and Central America, open, seasonally flooded wetlands, and dry grassland terrain. Of these habitats, the jaguar much prefers dense forest; the cat has lost range most rapidly in regions of drier habitat, such as the Argentine pampas, the arid grasslands of Mexico, and the southwestern United States. The cat will range across tropical, subtropical, and dry deciduous forests (including, historically, oak forests in the United States). The jaguar prefers to live by rivers, swamps, and in dense rainforest with thick cover for stalking prey. Jaguars have been found at elevations as high as 3,800 m, but they typically avoid montane forest and are not found in the high plateau of central Mexico or in the Andes. The jaguars preferred habitats are usually swamps and wooded regions, but jaguars also live in scrublands and deserts. The adult jaguar is an apex predator, meaning it exists at the top of its food chain and is not preyed on in the wild. The jaguar has also been termed a keystone species, as it is assumed, through controlling the population levels of prey such as herbivorous and granivorous mammals, apex felids maintain the structural integrity of forest systems. However, accurately determining what effect species like the jaguar have on ecosystems is difficult, because data must be compared from regions where the species is absent as well as its current habitats, while controlling for the effects of human activity. It is accepted that mid-sized prey species undergo population increases in the absence of the keystone predators, and this has been hypothesized to have cascading negative effects. However, field work has shown this may be natural variability and the population increases may not be sustained. Thus, the keystone predator hypothesis is not accepted by all scientists. The jaguar also has an effect on other predators. The jaguar and the cougar, which is the next-largest feline of South America, but the biggest in Central or North America, are often sympatric (related species sharing overlapping territory) and have often been studied in conjunction. The jaguar tends to take larger prey, usually over and the cougar smaller, usually between, reducing the latter's size. This situation may be advantageous to the cougar. Its broader prey niche, including its ability to take smaller prey, may give it an advantage over the jaguar in human-altered landscapes; while both are classified as near-threatened species, the cougar has a significantly larger current distribution. Depending on the availability of prey, the cougar and jaguar may even share it. Jaguar females reach sexual maturity at about two years of age, and males at three or four. The cat probably mates throughout the year in the wild, with births increasing when prey is plentiful. Research on captive male jaguars supports the year-round mating hypothesis, with no seasonal variation in semen traits and ejaculatory quality; low reproductive success has also been observed in captivity. Generation length of the jaguar is 9.8 years. Female estrus is 6–17 days out of a full 37-day cycle, and females will advertise fertility with urinary scent marks and increased vocalization. Females range more widely than usual during courtship. Pairs separate after mating, and females provide all parenting. The gestation period lasts 93–105 days; females give birth to up to four cubs, and most commonly to two. The mother will not tolerate the presence of males after the birth of cubs, given a risk of infanticide; this behavior is also found in the tiger. The young are born blind, gaining sight after two weeks. Cubs are weaned at three months, but remain in the birth den for six months before leaving to accompany their mother on hunts. They will continue in their mother's company for one to two years before leaving to establish a territory for themselves. Young males are at first nomadic, jostling with their older counterparts until they succeed in claiming a territory. Typical lifespan in the wild is estimated at around 12–15 years; in captivity, the jaguar lives up to 23 years, placing it among the longest-lived cats. Like most cats, the jaguar is solitary outside mother–cub groups. Adults generally meet only to court and mate (though limited noncourting socialization has been observed anecdotally) and carve out large territories for themselves. Female territories, which range from 25 to 40 km in size, may overlap, but the animals generally avoid one another. Male ranges cover roughly twice as much area, varying in size with the availability of game and space, and do not overlap. The territory of a male can contain those of several females. The jaguar uses scrape marks, urine, and feces to mark its territory. Like the other big cats except the snow leopard, the jaguar is capable of roaring and does so to warn territorial and mating competitors away; intensive bouts of counter-calling between individuals have been observed in the wild. Their roar often resembles a repetitive cough, and they may also vocalize mews and grunts. Mating fights between males occur, but are rare, and aggression avoidance behavior has been observed in the wild. When it occurs, conflict is typically over territory: a male's range may encompass that of two or three females, and he will not tolerate intrusions by other adult males. The jaguar is often described as nocturnal, but is more specifically crepuscular (peak activity around dawn and dusk). Both sexes hunt, but males travel farther each day than females, befitting their larger territories. The jaguar may hunt during the day if game is available and is a relatively energetic feline, spending as much as 50–60 percent of its time active. The jaguar's elusive nature and the inaccessibility of much of its preferred habitat make it a difficult animal to sight, let alone study. Like all cats, the jaguar is an obligate carnivore, feeding only on meat. It is an opportunistic hunter and its diet encompasses at least 87 species. Range-wide, jaguars prefer prey weighing and the most significantly preferred species are capybara and giant anteater. Other commonly taken prey include wild boar, common caiman, collared peccary, deer in more northern parts of their range, frogs, fish, nine-banded armadillo and white-nosed coati. Other species like the agouti, other carnivorans, primates, common opossum and tapir are generally avoided. Jagaurs are unusual among large felids in that they do not have a special preference for even-toed ungulates. Some jaguars also prey on livestock and they will actively target horses, cattle, and llamas. The activity patterns of the jaguar have been found to coincide with the activity of their main prey species in their biomes. Camera trap studies have shown that jaguars primarily have a crepuscular–nocturnal activity pattern in all the biomes that they are found in; however jaguars have been recorded to have considerable diurnal activity in thickly forested regions of the Amazon Rainforest and the Pantanal, as well as purely nocturnal activity in other regions such as the Atlantic forest.. The jaguar is a stalk-and-ambush rather than a chase predator. The cat will walk slowly down forest paths, listening for and stalking prey before rushing or ambushing. The jaguar attacks from cover and usually from a target's blind spot with a quick pounce; the species' ambushing abilities are considered nearly peerless in the animal kingdom by both indigenous people and field researchers, and are probably a product of its role as an apex predator in several different environments. The ambush may include leaping into water after prey, as a jaguar is quite capable of carrying a large kill while swimming; its strength is such that carcasses as large as a heifer can be hauled up a tree to avoid flood levels. While the jaguar often employs the deep throat-bite and suffocation technique typical among "Panthera", it sometimes uses a killing method unique among cats: it pierces directly through the temporal bones of the skull between the ears of prey (especially the capybara) with its canine teeth, piercing the brain. This may be an adaptation to "cracking open" turtle shells; following the late Pleistocene extinctions, armored reptiles such as turtles would have formed an abundant prey base for the jaguar. After killing prey, the jaguar will drag the carcass to a thicket or other secluded spot. It begins eating at the neck and chest, rather than the midsection. The heart and lungs are consumed, followed by the shoulders. The daily food requirement of a animal, at the extreme low end of the species' weight range, has been estimated at. For captive animals in the range, more than of meat daily are recommended. In the wild, consumption is naturally more erratic; wild cats expend considerable energy in the capture and kill of prey, and they may consume up to of meat at one feeding, followed by periods of famine. Though carnivorous, there is evidence that wild jaguars consume the roots of "Banisteriopsis caapi". Jaguars very rarely attack humans. Upon catching the scent or sight of a human, overwhelmingly they run as fast as their legs can carry them or will climb a tree to hide rather than fight. They did not evolve eating large primates and do not normally see man as food. Experts have cited them as the least likely of all big cats to kill and eat man and the majority of attacks come when the feline has been cornered or wounded. However, such behavior appears to be more frequent where humans enter jaguar habitat and decrease prey. Captive jaguars sometimes attack zookeepers. When the conquistadors arrived in the Americas, they feared jaguars. Nevertheless, even in those times, the jaguar's chief prey was the capybara in South America and peccary further north. Charles Darwin reported a saying of Native Americans that people would not have to fear the jaguar as long as capybaras were abundant. Jaguar populations are rapidly declining. The species is listed as Near Threatened on the IUCN Red List. The loss of parts of its range, including its virtual elimination from its historic northern areas and the increasing fragmentation of the remaining range, have contributed to this status. Particularly significant declines occurred in the 1960s, when more than 15,000 jaguars were killed for their skins in the Brazilian Amazon yearly; the Convention on International Trade in Endangered Species of 1973 brought about a sharp decline in the pelt trade. Detailed work performed under the auspices of the Wildlife Conservation Society revealed the species has lost 37% of its historic range, with its status unknown in an additional 18% of the global range. More encouragingly, the probability of long-term survival was considered high in 70% of its remaining range, particularly in the Amazon basin and the adjoining Gran Chaco and Pantanal. The major risks to the jaguar include deforestation across its habitat, increasing competition for food with human beings, especially in dry and unproductive habitat, poaching, hurricanes in northern parts of its range, and the behavior of ranchers who will often kill the cat where it preys on livestock. When adapted to the prey, the jaguar has been shown to take cattle as a large portion of its diet; while land clearance for grazing is a problem for the species, the jaguar population may have increased when cattle were first introduced to South America, as the animals took advantage of the new prey base. This willingness to take livestock has induced ranch owners to hire full-time jaguar hunters. The skins of wild cats and other mammals have been highly valued by the fur trade for many decades. From the beginning of the 20th-century Jaguars were hunted in large numbers, but over-harvest and habitat destruction reduced the availability and induced hunters and traders to gradually shift to smaller species by the 1960s. The international trade of jaguar skins had its largest boom between the end of the Second World War and the early 1970, due to the growing economy and lack of regulations. From 1967 onwards, the regulations introduced by national laws and international agreements diminished the reported international trade from as high as 13000 skins in 1967, through 7000 skins in 1969, until it became negligible after 1976, although illegal trade and smuggling continue to be a problem. During this period, the biggest exporters were Brazil and Paraguay, and the biggest importers were the US and Germany. The jaguar is listed on CITES Appendix I, which means that all international trade in jaguars or their body parts is prohibited. Hunting jaguars is prohibited in Argentina, Brazil, Colombia, French Guiana, Honduras, Nicaragua, Panama, Paraguay, Suriname, the United States, and Venezuela. Hunting jaguars is restricted in Guatemala and Peru. Trophy hunting is still permitted in Bolivia, and it is not protected in Ecuador or Guyana. Jaguar conservation is complicated because of the species' large range spanning 18 countries with different policies and regulations. Specific areas of high importance for jaguar conservation, so-called "Jaguar Conservation Units" (JCU) were determined in 2000. These are large areas inhabited by at least 50 jaguars. Each unit was assessed and evaluated on the basis of size, connectivity, habitat quality for both jaguar and prey, and jaguar population status. That way, 51 Jaguar Conservation Units were determined in 36 geographic regions as priority areas for jaguar conservation including: Recent studies underlined that to maintain the robust exchange across the jaguar gene pool necessary for maintaining the species, it is important that jaguar habitats are interconnected. To facilitate this, a new project, the Paseo del Jaguar, has been established to connect several jaguar hotspots. In 1986, the Cockscomb Basin Wildlife Sanctuary was established in Belize as the world's first protected area for jaguar conservation. Given the inaccessibility of much of the species' range, particularly the central Amazon, estimating jaguar numbers is difficult. Researchers typically focus on particular bioregions, thus species-wide analysis is scant. In 1991, 600–1,000 (the highest total) were estimated to be living in Belize. A year earlier, 125–180 jaguars were estimated to be living in Mexico's 4,000-km (2400-mi) Calakmul Biosphere Reserve, with another 350 in the state of Chiapas. The adjoining Maya Biosphere Reserve in Guatemala, with an area measuring 15,000 km (9,000 mi), may have 465–550 animals. Work employing GPS telemetry in 2003 and 2004 found densities of only six to seven jaguars per 100 km in the critical Pantanal region, compared with 10 to 11 using traditional methods; this suggests the widely used sampling methods may inflate the actual numbers of cats. In setting up protected reserves, efforts generally also have to be focused on the surrounding areas, as jaguars are unlikely to confine themselves to the bounds of a reservation, especially if the population is increasing in size. Human attitudes in the areas surrounding reserves and laws and regulations to prevent poaching are essential to make conservation areas effective. To estimate population sizes within specific areas and to keep track of individual jaguars, camera trapping and wildlife tracking telemetry are widely used, and feces may be sought out with the help of detector dogs to study jaguar health and diet. Current conservation efforts often focus on educating ranch owners and promoting ecotourism. The jaguar is generally defined as an umbrella species – its home range and habitat requirements are sufficiently broad that, if protected, numerous other species of smaller range will also be protected. Umbrella species serve as "mobile links" at the landscape scale, in the jaguar's case through predation. Conservation organizations may thus focus on providing viable, connected habitat for the jaguar, with the knowledge other species will also benefit. Ecotourism setups are being used to generate public interest in charismatic animals such as the jaguar, while at the same time generating revenue that can be used in conservation efforts. Audits done in Africa have shown that ecotourism has helped in African cat conservation. As with large African cats, a key concern in jaguar ecotourism is the considerable habitat space the species requires, so if ecotourism is used to aid in jaguar conservation, some considerations need to be made as to how existing ecosystems will be kept intact, or how new ecosystems that are large enough to support a growing jaguar population will be put into place. The only extant cat native to North America that roars, the jaguar was recorded as an animal of the Americas by Thomas Jefferson in 1799. Jaguars are still occasionally sighted in Arizona and New Mexico, such as El Jefe, prompting actions for its conservation by authorities. For example, on 20 August 2012, the USFWS proposed setting aside 838,232 acres in Arizona and New Mexico – an area larger than Rhode Island – as critical jaguar habitat. In pre-Columbian Central and South America, the jaguar was a symbol of power and strength. Among the Andean cultures, a jaguar cult disseminated by the early Chavín culture became accepted over most of what is today Peru by 900 BC. The later Moche culture of northern Peru used the jaguar as a symbol of power in many of their ceramics. In the religion of the Muisca, who inhabited the cool Altiplano Cundiboyacense in the Colombian Andes, the jaguar was considered a sacred animal and during their religious rituals the people dressed in jaguar skins. The skins were traded with the lowland peoples of the tropical Llanos Orientales. The name of "zipa" Nemequene was derived from the Muysccubun words "nymy" and "quyne", meaning "force of the jaguar". In Mesoamerica, the Olmec—an early and influential culture of the Gulf Coast region roughly contemporaneous with the Chavín—developed a distinct "were-jaguar" motif of sculptures and figurines showing stylised jaguars or humans with jaguar characteristics. In the later Maya civilization, the jaguar was believed to facilitate communication between the living and the dead and to protect the royal household. The Maya saw these powerful felines as their companions in the spiritual world, and a number of Maya rulers bore names that incorporated the Mayan word for jaguar ("b'alam" in many of the Mayan languages). "Balam" ("Jaguar") remains a common Maya surname, and it is also the name of Chilam Balam, a legendary author to whom are attributed 17th and 18th-centuries Maya miscellanies preserving much important knowledge. The Aztec civilization shared this image of the jaguar as the representative of the ruler and as a warrior. The Aztecs formed an elite warrior class known as the Jaguar Knights. In Aztec mythology, the jaguar was considered to be the totem animal of the powerful deity Tezcatlipoca. Remains of jaguar bones were discovered in a burial site in Guatemala which indicates that Mayans kept jaguars as pets. The jaguar and its name are widely used as a symbol in contemporary culture. It is the national animal of Guyana, and is featured in its coat of arms. The flag of the Department of Amazonas, a Colombian department, features a black jaguar silhouette pouncing towards a hunter. The jaguar also appears in banknotes of Brazilian real. The jaguar is also a common fixture in the mythology of many contemporary native cultures in South America, usually being portrayed as the creature which gave humans the power over fire. Jaguar is widely used as a product name, most prominently for a British luxury car brand. The name has been adopted by sports franchises, including the NFL's Jacksonville Jaguars and the Mexican soccer club Chiapas F.C. The crest of Argentina's national federation in rugby union features a jaguar; however, because of a journalist error, the country's national team is nicknamed "Los Pumas". In the spirit of the ancient Mayan culture, the 1968 Olympics in Mexico City adopted a red jaguar as the first official Olympic mascot.

The jaguar ("Panthera onca") is a large felid species and the only extant member of the genus "Panthera" native to the Americas. The jaguar's present range extends from Southwestern United States and Mexico in North America, across much of Central America, and south to Paraguay and northern Argentina in South America. Though there are single cats now living within the Western United States, the species has largely been extirpated from the United States since the early 20th century. It is listed as Near Threatened on the IUCN Red List; and its numbers are declining. Threats include loss and fragmentation of habitat.

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summarize: The ancient Greek philosopher Archimedes discovered the center of gravity of a triangle. He also postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity. The Roman architect and engineer Vitruvius in "De Architectura" postulated that gravity of an object did not depend on weight but its "nature". In ancient India, Aryabhata first identified the force to explain why objects are not thrown outward as the earth rotates. Brahmagupta described gravity as an attractive force and used the term "gurutvaakarshan" for gravity. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitational acceleration is the same for all objects. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass fall more slowly in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity. In 1687, English mathematician Sir Isaac Newton published "Principia", which hypothesizes the inverse-square law of universal gravitation. In his own words, "I deduced that the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth; and found them answer pretty nearly." The equation is the following: formula_1 Where "F" is the force, "m" and "m" are the masses of the objects interacting, "r" is the distance between the centers of the masses and "G" is the gravitational constant. Newton's theory enjoyed its greatest success when it was used to predict the existence of Neptune based on motions of Uranus that could not be accounted for by the actions of the other planets. Calculations by both John Couch Adams and Urbain Le Verrier predicted the general position of the planet, and Le Verrier's calculations are what led Johann Gottfried Galle to the discovery of Neptune. A discrepancy in Mercury's orbit pointed out flaws in Newton's theory. By the end of the 19th century, it was known that its orbit showed slight perturbations that could not be accounted for entirely under Newton's theory, but all searches for another perturbing body (such as a planet orbiting the Sun even closer than Mercury) had been fruitless. The issue was resolved in 1915 by Albert Einstein's new theory of general relativity, which accounted for the small discrepancy in Mercury's orbit. This discrepancy was the advance in the perihelion of Mercury of 42.98 arcseconds per century. Although Newton's theory has been superseded by Albert Einstein's general relativity, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is simpler to work with and it gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies. The equivalence principle, explored by a succession of researchers including Galileo, Loránd Eötvös, and Einstein, expresses the idea that all objects fall in the same way, and that the effects of gravity are indistinguishable from certain aspects of acceleration and deceleration. The simplest way to test the weak equivalence principle is to drop two objects of different masses or compositions in a vacuum and see whether they hit the ground at the same time. Such experiments demonstrate that all objects fall at the same rate when other forces (such as air resistance and electromagnetic effects) are negligible. More sophisticated tests use a torsion balance of a type invented by Eötvös. Satellite experiments, for example STEP, are planned for more accurate experiments in space. Formulations of the equivalence principle include: In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground. In Newtonian physics, however, no such acceleration can occur unless at least one of the objects is being operated on by a force. Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. Like Newton's first law of motion, Einstein's theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, we are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us, and we are non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial. Einstein discovered the field equations of general relativity, which relate the presence of matter and the curvature of spacetime and are named after him. The Einstein field equations are a set of 10 simultaneous, non-linear, differential equations. The solutions of the field equations are the components of the metric tensor of spacetime. A metric tensor describes a geometry of spacetime. The geodesic paths for a spacetime are calculated from the metric tensor. Notable solutions of the Einstein field equations include: The tests of general relativity included the following: An open question is whether it is possible to describe the small-scale interactions of gravity with the same framework as quantum mechanics. General relativity describes large-scale bulk properties whereas quantum mechanics is the framework to describe the smallest scale interactions of matter. Without modifications these frameworks are incompatible. One path is to describe gravity in the framework of quantum field theory, which has been successful to accurately describe the other fundamental interactions. The electromagnetic force arises from an exchange of virtual photons, where the QFT description of gravity is that there is an exchange of virtual gravitons. This description reproduces general relativity in the classical limit. However, this approach fails at short distances of the order of the Planck length, where a more complete theory of quantum gravity (or a new approach to quantum mechanics) is required. Every planetary body (including the Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of the gravitational field is numerically equal to the acceleration of objects under its influence. The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities. For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures, under the International System of Units (SI). That value, denoted "g", is "g" = 9.80665 m/s (32.1740 ft/s). The standard value of 9.80665 m/s is the one originally adopted by the International Committee on Weights and Measures in 1901 for 45° latitude, even though it has been shown to be too high by about five parts in ten thousand. This value has persisted in meteorology and in some standard atmospheres as the value for 45° latitude even though it applies more precisely to latitude of 45°32'33". Assuming the standardized value for g and ignoring air resistance, this means that an object falling freely near the Earth's surface increases its velocity by 9.80665 m/s (32.1740 ft/s or 22 mph) for each second of its descent. Thus, an object starting from rest will attain a velocity of 9.80665 m/s (32.1740 ft/s) after one second, approximately 19.62 m/s (64.4 ft/s) after two seconds, and so on, adding 9.80665 m/s (32.1740 ft/s) to each resulting velocity. Also, again ignoring air resistance, any and all objects, when dropped from the same height, will hit the ground at the same time. According to Newton's 3rd Law, the Earth itself experiences a force equal in magnitude and opposite in direction to that which it exerts on a falling object. This means that the Earth also accelerates towards the object until they collide. Because the mass of the Earth is huge, however, the acceleration imparted to the Earth by this opposite force is negligible in comparison to the object's. If the object does not bounce after it has collided with the Earth, each of them then exerts a repulsive contact force on the other which effectively balances the attractive force of gravity and prevents further acceleration. The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the centrifugal force caused by the Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s at the Equator to about 9.832 m/s at the poles. Under an assumption of constant gravitational attraction, Newton's law of universal gravitation simplifies to "F" = "mg", where "m" is the mass of the body and "g" is a constant vector with an average magnitude of 9.81 m/s on Earth. This resulting force is the object's weight. The acceleration due to gravity is equal to this "g". An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first of a second the ball drops one unit of distance (here, a unit is about 12 mm); by it has dropped at total of 4 units; by, 9 units and so on. Under the same constant gravity assumptions, the potential energy, "E", of a body at height "h" is given by "E" = "mgh" (or "E" = "Wh", with "W" meaning weight). This expression is valid only over small distances "h" from the surface of the Earth. Similarly, the expression formula_2 for the maximum height reached by a vertically projected body with initial velocity "v" is useful for small heights and small initial velocities only. The application of Newton's law of gravity has enabled the acquisition of much of the detailed information we have about the planets in the Solar System, the mass of the Sun, and details of quasars; even the existence of dark matter is inferred using Newton's law of gravity. Although we have not traveled to all the planets nor to the Sun, we know their masses. These masses are obtained by applying the laws of gravity to the measured characteristics of the orbit. In space an object maintains its orbit because of the force of gravity acting upon it. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters. The force of gravity exerted on one object by another is directly proportional to the product of those objects' masses and inversely proportional to the square of the distance between them. The earliest gravity (possibly in the form of quantum gravity, supergravity or a gravitational singularity), along with ordinary space and time, developed during the Planck epoch (up to 10 seconds after the birth of the Universe), possibly from a primeval state (such as a false vacuum, quantum vacuum or virtual particle), in a currently unknown manner. General relativity predicts that energy can be transported out of a system through gravitational radiation. Any accelerating matter can create curvatures in the space-time metric, which is how the gravitational radiation is transported away from the system. Co-orbiting objects can generate curvatures in space-time such as the Earth-Sun system, pairs of neutron stars, and pairs of black holes. Another astrophysical system predicted to lose energy in the form of gravitational radiation are exploding supernovae. The first indirect evidence for gravitational radiation was through measurements of the Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993. The first direct evidence for gravitational radiation was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion-light years from Earth were measured. This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including the Big Bang. Neutron star and black hole formation also create detectable amounts of gravitational radiation. This research was awarded the Nobel Prize in physics in 2017. , the gravitational radiation emitted by the Solar System is far too small to measure with current technology. In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light. This means that if the Sun suddenly disappeared, the Earth would keep orbiting it normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in the Chinese Science Bulletin in February 2013. In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from the same direction. This confirmed that the speed of gravitational waves was the same as the speed of light. There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways.

Gravity (), or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or "gravitate" toward) one another. On Earth, gravity gives weight to physical objects, and the Moon's gravity causes the ocean tides. The gravitational attraction of the original gaseous matter present in the Universe caused it to begin coalescing and forming stars and caused the stars to group together into galaxies, so gravity is responsible for many of the large-scale structures in the Universe. Gravity has an infinite range, although its effects become increasingly weaker as objects get further away.

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summarize: The "Belgae" were the inhabitants of the northernmost part of Gaul, which was significantly bigger than modern Belgium. Caesar used the word ""Belgium"" once, to refer to their region. "Gallia Belgica", as it was more commonly called, became a Roman province as a result of his conquests. Areas closer to the Rhine frontier, including the eastern part of modern Belgium, eventually became part of the province of "Germania Inferior", which interacted with Germanic tribes outside the empire. At the time when central government collapsed in the Western Roman Empire, the region of Belgium was inhabited by a mix of Frankish tribes and a more Romanized population. During the 5th century the area came under the rule of the Merovingian kings, who had already seized power in what is northern France. A gradual shift of power during the 8th century led the kingdom of the Franks to evolve into the Carolingian Empire. The Treaty of Verdun in 843 divided the Carolingian empire into three kingdoms, whose borders had a lasting impact on medieval political boundaries. Most of modern Belgium was in the Middle Kingdom, later known as Lotharingia. In 1830, the Belgian Revolution led to the separation of the Southern Provinces from the Netherlands and to the establishment of a Catholic and bourgeois, officially French-speaking and neutral, independent Belgium under a provisional government and a national congress. Since the installation of Leopold I as king on 1831, now celebrated as Belgium's National Day, Belgium has been a constitutional monarchy and parliamentary democracy, with a laicist constitution based on the Napoleonic code. Although the franchise was initially restricted, universal suffrage for men was introduced after the general strike of 1893 (with Belgium shares borders with France (), Germany (), Luxembourg () and the Netherlands (). Its total surface, including water area, is. Before 2018, its total area was believed to be. However, when the country's statistics were measured in 2018, a new calculation method was used. Unlike previous calculations, this one included the area from the coast to the low-water line, revealing the country to be larger in surface area than previously thought. Its land area alone is 30,278 km. It lies between latitudes 49°30' and 51°30' N, and longitudes 2°33' and 6°24' E. Belgium has three main geographical regions; the coastal plain in the northwest and the central plateau both belong to the Anglo-Belgian Basin, and the Ardennes uplands in the southeast to the Hercynian orogenic belt. The Paris Basin reaches a small fourth area at Belgium's southernmost tip, Belgian Lorraine. The coastal plain consists mainly of sand dunes and polders. Further inland lies a smooth, slowly rising landscape irrigated by numerous waterways, with fertile valleys and the northeastern sandy plain of the Campine ("Kempen"). The thickly forested hills and plateaus of the Ardennes are more rugged and rocky with caves and small gorges. Extending westward into France, this area is eastwardly connected to the Eifel in Germany by the High Fens plateau, on which the Signal de Botrange forms the country's highest point at. The climate is maritime temperate with significant precipitation in all seasons (Köppen climate classification: "Cfb"), like most of northwest Europe. The average temperature is lowest in January at and highest in July at. The average precipitation per month varies between for February and April, to for July. Averages for the years 2000 to 2006 show daily temperature minimums of and maximums of and monthly rainfall of ; these are about 1 °C and nearly 10 millimetres above last century's normal values, respectively. Phytogeographically, Belgium is shared between the Atlantic European and Central European provinces of the Circumboreal Region within the Boreal Kingdom. According to the World Wide Fund for Nature, the territory of Belgium belongs to the ecoregion of Atlantic mixed forests. Because of its high population density, industrialization and its location in the center of Western Europe, Belgium still faces some environmental problems. However, due to consistent efforts by the various levels of government in Belgium, the state of the environment in Belgium is gradually improving. This led to Belgium being ranked as one of the top 10 countries (9 out of 132) in terms of environmental protection trends, and to Belgium being ranked in 2012 as the 24th country out of 132 for environmental protection. Belgium moreover has one of Europe's highest waste recycling rates. In particular, the Flemish region of Belgium has the highest waste diversion rate in Europe. Almost 75 percent of the residential waste produced there is reused, recycled, or composted. Belgium is a constitutional, popular monarchy and a federal parliamentary democracy. The bicameral federal parliament is composed of a Senate and a Chamber of Representatives. The former is made up of 50 senators appointed by the parliaments of the communities and regions and 10 co-opted senators. Prior to 2014, most of the Senate's members were directly elected. The Chamber's 150 representatives are elected under a proportional voting system from 11 electoral districts. Belgium has compulsory voting and thus maintains one of the highest rates of voter turnout in the world. The King (currently Philippe) is the head of state, though with limited prerogatives. He appoints ministers, including a Prime Minister, that have the confidence of the Chamber of Representatives to form the federal government. The Council of Ministers is composed of no more than fifteen members. With the possible exception of the Prime Minister, the Council of Ministers is composed of an equal number of Dutch-speaking members and French-speaking members. The judicial system is based on civil law and originates from the Napoleonic code. The Court of Cassation is the court of last resort, with the courts of appeal one level below. Belgium's political institutions are complex; most political power is organized around the need to represent the main cultural communities. Since about 1970, the significant national Belgian political parties have split into distinct components that mainly represent the political and linguistic interests of these communities. The major parties in each community, though close to the political center, belong to three main groups: Christian Democrats, Liberals, and Social Democrats. Further notable parties came into being well after the middle of last century, mainly around linguistic, nationalist, or environmental themes and recently smaller ones of some specific liberal nature. A string of Christian Democrat coalition governments from 1958 was broken in 1999 after the Following a usage which can be traced back to the Burgundian and Habsburg courts, in the 19th century it was necessary to speak French to belong to the governing upper class, and those who could only speak Dutch were effectively second-class citizens. Late that century, and continuing into the 20th century, Flemish movements evolved to counter this situation. While the people in Southern Belgium spoke French or dialects of French, and most Brusselers adopted French as their first language, the Flemings refused to do so and succeeded progressively in making Dutch an equal language in the education system. Following World War II, Belgian politics became increasingly dominated by the autonomy of its two main linguistic communities. Intercommunal tensions rose and the constitution was amended to minimize the potential for conflict. The Federal State's authority includes justice, defense, federal police, social security, nuclear energy, monetary policy and public debt, and other aspects of public finances. State-owned companies include the Belgian Post Group and Belgian Railways. The Federal Government is responsible for the obligations of Belgium and its federalized institutions towards the European Union and NATO. It controls substantial parts of public health, home affairs and foreign affairs. The budget—without the debt—controlled by the federal government amounts to about 50% of the national fiscal income. The federal government employs around 12% of the civil servants. Communities exercise their authority only within linguistically determined geographical boundaries, originally oriented towards the individuals of a Community's language: culture (including audiovisual Because of its location at the crossroads of Western Europe, Belgium has historically been the route of invading armies from its larger neighbors. With virtually defenseless The Belgian Armed Forces have about 47,000 active troops. In 2010, Belgium's defense budget totaled €3.95 billion (representing 1.12% of its GDP). They are organized into one unified structure which consists of four main components: Land Component, or the Army; Air Component, or the Air Force; Naval Component, or the Navy; Medical Component. The operational commands of the four components are subordinate to the Staff Department for Operations and Training of the Ministry of Defense, which is headed by the Assistant Belgium's strongly globalized economy and its transport infrastructure are integrated with the rest of Europe. Its location at the heart of a highly industrialized region helped make it the world's 15th largest trading nation in 2007. The economy is characterized by a highly productive work force, high GNP and high exports per capita. Belgium's main imports are raw materials, machinery and equipment, chemicals, raw diamonds, pharmaceuticals, foodstuffs, transportation equipment, and oil products. Its main exports are machinery and equipment, chemicals, finished diamonds, metals and metal products, and foodstuffs. The Belgian economy is heavily service-oriented and shows a dual nature: a dynamic Flemish economy and a Walloon economy that lags behind. One of the founding members of the European Union, Belgium strongly supports an open economy and the extension of the powers of EU institutions to integrate member economies. Since 1922, through the Belgium-Luxembourg Economic Union, Belgium and Luxembourg have been a single trade market with customs and currency union. Belgium was the first continental European country to undergo the Industrial Revolution, in the early 19th century. Liège and Charleroi rapidly developed mining and steelmaking, which flourished until the mid-20th century in the Sambre and Meuse valley and made Belgium one of the three most industrialized nations in the world from 1830 to 1910. However, by the 1840s the textile industry of Flanders was in severe crisis, and the region experienced famine from 1846 to 1850. After World War II, Ghent and Antwerp experienced a rapid expansion of the chemical and petroleum industries. The 1973 and 1979 oil crises sent the economy into a recession; it was particularly prolonged in Wallonia, where the steel industry had become less competitive and experienced a serious decline. In the 1980s and 1990s, the economic center of the country continued to shift northwards and is now concentrated in the populous Flemish Diamond area. By the end of the 1980s, Belgian macroeconomic policies had resulted in a cumulative government debt of about 120% of GDP., the budget was balanced and public debt was equal to 90.30% of GDP. In 2005 and 2006, real GDP growth rates of 1.5% and 3.0%, respectively, were slightly above the average for the Euro area. Unemployment rates of 8.4% in 2005 and 8.2% in 2006 were close to the area average. By, this had grown to 8.5% compared to an average rate of 9.6% for the European Union as a whole (EU 27). From 1832 until 2002, Belgium's currency was the Belgian franc. Belgium switched to the euro in 2002, with the first sets of euro coins being minted in 1999. The standard Belgian euro coins designated for circulation show the portrait of the monarch (first King Albert II, since 2013 King Philippe). Despite an 18% decrease observed from 1970 to 1999, Belgium still had in 1999 the highest rail network density within the European Union with 113.8 km/1 000 km. On the other hand, the same period, 1970–1999, has seen a huge growth (+56%) of the motorway network. In 1999, the density of km motorways per 1000 km and 1000 inhabitants amounted to 55.1 and 16.5 respectively and were significantly superior to the EU's means of 13.7 and 15.9. From a biological resource perspective, Belgium has a low endowment: Belgium's biocapacity adds up to only 0.8 global hectares in 2016, just about half of the 1.6 global hectares of biocapacity available per person worldwide. In contrast, in 2016, Belgians used on average 6.3 global hectares of biocapacity - their ecological footprint of consumption. This means they required about eight times as much biocapacity as Belgium contains. As a result, Belgium was running a biocapacity deficit of 5.5 global hectares per person in 2016. Belgium experiences some of the most congested traffic in Europe. In 2010, commuters to the cities of Brussels and Antwerp spent respectively 65 and 64 hours a year in traffic jams. Like in most small European countries, more than 80% of the airways traffic is handled by a single airport, the Brussels Airport. The ports of Antwerp and Zeebrugge (Bruges) share more than 80% of Belgian maritime traffic, Antwerp being the second European harbor with a gross weight of goods handled of 115 988 000 t in 2000 after a growth of 10.9% over the preceding five years. In 2016, the port of Antwerp handled 214 million tons after a year-on-year growth of 2.7%. There is a large economic gap between Flanders and Wallonia. Wallonia was historically wealthy compared to Flanders, mostly due to its heavy industries, but the decline of the steel industry post-World War II led to the region's rapid decline, whereas Flanders rose swiftly. Since then, Flanders has been prosperous, among the wealthiest regions in Europe, whereas Wallonia has been languishing. As of 2007, the unemployment rate of Wallonia is over double that of Flanders. The divide has played a key part in the tensions between the Flemish and Walloons in addition to the already-existing language divide. Pro-independence movements have gained high popularity in Flanders as a consequence. The separatist New Flemish Alliance (N-VA) party, for instance, is the largest party in Belgium. As of 1 January 2020, the total population of Belgium according to its population register was 11,492,641. The population density of Belgium is as of January 2019, making it the 22nd most densely populated country in the world, and the 6th most densely populated country in Europe. The most densily populated province is Antwerp, the least densily populated province is Luxembourg. As of January 2019, the Flemish Region had a population of 6,589,069 (57.6% of Belgium), its most populous cities being Antwerp (523,248), Ghent (260,341) and Bruges (118,284). Wallonia had a population of 3,633,795 (31.8% of Belgium) with Charleroi (201,816), Liège (197,355) and Namur (110,939), its most populous cities. The Brussels Capital Region has 1,208,542 inhabitants (10.6% of Belgium) in the 19 municipalities, three of which have over 100,000 residents. In 2017 the average total fertility rate (TFR) across Belgium was 1.64 children per woman, below the replacement rate of 2.1, it remains considerably below the high of 4.87 children born per woman in 1873. Belgium subsequently has one of the oldest populations in the world, with the average age of 41.5 years. , nearly 92% of the population had Belgian citizenship, and other European Union member citizens account for around 6%. The prevalent foreign nationals were Italian (171,918), French (125,061), Dutch (116,970), Moroccan (80,579), Portuguese (43,509), Spanish (42,765), Turkish (39,419) and German (37,621). In 2007, there were 1.38 million foreign-born residents in Belgium, corresponding to 12.9% of the total population. Of these, 685,000 (6.4%) were born outside the EU and 695,000 (6.5%) were born in another EU Member Belgium has three official languages: Dutch, French and German. A number of non-official minority languages are spoken as well. As no census exists, there are no official statistical data regarding the distribution or usage of Belgium's three official languages or their dialects. However, various criteria, including the language(s) of parents, of education, or the second-language status of foreign born, may provide suggested figures. An estimated 60% of the Belgian population are native speakers of Dutch (often referred to as Flemish), and 40% of the population speaks French natively. French-speaking Belgians are often referred to as Walloons, although the French speakers in Brussels are not Walloons. The total number Since the country's independence, Roman Catholicism, counterbalanced by strong freethought movements, has had an important role in Belgium's politics. However Belgium is largely a secular country as the constitution provides for freedom of religion, and the government generally respects this right in practice. During the reigns of Albert I and Baudouin, the Belgian royal family had a reputation of deeply rooted Catholicism. Roman Catholicism has traditionally been Belgium's majority religion; being especially strong in Flanders. However, by 2009 Sunday church attendance was 5% for Belgium in total; The Belgians enjoy good health. According to 2012 estimates, the average life expectancy is 79.65 years. Since 1960, life expectancy has, in line with the European average, grown by two months per year. Death in Belgium is mainly due to heart and vascular disorders, neoplasms, disorders of the respiratory system and unnatural causes of death (accidents, suicide). Non-natural causes of death and cancer are the most common causes of death for females up to age 24 and males up to age 44. Healthcare in Belgium is financed through both social security contributions and taxation. Health insurance is compulsory. Health care is delivered by a mixed public and private system Education is compulsory from 6 to 18 years of age for Belgians. Among OECD countries in 2002, Belgium had the third highest proportion of 18- to 21-year-olds enrolled in postsecondary education, at 42%. Though an estimated 99% of the adult population is literate, concern is rising over functional illiteracy. The Programme for International Student Assessment (PISA), coordinated by the OECD, currently ranks Belgium's education Despite its political and linguistic divisions, the region corresponding to today's Belgium has seen the flourishing of major artistic movements that have had tremendous influence on European art and culture. Nowadays, to a certain extent, cultural life is concentrated within each language Community, and a variety of barriers have made a shared cultural sphere less pronounced. Since the 1970s, there are no bilingual universities or colleges in the country except the Royal Military Academy and the Antwerp Maritime Academy, no common media and no single large cultural or scientific organization in which both main communities are represented. Contributions to painting and architecture have been especially rich. The Mosan art, the Early Netherlandish, the Flemish Renaissance and Baroque painting and major examples of Romanesque, Gothic, Renaissance and Baroque architecture are milestones in the history of art. While the 15th century's art in the Low Countries is dominated by the religious paintings of Jan van Eyck and Rogier van der Weyden, the 16th century is characterized by a broader panel of styles such as Peter Breughel's landscape paintings and Lambert Lombard's representation of the antique. Though the Baroque style of Peter Paul Rubens and Anthony van Dyck flourished in the early 17th century in the Southern Netherlands, it gradually declined thereafter. During the 19th and 20th centuries many original romantic, expressionist and surrealist Belgian painters emerged, including James Ensor and other artists belonging to the Les XX group, Constant Permeke, Paul Delvaux and René Magritte. The avant-garde CoBrA movement appeared in the 1950s, while the sculptor Panamarenko remains a remarkable figure in contemporary art. Multidisciplinary artists Jan Fabre, Wim Delvoye and the painter Luc Tuymans are other internationally renowned figures on the contemporary art scene. Belgian contributions to architecture also continued into the 19th and 20th centuries, including the work of Victor Horta and Henry van de Velde, who were major initiators of Folklore plays a major role in Belgium's cultural life: the country has a comparatively high number of processions, cavalcades, parades, 'ommegangs' and 'ducasses', 'kermesse' and other local festivals, nearly always with an originally religious or mythological background. The Carnival of Binche with its famous Gilles and the 'Processional Giants and Dragons' of Ath, Brussels, Dendermonde, Mechelen and Mons are Many highly ranked Belgian restaurants can be found in the most influential restaurant guides, such as the Michelin Guide. Belgium is famous for beer, chocolate, waffles and french fries with mayonnaise. Contrary to their name, french fries are claimed to have originated in Belgium, although their exact place of origin is uncertain. The national Since the 1970s, sports clubs and federations are organized separately within each language community. Association football is the most popular sport in both parts of Belgium; also very popular are cycling, tennis, swimming, judo and basketball. Belgians hold the most Tour de France victories of any country except France. They have also the most victories on the UCI Road World Championships. Philippe Gilbert is the 2012 world champion. Another modern well-known Belgian cyclist is Tom Boonen. With five victories in the Tour de France and numerous other cycling records, Belgian cyclist Eddy Merckx is regarded as one of the greatest cyclists of all time. Jean-Marie Pfaff, a former Belgian goalkeeper, is considered one of the greatest in the history of association

Belgium, officially the Kingdom of Belgium, is a country in Western Europe. It is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to the southwest, and the North Sea to the northwest. It covers an area of and has a population of more than 11.5 million, making it the 22nd most densely populated country in the world and the 6th most densely populated country in Europe, with a density of. The capital and largest city is Brussels; other major cities are Antwerp, Ghent, Charleroi and Liège.

en

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summarize: In three dimensions, any set of three-dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used. Commonly, one uses the familiar Cartesian coordinate system, or sometimes spherical polar coordinates, or cylindrical coordinates: where "t" is a parameter, owing to their rectangular or circular symmetry. These different coordinates and corresponding basis vectors represent the same position vector. More general curvilinear coordinates could be used instead and are in contexts like continuum mechanics and general relativity (in the latter case one needs an additional time coordinate). Linear algebra allows for the abstraction of an "n"-dimensional position vector. A position vector can be expressed as a linear combination of basis vectors: The set of all position vectors forms position space (a vector space whose elements are the position vectors), since positions can be added (vector addition) and scaled in length (scalar multiplication) to obtain another position vector in the space. The notion of "space" is intuitive, since each "x" ("i" = 1, 2,..., "n") can have any value, the collection of values defines a point in space. The "dimension" of the position space is "n" (also denoted dim("R") = "n"). The "coordinates" of the vector r with respect to the basis vectors e are "x". The vector of coordinates forms the coordinate vector or "n"-tuple ("x", "x",..., "x"). Each coordinate "x" may be parameterized a number of parameters "t". One parameter "x"("t") would describe a curved 1D path, two parameters "x"("t", "t") describes a curved 2D surface, three "x"("t", "t", "t") describes a curved 3D volume of space, and so on. The linear span of a basis set "B" = {e, e,..., e} equals the position space "R", denoted span("B") = "R". Position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter needs not be time, but can be (e.g.) arc length of the curve. In any equation of motion, the position vector r("t") is usually the most sought-after quantity because this function defines the motion of a particle (i.e. a point mass) – its location relative to a given coordinate system at some time "t". To define motion in terms of position, each coordinate may be parametrized by time; since each successive value of time corresponds to a sequence of successive spatial locations given by the coordinates, the continuum limit of many successive locations is a path the particle traces. In the case of one dimension, the position has only one component, so it effectively degenerates to a scalar coordinate. It could be, say, a vector in the "x" direction, or the radial "r" direction. Equivalent notations include For a position vector r that is a function of time "t", the time derivatives can be computed with respect to "t". These derivatives have common utility in the study of kinematics, control theory, engineering and other sciences. where dr is an infinitesimally small displacement (vector). These names for the first, second and third derivative of position are commonly used in basic kinematics. By extension, the higher-order derivatives can be computed in a similar fashion. Study of these higher-order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to accurately represent the displacement function as a sum of an infinite sequence, enabling several analytical techniques in engineering and physics.

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point "P" in space in relation to an arbitrary reference origin "O". Usually denoted x, r, or s, it corresponds to the straight line segment from "O" to "P". In other words, it is the displacement or translation that maps the origin to "P":

en

89

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summarize: The speed of light in a fluid is slower than the speed of light in vacuum, and it changes if the fluid is moving along with the light. In 1851, Fizeau measured the speed of light in a fluid moving parallel to the light using a interferometer. Fizeau's results were not in accord with the then-prevalent theories. Fizeau experimentally correctly determined the zeroth term of an expansion of the relativistically correct addition law in terms of as is described below. Fizeau's result led physicists to accept the empirical validity of the rather unsatisfactory theory by Fresnel that a fluid moving with respect to the stationary aether "partially" drags light with it, i.e. the speed is instead of, where is the speed of light in the aether, and is the speed of the fluid with respect to the aether. The aberration of light, of which the easiest explanation is the relativistic velocity addition formula, together with Fizeau's result, triggered the development of theories like Lorentz aether theory of electromagnetism in 1892. In 1905 Albert Einstein, with the advent of special relativity, derived the standard configuration formula ( in the ) for the addition of relativistic velocities. The issues involving aether were, gradually over the years, settled in favor of special relativity. It was observed by Galilei that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward. This observation is now regarded as the first clear statement of the principle of mechanical relativity. Galilei saw that from the point of view of a person standing on the shore, the motion of falling downwards on the ship would be combined with, or added to, the forward motion of the ship. In terms of velocities it can be said that the velocity of the falling body relative to the shore equals the velocity of that body relative to ship plus the velocity of the ship relative to the shore. In general for three objects A (e.g. Galilei on the shore), B (e.g. ship), C (e.g. falling body on ship) the velocity vector formula_1 of C relative to A (velocity of falling object as Galilei sees it) is the sum of the velocity formula_2 of C relative to B (velocity of falling object relative to ship) plus the velocity of B relative to A (ship's velocity away from the shore). The addition here is the vector addition of vector algebra and the resulting velocity is usually represented in the form The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of Galilean transformations. The relativity principle is called Galilean relativity. It is obeyed by Newtonian mechanics. According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. This change is not noticeable at low velocities but as the velocity increases towards the speed of light it becomes important. The addition law is also called a composition law for velocities. For collinear motions, the speed of the object (e.g. a cannonball fired horizontally out to sea) as measured from the ship would be measured by someone standing on the shore and watching the whole scene through a telescope as The composition formula can take an algebraically equivalent form, which can be easily derived by using only the principle of constancy of the speed of light, The cosmos of special relativity consists of Minkowski spacetime and the addition of velocities corresponds to composition of Lorentz transformations. In the special theory of relativity Newtonian mechanics is modified into relativistic mechanics. The formulas for boosts in the standard configuration follow most straightforwardly from taking differentials of the inverse Lorentz boost in standard configuration. If the primed frame is travelling with speed formula_6 with Lorentz factor formula_7 in the positive relative to the unprimed frame, then the differentials are Divide the first three equations by the fourth, or which is u_y'}{1 + \frac{v}{c^2}u_x'}, \quad u_y' = \frac{\sqrt{1-\frac{v^2}{c^2}}u_y}{1 - \frac{v}{c^2}u_x},</math> in which expressions for the primed velocities were obtained using the standard recipe by replacing by and swapping primed and unprimed coordinates. If coordinates are chosen so that all velocities lie in a (common) plane, then velocities may be expressed as (see polar coordinates) and one finds \tan \theta &= \frac{u_y}{u_x} = \frac{\sqrt{1-\frac{v^2}{c^2}}u_y'}{u_x' + v} = \frac{\sqrt{1-\frac{v^2}{c^2}}u'\sin \theta'}{u'\cos \theta' + v}.\end{align}</math> The proof as given is highly formal. There are other more involved proofs that may be more enlightening, such as the one below. Since a relativistic transformation rotates space and time into each other much as geometric rotations in the plane rotate the - and -axes, it is convenient to use the same units for space and time, otherwise a unit conversion factor appears throughout relativistic formulae, being the speed of light. In a system where lengths and times are measured in the same units, the speed of light is dimensionless and equal to. A velocity is then expressed as fraction of the speed of light. To find the relativistic transformation law, it is useful to introduce the four-velocities, which is the motion of the ship away from the shore, as measured from the shore, and which is the motion of the fly away from the ship, as measured from the ship. The four-velocity is defined to be a four-vector with relativistic length equal to, future-directed and tangent to the world line of the object in spacetime. Here, corresponds to the time component and to the component of the ship's velocity as seen from the shore. It is convenient to take the -axis to be the direction of motion of the ship away from the shore, and the -axis so that the plane is the plane spanned by the motion of the ship and the fly. This results in several components of the velocities being zero;. The ordinary velocity is the ratio of the rate at which the space coordinates are increasing to the rate at which the time coordinate is increasing, Since the relativistic length of is, so The Lorentz transformation matrix that converts velocities measured in the ship frame to the shore frame is the "inverse" of the transformation described on the Lorentz transformation page, so the minus signs that appear there must be inverted here: This matrix rotates the a pure time-axis vector to, and all its columns are relativistically orthogonal to one another, so it defines a Lorentz transformation. If a fly is moving with four-velocity in the ship frame, and it is boosted by multiplying by the matrix above, the new four-velocity in the shore frame is, Dividing by the time component and substituting for the components of the four-vectors and in terms of the components of the three-vectors and gives the relativistic composition law as The form of the relativistic composition law can be understood as an effect of the failure of simultaneity at a distance. For the parallel component, the time dilation decreases the speed, the length contraction increases it, and the two effects cancel out. The failure of simultaneity means that the fly is changing simultaneity slices as the projection of onto. Since this effect is entirely due to the time slicing, the same factor multiplies the perpendicular component, but for the perpendicular component there is no length contraction, so the time dilation multiplies by a factor of. Starting from the expression in coordinates for parallel to the, expressions for the perpendicular and parallel components can be cast in vector form as follows, a trick which also works for Lorentz transformations of other 3d physical quantities originally in set up standard configuration. Introduce the velocity vector in the unprimed frame and in the primed frame, and split them into components parallel (∥) and perpendicular (⊥) to the relative velocity vector (see hide box below) thus then with the usual Cartesian unit basis vectors, set the velocity in the unprimed frame to be which gives, using the results for the standard configuration, where · is the dot product. Since these are vector equations, they still have the same form for in "any" direction. The only difference from the coordinate expressions is that the above expressions refers to "vectors", not components. One obtains where is the reciprocal of the Lorentz factor. The ordering of operands in the definition is chosen to coincide with that of the standard configuration from which the formula is derived. Either the parallel or the perpendicular component for each vector needs to be found, since the other component will be eliminated by substitution of the full vectors. The parallel component of can be found by projecting the full vector into the direction of the relative motion and the perpendicular component of can be found by the geometric properties of the cross product (see figure above right), In each case, is a unit vector in the direction of relative motion. The expressions for and can be found in the same way. Substituting the parallel component into results in the above equation. Using an identity in formula_28 and formula_29, \left[\mathbf v + \frac{\mathbf u'}{\gamma_v} + \frac{1}{c^2}\frac{\gamma_v}{1+\gamma_v}(\mathbf u' \cdot \mathbf v)\mathbf v\right]\\ &= \frac{1}{1 + \frac{\mathbf u' \cdot \mathbf v}{c^2}}\left[\mathbf v + \mathbf u' + \frac{1}{c^2}\frac{\gamma_v}{1+\gamma_v} \mathbf v \times(\mathbf v \times \mathbf u')\right],\end{align}</math> where the last expression is by the standard vector analysis formula. The first expression extends to any number of spatial dimensions, but the cross product is defined in three dimensions only. The objects with having velocity relative to and having velocity relative to can be anything. In particular, they can be three frames, or they could be the laboratory, a decaying particle and one of the decay products of the decaying particle. The relativistic addition of 3-velocities is non-linear for any real numbers and, although it is true that Also, due to the last terms, is in general neither commutative nor associative It deserves special mention that if and refer to velocities of pairwise parallel frames (primed parallel to unprimed and doubly primed parallel to primed), then, according to Einstein's velocity reciprocity principle, the unprimed frame moves with velocity relative to the primed frame, and the primed frame moves with velocity relative to the doubly primed frame hence is the velocity of the unprimed frame relative to the doubly primed frame, and one might expect to have by naive application of the reciprocity principle. This does not hold, though the magnitudes are equal. The unprimed and doubly primed frames are "not" parallel, but related through a rotation. This is related to the phenomenon of Thomas precession, and is not dealt with further here. The norms are given by and Reverse formula found by using standard procedure of swapping for and for. It is clear that the non-commutativity manifests itself as an additional "rotation" of the coordinate frame when two boosts are involved, since the norm squared is the same for both orders of boosts. The gamma factors for the combined velocities are computed as Reverse formula found by using standard procedure of swapping for and for. Notations and conventions for the velocity addition vary from author to author. Different symbols may be used for the operation, or for the velocities involved, and the operands may be switched for the same expression, or the symbols may be switched for the same velocity. A completely separate symbol may also be used for the transformed velocity, rather than the prime used here. Since the velocity addition is non-commutative, one cannot switch the operands or symbols without changing the result. Examples of alternative notation include: Some classical applications of velocity-addition formulas, to the Doppler shift, to the aberration of light, and to the dragging of light in moving water, yielding relativistically valid expressions for these phenomena are detailed below. It is also possible to use the velocity addition formula, assuming conservation of momentum (by appeal to ordinary rotational invariance), the correct form of the -vector part of the momentum four-vector, without resort to electromagnetism, or a priori not known to be valid, relativistic versions of the Lagrangian formalism. This involves experimentalist bouncing off relativistic billiard balls from each other. This is not detailed here, but see for reference (primary source) and. When light propagates in a medium, its speed is reduced, in the rest frame of the medium, to, where is the index of refraction of the medium. The speed of light in a medium uniformly moving with speed in the positive -direction as measured in the lab frame is given directly by the velocity addition formulas. For the forward direction (standard configuration, drop index on ) one gets, Collecting the largest contributions explicitly, Fizeau found the first three terms. The classical result is the first two terms. Another basic application is to consider the deviation of light, i.e. change of its direction, when transforming to a new reference frame with parallel axes, called aberration of light. In this case,, and insertion in the formula for yields For this case one may also compute and from the standard formulae, the trigonometric manipulations essentially being identical in the case to the manipulations in the case. Consider the difference, correct to order. Employ in order to make small angle approximations a trigonometric formula, where were used. Thus the quantity the classical aberration angle, is obtained in the limit. Here "velocity components" will be used as opposed to "speed" for greater generality, and in order to avoid perhaps seemingly ad hoc introductions of minus signs. Minus signs occurring here will instead serve to illuminate features when speeds less than that of light are considered. For light waves in vacuum, time dilation together with a simple geometrical observation alone suffices to calculate the Doppler shift in standard configuration (collinear relative velocity of emitter and observer as well of observed light wave). All velocities in what follows are parallel to the common positive, so subscripts on velocity components are dropped. In the observers frame, introduce the geometrical observation as the spatial distance, or wavelength, between two pulses (wave crests), where is the time elapsed between the emission of two pulses. The time elapsed between the passage of two pulses "at the same point in space" is the "time period", and its inverse is the observed (temporal) frequency. The corresponding quantities in the emitters frame are endowed with primes. For light waves and the observed frequency is where is standard time dilation formula. Suppose instead that the wave is not composed of light waves with speed, but instead, for easy visualization, bullets fired from a relativistic machine gun, with velocity in the frame of the emitter. Then, in general, the geometrical observation is "precisely the same". But now,, and is given by velocity addition, The calculation is then essentially the same, except that here it is easier carried out upside down with instead of. One finds \right), \quad \nu = \gamma_{_V}\nu'\left(1+{V\over s'}\right)</math> Observe that in the typical case, the that enters is "negative". The formula has general validity though. When, the formula reduces to the formula calculated directly for light waves above, If the emitter is not firing bullets in empty space, but emitting waves in a medium, then the "formula still applies", but now, it may be necessary to first calculate from the velocity of the emitter relative to the medium. Returning to the case of a light emitter, in the case the observer and emitter are not collinear, the result has little modification, where is the angle between the light emitter and the observer. This reduces to the previous result for collinear motion when, but for transverse motion corresponding to, the frequency is shifted by the Lorentz factor. This does not happen in the classical optical Doppler effect. Associated to the relativistic velocity formula_60 of an object is a quantity formula_61 whose norm is called rapidity. These are related through where the vector formula_63 is thought of as being Cartesian coordinates on a 3-dimensional subspace of the Lie algebra formula_64 of the Lorentz group spanned by the boost generators formula_65. This space, call it "rapidity space", is isomorphic to as a vector space, and is mapped to the open unit ball, formula_66, "velocity space", via the above relation. The addition law on collinear form coincides with the law of addition of hyperbolic tangents with where the speed of light is set to unity so that formula_69 and formula_70 agree. It this expression, formula_71 and formula_72 are velocities of two objects in any one given frame. The quantity formula_73 is the speed of one or the other object "relative" to the other object as seen "in the given frame". The expression is Lorentz invariant, i.e. independent of which frame is the given frame, but the quantity it calculates is "not". For instance, if the given frame is the rest frame of object one, then formula_74. The line element is found by putting formula_75 or equivalently formula_76, with and the usual spherical angle coordinates for formula_60 taken in the -direction. Now introduce through and the line element on rapidity space formula_80 becomes In scattering experiments the primary objective is to measure the invariant scattering cross section. This enters the formula for scattering of two particle types into a final state formula_82 assumed to have two or more particles, where The objective is to find a correct expression for "relativistic relative speed" formula_95 and an invariant expression for the incident flux. Non-relativistically, one has for relative speed formula_96. If the system in which velocities are measured is the rest frame of particle type formula_97, it is required that formula_98 Setting the speed of light formula_99, the expression for formula_95 follows immediately from the formula for the norm (second formula) in the "general configuration" as The formula reduces in the classical limit to formula_102 as it should, and gives the correct result in the rest frames of the particles. The relative velocity is "incorrectly given" in most, perhaps "all" books on particle physics and quantum field theory. This is mostly harmless, since if either one particle type is stationary or the relative motion is collinear, then the right result is obtained from the incorrect formulas. The formula is invariant, but not manifestly so. It can be rewritten in terms of four-velocities as The correct expression for the flux, published by Christian Møller in 1945, is given by One notes that for collinear velocities, formula_105. In order to get a "manifestly" Lorentz invariant expression one writes formula_106 with formula_107, where formula_108is the density in the rest frame, for the individual particle fluxes and arrives at In the literature the quantity formula_110 as well as formula_73 are both referred to as the relative velocity. In some cases (statistical physics and dark matter literature), formula_110 is referred to as the "Møller velocity", in which case formula_73 means relative velocity. The true relative velocity is at any rate formula_95. The discrepancy between formula_95 and formula_73 is relevant though in most cases velocities are collinear. At LHC the crossing angle is small, around 300 rad, but at the old Intersecting Storage Ring at CERN, it was about 18.

In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as Thomas precession, whereby successive non-collinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.

en

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summarize: Prior to the Renaissance, the most generally accepted theory of motion in Western philosophy was based on Aristotle who around about 335 BC to 322 BC said that, in the absence of an external motive power, all objects (on Earth) would come to rest and that moving objects only continue to move so long as there is a power inducing them to do so. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, which continues to move the projectile in some way. Aristotle concluded that such violent motion in a void was impossible. Despite its general acceptance, Aristotle's concept of motion was disputed on several occasions by notable philosophers over nearly two millennia. For example, Lucretius (following, presumably, Epicurus) stated that the "default state" of matter was motion, not stasis. In the 6th century, John Philoponus criticized the inconsistency between Aristotle's discussion of projectiles, where the medium keeps projectiles going, and his discussion of the void, where the medium would hinder a body's motion. Philoponus proposed that motion was not maintained by the action of a surrounding medium, but by some property imparted to the object when it was set in motion. Although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was strongly opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, where Philoponus did have several supporters who further developed his ideas. In the 11th century, Persian polymath Ibn Sina (Avicenna) claimed that a projectile in a vacuum would not stop unless acted upon. In the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named "impetus", dissipated spontaneously. Buridan's position was that a moving object would be arrested by the resistance of the air and the weight of the body which would oppose its impetus. Buridan also maintained that impetus increased with speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Despite the obvious similarities to more modern ideas of inertia, Buridan saw his theory as only a modification to Aristotle's basic philosophy, maintaining many other peripatetic views, including the belief that there was still a fundamental difference between an object in motion and an object at rest. Buridan also believed that impetus could be not only linear, but also circular in nature, causing objects (such as celestial bodies) to move in a circle. Buridan's thought was followed up by his pupil Albert of Saxony (1316–1390) and the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs. Shortly before Galileo's theory of inertia, Giambattista Benedetti modified the growing theory of impetus to involve linear motion alone: Benedetti cites the motion of a rock in a sling as an example of the inherent linear motion of objects, forced into circular motion. According to historian of science Charles Coulston Gillispie, inertia "entered science as a physical consequence of Descartes' geometrization of space-matter, combined with the immutability of God." The principle of inertia, which originated with Aristotle for "motions in a void", states that an object tends to resist a change in motion. According to Newton, an object will stay at rest or stay in motion (i.e. maintain its velocity) unless acted on by a net external force, whether it results from gravity, friction, contact, or some other force. The Aristotelian division of motion into mundane and celestial became increasingly problematic in the face of the conclusions of Nicolaus Copernicus in the 16th century, who argued that the Earth is never at rest, but is actually in constant motion around the Sun. Galileo, in his further development of the Copernican model, recognized these problems with the then-accepted nature of motion and, at least partially as a result, included a restatement of Aristotle's description of motion in a void as a basic physical principle: A body moving on a level surface will continue in the same direction at a constant speed unless disturbed. Galileo writes that "all external impediments removed, a heavy body on a spherical surface concentric with the earth will maintain itself in that state in which it has been; if placed in movement towards the west (for example), it will maintain itself in that movement." This notion which is termed "circular inertia" or "horizontal circular inertia" by historians of science, is a precursor to, but distinct from, Newton's notion of rectilinear inertia. For Galileo, a motion is "horizontal" if it does not carry the moving body towards or away from the centre of the earth, and for him, "a ship, for instance, having once received some impetus through the tranquil sea, would move continually around our globe without ever stopping." It is also worth noting that Galileo later (in 1632) concluded that based on this initial premise of inertia, it is impossible to tell the difference between a moving object and a stationary one without some outside reference to compare it against. This observation ultimately came to be the basis for Albert Einstein to develop the theory of special relativity. The first physicist to completely break away from the Aristotelian model of motion was Isaac Beeckman in 1614. Concepts of inertia in Galileo's writings would later come to be refined, modified and codified by Isaac Newton as the first of his Laws of Motion (first published in Newton's work, "Philosophiae Naturalis Principia Mathematica", in 1687): Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon. Since initial publication, Newton's Laws of Motion (and by inclusion, this first law) have come to form the basis for the branch of physics known as classical mechanics. The term "inertia" was first introduced by Johannes Kepler in his "Epitome Astronomiae Copernicanae" (published in three parts from 1617–1621); however, the meaning of Kepler's term (which he derived from the Latin word for "idleness" or "laziness") was not quite the same as its modern interpretation. Kepler defined inertia only in terms of a resistance to movement, once again based on the presumption that rest was a natural state which did not need explanation. It was not until the later work of Galileo and Newton unified rest and motion in one principle that the term "inertia" could be applied to these concepts as it is today. Nevertheless, despite defining the concept so elegantly in his laws of motion, even Newton did not actually use the term "inertia" to refer to his First Law. In fact, Newton originally viewed the phenomenon he described in his First Law of Motion as being caused by "innate forces" inherent in matter, which resisted any acceleration. Given this perspective, and borrowing from Kepler, Newton attributed the term "inertia" to mean "the innate force possessed by an object which resists changes in motion"; thus, Newton defined "inertia" to mean the cause of the phenomenon, rather than the phenomenon itself. However, Newton's original ideas of "innate resistive force" were ultimately problematic for a variety of reasons, and thus most physicists no longer think in these terms. As no alternate mechanism has been readily accepted, and it is now generally accepted that there may not be one which we can know, the term "inertia" has come to mean simply the phenomenon itself, rather than any inherent mechanism. Thus, ultimately, "inertia" in modern classical physics has come to be a name for the same phenomenon described by Newton's First Law of Motion, and the two concepts are now considered to be equivalent. Albert Einstein's theory of special relativity, as proposed in his 1905 paper entitled "On the Electrodynamics of Moving Bodies" was built on the understanding of inertial reference frames developed by Galileo and Newton. While this revolutionary theory did significantly change the meaning of many Newtonian concepts such as mass, energy, and distance, Einstein's concept of inertia remained unchanged from Newton's original meaning. However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to inertial reference frames. To address this limitation, Einstein developed his general theory of relativity ("The Foundation of the General Theory of Relativity", 1916), which provided a theory including "noninertial" (accelerated) reference frames. A quantity related to inertia is "rotational inertia" (→ moment of inertia), the property that a rotating rigid body maintains its state of uniform rotational motion. Its angular momentum remains unchanged, unless an external torque is applied; this is also called conservation of angular momentum. Rotational inertia is often considered in relation to the a rigid body. For example, a gyroscope uses the property that it resists any change in the axis of rotation.

Inertia is the resistance of any physical object to any change in its velocity. This includes changes to the object's speed, or direction of motion. An aspect of this property is the tendency of objects to keep moving in a straight line at a constant speed, when no forces act upon them.

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summarize: Momentum is a vector quantity: it has both magnitude and direction. Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Below, the basic properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations (see multiple dimensions). The momentum of a particle is conventionally represented by the letter. It is the product of two quantities, the particle's mass (represented by the letter ) and its velocity (): The unit of momentum is the product of the units of mass and velocity. In SI units, if the mass is in kilograms and The momentum of a system of particles is the vector sum of their momenta. If two particles have respective masses and, and velocities and, the total momentum is The momenta of more than two particles can be added more generally with the following: A system of particles has a If the net force applied to a particle is constant, and is applied for a time interval, the momentum of the particle changes by an amount In differential form, this is Newton's second law; the rate of change of the momentum of a particle is equal to the instantaneous force acting on it, If the net force experienced by a particle changes as a function of time,, the change in momentum (or impulse ) between In a closed system (one that does not exchange any matter with its surroundings and is not acted on by external forces) the total momentum is constant. This fact, known as the "law of conservation of momentum", is implied by Newton's laws of motion. Suppose, for example, that two particles interact. Because of the third law, the forces between them are equal and opposite. If the particles are numbered 1 and 2, the second Momentum is a measurable quantity, and the measurement depends on the motion of the observer. For example: if an apple is sitting in a glass elevator that is descending, an outside observer, looking into the elevator, sees the apple moving, so, to that observer, the apple has a non-zero momentum. To someone inside the elevator, the apple does not move, so, it has zero momentum. The two observers each have a frame of reference, in which, they observe motions, and, if the elevator is descending steadily, they will see behavior that is consistent with those same physical laws. Suppose a particle has position in a stationary frame of reference. From the point of view of By itself, the law of conservation of momentum is not enough to determine the motion of particles after a collision. Another property of the motion, kinetic energy, must be known. This is not necessarily conserved. If it is conserved, the collision is called an "elastic collision"; if not, it is an "inelastic collision". An elastic collision is one in which no kinetic energy is absorbed in the collision. Perfectly elastic "collisions" can occur when the objects do not touch each other, as for example in atomic or nuclear scattering where electric repulsion keeps them apart. A slingshot maneuver of a satellite around a planet can also be viewed as a perfectly elastic collision. A collision between two pool balls is a good example of an "almost" totally elastic collision, due to their high rigidity, but when bodies come in contact there is always some dissipation. A head-on elastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision and and after, the equations In an inelastic collision, some of the kinetic energy of the colliding bodies is converted into other forms of energy (such as heat or sound). Examples include traffic collisions, in which the effect of loss of kinetic energy can be seen in the damage to the vehicles; electrons losing some of their energy to atoms (as in the Franck–Hertz experiment); and particle accelerators in which the kinetic energy is converted into mass in the form of new particles. In a perfectly inelastic collision (such as a bug hitting a windshield), both bodies have the same motion afterwards. A head-on inelastic collision between two bodies can be represented by velocities in one dimension, along a line passing through the bodies. If the velocities are and before the collision then in a perfectly inelastic collision both bodies will be travelling with velocity after the Real motion has both direction and velocity and must be represented by a vector. In a coordinate system with axes, velocity has components in the -direction, in the -direction, in the -direction. The vector is represented by a boldface symbol: Similarly, the momentum is a vector quantity and is represented by a boldface symbol: The equations in the previous sections, work in vector form if the scalars and are replaced by vectors and. Each vector equation The concept of momentum plays a fundamental role in explaining the behavior of variable-mass objects such as a rocket ejecting fuel or a star accreting gas. In analyzing such an object, one treats the object's mass as a function that varies with time:. The momentum of the object at time is therefore. One might then try to invoke Newton's second law of motion by saying that the external force on the object is related to Newtonian physics assumes that absolute time and space exist outside of any observer; this gives rise to Galilean invariance. It also results in a prediction that the speed of light can vary from one reference frame to another. This is contrary to observation. In the special theory of relativity, Einstein keeps the postulate that the equations of motion do not depend on the reference frame, but assumes that the speed of light is invariant. As a result, position and In the theory of special relativity, physical quantities are expressed in terms of four-vectors that include time as a fourth coordinate along with the three space coordinates. These vectors are generally represented by capital letters, for example for position. The expression for the "four-momentum" depends on how the coordinates are expressed. Time may be given in its normal units or multiplied by the speed of light so that all the components of the four-vector have dimensions of length. If the latter scaling is used, an interval of proper time,, defined by is invariant under Lorentz transformations (in this expression and in what follows the metric signature has been used, different authors use different conventions). Mathematically this invariance can be ensured in one of two ways: by treating the four-vectors as Euclidean vectors and multiplying time Newton's laws can be difficult to apply to many kinds of motion because the motion is limited by "constraints". For example, a bead on an abacus is constrained to move along its wire and a pendulum bob is constrained to swing at a fixed distance from the pivot. Many such constraints can be incorporated by changing the normal Cartesian coordinates to a set of "generalized coordinates" that may be fewer in number. Refined mathematical methods have been developed for solving mechanics problems in generalized coordinates. They introduce a "generalized momentum", also known as the "canonical" or "conjugate momentum", that extends the concepts of both linear momentum and angular momentum. To distinguish it from generalized momentum, the product of mass and velocity is also referred to as "mechanical", "kinetic" or "kinematic momentum". The two main methods are described below. In Lagrangian mechanics, a Lagrangian is defined as the difference between the kinetic energy and the potential energy : If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion (known as the Lagrange or Euler–Lagrange equations) are a set of equations: If a coordinate is not a Cartesian coordinate, the associated generalized momentum component does not necessarily have the dimensions of linear momentum. Even In Hamiltonian mechanics, the Lagrangian (a function of generalized coordinates and their derivatives) is replaced by a Hamiltonian that is a function of generalized coordinates and momentum. The Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate In Maxwell's equations, the forces between particles are mediated by electric and magnetic fields. The electromagnetic force ("Lorentz force") on a particle with charge due to a combination of electric field and magnetic field is (in SI units). It has an electric potential and magnetic vector potential. In the non-relativistic regime, its generalized momentum is In Newtonian mechanics, the law of conservation of momentum can be derived from the law of action and reaction, which states that every force has a reciprocating equal and opposite force. Under some circumstances, moving charged particles can exert forces on each other in non-opposite directions. Nevertheless, the combined momentum of the particles and the electromagnetic field is conserved. The Lorentz force imparts a momentum to the particle, so by Newton's second law the particle must impart a momentum to the electromagnetic fields. In a vacuum, the momentum per unit volume is where is the vacuum permeability and is the speed of light. The momentum density is proportional to the Poynting vector which gives the directional rate of energy transfer per unit area: If momentum is to be conserved over the volume The above results are for the "microscopic" Maxwell equations, applicable to electromagnetic forces in a vacuum (or on a very small scale in media). It is more difficult to define momentum density in media because the division into electromagnetic and mechanical is arbitrary. The definition of electromagnetic momentum density is modified to where the H-field is related to the B-field and the magnetization by The electromagnetic stress tensor depends on the properties of the media. In quantum mechanics, momentum is defined as a self-adjoint operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables. For a single particle described in the position basis the momentum operator can be written as where is the gradient operator, is the reduced Planck constant, and is the imaginary unit. This is a commonly encountered form of the momentum operator, though In fields such as fluid dynamics and solid mechanics, it is not feasible to follow the motion of individual atoms or molecules. Instead, the materials must be approximated by a continuum in which there is a particle or fluid parcel at each point that is assigned the average of the properties of atoms in a small region nearby. In particular, it has a density and velocity that depend on time and position. The momentum per unit volume is. Consider a column of water A disturbance in a medium gives rise to oscillations, or waves, that propagate away from their source. In a fluid, small changes in pressure can often be described by the acoustic wave equation: where is the speed of sound. In a solid, similar equations can be obtained for propagation In about 530 AD, working in Alexandria, Byzantine philosopher John Philoponus developed a concept of momentum in his commentary to Aristotle's "Physics". Aristotle claimed that everything that is moving must be kept moving by something. For example, a thrown ball must be kept moving by motions of the air. Most writers continued to accept Aristotle's theory until the time of Galileo, but a few were skeptical. Philoponus pointed out the absurdity in Aristotle's claim that motion of an object is promoted by the same air that is resisting its passage. He proposed instead that an impetus was imparted to the object in the act of throwing it. Ibn Sīnā (also known by his Latinized name Avicenna) read Philoponus and published his own theory of motion in "The Book of Healing" in 1020. He agreed that an impetus is imparted to a projectile by the thrower; but unlike Philoponus, who believed that it was a temporary virtue that would decline even in a vacuum, he viewed it as a persistent, requiring external forces such as air resistance to dissipate it. The work of Philoponus, and possibly that of Ibn Sīnā, was read and refined by the European philosophers Peter Olivi and Jean Buridan. Buridan, who in about 1350 was made rector of the University of Paris, referred to impetus being proportional to the weight times the speed. Moreover, Buridan's theory was different from his predecessor's in that he did not consider impetus to be self-dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus. René Descartes believed that the total "quantity of motion" () in the universe is conserved, where the quantity of motion is understood as the product of size and speed. This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more important, he believed that it is speed rather than velocity that is conserved. So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion. Galileo, in his "Two New Sciences", used the Italian word "impeto" to similarly describe Descartes' quantity of motion. Leibniz, in his "Discourse on Metaphysics", gave an argument against Descartes' construction of the conservation of the "quantity of motion" using an example of dropping blocks of different sizes different distances. He points out that force is conserved but quantity of motion, construed as the product of size and speed of an object, is not conserved. Christiaan Huygens concluded quite early that Descartes's laws for the elastic collision of two bodies must be wrong, and he formulated the correct laws. An important step was his recognition of the Galilean invariance of the problems. His views then took many years to be circulated. He passed them on in person to William Brouncker and Christopher Wren in London, in 1661. What Spinoza wrote to Henry Oldenburg about them, in 1666 which was during the Second Anglo-Dutch War, was guarded. Huygens had actually worked them out in a manuscript "De motu corporum ex percussione" in the period 1652–6. The war ended in 1667, and Huygens announced his results to the Royal Society in 1668. He published them in the "Journal des sçavans" in 1669. The first correct statement of the law of conservation of momentum was by English mathematician John Wallis in his 1670 work, "Mechanica sive De Motu, Tractatus Geometricus": "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result". Wallis used "momentum" for quantity of motion, and "vis" for force. Newton's "Philosophiæ Naturalis Principia Mathematica", when it was first published in 1687, showed a similar casting around for words to use for the mathematical momentum. His Definition II defines "quantitas motus", "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum. Thus when in Law II he refers to "mutatio motus", "change of motion", being proportional to the force impressed, he is generally taken to mean momentum and not motion. It remained only to assign a standard term to the quantity of motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jennings's "Miscellanea" in 1721, five years before the final edition of Newton's "Principia Mathematica", momentum or "quantity of motion" was being defined for students as "a rectangle", the product of and, where is "quantity of material" and is "velocity",.

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum is: formula_1 In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).

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summarize: Impulse J produced from time "t" to "t" is defined to be where F is the resultant force applied from "t" to "t". From Newton's second law, force is related to momentum p by Therefore, where Δp is the change in linear momentum from time "t" to "t". This is often called the impulse-momentum theorem (analogous to the work-energy theorem). As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant: where Impulse has the same units and dimensions as momentum. In the International System of Units, these are. In English engineering units, they are. The term "impulse" is also used to refer to a fast-acting force or impact. This type of impulse is often "idealized" so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in game physics engines). Additionally, in rocketry, the term "total impulse" is commonly used and is considered synonymous with the term "impulse". The application of Newton's second law for variable mass allows impulse and momentum to be used as analysis tools for jet- or rocket-propelled vehicles. In the case of rockets, the impulse imparted can be normalized by unit of propellant expended, to create a performance parameter, specific impulse. This fact can be used to derive the Tsiolkovsky rocket equation, which relates the vehicle's propulsive change in velocity to the engine's specific impulse (or nozzle exhaust velocity) and the vehicle's propellant-mass ratio.

In classical mechanics, impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction. The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg⋅m/s). The corresponding English engineering units are the pound-second (lbf⋅s) and the slug-foot per second (slug⋅ft/s).

en

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summarize: The role of fictitious forces in Newtonian mechanics is described by Tonnelat: Fictitious forces arise in classical mechanics and special relativity in all non-inertial frames. Inertial frames are privileged over non-inertial frames because they do not have physics whose causes are outside of the system, while non-inertial frames do. Fictitious forces, or physics whose cause is outside of the system, are no longer necessary in general relativity, since these physics are explained with the geodesics of spacetime. The surface of the Earth is a rotating reference frame. To solve classical mechanics problems exactly in an Earth-bound reference frame, three fictitious forces must be introduced: the Coriolis force, the centrifugal force (described below) and the Euler force. The Euler force is typically ignored because the variations in the angular velocity of the rotating Earth surface are usually insignificant. Both of the other fictitious forces are weak compared to most typical forces in everyday life, but they can be detected under careful conditions. For example, Léon Foucault used his Foucault pendulum to show that a Coriolis force results from the Earth's rotation. If the Earth were to rotate twenty times faster (making each day only ~72 minutes long), people could easily get the impression that such fictitious forces were pulling on them, as on a spinning carousel; people in temperate and tropical latitudes would, in fact, need to hold on in order to avoid being launched into orbit by the centrifugal force. Observers inside a closed box that is moving with a constant velocity cannot detect their own motion; however, observers within an accelerating reference frame can detect that they are in a non-inertial reference frame from the fictitious forces that arise. For example, for straight-line acceleration Vladimir Arnold presents the following theorem: Other accelerations also give rise to fictitious forces, as described mathematically below. The physical explanation of motions in an inertial frame is the simplest possible, requiring no fictitious forces: fictitious forces are zero, providing a means to distinguish inertial frames from others. An example of the detection of a non-inertial, rotating reference frame is the precession of a Foucault pendulum. In the non-inertial frame of the Earth, the fictitious Coriolis force is necessary to explain observations. In an inertial frame outside the Earth, no such fictitious force is necessary. Figure 1 (top) shows an accelerating car. When a car accelerates, a passenger feels like they're being pushed back into the seat. In an inertial frame of reference attached to the road, there is no physical force moving the rider backward. However, in the rider's non-inertial reference frame attached to the accelerating car, there "is" a backward fictitious force. We mention two possible reasons for the force to clarify its (the force's) existence: How can the accelerating frame be discovered to be non-inertial? In the accelerating frame, everything appears to be subject to zero net force, and nothing moves. Nonetheless, compression of the seat is observed and is explained in the accelerating frame (and in an inertial frame) by the force of acceleration on the seat from the car on one side, and the opposing force of reaction to acceleration by the passenger on the other. Identification of the accelerating frame as non-inertial cannot be based simply on the compression of the seat, which all observers can explain; rather it is based on the "simplicity" of the physical explanation for this compression. The explanation of the seat compression in the accelerating frame requires not only the thrust from the axle of the car, but additional (fictitious) forces. In an inertial frame, only the thrust from the axle is necessary. Therefore, the inertial frame has a "simpler" physical explanation (not necessarily a simpler mathematical formulation, however), indicating the accelerating frame is a non-inertial frame of reference. In other words, in the inertial frame, fictitious forces are zero. See inertial frame for more detail. This example illustrates how fictitious forces arise from switching from an inertial to a non-inertial reference frame. Calculations of physical quantities (compression of the seat, required force from the axle) made in any frame give the same answers, but in some cases calculations are easier to make in a non-inertial frame. (In this simple example, the calculations are equally complex for the two frames described.) A similar effect occurs in circular motion, circular from the standpoint of an inertial frame of reference attached to the road. When seen from a non-inertial frame of reference attached to the car, the fictitious force called the centrifugal force appears. If the car is moving at constant speed around a circular section of road, the occupants will feel pushed outside by this centrifugal force, away from the center of the turn. Again the situation can be viewed from inertial or non-inertial frames: A classic example of fictitious force in circular motion is the experiment of rotating spheres tied by a cord and spinning around their center of mass. In this case, as with the linearly accelerating car example, the identification of a rotating, non-inertial frame of reference can be based upon the vanishing of fictitious forces. In an inertial frame, fictitious forces are not necessary to explain the tension in the string joining the spheres. In a rotating frame, Coriolis and centrifugal forces must be introduced to predict the observed tension. In the rotating reference frame perceived on the surface of the Earth, centrifugal force reduces the apparent force of gravity by about one part in a thousand, depending on latitude. This reduction is zero at the poles, maximum at the equator. The fictitious Coriolis force, which is observed in rotational frames, is ordinarily visible only in very large-scale motion like the projectile motion of long-range guns or the circulation of the Earth's atmosphere (see Rossby number). Neglecting air resistance, an object dropped from a 50-meter-high tower at the equator will fall 7.7 millimeters eastward of the spot below where it is dropped because of the Coriolis force. In the case of distant objects and a rotating reference frame, what must be taken into account is the resultant force of centrifugal and Coriolis force. Consider a distant star observed from a rotating spacecraft. In the reference frame co-rotating with the spacecraft, the distant star appears to move along a circular trajectory around the spacecraft. The apparent motion of the star is an apparent centripetal acceleration. Just like in the example above of the car in circular motion, the centrifugal force has the same magnitude as the fictitious centripetal force, but is directed in the opposite, centrifugal direction. In this case the Coriolis force is twice the magnitude of the centrifugal force, and it points in centripetal direction. The vector sum of the centrifugal force and the Coriolis force is the total fictitious force, which in this case points in centripetal direction. Fictitious forces can be considered to do work, provided that they move an object on a trajectory that changes its energy from potential to kinetic. For example, consider a person in a rotating chair holding a weight in their outstretched hand. If they pull their hand inward toward their body, from the perspective of the rotating reference frame, they have done work against the centrifugal force. When the weight is let go, it spontaneously flies outward relative to the rotating reference frame, because the centrifugal force does work on the object, converting its potential energy into kinetic. From an inertial viewpoint, of course, the object flies away from them because it is suddenly allowed to move in a straight line. This illustrates that the work done, like the total potential and kinetic energy of an object, can be different in a non-inertial frame than an inertial one. The notion of "fictitious force" comes up in Einstein's general theory of relativity. All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity. This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, freefalling reference frames are equivalent to an inertial reference frame (the equivalence principle). Following up on this insight, Einstein was able to formulate a theory with gravity as a fictitious force and attributing the apparent acceleration of gravity to the curvature of spacetime. This idea underlies Einstein's theory of general relativity. See Eötvös experiment. Many problems require use of noninertial reference frames, for example, those involving satellites and particle accelerators. Figure 2 shows a particle with mass "m" and position vector x("t") in a particular inertial frame A. Consider a non-inertial frame B whose origin relative to the inertial one is given by X("t"). Let the position of the particle in frame B be x("t"). What is the force on the particle as expressed in the coordinate system of frame B? To answer this question, let the coordinate axis in B be represented by unit vectors u with "j" any of { 1, 2, 3 } for the three coordinate axes. Then The interpretation of this equation is that x is the vector displacement of the particle as expressed in terms of the coordinates in frame B at time "t". From frame A the particle is located at: As an aside, the unit vectors { u } cannot change magnitude, so derivatives of these vectors express only rotation of the coordinate system B. On the other hand, vector X simply locates the origin of frame B relative to frame A, and so cannot include rotation of frame B. Taking a time derivative, the velocity of the particle is: The second term summation is the velocity of the particle, say v as measured in frame B. That is: The interpretation of this equation is that the velocity of the particle seen by observers in frame A consists of what observers in frame B call the velocity, namely v, plus two extra terms related to the rate of change of the frame-B coordinate axes. One of these is simply the velocity of the moving origin v. The other is a contribution to velocity due to the fact that different locations in the non-inertial frame have different apparent velocities due to rotation of the frame; a point seen from a rotating frame has a rotational component of velocity that is greater the further the point is from the origin. To find the acceleration, another time differentiation provides: Using the same formula already used for the time derivative of x, the velocity derivative on the right is: Consequently, The interpretation of this equation is as follows: the acceleration of the particle in frame A consists of what observers in frame B call the particle acceleration a, but in addition there are three acceleration terms related to the movement of the frame-B coordinate axes: one term related to the acceleration of the origin of frame B, namely a, and two terms related to rotation of frame B. Consequently, observers in B will see the particle motion as possessing "extra" acceleration, which they will attribute to "forces" acting on the particle, but which observers in A say are "fictitious" forces arising simply because observers in B do not recognize the non-inertial nature of frame B. The factor of two in the Coriolis force arises from two equal contributions: (i) the apparent change of an inertially constant velocity with time because rotation makes the direction of the velocity seem to change (a "d"v/d"t" term) and (ii) an apparent change in the velocity of an object when its position changes, putting it nearer to or further from the axis of rotation (the change in formula_7 due to change in "x " ). To put matters in terms of forces, the accelerations are multiplied by the particle mass: The force observed in frame B, F = "m"a is related to the actual force on the particle, F, by where: Thus, we can solve problems in frame B by assuming that Newton's second law holds (with respect to quantities in that frame) and treating F as an additional force. Below are a number of examples applying this result for fictitious forces. More examples can be found in the article on centrifugal force. A common situation in which noninertial reference frames are useful is when the reference frame is rotating. Because such rotational motion is non-inertial, due to the acceleration present in any rotational motion, a fictitious force can always be invoked by using a rotational frame of reference. Despite this complication, the use of fictitious forces often simplifies the calculations involved. To derive expressions for the fictitious forces, derivatives are needed for the apparent time rate of change of vectors that take into account time-variation of the coordinate axes. If the rotation of frame 'B' is represented by a vector Ω pointed along the axis of rotation with orientation given by the right-hand rule, and with magnitude given by then the time derivative of any of the three unit vectors describing frame B is and as is verified using the properties of the vector cross product. These derivative formulas now are applied to the relationship between acceleration in an inertial frame, and that in a coordinate frame rotating with time-varying angular velocity ω("t"). From the previous section, where subscript A refers to the inertial frame and B to the rotating frame, setting a = 0 to remove any translational acceleration, and focusing on only rotational properties (see Eq. 1): Collecting terms, the result is the so-called "acceleration transformation formula": The physical acceleration a due to what observers in the inertial frame A call "real external forces" on the object is, therefore, not simply the acceleration a seen by observers in the rotational frame B, but has several additional geometric acceleration terms associated with the rotation of B. As seen in the rotational frame, the acceleration a of the particle is given by rearrangement of the above equation as: The net force upon the object according to observers in the rotating frame is F = "m"a. If their observations are to result in the correct force on the object when using Newton's laws, they must consider that the additional force F is present, so the end result is F = F + F. Thus, the fictitious force used by observers in B to get the correct behavior of the object from Newton's laws equals: Here, the first term is the "Coriolis force", the second term is the "centrifugal force", and the third term is the "Euler force". As a related example, suppose the moving coordinate system "B" rotates with a constant angular speed ω in a circle of radius "R" about the fixed origin of inertial frame "A", but maintains its coordinate axes fixed in orientation, as in Figure 3. The acceleration of an observed body is now (see Eq. 1): where the summations are zero inasmuch as the unit vectors have no time dependence. The origin of system "B" is located according to frame "A" at: leading to a velocity of the origin of frame "B" as: leading to an acceleration of the origin of "B" given by: Because the first term, which is is of the same form as the normal centrifugal force expression: it is a natural extension of standard terminology (although there is no standard terminology for this case) to call this term a "centrifugal force". Whatever terminology is adopted, the observers in frame "B" must introduce a fictitious force, this time due to the acceleration from the orbital motion of their entire coordinate frame, that is radially outward away from the center of rotation of the origin of their coordinate system: and of magnitude: Notice that this "centrifugal force" has differences from the case of a rotating frame. In the rotating frame the centrifugal force is related to the distance of the object from the origin of frame "B", while in the case of an orbiting frame, the centrifugal force is independent of the distance of the object from the origin of frame "B", but instead depends upon the distance of the origin of frame "B" from "its" center of rotation, resulting in the "same" centrifugal fictitious force for "all" objects observed in frame "B". As a combination example, Figure 4 shows a coordinate system "B" that orbits inertial frame "A" as in Figure 3, but the coordinate axes in frame "B" turn so unit vector u always points toward the center of rotation. This example might apply to a test tube in a centrifuge, where vector u points along the axis of the tube toward its opening at its top. It also resembles the Earth-Moon system, where the Moon always presents the same face to the Earth. In this example, unit vector u retains a fixed orientation, while vectors u, u rotate at the same rate as the origin of coordinates. That is, Hence, the acceleration of a moving object is expressed as (see Eq. 1): where the angular acceleration term is zero for constant rate of rotation. Because the first term, which is is of the same form as the normal centrifugal force expression: it is a natural extension of standard terminology (although there is no standard terminology for this case) to call this term the "centrifugal force". Applying this terminology to the example of a tube in a centrifuge, if the tube is far enough from the center of rotation, |X| = "R" ≫ |x|, all the matter in the test tube sees the same acceleration (the same centrifugal force). Thus, in this case, the fictitious force is primarily a uniform centrifugal force along the axis of the tube, away from the center of rotation, with a value |F| = ω "R", where "R" is the distance of the matter in the tube from the center of the centrifuge. It is standard specification of a centrifuge to use the "effective" radius of the centrifuge to estimate its ability to provide centrifugal force. Thus, a first estimate of centrifugal force in a centrifuge can be based upon the distance of the tubes from the center of rotation, and corrections applied if needed. Also, the test tube confines motion to the direction down the length of the tube, so v is opposite to u and the Coriolis force is opposite to u, that is, against the wall of the tube. If the tube is spun for a long enough time, the velocity v drops to zero as the matter comes to an equilibrium distribution. For more details, see the articles on sedimentation and the Lamm equation. A related problem is that of centrifugal forces for the Earth-Moon-Sun system, where three rotations appear: the daily rotation of the Earth about its axis, the lunar-month rotation of the Earth-Moon system about their center of mass, and the annual revolution of the Earth-Moon system about the Sun. These three motions influence the tides. Figure 5 shows another example comparing the observations of an inertial observer with those of an observer on a rotating carousel. The carousel rotates at a constant angular velocity represented by the vector Ω with magnitude ω, pointing upward according to the right-hand rule. A rider on the carousel walks radially across it at constant speed, in what appears to the walker to be the straight line path inclined at 45° in Figure 5. To the stationary observer, however, the walker travels a spiral path. The points identified on both paths in Figure 5 correspond to the same times spaced at equal time intervals. We ask how two observers, one on the carousel and one in an inertial frame, formulate what they see using Newton's laws. The observer at rest describes the path followed by the walker as a spiral. Adopting the coordinate system shown in Figure 5, the trajectory is described by r("t"): where the added π/4 sets the path angle at 45° to start with (just an arbitrary choice of direction), u is a unit vector in the radial direction pointing from the center of the carousel to the walker at time "t". The radial distance "R"("t") increases steadily with time according to: with "s" the speed of walking. According to simple kinematics, the velocity is then the first derivative of the trajectory: with u a unit vector perpendicular to u at time "t" (as can be verified by noticing that the vector dot product with the radial vector is zero) and pointing in the direction of travel. The acceleration is the first derivative of the velocity: The last term in the acceleration is radially inward of magnitude ω "R", which is therefore the instantaneous centripetal acceleration of circular motion. The first term is perpendicular to the radial direction, and pointing in the direction of travel. Its magnitude is 2"s"ω, and it represents the acceleration of the walker as the edge of the carousel is neared, and the arc of circle traveled in a fixed time increases, as can be seen by the increased spacing between points for equal time steps on the spiral in Figure 5 as the outer edge of the carousel is approached. Applying Newton's laws, multiplying the acceleration by the mass of the walker, the inertial observer concludes that the walker is subject to two forces: the inward, radially directed centripetal force, and another force perpendicular to the radial direction that is proportional to the speed of the walker. The rotating observer sees the walker travel a straight line from the center of the carousel to the periphery, as shown in Figure 5. Moreover, the rotating observer sees that the walker moves at a constant speed in the same direction, so applying Newton's law of inertia, there is "zero" force upon the walker. These conclusions do not agree with the inertial observer. To obtain agreement, the rotating observer has to introduce fictitious forces that appear to exist in the rotating world, even though there is no apparent reason for them, no apparent gravitational mass, electric charge or what have you, that could account for these fictitious forces. To agree with the inertial observer, the forces applied to the walker must be exactly those found above. They can be related to the general formulas already derived, namely: In this example, the velocity seen in the rotating frame is: with u a unit vector in the radial direction. The position of the walker as seen on the carousel is: and the time derivative of Ω is zero for uniform angular rotation. Noticing that and we find: To obtain a straight-line motion in the rotating world, a force exactly opposite in sign to the fictitious force must be applied to reduce the net force on the walker to zero, so Newton's law of inertia will predict a straight line motion, in agreement with what the rotating observer sees. The fictitious forces that must be combated are the Coriolis force (first term) and the centrifugal force (second term). (These terms are approximate.) By applying forces to counter these two fictitious forces, the rotating observer ends up applying exactly the same forces upon the walker that the inertial observer predicted were needed. Because they differ only by the constant walking velocity, the walker and the rotational observer see the same accelerations. From the walker's perspective, the fictitious force is experienced as real, and combating this force is necessary to stay on a straight line radial path holding constant speed. It's like battling a crosswind while being thrown to the edge of the carousel. Notice that this kinematical discussion does not delve into the mechanism by which the required forces are generated. That is the subject of kinetics. In the case of the carousel, the kinetic discussion would involve perhaps a study of the walker's shoes and the friction they need to generate against the floor of the carousel, or perhaps the dynamics of skateboarding, if the walker switched to travel by skateboard. Whatever the means of travel across the carousel, the forces calculated above must be realized. A very rough analogy is heating your house: you must have a certain temperature to be comfortable, but whether you heat by burning gas or by burning coal is another problem. Kinematics sets the thermostat, kinetics fires the furnace.

A fictitious force (also called a pseudo force, d'Alembert force, or inertial force) is a force that appears to act on a mass whose motion is described using a non-inertial frame of reference, such as an accelerating or rotating reference frame. An example is seen in a passenger vehicle that is accelerating in the forward direction - passengers perceive that they are acted upon by a force in the rearward direction pushing them back into their seats. An example in a rotating reference frame is the force that appears to push objects outwards towards the rim of a centrifuge. These apparent forces are examples of fictitious forces.

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70, 2258, 23, 115339, 78112, 4, 70, 69514, 3125, 2870, 37772, 1556, 70, 5701, 101668, 13, 237, 70, 6, 20941, 31821, 10821, 69514, 5408, 289, 37772, 4, 1284, 83, 8951, 297, 23, 70, 198274, 4, 69514, 3125, 2870, 48225, 5, 360, 903, 7225, 70, 5631, 846, 4086, 37772, 83, 186351, 70, 101668, 13, 111, 70, 69514, 3125, 2870, 37772, 4, 136, 442, 26847, 23, 69514, 5408, 289, 48225, 5, 581, 173, 18770, 10554, 111, 70, 69514, 3125, 2870, 37772, 136, 70, 5631, 846, 4086, 37772, 83, 70, 3622, 6, 20941, 31821, 10821, 37772, 4, 3129, 23, 903, 7225, 26847, 23, 69514, 5408, 289, 48225, 5, 3698, 23835, 5565, 223, 84616, 831, 186, 90698, 47, 54, 4488, 4, 62952, 450, 1836, 25813, 142, 36746, 98, 10, 182418, 30675, 450, 65572, 6863, 48302, 1295, 38516, 47, 200, 86, 9523, 5, 1326, 27781, 4, 16916, 10, 3445, 23, 10, 47014, 1916, 80923, 104064, 10, 57888, 23, 2363, 1810, 50768, 74694, 3535, 5, 4263, 1836, 50065, 2363, 3535, 23, 19364, 154732, 2363, 14361, 4, 1295, 70, 80280, 111, 70, 47014, 1916, 91067, 123789, 4, 1836, 765, 16940, 4488, 26548, 70, 69514, 3125, 2870, 37772, 5, 14847, 70, 57888, 83, 2633, 738, 4, 442, 150189, 79850, 33977, 90, 1810, 19364, 35845, 47, 70, 47014, 1916, 91067, 123789, 4, 6637, 70, 69514, 3125, 2870, 37772, 14602, 4488, 98, 70, 36746, 4, 96760, 214, 6863, 38516, 48302, 3934, 200, 86, 9523, 5, 28090, 142, 23, 2529, 15403, 21455, 38496, 4, 111, 15411, 4, 70, 36746, 33977, 90, 16065, 1295, 2856, 6637, 442, 83, 186683, 107003, 47, 25813, 23, 10, 80560, 13315, 5, 3293, 58755, 1636, 450, 70, 4488, 16940, 4, 1884, 70, 3622, 38516, 136, 200, 86, 9523, 48302, 111, 142, 36746, 4, 831, 186, 12921, 23, 10, 351, 9, 20037, 118, 289, 123789, 3501, 142, 23, 2529, 15403, 1632, 5, 581, 110, 1363, 111, 44, 20941, 31821, 10821, 37772, 58, 32497, 1257, 23, 119225, 25, 7, 4537, 154453, 111, 90816, 939, 5, 3164, 6, 20941, 31821, 10821, 84616, 621, 123875, 289, 47, 70, 46889, 111, 70, 36746, 54799, 3129, 1836, 27992, 4, 3129, 83, 2843, 29568, 100, 64002, 939, 5, 3293, 12441, 24748, 119225, 47, 32195, 36766, 64002, 939, 509, 10, 6, 20941, 31821, 10821, 37772, 237, 5299, 5, 1529, 959, 297, 450, 10, 4092, 9146, 214, 160073, 23, 10, 155738, 16530, 2806, 959, 186, 19048, 47, 96391, 70, 37772, 111, 64002, 939, 74, 8311, 329, 4, 4092, 9146, 214, 91067, 2674, 90, 621, 183234, 47, 142, 23, 2529, 15403, 91067, 123789, 15, 2347, 224743, 3956, 24702, 133, 194, 77168, 214, 1257, 98, 903, 149201, 4, 119225, 509, 19048, 47, 26168, 67, 10, 154453, 678, 64002, 939, 237, 10, 6, 20941, 31821, 10821, 37772, 136, 150380, 214, 70, 173676, 197108, 1830, 111, 64002, 939, 47, 70, 130661, 6644, 111, 32628, 6032, 5, 3293, 6528, 1379, 25720, 119225, 25, 7, 154453, 111, 4537, 90816, 939, 5, 6872, 241, 16463, 68709, 7, 28007, 5, 52455, 44402, 64209, 4527, 111, 351, 20037, 118, 289, 91067, 2674, 90, 4, 100, 27781, 4, 8382, 23, 3784, 6496, 99675, 90, 136, 915, 26147, 197108, 25251, 5, 55412, 13, 116, 45831, 10, 915, 26147, 678, 46889, 44, 39, 58, 136, 19069, 173, 18770, 1022, 132, 58, 18, 18939, 23, 10, 17311, 23, 2529, 15403, 123789, 62, 5, 137399, 10, 351, 9, 20037, 118, 289, 123789, 335, 124901, 59665, 35845, 47, 70, 23, 2529, 15403, 1632, 83, 34475, 390, 1193, 132, 58, 18, 51029, 10842, 70, 19069, 111, 70, 915, 26147, 23, 123789, 335, 186, 1022, 132, 58, 18, 51029, 4865, 83, 70, 37772, 98, 70, 915, 26147, 237, 36510, 297, 23, 70, 176866, 13, 5426, 111, 123789, 335, 32, 717, 35166, 903, 9655, 4, 2633, 70, 176866, 13, 10, 33102, 23, 335, 186, 33636, 297, 390, 25072, 22834, 22230, 75, 678, 44, 170, 58, 2499, 111, 10666, 106, 4, 116, 4, 138, 51912, 100, 70, 17262, 176866, 13, 10, 31195, 5, 47009, 581, 206019, 111, 903, 28, 5490, 2320, 83, 450, 1022, 83, 70, 173, 18770, 2837, 23935, 674, 111, 70, 915, 26147, 237, 36510, 297, 23, 69407, 111, 70, 176866, 90, 23, 123789, 335, 99, 1733, 44, 18, 740, 28090, 123789, 62, 70, 915, 26147, 83, 105866, 99, 12, 1301, 142, 10, 8752, 4, 70, 25072, 22834, 22230, 10666, 75, 51912, 53418, 15549, 101668, 13, 4, 221, 30057, 42991, 111, 6097, 22834, 22230, 36510, 4734, 2062, 22062, 111, 70, 176866, 13, 5426, 335, 5, 2161, 70, 3789, 3535, 4, 173, 18770, 1193, 42856, 64040, 1636, 70, 59665, 111, 123789, 335, 35845, 47, 123789, 62, 4, 136, 221, 53418, 26698, 2062, 22062, 111, 123789, 335, 5, 2561, 214, 10, 1733, 30057, 4935, 4, 70, 191060, 939, 111, 70, 915, 26147, 83, 12, 581, 17932, 13579, 29334, 1363, 83, 70, 191060, 939, 111, 70, 915, 26147, 4, 5154, 81, 237, 72350, 71, 23, 123789, 335, 5, 9925, 83, 12, 581, 206019, 111, 903, 28, 5490, 2320, 83, 450, 70, 191060, 939, 111, 70, 915, 26147, 51592, 390, 160073, 7, 23, 123789, 62, 58055, 7, 111, 2367, 160073, 7, 23, 123789, 335, 11782, 70, 191060, 939, 4, 24, 110987, 81, 4, 1001, 6626, 4173, 69407, 62548, 47, 70, 34515, 111, 15549, 111, 70, 123789, 9, 571, 176866, 13, 10, 31195, 5, 6561, 111, 6097, 83, 42856, 70, 191060, 939, 111, 70, 98567, 59665, 81, 5, 581, 3789, 83, 10, 127752, 47, 191060, 939, 4743, 47, 70, 15824, 450, 12921, 31913, 7, 23, 70, 351, 9, 20037, 118, 289, 123789, 765, 12921, 173676, 191060, 2449, 4743, 47, 2062, 22062, 111, 70, 123789, 74, 10, 6275, 51592, 1295, 10, 47014, 1916, 123789, 1556, 10, 47014, 43315, 82761, 111, 191060, 939, 450, 83, 117396, 70, 53333, 70, 6275, 83, 1295, 70, 59665, 5, 717, 7413, 70, 197108, 1830, 4, 15700, 1733, 99710, 2320, 87344, 12, 345, 6953, 70, 5701, 26168, 21771, 11814, 100, 70, 1733, 30057, 4935, 111, 1022, 4, 70, 191060, 939, 30057, 4935, 98, 70, 7108, 83, 12, 1657, 184, 26513, 18, 538, 4, 581, 206019, 111, 903, 28, 5490, 2320, 83, 237, 28960, 7, 12, 70, 197108, 1830, 111, 70, 915, 26147, 23, 123789, 62, 58055, 7, 111, 2367, 160073, 7, 23, 123789, 335, 11782, 70, 915, 26147, 197108, 1830, 10, 4, 1284, 23, 66044, 2685, 621, 17262, 197108, 1830, 69407, 62548, 47, 70, 112664, 111, 70, 123789, 9, 571, 176866, 13, 10, 31195, 12, 1632, 13579, 62548, 47, 70, 197108, 1830, 111, 70, 59665, 111, 123789, 335, 4, 24, 110987, 10, 4, 136, 6626, 69407, 62548, 47, 2062, 22062, 111, 123789, 335, 5, 1657, 184, 26513, 18, 538, 4, 160073, 7, 23, 335, 1221, 1957, 70, 915, 26147, 78112, 237, 158566, 214, 44, 112779, 58, 197108, 1830, 4, 3129, 1836, 1221, 150380, 13, 47, 44, 50930, 7, 58, 1030, 1916, 98, 70, 915, 26147, 4, 1284, 3129, 160073, 7, 23, 62, 5154, 621, 44, 20941, 31821, 10821, 58, 84616, 187, 72219, 42856, 6637, 160073, 7, 23, 335, 54, 959, 125296, 70, 351, 9, 20037, 118, 289, 31425, 111, 123789, 335, 5, 581, 31461, 111, 6626, 23, 70, 5631, 846, 4086, 37772, 187, 62093, 1295, 6626, 105950, 127752, 7, 12, 15, 14, 16, 70, 173676, 15549, 111, 142, 23, 56, 118, 25958, 53697, 191060, 939, 678, 1733, 6637, 2062, 22062, 30482, 70, 48225, 111, 70, 191060, 939, 48903, 47, 15549, 15, 11, 44, 71, 58, 334, 64, 71, 58, 18, 58, 13579, 16, 136, 15, 1573, 16, 142, 173676, 15549, 23, 70, 191060, 939, 111, 142, 36746, 3229, 6863, 19069, 65572, 4, 118620, 442, 43573, 56, 47, 707, 53333, 1295, 70, 10, 33102, 111, 2062, 22062, 15, 2347, 15549, 23, 26168, 454, 966, 4743, 47, 15549, 23, 44, 425, 44, 6, 194, 717, 3884, 26866, 7, 23, 69407, 111, 84616, 4, 70, 197108, 17514, 621, 118126, 297, 390, 70, 915, 26147, 46889, 12, 581, 37772, 139999, 71, 23, 123789, 335, 4, 563, 2203, 44, 39, 58, 11, 83, 62548, 47, 70, 8561, 37772, 98, 70, 915, 26147, 4, 563, 4, 390, 7440, 12, 12613, 7, 4, 642, 831, 86869, 44402, 23, 123789, 335, 390, 10, 66596, 214, 450, 145076, 25, 7, 17932, 27165, 16401, 7, 15, 76228, 15072, 47, 102134, 2449, 23, 450, 123789, 16, 136, 85689, 214, 563, 237, 142, 78301, 37772, 5, 873, 17336, 621, 10, 14012, 111, 27781, 7, 59911, 214, 903, 16750, 100, 6, 20941, 31821, 10821, 84616, 5, 5455, 27781, 7, 831, 186, 14037, 23, 70, 5582, 98, 69514, 3125, 2870, 37772, 5, 62, 39210, 16648, 23, 3129, 351, 20037, 118, 289, 91067, 2674, 90, 621, 80234, 83, 3229, 70, 91067, 123789, 83, 47014, 1916, 5, 88949, 6044, 47014, 43315, 78112, 83, 351, 9, 20037, 118, 289, 4, 4743, 47, 70, 197108, 1830, 13379, 23, 2499, 47014, 43315, 78112, 4, 10, 6, 20941, 31821, 10821, 37772, 831, 11343, 186, 23, 23253, 297, 390, 17368, 10, 47014, 43315, 123789, 111, 91067, 5, 262, 61518, 903, 51455, 1363, 4, 70, 4527, 111, 6, 20941, 31821, 10821, 84616, 27983, 112892, 1029, 90, 70, 74481, 5256, 75412, 5, 717, 122, 5844, 125195, 7, 100, 70, 6, 20941, 31821, 10821, 84616, 4, 30057, 42991, 621, 44841, 100, 70, 173676, 1733, 34515, 111, 15549, 111, 22834, 22230, 450, 5646, 3934, 15426, 1733, 9, 21690, 2320, 111, 70, 176866, 13, 10, 31195, 5, 4263, 70, 2062, 22062, 111, 123789, 242, 571, 25, 83, 33636, 297, 390, 10, 173, 18770, 6, 20723, 6275, 297, 33233, 70, 10, 33102, 111, 2062, 22062, 678, 6, 180324, 34475, 390, 70, 7108, 9, 12336, 79986, 4, 136, 678, 101668, 13, 34475, 390, 7068, 70, 1733, 30057, 4935, 111, 2499, 111, 70, 17262, 25072, 22834, 22230, 28852, 23709, 123789, 335, 83, 136, 237, 83, 493, 47314, 17368, 70, 183871, 111, 70, 173, 18770, 41421, 12996, 5, 32255, 30057, 4935, 26168, 7, 5036, 621, 190659, 47, 70, 76755, 17721, 197108, 1830, 23, 142, 23, 2529, 15403, 123789, 4, 136, 450, 23, 10, 176866, 13, 123789, 47014, 1916, 678, 1733, 9, 1961, 38543, 348, 35975, 191060, 939, 6, 2778, 132, 58, 18, 51029, 28090, 70, 96362, 40059, 4, 7440, 1614, 32032, 62, 15005, 7, 47, 70, 23, 2529, 15403, 123789, 136, 335, 47, 70, 47014, 1916, 123789, 4, 53550, 10, 2203, 757, 47, 87388, 2499, 153648, 289, 197108, 1830, 4, 136, 32153, 214, 98, 4734, 47014, 43315, 183871, 15, 21231, 241, 864, 5, 4879, 12, 138521, 214, 69407, 4, 70, 16750, 83, 70, 221, 9, 85763, 297, 44, 151932, 1363, 167201, 26168, 58, 12, 581, 72761, 197108, 1830, 10, 4743, 47, 2367, 160073, 7, 23, 70, 23, 2529, 15403, 123789, 62, 11782, 44, 30544, 173591, 84616, 58, 98, 70, 36746, 83, 4, 127298, 4, 959, 42856, 70, 197108, 1830, 10, 51592, 390, 160073, 7, 23, 70, 47014, 43315, 123789, 335, 4, 1284, 1556, 40368, 78301, 84183, 238, 197108, 1830, 69407, 137272, 678, 70, 2062, 22062, 111, 335, 5, 1301, 51592, 23, 70, 47014, 43315, 123789, 4, 70, 197108, 1830, 10, 111, 70, 915, 26147, 83, 34475, 390, 456, 225628, 111, 70, 36917, 28, 5490, 2320, 237, 12, 581, 2043, 37772, 54799, 70, 36746, 59499, 47, 160073, 7, 23, 70, 47014, 1916, 123789, 83, 563, 2203, 44, 39, 58, 11, 5, 4263, 2363, 150556, 7, 621, 47, 16750, 23, 70, 26785, 37772, 98, 70, 36746, 3229, 17368, 145076, 25, 7, 131703, 4, 1836, 8110, 16916, 450, 70, 78301, 37772, 563, 83, 13379, 4, 221, 70, 3564, 16750, 83, 563, 2203, 563, 997, 563, 5, 12613, 7, 4, 70, 6, 20941, 31821, 10821, 37772, 11814, 390, 160073, 7, 23, 335, 47, 2046, 70, 26785, 123166, 111, 70, 36746, 1295, 145076, 25, 7, 131703, 105950, 7, 12, 11853, 4, 70, 5117, 13579, 83, 70, 44, 50886, 846, 4086, 37772, 830, 70, 17932, 13579, 83, 70, 44, 46899, 45862, 2870, 37772, 830, 136, 70, 50960, 13579, 83, 70, 44, 52283, 603, 37772, 740, 1301, 10, 62548, 27781, 4, 139124, 70, 98567, 176866, 13, 5426, 44, 571, 58, 47014, 1636, 678, 10, 53697, 348, 35975, 38352, 6, 2778, 23, 10, 42154, 133, 111, 4567, 223, 44, 1052, 58, 1672, 70, 188347, 59665, 111, 23, 2529, 15403, 123789, 44, 284, 830, 1284, 76104, 7, 6863, 176866, 13, 10, 31195, 188347, 23, 6, 180324, 4, 237, 23, 55412, 13, 1031, 581, 197108, 1830, 111, 142, 139999, 71, 14361, 83, 5036, 15, 21231, 241, 864, 5, 4879, 12, 7440, 70, 29334, 5256, 621, 45234, 23, 162, 561, 206, 237, 70, 25072, 22834, 22230, 765, 110, 1733, 6, 215131, 5, 581, 59665, 111, 5426, 44, 571, 58, 83, 105866, 59499, 47, 123789, 44, 284, 58, 99, 12, 105207, 47, 10, 191060, 939, 111, 70, 59665, 111, 123789, 44, 571, 58, 237, 12, 105207, 47, 142, 197108, 1830, 111, 70, 59665, 111, 44, 571, 58, 34475, 390, 12, 88949, 70, 5117, 13579, 4, 3129, 83, 83, 111, 70, 5701, 3173, 237, 70, 3638, 69514, 3125, 2870, 37772, 125195, 12, 442, 83, 10, 6083, 111938, 111, 5570, 18614, 25443, 15, 289, 197271, 2685, 83, 110, 5570, 18614, 25443, 100, 903, 7225, 16, 47, 11782, 903, 13579, 10, 44, 46899, 45862, 2870, 37772, 740, 4865, 30441, 18614, 25443, 83, 30666, 297, 4, 70, 160073, 7, 23, 123789, 44, 571, 58, 8110, 65508, 10, 6, 20941, 31821, 10821, 37772, 4, 903, 1733, 4743, 47, 70, 197108, 1830, 1295, 70, 103173, 289, 78112, 111, 2363, 64194, 176866, 13, 123789, 4, 450, 83, 4567, 25958, 1810, 19364, 16065, 1295, 70, 27585, 111, 2062, 22062, 111, 70, 59665, 111, 2363, 176866, 13, 5426, 12, 136, 111, 101668, 13, 12, 438, 24494, 450, 903, 44, 46899, 45862, 2870, 37772, 58, 1556, 60212, 7, 1295, 70, 7225, 111, 10, 47014, 1916, 123789, 5, 360, 70, 47014, 1916, 123789, 70, 69514, 3125, 2870, 37772, 83, 62548, 47, 70, 62488, 111, 70, 36746, 1295, 70, 59665, 111, 123789, 44, 571, 830, 12960, 23, 70, 7225, 111, 142, 103173, 214, 123789, 4, 70, 69514, 3125, 2870, 37772, 83, 41371, 111, 70, 62488, 111, 70, 36746, 1295, 70, 59665, 111, 123789, 44, 571, 830, 1284, 64457, 56566, 7, 54799, 70, 62488, 111, 70, 59665, 111, 123789, 44, 571, 58, 1295, 44, 14481, 58, 27585, 111, 2062, 22062, 4, 16750, 214, 23, 70, 44, 40175, 58, 69514, 3125, 2870, 6, 20941, 31821, 10821, 37772, 100, 44, 5584, 58, 36746, 7, 139999, 71, 23, 123789, 44, 571, 740, 1301, 10, 162515, 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summarize: Specifically, the term "Galilean invariance" today usually refers to this principle as applied to Newtonian mechanics, that is, Newton’s laws hold in all frames related to one another by a Galilean transformation. In other words, all frames related to one another by such a transformation are inertial (meaning, Newton's equation of motion is valid in these frames). In this context it is sometimes called "Newtonian relativity". Among the axioms from Newton's theory are: Galilean relativity can be shown as follows. Consider two inertial frames "S" and "S' ". A physical event in "S" will have position coordinates "r" = ("x", "y", "z") and time "t" in "S", and "r' " = ("x' ", "y' ", "z' ") and time "t' " in "S' ". By the second axiom above, one can synchronize the clock in the two frames and assume "t" = "t' ". Suppose "S' " is in relative uniform motion to "S" with velocity "v". Consider a point object whose position is given by functions "r' "("t") " in "S' " and r"("t") in "S". We see that The velocity of the particle is given by the time derivative of the position: Another differentiation gives the acceleration in the two frames: It is this simple but crucial result that implies Galilean relativity. Assuming that mass is invariant in all inertial frames, the above equation shows Newton's laws of mechanics, if valid in one frame, must hold for all frames. But it is assumed to hold in absolute space, therefore Galilean relativity holds. A comparison can be made between Newtonian relativity and special relativity. Some of the assumptions and properties of Newton's theory are: In comparison, the corresponding statements from special relativity are as follows: Notice both theories assume the existence of inertial frames. In practice, the size of the frames in which they remain valid differ greatly, depending on gravitational tidal forces. In the appropriate context, a "local Newtonian inertial frame", where Newton's theory remains a good model, extends to, roughly, 10 light years. In special relativity, one considers "Einstein's cabins", cabins that fall freely in a gravitational field. According to Einstein's thought experiment, a man in such a cabin experiences (to a good approximation) no gravity and therefore the cabin is an approximate inertial frame. However, one has to assume that the size of the cabin is sufficiently small so that the gravitational field is approximately parallel in its interior. This can greatly reduce the sizes of such approximate frames, in comparison to Newtonian frames. For example, an artificial satellite orbiting around earth can be viewed as a cabin. However, reasonably sensitive instruments would detect "microgravity" in such a situation because the "lines of force" of the Earth's gravitational field converge. In general, the convergence of gravitational fields in the universe dictates the scale at which one might consider such (local) inertial frames. For example, a spaceship falling into a black hole or neutron star would (at a certain distance) be subjected to tidal forces so strong that it would be crushed in width and torn apart in length. In comparison, however, such forces might only be uncomfortable for the astronauts inside (compressing their joints, making it difficult to extend their limbs in any direction perpendicular to the gravity field of the star). Reducing the scale further, the forces at that distance might have almost no effects at all on a mouse. This illustrates the idea that all freely falling frames are locally inertial (acceleration and gravity-free) if the scale is chosen correctly. Maxwell's equations governing electromagnetism possess a different symmetry, Lorentz invariance, under which lengths and times "are" affected by a change in velocity, which is then described mathematically by a Lorentz transformation. Albert Einstein's central insight in formulating special relativity was that, for full consistency with electromagnetism, mechanics must also be revised such that Lorentz invariance replaces Galilean invariance. At the low relative velocities characteristic of everyday life, Lorentz invariance and Galilean invariance are nearly the same, but for relative velocities close to that of light they are very different. Because the distance covered while applying a force to an object depends on the inertial frame of reference, so does the work done. Due to Newton's law of reciprocal actions there is a reaction force; it does work depending on the inertial frame of reference in an opposite way. The total work done is independent of the inertial frame of reference. Correspondingly the kinetic energy of an object, and even the change in this energy due to a change in velocity, depends on the inertial frame of reference. The total kinetic energy of an isolated system also depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass. Due to the conservation of momentum the latter does not change with time, so changes with time of the total kinetic energy do not depend on the inertial frame of reference. By contrast, while the momentum of an object also depends on the inertial frame of reference, its change due to a change in velocity does not.

Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 in his "Dialogue Concerning the Two Chief World Systems" using the example of a ship travelling at constant velocity, without rocking, on a smooth sea; any observer below the deck would not be able to tell whether the ship was moving or stationary.

en

76

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summarize: The motion of a body can only be described relative to something else—other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body that has no external forces acting on it is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, a coordinate system could describe the simple flight of a free body in space as a complicated zig-zag in its coordinate system. Indeed, an intuitive summary of inertial frames can be given: in an inertial reference frame, the laws of mechanics take their simplest form. In an inertial frame, Newton's first law, the "law of inertia", is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form: with F the net force (a vector), "m" the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame. The force F is the vector sum of all "real" forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate "Ω" about an axis, takes the form: which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics): where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation "Ω", symbol × denotes the vector cross product, vector x locates the body and vector v is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer). The extra terms in the force F′ are the "fictitious" forces for this frame, whose causes are external to the system in the frame. The first extra term is the Coriolis force, the second the centrifugal force, and the third the Euler force. These terms all have these properties: they vanish when "Ω" = 0; that is, they are zero for an inertial frame (which, of course, does not rotate); they take on a different magnitude and direction in every rotating frame, depending upon its particular value of Ω; they are ubiquitous in the rotating frame (affect every particle, regardless of circumstance); and they have no apparent source in identifiable physical sources, in particular, matter. Also, fictitious forces do not drop off with distance (unlike, for example, nuclear forces or electrical forces). For example, the centrifugal force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis. All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present. In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force. Two experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking two spheres rotating about their center of gravity, and the example of the curvature of the surface of water in a rotating bucket. In both cases, application of Newton's second law would not work for the rotating observer without invoking centrifugal and Coriolis forces to account for their observations (tension in the case of the spheres; parabolic water surface in the case of the rotating bucket). As we now know, the fixed stars are not fixed. Those that reside in the Milky Way turn with the galaxy, exhibiting proper motions. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to expansion of the universe, and partly due to peculiar velocities. The Andromeda Galaxy is on collision course with the Milky Way at a speed of 117 km/s. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property. In practice, although not a requirement, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces very little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun about the galactic center. To illustrate further, consider the question: "Does our Universe rotate?" To answer, we might attempt to explain the shape of the Milky Way galaxy using the laws of physics, although other observations might be more definitive, that is, provide larger discrepancies or less measurement uncertainty, like the anisotropy of the microwave background radiation or Big Bang nucleosynthesis. The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If we attribute its apparent rate of rotation entirely to rotation in an inertial frame, a different "flatness" is predicted than if we suppose part of this rotation actually is due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example, dark matter is invoked to explain the galactic rotation curve. So far, observations show any rotation of the universe is very slow, no faster than once every 60·10 years (10 rad/yr), and debate persists over whether there is "any" rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter along the geodesics in general relativity. When quantum effects are important, there are additional conceptual complications that arise in quantum reference frames. According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation: This simplicity manifests in that inertial frames have self-contained physics without the need for external causes, while physics in non-inertial frames have external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity; see Nagel and also Blagojević. In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame. According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup. In Newtonian mechanics, which can be viewed as a limiting case of special relativity in which the speed of light is infinite, inertial frames of reference are related by the Galilean group of symmetries. Newton posited an absolute space considered well approximated by a frame of reference stationary relative to the fixed stars. An inertial frame was then one in uniform translation relative to absolute space. However, some scientists (called "relativists" by Mach), even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced. Indeed, the expression "inertial frame of reference" () was coined by Ludwig Lange in 1885, to replace Newton's definitions of "absolute space and time" by a more operational definition. As translated by Iro, Lange proposed the following definition: A discussion of Lange's proposal can be found in Mach. The inadequacy of the notion of "absolute space" in Newtonian mechanics is spelled out by Blagojević: The utility of operational definitions was carried much further in the special theory of relativity. Some historical background including Lange's definition is provided by DiSalle, who says in summary: Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame, is one in which Newton's first law of motion is valid. However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton's first law. Newton viewed the first law as valid in any reference frame that is in uniform motion relative to the fixed stars; that is, neither rotating nor accelerating relative to the stars. Today the notion of "absolute space" is abandoned, and an inertial frame in the field of classical mechanics is defined as: Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed. Newtonian inertial frames transform among each other according to the Galilean group of symmetries. If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then we have to be able to determine when zero net force is applied. The problem was summarized by Einstein: There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that a body is far enough away from all sources to ensure that no force is present. A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is that we might miss something, or account inappropriately for their influence, perhaps, again, due to Mach's principle and an incomplete understanding of the universe. A third approach is to look at the way the forces transform when we shift reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames, and have complicated rules of transformation in general cases. On the basis of universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces. Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion: This principle differs from the special principle in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares with the special principle the invariance of the form of the description among mutually translating reference frames. The role of fictitious forces in classifying reference frames is pursued further below. Inertial and non-inertial reference frames can be distinguished by the absence or presence of fictitious forces, as explained shortly. The presence of fictitious forces indicates the physical laws are not the simplest laws available so, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame: Bodies in non-inertial reference frames are subject to so-called "fictitious" forces (pseudo-forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames. How then, are "fictitious" forces to be separated from "real" forces? It is hard to apply the Newtonian definition of an inertial frame without this separation. For example, consider a stationary object in an inertial frame. Being at rest, no net force is applied. But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force (which is made up of the Coriolis force and the centrifugal force). How can we decide that the rotating frame is a non-inertial frame? There are two approaches to this resolution: one approach is to look for the origin of the fictitious forces (the Coriolis force and the centrifugal force). We will find there are no sources for these forces, no associated force carriers, no originating bodies. A second approach is to look at a variety of frames of reference. For any inertial frame, the Coriolis force and the centrifugal force disappear, so application of the principle of special relativity would identify these frames where the forces disappear as sharing the same and the simplest physical laws, and hence rule that the rotating frame is not an inertial frame. Newton examined this problem himself using rotating spheres, as shown in Figure 2 and Figure 3. He pointed out that if the spheres are not rotating, the tension in the tying string is measured as zero in every frame of reference. If the spheres only appear to rotate (that is, we are watching stationary spheres from a rotating frame), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed. If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion. Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value. That is, the inertial frame is the one where the fictitious forces vanish. So much for fictitious forces due to rotation. However, for linear acceleration, Newton expressed the idea of undetectability of straight-line accelerations held in common: This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, we can define inertial frames collectively as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set. For these ideas to apply, everything observed in the frame has to be subject to a base-line, common acceleration shared by the frame itself. That situation would apply, for example, to the elevator example, where all objects are subject to the same gravitational acceleration, and the elevator itself accelerates at the same rate. Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it. Three orthogonal gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position. Thus, inertial navigation is a form of dead reckoning that requires no external input, and therefore cannot be jammed by any external or internal signal source. A gyrocompass, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour. Classical theories that use the Galilean transformation postulate the equivalence of all inertial reference frames. Some theories may even postulate the existence of a privileged frame which provides absolute space and absolute time. The Galilean transformation transforms coordinates from one inertial reference frame, formula_4, to another, formula_5, by simple addition or subtraction of coordinates: where r and "t" represent shifts in the origin of space and time, and v is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time "t" − "t" between two events is the same for all reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, |r − r|) is also the same. Einstein's theory of special relativity, like Newtonian mechanics, postulates the equivalence of all inertial reference frames. However, because special relativity postulates that the speed of light in free space is invariant, the transformation between inertial frames is the Lorentz transformation, not the Galilean transformation which is used in Newtonian mechanics. The invariance of the speed of light leads to counter-intuitive phenomena, such as time dilation and length contraction, and the relativity of simultaneity, which have been extensively verified experimentally. The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero. General relativity is based upon the principle of equivalence: This idea was introduced in Einstein's 1907 article "Principle of Relativity and Gravitation" and later developed in 1911. Support for this principle is found in the Eötvös experiment, which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 10. For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin. Einstein's general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature. In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity. However, the general theory reduces to the special theory over sufficiently small regions of spacetime, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a "local theory". "Local" can encompass, for example, the entire Milky Way galaxy: The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the solar system. Schwarzschild pointed out that that was invariably seen: the direction of the angular momentum of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is approximately Galilean or Minkowskian.

An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant velocity. An inertial frame of reference can be defined in analytical terms as a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Conceptually, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.

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summarize: The position of a rigid body is the position of all the particles of which it is composed. To simplify the description of this position, we exploit the property that the body is rigid, namely that all its particles maintain the same distance relative to each other. If the body is rigid, it is sufficient to describe the position of at least three non-collinear particles. This makes it possible to reconstruct the position of all the other particles, provided that their time-invariant position relative to the three selected particles is known. However, typically a different, mathematically more convenient, but equivalent approach is used. The position of the whole body is represented by: Thus, the position of a rigid body has two components: linear and angular, respectively. The same is true for other kinematic and kinetic quantities describing the motion of a rigid body, such as linear and angular velocity, acceleration, momentum, impulse, and kinetic energy. The linear position can be represented by a vector with its tail at an arbitrary reference point in space (the origin of a chosen coordinate system) and its tip at an arbitrary point of interest on the rigid body, typically coinciding with its center of mass or centroid. This reference point may define the origin of a coordinate system fixed to the body. There are several ways to numerically describe the orientation of a rigid body, including a set of three Euler angles, a quaternion, or a direction cosine matrix (also referred to as a rotation matrix). All these methods actually define the orientation of a basis set (or coordinate system) which has a fixed orientation relative to the body (i.e. rotates together with the body), relative to another basis set (or coordinate system), from which the motion of the rigid body is observed. For instance, a basis set with fixed orientation relative to an airplane can be defined as a set of three orthogonal unit vectors "b", "b", "b", such that "b" is parallel to the chord line of the wing and directed forward, "b" is normal to the plane of symmetry and directed rightward, and "b" is given by the cross product formula_1. In general, when a rigid body moves, both its position and orientation vary with time. In the kinematic sense, these changes are referred to as "translation" and "rotation", respectively. Indeed, the position of a rigid body can be viewed as a hypothetic translation and rotation (roto-translation) of the body starting from a hypothetic reference position (not necessarily coinciding with a position actually taken by the body during its motion). Velocity (also called linear velocity) and angular velocity are measured with respect to a frame of reference. The linear velocity of a rigid body is a vector quantity, equal to the time rate of change of its linear position. Thus, it is the velocity of a reference point fixed to the body. During purely translational motion (motion with no rotation), all points on a rigid body move with the same velocity. However, when motion involves rotation, the instantaneous velocity of any two points on the body will generally not be the same. Two points of a rotating body will have the same instantaneous velocity only if they happen to lie on an axis parallel to the instantaneous axis of rotation. Angular velocity is a vector quantity that describes the angular speed at which the orientation of the rigid body is changing and the instantaneous axis about which it is rotating (the existence of this instantaneous axis is guaranteed by the Euler's rotation theorem). All points on a rigid body experience the same angular velocity at all times. During purely rotational motion, all points on the body change position except for those lying on the instantaneous axis of rotation. The relationship between orientation and angular velocity is not directly analogous to the relationship between position and velocity. Angular velocity is not the time rate of change of orientation, because there is no such concept as an orientation vector that can be differentiated to obtain the angular velocity. The angular velocity of a rigid body B in a reference frame N is equal to the sum of the angular velocity of a rigid body D in N and the angular velocity of B with respect to D: In this case, rigid bodies and reference frames are indistinguishable and completely interchangeable. For any set of three points P, Q, and R, the position vector from P to R is the sum of the position vector from P to Q and the position vector from Q to R: The velocity of point P in reference frame N is defined as the time derivative in N of the position vector from O to P: where O is any arbitrary point fixed in reference frame N, and the N to the left of the d/d"t" operator indicates that the derivative is taken in reference frame N. The result is independent of the selection of O so long as O is fixed in N. The acceleration of point P in reference frame N is defined as the time derivative in N of its velocity: For two points P and Q that are fixed on a rigid body B, where B has an angular velocity formula_6 in the reference frame N, the velocity of Q in N can be expressed as a function of the velocity of P in N: where formula_8 is the position vector from Q to P. By differentiating the equation for the Velocity of two points fixed on a rigid body in N with respect to time, the acceleration in reference frame N of a point Q fixed on a rigid body B can be expressed as where formula_10 is the angular acceleration of B in the reference frame N. As mentioned above, all points on a rigid body B have the same angular velocity formula_11 in a fixed reference frame N, and thus the same angular acceleration formula_12 If the point R is moving in rigid body B while B moves in reference frame N, then the velocity of R in N is where Q is the point fixed in B that is instantaneously coincident with R at the instant of interest. This relation is often combined with the relation for the Velocity of two points fixed on a rigid body. The acceleration in reference frame N of the point R moving in body B while B is moving in frame N is given by where Q is the point fixed in B that instantaneously coincident with R at the instant of interest. This equation is often combined with Acceleration of two points fixed on a rigid body. If "C" is the origin of a local coordinate system "L", attached to the body, where In 2D, the angular velocity is a scalar, and matrix A(t) simply represents a rotation in the "xy"-plane by an angle which is the integral of the angular velocity over time. Vehicles, walking people, etc., usually rotate according to changes in the direction of the velocity: they move forward with respect to their own orientation. Then, if the body follows a closed orbit in a plane, the angular velocity integrated over a time interval in which the orbit is completed once, is an integer times 360°. This integer is the winding number with respect to the origin of the velocity. Compare the amount of rotation associated with the vertices of a polygon. Any point that is rigidly connected to the body can be used as reference point (origin of coordinate system "L") to describe the linear motion of the body (the linear position, velocity and acceleration vectors depend on the choice). However, depending on the application, a convenient choice may be: When the center of mass is used as reference point: Two rigid bodies are said to be different (not copies) if there is no proper rotation from one to the other. A rigid body is called chiral if its mirror image is different in that sense, i.e., if it has either no symmetry or its symmetry group contains only proper rotations. In the opposite case an object is called achiral: the mirror image is a copy, not a different object. Such an object may have a symmetry plane, but not necessarily: there may also be a plane of reflection with respect to which the image of the object is a rotated version. The latter applies for "S, of which the case "n" = 1 is inversion symmetry. For a (rigid) rectangular transparent sheet, inversion symmetry corresponds to having on one side an image without rotational symmetry and on the other side an image such that what shines through is the image at the top side, upside down. We can distinguish two cases: A sheet with a through and through image is achiral. We can distinguish again two cases: The configuration space of a rigid body with one point fixed (i.e., a body with zero translational motion) is given by the underlying manifold of the rotation group SO(3). The configuration space of a nonfixed (with non-zero translational motion) rigid body is "E"(3), the subgroup of direct isometries of the Euclidean group in three dimensions (combinations of translations and rotations).

In physics, a rigid body (also known as a rigid object ) is a solid body in which deformation is zero or so small it can be neglected. The distance between any two given points on a rigid body remains constant in time regardless of external forces exerted on it. A rigid body is usually considered as a continuous distribution of mass.

en

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summarize: A couple is a pair of forces, equal in magnitude, oppositely directed, and displaced by perpendicular distance or moment. The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. This is called a "simple couple". The forces have a turning effect or moment called a torque about an axis which is normal (perpendicular) to the plane of the forces. The SI unit for the torque of the couple is newton metre. If the two forces are F and −F, then the magnitude of the torque is given by the following formula: where The magnitude of the torque is equal to "F d", with the direction of the torque given by the unit vector formula_3, which is perpendicular to the plane containing the two forces and positive being a counter-clockwise couple. When d is taken as a vector between the points of action of the forces, then the torque is the cross product of d and F, i.e. The moment of a force is only defined with respect to a certain point "P" (it is said to be the "moment about "P"") and, in general, when "P" is changed, the moment changes. However, the moment (torque) of a "couple" is "independent" of the reference point "P": Any point will give the same moment. In other words, a torque vector, unlike any other moment vector, is a "free vector". The proof of this claim is as follows: Suppose there are a set of force vectors F, F, etc. that form a couple, with position vectors (about some origin "P") r, r, etc., respectively. The moment about "P" is Now we pick a new reference point "P that differs from "P" by the vector r"'. The new moment is Now the distributive property of the cross product implies However, the definition of a force couple means that Therefore, This proves that the moment is independent of reference point, which is proof that a couple is a free vector. A force "F" applied to a rigid body at a distance "d" from the center of mass has the same effect as the same force applied directly to the center of mass and a couple "Cl = Fd". The couple produces an angular acceleration of the rigid body at right angles to the plane of the couple. The force at the center of mass accelerates the body in the direction of the force without change in orientation. The general theorems are: Couples are very important in mechanical engineering and the physical sciences. A few examples are: In a liquid crystal it is the rotation of an optic axis called the "director" that produces the functionality of these compounds. As Jerald Ericksen explained

In mechanics, a couple refers to two parallel forces that are equal in magnitude, opposite in direction and do not share a line of action.

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summarize: An important property of systems at mechanical equilibrium is their stability. If we have a function which describes the system's potential energy, we can determine the system's equilibria using calculus. A system is in mechanical equilibrium at the critical points of the function describing the system's potential energy. We can locate these points using the fact that the derivative of the function is zero at these points. To determine whether or not the system is stable or unstable, we apply the second derivative test: When considering more than one dimension, it is possible to get different results in different directions, for example stability with respect to displacements in the "x"-direction but instability in the "y"-direction, a case known as a saddle point. Generally an equilibrium is only referred to as stable if it is stable in all directions. Sometimes there is not enough information about the forces acting on a body to determine if it is in equilibrium or not. This makes it a statically indeterminate system. A stationary object (or set of objects) is in "static equilibrium," which is a special case of mechanical equilibrium. A paperweight on a desk is an example of static equilibrium. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing. Objects in motion can also be in equilibrium. A child sliding down a slide at constant speed would be in mechanical equilibrium, but not in static equilibrium (in the reference frame of the earth or slide). Another example of mechanical equilibrium is a person pressing a spring to a defined point. He or she can push it to an arbitrary point and hold it there, at which point the compressive load and the spring reaction are equal. In this state the system is in mechanical equilibrium. When the compressive force is removed the spring returns to its original state. The minimal number of static equilibria of homogeneous, convex bodies (when resting under gravity on a horizontal surface) is of special interest. In the planar case, the minimal number is 4, while in three dimensions one can build an object with just one stable and one unstable balance point. Such an object is called a gömböc.

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.

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summarize: Each median of a triangle passes through the triangle's centroid, which is the center of mass of an infinitely thin object of uniform density coinciding with the triangle. Thus the object would balance on the intersection point of the medians. The centroid is twice as close along any median to the side that the median intersects as it is to the vertex it emanates from. Each median divides the area of the triangle in half; hence the name, and hence a triangular object of uniform density would balance on any median. (Any other lines which divide the area of the triangle into two equal parts do not pass through the centroid.) The three medians divide the triangle into six smaller triangles of equal area. Consider a triangle "ABC". Let "D" be the midpoint of formula_1, "E" be the midpoint of formula_2, "F" be the midpoint of formula_3, and "O" be the centroid (most commonly denoted "G"). By definition, formula_4. Thus formula_5 and formula_6, where formula_7 represents the area of triangle formula_8 ; these hold because in each case the two triangles have bases of equal length and share a common altitude from the (extended) base, and a triangle's area equals one-half its base times its height. We have: Thus, formula_11 and formula_12 Since formula_13, therefore, formula_14. Using the same method, one can show that formula_15. The lengths of the medians can be obtained from Apollonius' theorem as: where "a", "b" and "c" are the sides of the triangle with respective medians "m", "m", and "m" from their midpoints. Thus we have the relationships: Let "ABC" be a triangle, let "G" be its centroid, and let "D", "E", and "F" be the midpoints of "BC", "CA", and "AB", respectively. For any point "P" in the plane of "ABC" then The centroid divides each median into parts in the ratio 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. For any triangle with sides formula_23 and medians formula_24 and The medians from sides of lengths "a" and "b" are perpendicular if and only if formula_27 The medians of a right triangle with hypotenuse "c" satisfy formula_28 Any triangle's area "T" can be expressed in terms of its medians formula_29, and formula_30 as follows. Denoting their semi-sum as σ, we have A tetrahedron is a three-dimensional object having four triangular faces. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a "median" of the tetrahedron. There are four medians, and they are all concurrent at the "centroid" of the tetrahedron. As in the two-dimensional case, the centroid of the tetrahedron is the center of mass. However contrary to the two-dimensional case the centroid divides the medians not in a 2:1 ratio but in a 3:1 ratio (Commandino's theorem).

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.

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summarize: Fluids display properties such as: These properties are typically a function of their inability to support a shear stress in static equilibrium. In contrast, solids respond to shear either with a spring-like restoring force, which means that deformations are reversible, or they require a certain initial stress before they deform (see plasticity). Solids respond with restoring forces to both shear stresses and to normal stresses—both compressive and tensile. In contrast, ideal fluids only respond with restoring forces to normal stresses, called pressure: fluids can be subjected to both compressive stress, corresponding to positive pressure, and to tensile stress, corresponding to negative pressure. Both solids and liquids also have tensile strengths, which when exceeded in solids makes irreversible deformation and fracture, and in liquids causes the onset of cavitation. Both solids and liquids have free surfaces, which cost some amount of free energy to form. In the case of solids, the amount of free energy to form a given unit of surface area is called surface energy, whereas for liquids the same quantity is called surface tension. The ability of liquids to flow results in different behaviour in response to surface tension than in solids, although in equilibrium both will try to minimise their surface energy: liquids tend to form rounded droplets, whereas pure solids tend to form crystals. Gases do not have free surfaces, and freely diffuse. In a solid, shear stress is a function of strain, but in a fluid, shear stress is a function of strain rate. A consequence of this behavior is Pascal's law which describes the role of pressure in characterizing a fluid's state. Depending on the relationship between shear stress, and the rate of strain and its derivatives, fluids can be characterized as one of the following: The behavior of fluids can be described by the Navier–Stokes equations—a set of partial differential equations which are based on: The study of fluids is fluid mechanics, which is subdivided into fluid dynamics and fluid statics depending on whether the fluid is in motion.

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress, or external force. Fluids are a phase of matter and include liquids, gases and plasmas. They are substances with zero shear modulus, or, in simpler terms, substances which cannot resist any shear force applied to them.

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summarize: In 1954, Zamecnik and Hoagland discovered tRNA. In 1955, George E. Palade discovered ribosomes. The basic process of translation is the addition of one amino acid at a time to the end of the polypeptide being formed. This process takes place inside the ribosome. A ribosome is made up of a subunit, a small 40S subunit or a large 60S subunit. These subunits come together before translation of mRNA into a protein to provide a location for translation to be carried out and a polypeptide to be produced. The choice of amino acid type to be added is determined by the genetic code on the mRNA molecule. Each amino acid added is matched to a three nucleotide subsequence of the mRNA. For each such triplet possible, the corresponding amino acid is accepted. The successive amino acids added to the chain are matched to successive nucleotide triplets in the mRNA. In this way, the sequence of nucleotides in the template mRNA chain determines the sequence of amino acids in the generated polypeptide. Addition of an amino acid occurs at the C-terminus of the peptide and thus translation is said to be amino-to-carboxyl directed. The mRNA carries genetic information encoded as a DNA sequence from the chromosomes to the nucleolus. The ribonucleotides are "read" by translational machinery in a sequence of nucleotide triplets called codons. Each of those triplets codes for a specific amino acid. The ribosome translates this code to a specific sequence of amino acids. The ribosome is a multi-subunit structure containing rRNA and proteins. It is the "factory" where amino acids are assembled into proteins. tRNAs are small noncoding RNA chains (75-90 nucleotides) that transport amino acids to the ribosome. tRNAs have a site for amino acid attachment, and a site called an anticodon. The anticodon is an RNA triplet complementary to the mRNA triplet that codes for their cargo amino acid. Aminoacyl tRNA synthetases (enzymes) catalyze the bonding between specific tRNAs and the amino acids that their anticodon sequences call for. The product of this reaction is an aminoacyl-tRNA. In prokaryotes, this aminoacyl-tRNA is carried to the ribosome by EF-Tu, where mRNA codons are matched through complementary base pairing to specific tRNA anticodons. Aminoacyl-tRNA synthetases that mispair tRNAs with the wrong amino acids can produce mischarged aminoacyl-tRNAs, which can result in inappropriate amino acids at the respective position in protein. This "mistranslation" of the genetic code naturally occurs at low levels in most organisms, but certain cellular environments cause an increase in permissive mRNA decoding, sometimes to the benefit of the cell. The ribosome has three sites for tRNA to bind. They are the aminoacyl site (abbreviated A), the peptidyl site (abbreviated P) and the exit site (abbreviated E). With respect to the mRNA, the three sites are oriented 5’ to 3’ E-P-A, because ribosomes move toward the 3' end of mRNA. The A-site binds the incoming tRNA with the complementary codon on the mRNA. The P-site holds the tRNA with the growing polypeptide chain. The E-site holds the tRNA without its amino acid, and the tRNA is then released. When an aminoacyl-tRNA initially binds to its corresponding codon on the mRNA, it is in the A site. Then, a peptide bond forms between the amino acid of the tRNA in the A site and the amino acid of the charged tRNA in the P site. The growing polypeptide chain is transferred to the tRNA in the A site. Translocation occurs, moving the tRNA in the P site, now without an amino acid, to the E site; the tRNA that was in the A site, now charged with the polypeptide chain, is moved to the P site. The tRNA in the E site leaves and another aminoacyl-tRNA enters the A site to repeat the process. After the new amino acid is added to the chain, and after the mRNA is released out of the nucleus and into the ribosome's core, the energy provided by the hydrolysis of an ATP bound to the translocase EF-G (in prokaryotes) and eEF-2 (in eukaryotes) moves the ribosome down one codon towards the 3' end. The energy required for translation of proteins is significant. For a protein containing "n" amino acids, the number of high-energy phosphate bonds required to translate it is 4"n"+1. The rate of translation varies; it is significantly higher in prokaryotic cells (up to 17-21 amino acid residues per second) than in eukaryotic cells (up to 6-9 amino acid residues per second). Even though the ribosomes are usually considered accurate, processive machines, the translation process is subject to errors that can lead either to the synthesis of erroneous proteins or to the premature abandonment of translation. The rate of error in synthesizing proteins has been estimated to be between 1/10 and 1/10 misincorporated amino acids, depending on the experimental conditions. The rate of premature translation abandonment, instead, has been estimated to be of the order of magnitude of 10 events per translated codon. The correct amino acid is covalently bonded to the correct transfer RNA (tRNA) by amino acyl transferases. The amino acid is joined by its carboxyl group to the 3' OH of the tRNA by an ester bond. When the tRNA has an amino acid linked to it, the tRNA is termed "charged". Initiation involves the small subunit of the ribosome binding to the 5' end of mRNA with the help of initiation factors (IF). In prokaryotes, initiation of protein synthesis involves the recognition of a purine-rich initiation sequence on the mRNA called the Shine-Dalgarno sequence. The Shine-Dalgarno sequence binds to a complementary pyrimidine-rich sequence on the 3' end of the 16S rRNA part of the 30S ribosomal subunit. The binding of these complementary sequences ensures that the 30S ribosomal subunit is bound to the mRNA and is aligned such that the initiation codon is placed in the 30S portion of the P-site. Once the mRNA and 30S subunit are properly bound, an initiation factor brings the initiator tRNA-amino acid complex, f-Met-tRNA, to the 30S P site. The initiation phase is completed once a 50S subunit joins the 30 subunit, forming an active 70S ribosome. Termination of the polypeptide occurs when the A site of the ribosome is occupied by a stop codon (UAA, UAG, or UGA) on the mRNA. tRNA usually cannot recognize or bind to stop codons. Instead, the stop codon induces the binding of a release factor protein (RF1 & RF2) that prompts the disassembly of the entire ribosome/mRNA complex by the hydrolysis of the polypeptide chain from the peptidyl transferase center of the ribosome. Drugs or special sequence motifs on the mRNA can change the ribosomal structure so that near-cognate tRNAs are bound to the stop codon instead of the release factors. In such cases of 'translational readthrough', translation continues until the ribosome encounters the next stop codon. The process of translation is highly regulated in prokaryotic and eukaryotic organisms. Regulation of translation can impact the global rate of protein synthesis which is closely coupled to the metabolic and proliferative state of a cell. In addition, recent work has revealed that genetic differences and their subsequent expression as mRNAs can also impact translation rate in an RNA-specific manner. The transcription-translation process description, mentioning only the most basic ”elementary” processes, consists of: The process of protein synthesis and translation is a subject of mathematical modeling for a long time starting from the first detailed kinetic models such as or others taking into account stochastic aspects of translation and using computer simulations. Many chemical kinetics-based models of protein synthesis have been developed and analyzed in the last four decades. Beyond chemical kinetics, various modeling formalisms such as Totally Asymmetric Simple Exclusion Process (TASEP) Probabilistic Boolean Networks (PBN), Petri Nets and max-plus algebra have been applied to model the detailed kinetics of protein synthesis or some of its stages. A basic model of protein synthesis that took into account all eight 'elementary' processes has been developed, following the paradigm that "useful models are simple and extendable". The simplest model "M0" is represented by the reaction kinetic mechanism (Figure M0). It was generalised to include 40S, 60S and initiation factors (IF) binding (Figure M1'). It was extended further to include effect of microRNA on protein synthesis. Most of models in this hierarchy can be solved analytically. These solutions were used to extract 'kinetic signatures' of different specific mechanisms of synthesis regulation. Whereas other aspects such as the 3D structure, called tertiary structure, of protein can only be predicted using sophisticated algorithms, the amino acid sequence, called primary structure, can be determined solely from the nucleic acid sequence with the aid of a translation table. This approach may not give the correct amino acid composition of the protein, in particular if unconventional amino acids such as selenocysteine are incorporated into the protein, which is coded for by a conventional stop codon in combination with a downstream hairpin (SElenoCysteine Insertion Sequence, or SECIS). There are many computer programs capable of translating a DNA/RNA sequence into a protein sequence. Normally this is performed using the Standard Genetic Code, however, few programs can handle all the "special" cases, such as the use of the alternative initiation codons. For instance, the rare alternative start codon CTG codes for methionine when used as a start codon, and for leucine in all other positions. Example: Condensed translation table for the Standard Genetic Code (from the NCBI Taxonomy webpage). The "Starts" row indicate three start codons, UUG, CUG, and the very common AUG. It also indicates the first amino acid residue when interpreted as a start: in this case it is all methionine. Even when working with ordinary eukaryotic sequences such as the yeast genome, it is often desired to be able to use alternative translation tables—namely for translation of the mitochondrial genes. Currently the following translation tables are defined by the NCBI Taxonomy Group for the translation of the sequences in GenBank:

In molecular biology and genetics, translation is the process in which ribosomes in the cytoplasm or ER synthesize proteins after the process of transcription of DNA to RNA in the cell's nucleus. The entire process is called gene expression.

en

43

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summarize: There are three basic classes of ideal gas: The classical ideal gas can be separated into two types: The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. Both are essentially the same, except that the classical thermodynamic ideal gas is based on classical statistical mechanics, and certain thermodynamic parameters such as the entropy are only specified to within an undetermined additive constant. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas and quantum Fermi gas in the limit of high temperature to specify these additive constants. The behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur–Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma. The classical thermodynamic properties of an ideal gas can be described by two equations of state: The ideal gas law is the equation of state for an ideal gas, given by: where The ideal gas law is an extension of experimentally discovered gas laws. It can also be derived from microscopic considerations. Real fluids at low density and high temperature approximate the behavior of a classical ideal gas. However, at lower temperatures or a higher density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or as it deposits from a gas into a solid. This deviation is expressed as a compressibility factor. This equation is derived from After combining three laws we get That is: The other equation of state of an ideal gas must express Joule's law, that the internal energy of a fixed mass of ideal gas is a function only of its temperature. For the present purposes it is convenient to postulate an exemplary version of this law by writing: where That for an ideal gas depends only on temperature is a consequence of the ideal gas law, although in the general case depends on temperature and an integral is needed to compute. In order to switch from macroscopic quantities (left hand side of the following equation) to microscopic ones (right hand side), we use where The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution. The ideal gas model depends on the following assumptions: The assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas. The following three assumptions are very related: molecules are hard, collisions are elastic, and there are no inter-molecular forces. The assumption that the space between particles is much larger than the particles themselves is of paramount importance, and explains why the ideal gas approximation fails at high pressures. The dimensionless heat capacity at constant volume is generally defined by where is the entropy. This quantity is generally a function of temperature due to intermolecular and intramolecular forces, but for moderate temperatures it is approximately constant. Specifically, the Equipartition Theorem predicts that the constant for a monatomic gas is = while for a diatomic gas it is = if vibrations are neglected (which is often an excellent approximation). Since the heat capacity depends on the atomic or molecular nature of the gas, macroscopic measurements on heat capacity provide useful information on the microscopic structure of the molecules. The dimensionless heat capacity at constant pressure of an ideal gas is: where is the enthalpy of the gas. Sometimes, a distinction is made between an ideal gas, where and could vary with temperature, and a perfect gas, for which this is not the case. The ratio of the constant volume and constant pressure heat capacity is the adiabatic index For air, which is a mixture of gases, this ratio is 1.4. Using the results of thermodynamics only, we can go a long way in determining the expression for the entropy of an ideal gas. This is an important step since, according to the theory of thermodynamic potentials, if we can express the entropy as a function of ( is a thermodynamic potential), volume and the number of particles, then we will have a complete statement of the thermodynamic behavior of the ideal gas. We will be able to derive both the ideal gas law and the expression for internal energy from it. Since the entropy is an exact differential, using the chain rule, the change in entropy when going from a reference state 0 to some other state with entropy may be written as where: where the reference variables may be functions of the number of particles. Using the definition of the heat capacity at constant volume for the first differential and the appropriate Maxwell relation for the second we have: Expressing in terms of as developed in the above section, differentiating the ideal gas equation of state, and integrating yields: which implies that the entropy may be expressed as: where all constants have been incorporated into the logarithm as which is some function of the particle number having the same dimensions as in order that the argument of the logarithm be dimensionless. We now impose the constraint that the entropy be extensive. This will mean that when the extensive parameters ( and ) are multiplied by a constant, the entropy will be multiplied by the same constant. Mathematically: From this we find an equation for the function Differentiating this with respect to, setting equal to 1, and then solving the differential equation yields : where may vary for different gases, but will be independent of the thermodynamic state of the gas. It will have the dimensions of. Substituting into the equation for the entropy: and using the expression for the internal energy of an ideal gas, the entropy may be written: Since this is an expression for entropy in terms of,, and, it is a fundamental equation from which all other properties of the ideal gas may be derived. This is about as far as we can go using thermodynamics alone. Note that the above equation is flawed – as the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics. In the above "ideal" development, there is a critical point, not at absolute zero, at which the argument of the logarithm becomes unity, and the entropy becomes zero. This is unphysical. The above equation is a good approximation only when the argument of the logarithm is much larger than unity – the concept of an ideal gas breaks down at low values of. Nevertheless, there will be a "best" value of the constant in the sense that the predicted entropy is as close as possible to the actual entropy, given the flawed assumption of ideality. A quantum-mechanical derivation of this constant is developed in the derivation of the Sackur–Tetrode equation which expresses the entropy of a monatomic ( = ) ideal gas. In the Sackur–Tetrode theory the constant depends only upon the mass of the gas particle. The Sackur–Tetrode equation also suffers from a divergent entropy at absolute zero, but is a good approximation for the entropy of a monatomic ideal gas for high enough temperatures. An alternative way of expressing the change in entropy: formula_22 Expressing the entropy as a function of,, and : The chemical potential of the ideal gas is calculated from the corresponding equation of state (see thermodynamic potential): where is the Gibbs free energy and is equal to so that: The chemical potential is usually referenced to the potential at some standard pressure "P" so that, with formula_26: For a mixture ("j"=1,2...) of ideal gases, each at partial pressure "P", it can be shown that the chemical potential "μ" will be given by the above expression with the pressure "P" replaced by "P". The thermodynamic potentials for an ideal gas can now be written as functions of,, and as: where, as before, The most informative way of writing the potentials is in terms of their natural variables, since each of these equations can be used to derive all of the other thermodynamic variables of the system. In terms of their natural variables, the thermodynamic potentials of a single-species ideal gas are: In statistical mechanics, the relationship between the Helmholtz free energy and the partition function is fundamental, and is used to calculate the thermodynamic properties of matter; see configuration integral for more details. The speed of sound in an ideal gas is given by the Newton-Laplace formula: where the isentropic Bulk modulus formula_34. For an isentropic process of an ideal gas, formula_35, therefore Here, In the above-mentioned Sackur–Tetrode equation, the best choice of the entropy constant was found to be proportional to the quantum thermal wavelength of a particle, and the point at which the argument of the logarithm becomes zero is roughly equal to the point at which the average distance between particles becomes equal to the thermal wavelength. In fact, quantum theory itself predicts the same thing. Any gas behaves as an ideal gas at high enough temperature and low enough density, but at the point where the Sackur–Tetrode equation begins to break down, the gas will begin to behave as a quantum gas, composed of either bosons or fermions. (See the gas in a box article for a derivation of the ideal quantum gases, including the ideal Boltzmann gas.) Gases tend to behave as an ideal gas over a wider range of pressures when the temperature reaches the Boyle temperature. The ideal Boltzmann gas yields the same results as the classical thermodynamic gas, but makes the following identification for the undetermined constant : where is the thermal de Broglie wavelength of the gas and is the degeneracy of states. An ideal gas of bosons (e.g. a photon gas) will be governed by Bose–Einstein statistics and the distribution of energy will be in the form of a Bose–Einstein distribution. An ideal gas of fermions will be governed by Fermi–Dirac statistics and the distribution of energy will be in the form of a Fermi–Dirac distribution.

An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.

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summarize: Some principles of hydrostatics have been known in an empirical and intuitive sense since antiquity, by the builders of boats, cisterns, aqueducts and fountains. Archimedes is credited with the discovery of Archimedes' Principle, which relates the buoyancy force on an object that is submerged in a fluid to the weight of fluid displaced by the object. The Roman engineer Vitruvius warned readers about lead pipes bursting under hydrostatic pressure. The concept of pressure and the way it is transmitted by fluids was formulated by the French mathematician and philosopher Blaise Pascal in 1647. The "fair cup" or Pythagorean cup, which dates from about the 6th century BC, is a hydraulic technology whose invention is credited to the Greek mathematician and geometer Pythagoras. It was used as a learning tool. The cup consists of a line carved into the interior of the cup, and a small vertical pipe in the center of the cup that leads to the bottom. The height of this pipe is the same as the line carved into the interior of the cup. The cup may be filled to the line without any fluid passing into the pipe in the center of the cup. However, when the amount of fluid exceeds this fill line, fluid will overflow into the pipe in the center of the cup. Due to the drag that molecules exert on one another, the cup will be emptied. Heron's fountain is a device invented by Heron of Alexandria that consists of a jet of fluid being fed by a reservoir of fluid. The fountain is constructed in such a way that the height of the jet exceeds the height of the fluid in the reservoir, apparently in violation of principles of hydrostatic pressure. The device consisted of an opening and two containers arranged one above the other. The intermediate pot, which was sealed, was filled with fluid, and several cannula (a small tube for transferring fluid between vessels) connecting the various vessels. Trapped air inside the vessels induces a jet of water out of a nozzle, emptying all water from the intermediate reservoir. Pascal made contributions to developments in both hydrostatics and hydrodynamics. Pascal's Law is a fundamental principle of fluid mechanics that states that any pressure applied to the surface of a fluid is transmitted uniformly throughout the fluid in all directions, in such a way that initial variations in pressure are not changed. Due to the fundamental nature of fluids, a fluid cannot remain at rest under the presence of a shear stress. However, fluids can exert pressure normal to any contacting surface. If a point in the fluid is thought of as an infinitesimally small cube, then it follows from the principles of equilibrium that the pressure on every side of this unit of fluid must be equal. If this were not the case, the fluid would move in the direction of the resulting force. Thus, the pressure on a fluid at rest is isotropic; i.e., it acts with equal magnitude in all directions. This characteristic allows fluids to transmit force through the length of pipes or tubes; i.e., a force applied to a fluid in a pipe is transmitted, via the fluid, to the other end of the pipe. This principle was first formulated, in a slightly extended form, by Blaise Pascal, and is now called Pascal's law. In a fluid at rest, all frictional and inertial stresses vanish and the state of stress of the system is called "hydrostatic". When this condition of is applied to the Navier–Stokes equations, the gradient of pressure becomes a function of body forces only. For a barotropic fluid in a conservative force field like a gravitational force field, the pressure exerted by a fluid at equilibrium becomes a function of force exerted by gravity. The hydrostatic pressure can be determined from a control volume analysis of an infinitesimally small cube of fluid. Since pressure is defined as the force exerted on a test area (, with : pressure, : force normal to area, : area), and the only force acting on any such small cube of fluid is the weight of the fluid column above it, hydrostatic pressure can be calculated according to the following formula: where: For water and other liquids, this integral can be simplified significantly for many practical applications, based on the following two assumptions: Since many liquids can be considered incompressible, a reasonable good estimation can be made from assuming a constant density throughout the liquid. (The same assumption cannot be made within a gaseous environment.) Also, since the height of the fluid column between and is often reasonably small compared to the radius of the Earth, one can neglect the variation of. Under these circumstances, the integral is simplified into the formula: where is the height of the liquid column between the test volume and the zero reference point of the pressure. This formula is often called Stevin's law. Note that this reference point should lie at or below the surface of the liquid. Otherwise, one has to split the integral into two (or more) terms with the constant and. For example, the absolute pressure compared to vacuum is: where is the total height of the liquid column above the test area to the surface, and is the atmospheric pressure, i.e., the pressure calculated from the remaining integral over the air column from the liquid surface to infinity. This can easily be visualized using a pressure prism. Hydrostatic pressure has been used in the preservation of foods in a process called pascalization. In medicine, hydrostatic pressure in blood vessels is the pressure of the blood against the wall. It is the opposing force to oncotic pressure. Statistical mechanics shows that, for a gas of constant temperature, "T", its pressure, "p" will vary with height, "h", as: where: This is known as the barometric formula, and maybe derived from assuming the pressure is hydrostatic. If there are multiple types of molecules in the gas, the partial pressure of each type will be given by this equation. Under most conditions, the distribution of each species of gas is independent of the other species. Anybody of arbitrary shape which is immersed, partly or fully, in a fluid will experience the action of a net force in the opposite direction of the local pressure gradient. If this pressure gradient arises from gravity, the net force is in the vertical direction opposite that of the gravitational force. This vertical force is termed buoyancy or buoyant force and is equal in magnitude, but opposite in direction, to the weight of the displaced fluid. Mathematically, where is the density of the fluid, is the acceleration due to gravity, and is the volume of fluid directly above the curved surface. In the case of a ship, for instance, its weight is balanced by pressure forces from the surrounding water, allowing it to float. If more cargo is loaded onto the ship, it would sink more into the water – displacing more water and thus receive a higher buoyant force to balance the increased weight. Discovery of the principle of buoyancy is attributed to Archimedes. The horizontal and vertical components of the hydrostatic force acting on a submerged surface are given by the following: where: Liquids can have free surfaces at which they interface with gases, or with a vacuum. In general, the lack of the ability to sustain a shear stress entails that free surfaces rapidly adjust towards an equilibrium. However, on small length scales, there is an important balancing force from surface tension. When liquids are constrained in vessels whose dimensions are small, compared to the relevant length scales, surface tension effects become important leading to the formation of a meniscus through capillary action. This capillary action has profound consequences for biological systems as it is part of one of the two driving mechanisms of the flow of water in plant xylem, the transpirational pull. Without surface tension, drops would not be able to form. The dimensions and stability of drops are determined by surface tension. The drop's surface tension is directly proportional to the cohesion property of the fluid.

Fluid statics or hydrostatics is the branch of fluid mechanics that studies "fluids at rest and the pressure in a fluid or exerted by a fluid on an immersed body".

en

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summarize: Newton's laws are applied to objects which are idealised as single point masses, in the sense that the size and shape of the object's body are neglected to focus on its motion more easily. This can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newton's laws of motion for rigid bodies called Euler's laws of motion, later applied as well for deformable bodies assumed as a continuum. If a body is represented as an assemblage of discrete particles, each governed by Newton's laws of motion, then Euler's laws can be derived from Newton's laws. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Some authors interpret the first law as defining what an inertial reference frame is; from this point of view, the second law holds only when the observation is made from an inertial reference frame, and therefore the first law cannot be proved as a special case of the second. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given interpretation mass, acceleration, momentum, and (most importantly) force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is still useful as an approximation when the speeds involved are much slower than the speed of light. One translation of Newton's laws reads: Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed. Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd. Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. The first law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant. Velocity is a vector quantity which expresses both the object's speed and the direction of its motion; therefore, the statement that the object's velocity is constant is a statement that both its speed and the direction of its motion are constant. The first law can be stated mathematically when the mass is a non-zero constant, as, Consequently, This is known as "uniform motion". An object "continues" to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest (demonstrated when a tablecloth is skilfully whipped from under dishes on a tabletop and the dishes remain in their initial state of rest). If an object is moving, it continues to move without turning or changing its speed. This is evident in space probes that continuously move in outer space. Changes in motion must be imposed against the tendency of an object to retain its state of motion. In the absence of net forces, a moving object tends to move along a straight line path indefinitely. Newton placed the first law of motion to establish frames of reference for which the other laws are applicable. However, Newton implicitly referred to the absolute co-ordinate of cosmos for this frame. Since we cannot precisely measure our velocity relative to a far star, Newton's frame is based on a pure imagination, not based on measurable physics. In current physics, an observer defines himself as in inertial frame by preparing one stone hooked by a spring, and rotating the spring to any direction, and observing the stone static and the length of that spring unchanged. By Einstein's equivalence principle, if there was one such observer A and another observer B moving in a constant velocity related to A, then A and B will both observe the same physics phenomena. if A verified the first law, then B will verify it too. In this way, the definition of inertial can get rid of absolute space or far star, and only refer to the objects locally reachable and measurable. A particle not subject to forces moves (related to inertial frame) in a straight line at a constant speed. Newton's first law is often referred to as the "law of inertia". Thus, a condition necessary for the uniform motion of a particle relative to an inertial reference frame is that the total net force acting on it is zero. In this sense, the first law can be restated as: Newton's first and second laws are valid only in an inertial reference frame. Any reference frame that is in uniform motion with respect to an inertial frame is also an inertial frame, i.e. Galilean invariance or the principle of Newtonian relativity. The second law states that the rate of change of momentum of a body is directly proportional to the force applied, and this change in momentum takes place in the direction of the applied force. The second law can also be stated in terms of an object's acceleration. Since Newton's second law is valid only for constant-mass systems, can be taken outside the differentiation operator by the constant factor rule in differentiation. Thus, where F is the net force applied, is the mass of the body, and a is the body's acceleration. Thus, the net force applied to a body produces a proportional acceleration. In other words, if a body is accelerating, then there is a force on it. The above statements hint that the second law is merely a definition of formula_4, not a precious observation of nature. However, current physics restate the second law in measurable steps: (1)defining the term 'one unit of mass' by a specified stone, (2)defining the term 'one unit of force' by a specified spring with specified length, (3)measuring by experiment or proving by theory (with a principle that every direction of space are equivalent), that force can be added as a mathematical vector, (4)finally conclude that formula_5. These steps hint the second law is a precious feature of nature. The second law also implies the conservation of momentum: when the net force on the body is zero, the momentum of the body is constant. Any net force is equal to the rate of change of the momentum. Any mass that is gained or lost by the system will cause a change in momentum that is not the result of an external force. A different equation is necessary for variable-mass systems (see below). Newton's second law is an approximation that is increasingly worse at high speeds because of relativistic effects. According to modern ideas of how Newton was using his terminology, the law is understood, in modern terms, as an equivalent of: This may be expressed by the formula formula_6, where formula_7 is the time derivative of the momentum formula_8. This equation can be seen clearly in the Wren Library of Trinity College, Cambridge, in a glass case in which Newton's manuscript is open to the relevant page. Motte's 1729 translation of Newton's Latin continued with Newton's commentary on the second law of motion, reading: The sense or senses in which Newton used his terminology, and how he understood the second law and intended it to be understood, have been extensively discussed by historians of science, along with the relations between Newton's formulation and modern formulations. An impulse J occurs when a force F acts over an interval of time Δ"t", and it is given by Since force is the time derivative of momentum, it follows that This relation between impulse and momentum is closer to Newton's wording of the second law. Impulse is a concept frequently used in the analysis of collisions and impacts. Variable-mass systems, like a rocket burning fuel and ejecting spent gases, are not closed and cannot be directly treated by making mass a function of time in the second law; that is, the following formula is wrong: The falsehood of this formula can be seen by noting that it does not respect Galilean invariance: a variable-mass object with F = 0 in one frame will be seen to have F ≠ 0 in another frame. The correct equation of motion for a body whose mass "m" varies with time by either ejecting or accreting mass is obtained by applying the second law to the entire, constant-mass system consisting of the body and its ejected/accreted mass; the result is where u is the velocity of the escaping or incoming mass relative to the body. From this equation one can derive the equation of motion for a varying mass system, for example, the Tsiolkovsky rocket equation. Under some conventions, the quantity u d"m"/d"t" on the left-hand side, which represents the advection of momentum, is defined as a force (the force exerted on the body by the changing mass, such as rocket exhaust) and is included in the quantity F. Then, by substituting the definition of acceleration, the equation becomes F = "m"a. The third law states that all forces between two objects exist in equal magnitude and opposite direction: if one object "A" exerts a force F on a second object "B", then "B" simultaneously exerts a force F on "A", and the two forces are equal in magnitude and opposite in direction: F = −F. The third law means that all forces are "interactions" between different bodies, or different regions within one body, and thus that there is no such thing as a force that is not accompanied by an equal and opposite force. In some situations, the magnitude and direction of the forces are determined entirely by one of the two bodies, say Body "A"; the force exerted by Body "A" on Body "B" is called the "action", and the force exerted by Body "B" on Body "A" is called the "reaction". This law is sometimes referred to as the "action-reaction law", with F called the "action" and F the "reaction". In other situations the magnitude and directions of the forces are determined jointly by both bodies and it isn't necessary to identify one force as the "action" and the other as the "reaction". The action and the reaction are simultaneous, and it does not matter which is called the "action" and which is called "reaction"; both forces are part of a single interaction, and neither force exists without the other. The two forces in Newton's third law are of the same type (e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road). From a conceptual standpoint, Newton's third law is seen when a person walks: they push against the floor, and the floor pushes against the person. Similarly, the tires of a car push against the road while the road pushes back on the tires—the tires and road simultaneously push against each other. In swimming, a person interacts with the water, pushing the water backward, while the water simultaneously pushes the person forward—both the person and the water push against each other. The reaction forces account for the motion in these examples. These forces depend on friction; a person or car on ice, for example, may be unable to exert the action force to produce the needed reaction force. Newton used the third law to derive the law of conservation of momentum; from a deeper perspective, however, conservation of momentum is the more fundamental idea (derived via Noether's theorem from Galilean invariance), and holds in cases where Newton's third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics. The ancient Greek philosopher Aristotle had the view that all objects have a natural place in the universe: that heavy objects (such as rocks) wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed continually to propel it, otherwise it would stop moving. Galileo Galilei, however, realised that a force is necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its velocity. In other words, Galileo stated that, in the "absence" of a force, a moving object will continue moving. (The tendency of objects to resist changes in motion was what Johannes Kepler had called "inertia".) This insight was refined by Newton, who made it into his first law, also known as the "law of inertia"—no force means no acceleration, and hence the body will maintain its velocity. As Newton's first law is a restatement of the law of inertia which Galileo had already described, Newton appropriately gave credit to Galileo. Leonardo da Vinci understood that "An object offers as much resistance to the air as the air does to the object". The law of inertia apparently occurred to several different natural philosophers and scientists independently, including Thomas Hobbes in his "Leviathan" (1651). The 17th-century philosopher and mathematician René Descartes also formulated the law, although he did not perform any experiments to confirm it. Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena. These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton's laws (combined with universal gravitation and classical electrodynamics) are inappropriate for use in certain circumstances, most notably at very small scales, at very high speeds, or in very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a semiconductor, optical properties of substances, errors in non-relativistically corrected GPS systems and superconductivity. Explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory. In quantum mechanics, concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form F = dp/d"t", where F and p are four-vectors. In modern physics, the laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics. This can be stated simply, "Momentum, energy and angular momentum cannot be created or destroyed." Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g., quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forces originate out of exchange by virtual particles. Other forces, such as gravity and fermionic degeneracy pressure, also arise from the momentum conservation. Indeed, the conservation of 4-momentum in inertial motion via curved space-time results in what we call gravitational force in general relativity theory. The application of the space derivative (which is a momentum operator in quantum mechanics) to the overlapping wave functions of a pair of fermions (particles with half-integer spin) results in shifts of maxima of compound wavefunction away from each other, which is observable as the "repulsion" of the fermions. Newton stated the third law within a world-view that assumed instantaneous action at a distance between material particles. However, he was prepared for philosophical criticism of this action at a distance, and it was in this context that he stated the famous phrase "I feign no hypotheses". In modern physics, action at a distance has been completely eliminated, except for subtle effects involving quantum entanglement. (In particular, this refers to Bell's theorem—that no local model can reproduce the predictions of quantum theory.) Despite only being an approximation, in modern engineering and all practical applications involving the motion of vehicles and satellites, the concept of action at a distance is used extensively. The discovery of the second law of thermodynamics by Carnot in the 19th century showed that not every physical quantity is conserved over time, thus disproving the validity of inducing the opposite metaphysical view from Newton's laws. Hence, a "steady-state" worldview based solely on Newton's laws and the conservation laws does not take entropy into account.

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a quantitative measure of the force, and the third asserts that a single isolated force doesn't exist. These three laws have been expressed in several ways, over nearly three centuries, and can be summarised as follows:

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summarize: Alexander Cumming, a watchmaker and mechanic, has a claim to having made the first effective recording barograph in the 1760s using an aneroid cell. Cumming created a series of barometrical clocks, including one for King George III. However, this type of design fell out of favour. Since the amount of movement that can be generated by a single aneroid is minuscule, up to seven aneroids (so called Vidie-cans) are often stacked "in series" to amplify their motion. This type of barograph was invented in 1844 by the Frenchman Lucien Vidi (1805–1866). In such barographs one or more aneroid cells act through a gear or lever train to drive a recording arm that has at its extreme end either a scribe or a pen. A scribe records on smoked foil while a pen records on paper using ink, held in a nib. The recording material is mounted on a cylindrical drum which is rotated slowly by clockwork. Commonly, the drum makes one revolution per day, per week, or per month and the rotation rate can often be selected by the user. Various other types of barograph have also been invented. Karl Kreil described a machine in 1843 based on a syphon barometer, where a pencil marked a chart at uniform intervals. Francis Ronalds, the Honorary Director of the Kew Observatory, created the first successful barograph utilising photography in 1845. The changing height of the mercury in the barometer was recorded on a continuously moving photosensitive surface. By 1847, a sophisticated temperature-compensation mechanism was also employed. Ronalds’ barograph was utilised by the UK Meteorological Office for many years to assist in weather forecasting and the machines were supplied to numerous observatories around the world. Today, traditional recording barographs for meteorological use have commonly been superseded (though not all) by electronic weather instruments that use computer methods to record the barometric pressure. These are not only less expensive than earlier barographs but they may also offer both greater recording length and the ability to perform further data analysis on the captured data including automated use of the data to forecast the weather. Older mechanical barographs are highly prized by collectors as they make good display items, often being made of high quality woods and brass. The most common weather Barograph found in homes and public buildings these days are the 8-day type. Some important manufacturers of Barographs are Negretti and Zambra, Short and Mason, and Richard Ferris among others. The late Victorian to early 20th century is generally considered to be the heyday of Barograph manufacture, many important refinements were made at this time, including improved temperature compensation and modification of the pen arm, to allow less weight to be applied to the paper, allowing better registration of small pressure changes (i.e. less friction on the nib). Marine barographs (used on ships) often include damping, this evens out the motion of the ship so that a more stable reading can be obtained, this can be either oil damping of the mechanism or simple coiled spring feet on the base. But, newer solid state, digital barographs eliminate this issue altogether, since they use no moving parts. As atmospheric pressure responds in a predictable manner to changes in altitude, barographs may be used to record elevation changes during an aircraft flight. Barographs were required by the FAI to record certain tasks and record attempts associated with sailplanes. A continuously varying trace indicated that the sailplane had not landed during a task, while measurements from a calibrated trace could be used to establish the completion of altitude tasks or the setting of records. Examples of FAI approved sailplane barographs included the Replogle mechanical drum barograph and the EW electronic barograph (which may be used in conjunction with GPS). Mechanical barographs are not commonly used for flight documentation now, having been displaced by GNSS Flight Recorders. On the top right of the picture of the three-day barograph can be seen a silver knurled knob. This is to adjust the barograph so that it correctly reflects the station pressure. Barely visible below the knob is a small silver plunger. This is pressed every three hours to leave a time mark on the paper. The line between two of these marks is called the 'characteristic of barometric tendency' and is used by weather forecasters. The observer would first note if the pressure was lower or higher than three hours prior. Next, a code number would be chosen that best represents the three-hour trace. There are nine possible choices (0 to 8) and no single code has preference over another. In the case of the graph on the barograph, one of two codes could be picked. An 8 (steady then decreasing) or 6 (decreasing then steady). The observer should pick the 6 because it represents the last part of the trace and is thus most representative of the pressure change. In the bottom centre is the aneroid (large circular silver object). As the pressure increases, the aneroid is pushed down causing the arm to move up and leave a trace on the paper. As the pressure decreases, the spring lifts the aneroid and the arm moves down. After three days the drum to which the graph is attached is removed. At this point the clockwork motor is wound and if necessary corrections can be made to increase or decrease the speed and new chart is attached.

A barograph is a barometer that records the barometric pressure over time in graphical form. This instrument is also used to make a continuous recording of atmospheric pressure. The pressure-sensitive element, a partially evacuated metal cylinder, is linked to a pen arm in such a way that the vertical displacement of the pen is proportional to the changes in the atmospheric pressure.

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summarize: The word "barometer" is derived from the, and "meter" from Ancient Greek meaning "measure". Although Evangelista Torricelli is universally credited with inventing the barometer in 1643,<ref name="http://www.islandnet.com/~see/weather/history/barometerhistory1.htm"></ref><ref name="http://www.barometerfair.com/history_of_the_barometer.htm"></ref><ref name="http://www.juliantrubin.com/bigten/torricellibarometer.html"></ref> historical documentation also suggests Gasparo Berti, an Italian mathematician and astronomer, unintentionally built a water barometer sometime between 1640 and 1643. French scientist and philosopher René Descartes described the design of an experiment to determine atmospheric pressure as early as 1631, but there is no evidence that he built a working barometer at that time. On July 27, 1630, Giovanni Battista Baliani wrote a letter to Galileo Galilei explaining an experiment he had made in which a siphon, led over a hill about twenty-one meters high, failed to work. Galileo responded with an explanation of the phenomenon: he proposed that it was the power of a vacuum that held the water up, and at a certain height the amount of water simply became too much and the force could not hold any more, like a cord that can support only so much weight. This was a restatement of the theory of "horror vacui" ("nature abhors a vacuum"), which dates to Aristotle, and which Galileo restated as "resistenza del vacuo". Galileo's ideas reached Rome in December 1638 in his "Discorsi". Raffaele Magiotti and Gasparo Berti were excited by these ideas, and decided to seek a better way to attempt to produce a vacuum other than with a siphon. Magiotti devised such an experiment, and sometime between 1639 and 1641, Berti (with Magiotti, Athanasius Kircher and Niccolò Zucchi present) carried it out. Four accounts of Berti's experiment exist, but a simple model of his experiment consisted of filling with water a long tube that had both ends plugged, then standing the tube in a basin already full of water. The bottom end of the tube was opened, and water that had been inside of it poured out into the basin. However, only part of the water in the tube flowed out, and the level of the water inside the tube stayed at an exact level, which happened to be, the same height Baliani and Galileo had observed that was limited by the siphon. What was most important about this experiment was that the lowering water had left a space above it in the tube which had no intermediate contact with air to fill it up. This seemed to suggest the possibility of a vacuum existing in the space above the water. Torricelli, a friend and student of Galileo, interpreted the results of the experiments in a novel way. He proposed that the weight of the atmosphere, not an attracting force of the vacuum, held the water in the tube. In a letter to Michelangelo Ricci in 1644 concerning the experiments, he wrote: Many have said that a vacuum does not exist, others that it does exist in spite of the repugnance of nature and with difficulty; I know of no one who has said that it exists without difficulty and without a resistance from nature. I argued thus: If there can be found a manifest cause from which the resistance can be derived which is felt if we try to make a vacuum, it seems to me foolish to try to attribute to vacuum those operations which follow evidently from some other cause; and so by making some very easy calculations, I found that the cause assigned by me (that is, the weight of the atmosphere) ought by itself alone to offer a greater resistance than it does when we try to produce a vacuum. It was traditionally thought (especially by the Aristotelians) that the air did not have weight: that is, that the kilometers of air above the surface did not exert any weight on the bodies below it. Even Galileo had accepted the weightlessness of air as a simple truth. Torricelli questioned that assumption, and instead proposed that air had weight and that it was the latter (not the attracting force of the vacuum) which held (or rather, pushed) up the column of water. He thought that the level the water stayed at (c. 10.3 m) was reflective of the force of the air's weight pushing on it (specifically, pushing on the water in the basin and thus limiting how much water can fall from the tube into it). In other words, he viewed the barometer as a balance, an instrument for measurement (as opposed to merely being an instrument to create a vacuum), and because he was the first to view it this way, he is traditionally considered the inventor of the barometer (in the sense in which we now use the term). Because of rumors circulating in Torricelli's gossipy Italian neighborhood, which included that he was engaged in some form of sorcery or witchcraft, Torricelli realized he had to keep his experiment secret to avoid the risk of being arrested. He needed to use a liquid that was heavier than water, and from his previous association and suggestions by Galileo, he deduced by using mercury, a shorter tube could be used. With mercury, which is about 14 times denser than water, a tube only 80 cm was now needed, not 10.5 m. In 1646, Blaise Pascal along with Pierre Petit, had repeated and perfected Torricelli's experiment after hearing about it from Marin Mersenne, who himself had been shown the experiment by Torricelli toward the end of 1644. Pascal further devised an experiment to test the Aristotelian proposition that it was vapours from the liquid that filled the space in a barometer. His experiment compared water with wine, and since the latter was considered more "spiritous", the Aristotelians expected the wine to stand lower (since more vapours would mean more pushing down on the liquid column). Pascal performed the experiment publicly, inviting the Aristotelians to predict the outcome beforehand. The Aristotelians predicted the wine would stand lower. It did not. However, Pascal went even further to test the mechanical theory. If, as suspected by mechanical philosophers like Torricelli and Pascal, air had weight, the pressure would be less at higher altitudes. Therefore, Pascal wrote to his brother-in-law, Florin Perier, who lived near a mountain called the Puy de Dome, asking him to perform a crucial experiment. Perier was to take a barometer up the Puy de Dome and make measurements along the way of the height of the column of mercury. He was then to compare it to measurements taken at the foot of the mountain to see if those measurements taken higher up were in fact smaller. In September 1648, Perier carefully and meticulously carried out the experiment, and found that Pascal's predictions had been correct. The mercury barometer stood lower the higher one went. The concept that decreasing atmospheric pressure predicts stormy weather, postulated by Lucien Vidi, provides the theoretical basis for a weather prediction device called a "weather glass" or a "Goethe barometer" (named for Johann Wolfgang Von Goethe, the renowned German writer and polymath who developed a simple but effective weather ball barometer using the principles developed by Torricelli). The French name, "le baromètre Liègeois", is used by some English speakers. This name reflects the origins of many early weather glasses – the glass blowers of Liège, Belgium. The weather ball barometer consists of a glass container with a sealed body, half filled with water. A narrow spout connects to the body below the water level and rises above the water level. The narrow spout is open to the atmosphere. When the air pressure is lower than it was at the time the body was sealed, the water level in the spout will rise above the water level in the body; when the air pressure is higher, the water level in the spout will drop below the water level in the body. A variation of this type of barometer can be easily made at home. A mercury barometer has a vertical glass tube closed at the top sitting in an open mercury-filled basin at the bottom. Mercury in the tube adjusts until the weight of the mercury column balances the atmospheric force exerted on the reservoir. High atmospheric pressure places more force on the reservoir, forcing mercury higher in the column. Low pressure allows the mercury to drop to a lower level in the column by lowering the force placed on the reservoir. Since higher temperature levels around the instrument will reduce the density of the mercury, the scale for reading the height of the mercury is adjusted to compensate for this effect. The tube has to be at least as long as the amount dipping in the mercury + head space + the maximum length of the column. Torricelli documented that the height of the mercury in a barometer changed slightly each day and concluded that this was due to the changing pressure in the atmosphere. He wrote: "We live submerged at the bottom of an ocean of elementary air, which is known by incontestable experiments to have weight". Inspired by Torricelli, Otto von Guericke on 5 December 1660 found that air pressure was unusually low and predicted a storm, which occurred the next day. The mercury barometer's design gives rise to the expression of atmospheric pressure in inches or millimeters of mercury (mmHg). A torr was originally defined as 1 mmHg. The pressure is quoted as the level of the mercury's height in the vertical column. Typically, atmospheric pressure is measured between and of Hg. One atmosphere (1 atm) is equivalent to of mercury. Design changes to make the instrument more sensitive, simpler to read, and easier to transport resulted in variations such as the basin, siphon, wheel, cistern, Fortin, multiple folded, stereometric, and balance barometers. "Fitzroy" barometers combine the standard mercury barometer with a thermometer, as well as a guide of how to interpret pressure changes. Fortin barometers use a variable displacement mercury cistern, usually constructed with a thumbscrew pressing on a leather diaphragm bottom (V in the diagram). This compensates for displacement of mercury in the column with varying pressure. To use a Fortin barometer, the level of mercury is set to zero by using the thumbscrew to make an ivory pointer (O in the diagram) just touch the surface of the mercury. The pressure is then read on the column by adjusting the vernier scale so that the mercury just touches the sightline at Z.. Some models also employ a valve for closing the cistern, enabling the mercury column to be forced to the top of the column for transport. This prevents water-hammer damage to the column in transit. On June 5, 2007, a European Union directive was enacted to restrict the sale of mercury, thus effectively ending the production of new mercury barometers in Europe. Around 1810 the wheel barometer, which could be read from a great distance, became the first practical and commercial instrument favoured by farmers and the educated classes in the UK. The face of the barometer was circular with a simple dial pointing to an easily readable scale: "Rain - Change - Dry" with the "Change" at the top centre of the dial. Later models added a barometric scale with finer graduations "Stormy (28 inches of mercury), Much Rain (28.5), Rain (29), Change (29.5), Fair (30), Set fair (30.5), very dry(31)". Using vacuum pump oil as the working fluid in a barometer has led to the creation of the new "World's Tallest Barometer" in February 2013. The barometer at Portland State University (PSU) uses doubly distilled vacuum pump oil and has a nominal height of about 12.4 m for the oil column height; expected excursions are in the range of ±0.4 m over the course of a year. Vacuum pump oil has very low vapour pressure and it is available in a range of densities; the lowest density vacuum oil was chosen for the PSU barometer to maximize the oil column height. An aneroid barometer is an instrument used for measuring pressure as a method that does not involve liquid. Invented in 1844 by French scientist Lucien Vidi, the aneroid barometer uses a small, flexible metal box called an aneroid cell (capsule), which is made from an alloy of beryllium and copper. The evacuated capsule (or usually several capsules, stacked to add up their movements) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer. Many models include a manually set needle which is used to mark the current measurement so a change can be seen. This type of barometer is common in homes and in recreational boats. It is also used in meteorology, mostly in barographs and as a pressure instrument in radiosondes. A barograph is a recording aneroid barometer where the changes in atmospheric pressure are recorded on a paper chart. Principle & Working: The principle of the barograph is same as that of the aneroid barometer. A metal box partially exhausted of air will undergo changes of shape as the outside pressure varies. These small movements of the box are transmitted by a system of levers to a recording arm that has at its extreme end either a scribe or a pen. A scribe records on smoked foil while a pen records on paper using ink, held in a nib. The recording material is mounted on a cylindrical drum which is rotated slowly by a clock. Commonly, the drum makes one revolution per day, per week, or per month and the rotation rate can often be selected by the user. Micro Electro Mechanical Systems (or MEMS) barometers are extremely small devices between 1 and 100 micrometres in size (0.001 to 0.1 mm). They are created via photolithography or photochemical machining. Typical applications include miniaturized weather stations, electronic barometers and altimeters. A barometer can also be found in smartphones such as the Samsung Galaxy Nexus, Samsung Galaxy S3-S6, Motorola Xoom, Apple iPhone 6 smartphones, and Timex Expedition WS4 smartwatch, based on MEMS and piezoresistive pressure-sensing technologies. Inclusion of barometers on smartphones was originally intended to provide a faster GPS lock. However, third party researchers were unable to confirm additional GPS accuracy or lock speed due to barometric readings. The researchers suggest that the inclusion of barometers in smartphones may provide a solution for determining a user's elevation, but also suggest that several pitfalls must first be overcome. There are many other more unusual types of barometer. From variations on the storm barometer, such as the Collins Patent Table Barometer, to more traditional-looking designs such as Hooke's Otheometer and the Ross Sympiesometer. Some, such as the Shark Oil barometer, work only in a certain temperature range, achieved in warmer climates. Barometric pressure and the pressure tendency (the change of pressure over time) have been used in weather forecasting since the late 19th century. When used in combination with wind observations, reasonably accurate short-term forecasts can be made. Simultaneous barometric readings from across a network of weather stations allow maps of air pressure to be produced, which were the first form of the modern weather map when created in the 19th century. Isobars, lines of equal pressure, when drawn on such a map, give a contour map showing areas of high and low pressure. Localized high atmospheric pressure acts as a barrier to approaching weather systems, diverting their course. Atmospheric lift caused by low-level wind convergence into the surface brings clouds and sometimes precipitation. The larger the change in pressure, especially if more than 3.5 hPa (0.1 inHg), the greater the change in weather that can be expected. If the pressure drop is rapid, a low pressure system is approaching, and there is a greater chance of rain. Rapid pressure rises, such as in the wake of a cold front, are associated with improving weather conditions, such as clearing skies. With falling air pressure, gases trapped within the coal in deep mines can escape more freely. Thus low pressure increases the risk of firedamp accumulating. Collieries therefore keep track of the pressure. In the case of the Trimdon Grange colliery disaster of 1882 the mines inspector drew attention to the records and in the report stated "the conditions of atmosphere and temperature may be taken to have reached a dangerous point". Aneroid barometers are used in scuba diving. A submersible pressure gauge is used to keep track of the contents of the diver's air tank. Another gauge is used to measure the hydrostatic pressure, usually expressed as a depth of sea water. Either or both gauges may be replaced with electronic variants or a dive computer. The density of mercury will change with increase or decrease in temperature, so a reading must be adjusted for the temperature of the instrument. For this purpose a mercury thermometer is usually mounted on the instrument. Temperature compensation of an aneroid barometer is accomplished by including a bi-metal element in the mechanical linkages. Aneroid barometers sold for domestic use typically have no compensation under the assumption that they will be used within a controlled room temperature range. As the air pressure decreases at altitudes above sea level (and increases below sea level) the uncorrected reading of the barometer will depend on its location. The reading is then adjusted to an equivalent sea-level pressure for purposes of reporting. For example, if a barometer located at sea level and under fair weather conditions is moved to an altitude of 1,000 feet (305 m), about 1 inch of mercury (~35 hPa) must be added on to the reading. The barometer readings at the two locations should be the same if there are negligible changes in time, horizontal distance, and temperature. If this were not done, there would be a false indication of an approaching storm at the higher elevation. Aneroid barometers have a mechanical adjustment that allows the equivalent sea level pressure to be read directly and without further adjustment if the instrument is not moved to a different altitude. Setting an aneroid barometer is similar to resetting an analog clock that is not at the correct time. Its dial is rotated so that the current atmospheric pressure from a known accurate and nearby barometer (such as the local weather station) is displayed. No calculation is needed, as the source barometer reading has already been converted to equivalent sea-level pressure, and this is transferred to the barometer being set—regardless of its altitude. Though somewhat rare, a few aneroid barometers intended for monitoring the weather are calibrated to manually adjust for altitude. In this case, knowing "either" the altitude or the current atmospheric pressure would be sufficient for future accurate readings. The table below shows examples for three locations in the city of San Francisco, California. Note the corrected barometer readings are identical, and based on equivalent sea-level pressure. (Assume a temperature of 15 °C.) In 1787, during a scientific expedition on Mont Blanc, De Saussure undertook research and executed physical experiments on the boiling point of water at different heights. He calculated the height at each of his experiments by measuring how long it took an alcohol burner to boil an amount of water, and by these means he determined the height of the mountain to be 4775 metres. (This later turned out to be 32 metres less than the actual height of 4807 metres). For these experiments De Saussure brought specific scientific equipment, such as a barometer and thermometer. His calculated boiling temperature of water at the top of the mountain was fairly accurate, only off by 0.1 kelvin. Based on his findings, the altimeter could be developed as a specific application of the barometer. In the mid-19th century, this method was used by explorers. When atmospheric pressure is measured by a barometer, the pressure is also referred to as the "barometric pressure". Assume a barometer with a cross-sectional area "A", a height "h", filled with mercury from the bottom at Point B to the top at Point C. The pressure at the bottom of the barometer, Point B, is equal to the atmospheric pressure. The pressure at the very top, Point C, can be taken as zero because there is only mercury vapour above this point and its pressure is very low relative to the atmospheric pressure. Therefore, one can find the atmospheric pressure using the barometer and this equation: where ρ is the density of mercury, g is the gravitational acceleration, and h is the height of the mercury column above the free surface area. The physical dimensions (length of tube and cross-sectional area of the tube) of the barometer itself have no effect on the height of the fluid column in the tube. In thermodynamic calculations, a commonly used pressure unit is the "standard atmosphere". This is the pressure resulting from a column of mercury of 760 mm in height at 0 °C. For the density of mercury, use ρ = 13,595 kg/m and for gravitational acceleration use g = 9.807 m/s. If water were used (instead of mercury) to meet the standard atmospheric pressure, a water column of roughly 10.3 m (33.8 ft) would be needed. Standard atmospheric pressure as a function of elevation: Note: 1 torr = 133.3 Pa = 0.03937 inHg

A barometer is a scientific instrument that is used to measure air pressure in a certain environment. Pressure tendency can forecast short term changes in the weather. Many measurements of air pressure are used within surface weather analysis to help find surface troughs, pressure systems and frontal boundaries.

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summarize: Volumetric flow rate is defined by the limit: That is, the flow of volume of fluid through a surface per unit time. Since this is only the time derivative of volume, a scalar quantity, the volumetric flow rate is also a scalar quantity. The change in volume is the amount that flows "after" crossing the boundary for some time duration, not simply the initial amount of volume at the boundary minus the final amount at the boundary, since the change in volume flowing through the area would be zero for steady flow. Volumetric flow rate can also be defined by: where: The above equation is only true for flat, plane cross-sections. In general, including curved surfaces, the equation becomes a surface integral: This is the definition used in practice. The area required to calculate the volumetric flow rate is real or imaginary, flat or curved, either as a cross-sectional area or a surface. The vector area is a combination of the magnitude of the area through which the volume passes through,, and a unit vector normal to the area,. The relation is. The reason for the dot product is as follows. The only volume flowing "through" the cross-section is the amount normal to the area, that is, parallel to the unit normal. This amount is: where is the angle between the unit normal and the velocity vector of the substance elements. The amount passing through the cross-section is reduced by the factor. As increases less volume passes through. Substance which passes tangential to the area, that is perpendicular to the unit normal, does not pass through the area. This occurs when and so this amount of the volumetric flow rate is zero: These results are equivalent to the dot product between velocity and the normal direction to the area. When the mass flow rate is known, and the density can be assumed constant, this is an easy way to get formula_6. Where: In internal combustion engines, the time area integral is considered over the range of valve opening. The time lift integral is given by: where is the time per revolution, is the distance from the camshaft centreline to the cam tip, is the radius of the camshaft (that is, is the maximum lift), is the angle where opening begins, and is where the valve closes (seconds, mm, radians). This has to be factored by the width (circumference) of the valve throat. The answer is usually related to the cylinder's swept volume.

In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes per unit time; usually represented by the symbol (sometimes ). The SI unit is cubic metres per second (m/s). Another unit used is standard cubic centimetres per minute (sccm).

en

77

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summarize: Turbulence is characterized by the following features: "Turbulent diffusion" is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle. In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula. Via this energy cascade, turbulent flow can be realized as a superposition of a spectrum of flow velocity fluctuations and eddies upon a mean flow. The eddies are loosely defined as coherent patterns of flow velocity, vorticity and pressure. Turbulent flows may be viewed as made of an entire hierarchy of eddies over a wide range of length scales and the hierarchy can be described by the energy spectrum that measures the energy in flow velocity fluctuations for each length scale (wavenumber). The scales in the energy cascade are generally uncontrollable and highly non-symmetric. Nevertheless, based on these length scales these eddies can be divided into three categories. The integral time scale for a Lagrangian flow can be defined as: where "u"′ is the velocity fluctuation, and formula_2 is the time lag between measurements. Although it is possible to find some particular solutions of the Navier–Stokes equations governing fluid motion, all such solutions are unstable to finite perturbations at large Reynolds numbers. Sensitive dependence on the initial and boundary conditions makes fluid flow irregular both in time and in space so that a statistical description is needed. The Russian mathematician Andrey Kolmogorov proposed the first statistical theory of turbulence, based on the aforementioned notion of the energy cascade (an idea originally introduced by Richardson) and the concept of self-similarity. As a result, the Kolmogorov microscales were named after him. It is now known that the self-similarity is broken so the statistical description is presently modified. A complete description of turbulence is one of the unsolved problems in physics. According to an apocryphal story, Werner Heisenberg was asked what he would ask God, given the opportunity. His reply was: "When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." A similar witticism has been attributed to Horace Lamb in a speech to the British Association for the Advancement of Science: "I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic." The onset of turbulence can be, to some extent, predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe. A similar effect is created by the introduction of a stream of higher velocity fluid, such as the hot gases from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, as more kinetic energy is absorbed by a more viscous fluid. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation. This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full size version. Such scaling is not always linear and the application of Reynolds numbers to both situations allows scaling factors to be developed. A flow situation in which the kinetic energy is significantly absorbed due to the action of fluid molecular viscosity gives rise to a laminar flow regime. For this the dimensionless quantity the Reynolds number () is used as a guide. With respect to laminar and turbulent flow regimes: The Reynolds number is defined as where: While there is no theorem directly relating the non-dimensional Reynolds number to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In Poiseuille flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040; moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 4000. The transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased. When flow is turbulent, particles exhibit additional transverse motion which enhances the rate of energy and momentum exchange between them thus increasing the heat transfer and the friction coefficient. Assume for a two-dimensional turbulent flow that one was able to locate a specific point in the fluid and measure the actual flow velocity of every particle that passed through that point at any given time. Then one would find the actual flow velocity fluctuating about a mean value: and similarly for temperature () and pressure (), where the primed quantities denote fluctuations superposed to the mean. This decomposition of a flow variable into a mean value and a turbulent fluctuation was originally proposed by Osborne Reynolds in 1895, and is considered to be the beginning of the systematic mathematical analysis of turbulent flow, as a sub-field of fluid dynamics. While the mean values are taken as predictable variables determined by dynamics laws, the turbulent fluctuations are regarded as stochastic variables. The heat flux and momentum transfer (represented by the shear stress ) in the direction normal to the flow for a given time are where is the heat capacity at constant pressure, is the density of the fluid, is the coefficient of turbulent viscosity and is the turbulent thermal conductivity. Richardson's notion of turbulence was that a turbulent flow is composed by "eddies" of different sizes. The sizes define a characteristic length scale for the eddies, which are also characterized by flow velocity scales and time scales (turnover time) dependent on the length scale. The large eddies are unstable and eventually break up originating smaller eddies, and the kinetic energy of the initial large eddy is divided into the smaller eddies that stemmed from it. These smaller eddies undergo the same process, giving rise to even smaller eddies which inherit the energy of their predecessor eddy, and so on. In this way, the energy is passed down from the large scales of the motion to smaller scales until reaching a sufficiently small length scale such that the viscosity of the fluid can effectively dissipate the kinetic energy into internal energy. In his original theory of 1941, Kolmogorov postulated that for very high Reynolds numbers, the small-scale turbulent motions are statistically isotropic (i.e. no preferential spatial direction could be discerned). In general, the large scales of a flow are not isotropic, since they are determined by the particular geometrical features of the boundaries (the size characterizing the large scales will be denoted as ). Kolmogorov's idea was that in the Richardson's energy cascade this geometrical and directional information is lost, while the scale is reduced, so that the statistics of the small scales has a universal character: they are the same for all turbulent flows when the Reynolds number is sufficiently high. Thus, Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the kinematic viscosity and the rate of energy dissipation. With only these two parameters, the unique length that can be formed by dimensional analysis is This is today known as the Kolmogorov length scale (see Kolmogorov microscales). A turbulent flow is characterized by a hierarchy of scales through which the energy cascade takes place. Dissipation of kinetic energy takes place at scales of the order of Kolmogorov length, while the input of energy into the cascade comes from the decay of the large scales, of order. These two scales at the extremes of the cascade can differ by several orders of magnitude at high Reynolds numbers. In between there is a range of scales (each one with its own characteristic length ) that has formed at the expense of the energy of the large ones. These scales are very large compared with the Kolmogorov length, but still very small compared with the large scale of the flow (i.e. ). Since eddies in this range are much larger than the dissipative eddies that exist at Kolmogorov scales, kinetic energy is essentially not dissipated in this range, and it is merely transferred to smaller scales until viscous effects become important as the order of the Kolmogorov scale is approached. Within this range inertial effects are still much larger than viscous effects, and it is possible to assume that viscosity does not play a role in their internal dynamics (for this reason this range is called "inertial range"). Hence, a third hypothesis of Kolmogorov was that at very high Reynolds number the statistics of scales in the range are universally and uniquely determined by the scale and the rate of energy dissipation. The way in which the kinetic energy is distributed over the multiplicity of scales is a fundamental characterization of a turbulent flow. For homogeneous turbulence (i.e., statistically invariant under translations of the reference frame) this is usually done by means of the "energy spectrum function", where is the modulus of the wavevector corresponding to some harmonics in a Fourier representation of the flow velocity field : where is the Fourier transform of the flow velocity field. Thus, represents the contribution to the kinetic energy from all the Fourier modes with, and therefore, where is the mean turbulent kinetic energy of the flow. The wavenumber corresponding to length scale is. Therefore, by dimensional analysis, the only possible form for the energy spectrum function according with the third Kolmogorov's hypothesis is where would be a universal constant. This is one of the most famous results of Kolmogorov 1941 theory, and considerable experimental evidence has accumulated that supports it. In spite of this success, Kolmogorov theory is at present under revision. This theory implicitly assumes that the turbulence is statistically self-similar at different scales. This essentially means that the statistics are scale-invariant in the inertial range. A usual way of studying turbulent flow velocity fields is by means of flow velocity increments: that is, the difference in flow velocity between points separated by a vector (since the turbulence is assumed isotropic, the flow velocity increment depends only on the modulus of ). Flow velocity increments are useful because they emphasize the effects of scales of the order of the separation when statistics are computed. The statistical scale-invariance implies that the scaling of flow velocity increments should occur with a unique scaling exponent, so that when is scaled by a factor, should have the same statistical distribution as with independent of the scale. From this fact, and other results of Kolmogorov 1941 theory, it follows that the statistical moments of the flow velocity increments (known as "structure functions" in turbulence) should scale as where the brackets denote the statistical average, and the would be universal constants. There is considerable evidence that turbulent flows deviate from this behavior. The scaling exponents deviate from the value predicted by the theory, becoming a non-linear function of the order of the structure function. The universality of the constants have also been questioned. For low orders the discrepancy with the Kolmogorov value is very small, which explain the success of Kolmogorov theory in regards to low order statistical moments. In particular, it can be shown that when the energy spectrum follows a power law with, the second order structure function has also a power law, with the form Since the experimental values obtained for the second order structure function only deviate slightly from the value predicted by Kolmogorov theory, the value for is very near to (differences are about 2%). Thus the "Kolmogorov − spectrum" is generally observed in turbulence. However, for high order structure functions the difference with the Kolmogorov scaling is significant, and the breakdown of the statistical self-similarity is clear. This behavior, and the lack of universality of the constants, are related with the phenomenon of intermittency in turbulence. This is an important area of research in this field, and a major goal of the modern theory of turbulence is to understand what is really universal in the inertial range.

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.

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summarize: When a body is free to rotate around an axis, torque must be applied to change its angular momentum. The amount of torque needed to cause any given angular acceleration (the rate of change in angular velocity) is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram metre squared (kg·m) in SI units and pound-foot-second squared (lbf·ft·s) in imperial or US units. Moment of inertia plays the role in rotational kinetics that mass (inertia) plays in linear kinetics—both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like mass, the moment of inertia about some axis is given by formula_1, where formula_2 is the distance of the point from the axis, and formula_3 is the mass. For an extended rigid body, the moment of inertia is just the sum of all the small pieces of mass multiplied by the square of their distances from the axis in rotation. For an extended body of a regular shape Moment of inertia formula_4 is defined as the ratio of the net angular momentum formula_5 of a system to its angular velocity formula_6 around a principal axis, that is If the angular momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase. This occurs when spinning figure skaters pull in their outstretched arms or divers curl their bodies into a tuck position during a dive, to spin faster. If the shape of the body does not change, then its moment of inertia appears in Newton's law of motion as the ratio of an applied torque formula_8 on a body to the angular acceleration formula_9 around Moment of inertia can be measured using a simple pendulum, because it is the resistance to the rotation caused by gravity. Mathematically, the moment of inertia of the pendulum is the ratio of the torque due to gravity about the pivot of a pendulum to its angular acceleration about that pivot point. For a simple pendulum this is found to be the product of the mass of the particle formula_3 with the square of its distance formula_2 to the pivot, that is This can be shown as follows: The force of gravity on the mass of a simple pendulum generates a torque formula_27 around the axis perpendicular to the plane of the pendulum movement. Here formula_28 is the distance vector perpendicular to and from the force to the torque axis, and formula_29 is the net force on the mass. Associated A compound pendulum is a body formed from an assembly of particles of continuous shape that rotates rigidly around a pivot. Its moment of inertia is the sum of the moments of inertia of each of the particles that it is composed of. The natural frequency (formula_45) of a compound pendulum depends on its moment of inertia, formula_46, where formula_3 is the mass of the object, formula_49 is local acceleration of gravity, and formula_2 is the distance from the pivot point to the center of mass of the object. Measuring this frequency of oscillation over small angular displacements provides an effective way of measuring moment of inertia of a body. Thus, to determine the moment of inertia of the body, simply suspend it from a convenient pivot point formula_51 so that it swings freely in a plane perpendicular to the direction of the desired moment of inertia, then measure its natural frequency or period of oscillation (formula_52), to obtain where formula_52 is the period (duration) of oscillation (usually averaged over multiple periods). A simple pendulum that has the same natural frequency as a compound pendulum defines the length formula_5 from the pivot to a point called the center of oscillation of the compound pendulum. This point also corresponds to the center of percussion. The length formula_5 is determined from the formula, or The seconds pendulum, which provides the "tick" and "tock" of a grandfather clock, takes one second to swing from side-to-side. This is a period of two seconds, or a natural frequency of formula_59 for the pendulum. In this case, the distance to the center of oscillation, formula_5, can be computed to be Notice that the distance to the center of oscillation of the seconds pendulum must be adjusted to accommodate different values for the local acceleration of gravity. Kater's pendulum is a compound pendulum that uses this property to measure the local acceleration of gravity, and is called a gravimeter. The moment of inertia of a complex system such as a vehicle or airplane around its vertical axis can be measured by suspending the system from three points The moment of inertia about an axis of a body is calculated by summing formula_1 for every particle in the body, where formula_2 is the perpendicular distance to the specified axis. To see how moment of inertia arises in the study of the movement of an extended body, it is convenient to consider a rigid assembly of point masses. (This equation can be used for axes that are not principal axes provided that it is understood that this does not fully describe the moment of inertia.) Consider the kinetic energy of an assembly of formula_64 masses formula_65 that lie at the distances formula_66 from the pivot point formula_51, which is the nearest point on the axis of rotation. It is the sum of the kinetic energy of the individual masses, This shows that the moment of inertia of the body is the sum of each of the formula_1 terms, that is Thus, moment of inertia is a physical property that combines the mass and distribution of the particles around If a mechanical system is constrained to move parallel to a fixed plane, then the rotation of a body in the system occurs around an axis formula_34 perpendicular to this plane. In this case, the moment of inertia of the mass in this system is a scalar known as the "polar moment of inertia". The definition of the polar moment of inertia can be obtained by considering momentum, kinetic energy and Newton's laws for the planar movement of a rigid system of particles. If a system of formula_104 particles, formula_105, are assembled into a rigid body, then the momentum of the system can be written in terms of positions relative to a reference point formula_106, and absolute velocities formula_107: where formula_40 is the angular velocity of the system and formula_110 is the velocity of formula_106. For planar movement the angular velocity vector is directed along the unit The angular momentum vector for the planar movement of a rigid system of particles is given by Use the center of mass formula_119 as the reference point so and define the moment of inertia relative to the center of mass formula_121 as then the equation for angular momentum simplifies to The moment of inertia formula_121 about an axis perpendicular to the movement of the rigid system and The kinetic energy of a rigid system of particles moving in the plane is given by Let the reference point be the center of mass Newton's laws for a rigid system of formula_104 particles, formula_105, can be written in terms of a resultant force and torque at a reference point formula_106, to yield where formula_115 denotes the trajectory of each particle. The kinematics of a rigid body yields the formula for the acceleration of the particle formula_135 in terms of the position formula_106 and acceleration formula_137 of the reference particle as well as the angular velocity vector formula_40 and angular acceleration vector formula_30 of the rigid system The scalar moments of inertia appear as elements in a matrix when a system of particles is assembled into a rigid body that moves in three-dimensional space. This inertia matrix appears in the calculation of the angular momentum, kinetic energy and resultant torque of the rigid system of particles. Let the system of formula_104 particles, formula_105 be located at the coordinates formula_115 with velocities formula_107 relative to a fixed reference frame. For a (possibly moving) reference point formula_106, the relative positions are and the (absolute) velocities are where formula_40 is the angular velocity of the system, and formula_162 is the velocity of formula_106. Note that the cross product can be equivalently written as matrix multiplication by combining the first operand and the operator into a skew-symmetric matrix, formula_164, constructed from the components of formula_165: The inertia matrix is constructed by considering the angular momentum, with the reference point formula_106 The kinetic energy of a rigid system of particles can be formulated in terms of the center of mass and a matrix of mass moments of inertia of the system. Let the system of formula_104 particles formula_105 be located at the coordinates formula_115 with velocities formula_107, then the kinetic energy is where formula_173 The inertia matrix appears in the application of Newton's second law to a rigid assembly of particles. The resultant torque on this system is, where formula_192 is the acceleration of the particle formula_135. The kinematics of a rigid body yields the formula for the acceleration of the particle formula_135 in terms of the position formula_106 and acceleration formula_196 of the reference The inertia matrix of a body depends on the choice of the reference point. There is a useful relationship between the inertia matrix relative to the center of mass formula_119 and the inertia matrix relative to another point formula_106. This relationship is called the parallel axis theorem. Consider the inertia matrix formula_209 obtained for a rigid system of particles measured relative to a reference point formula_106, given by Let formula_119 be the center of mass of the rigid system, then where formula_214 is the vector from the center of mass formula_119 to the reference point formula_106. Use this equation to compute the inertia The scalar moment of inertia, formula_231, of a body about a specified axis whose direction is specified by the unit vector formula_34 and passes through the body at a point formula_106 is as follows: where formula_209 is the moment of inertia matrix of the system relative to the reference point formula_106, and formula_172 is the skew symmetric matrix obtained from the vector formula_159. This is derived as follows. Let a rigid assembly of formula_104 particles, formula_105, have coordinates formula_115. Choose formula_106 as a reference point and compute the moment of inertia around a line L defined by the unit vector formula_34 through the reference point formula_106, formula_245. The perpendicular vector from this line to the particle formula_135 is obtained from formula_247 by For the same object, different axes of rotation will have different moments of inertia about those axes. In general, the moments of inertia are not equal unless the object is symmetric about all axes. The moment of inertia tensor is a convenient way to summarize all moments of inertia of an object with one quantity. It may be calculated with respect to any point in space, although for practical purposes the center of mass is most commonly used. For a rigid object of formula_64 point masses formula_270, the moment of inertia tensor is given by Its components are defined as where Note that, by the definition, formula_281 is a symmetric tensor. The diagonal elements are more succinctly written as while the off-diagonal elements, also called the products of inertia, are Here formula_288 denotes the moment of inertia around the formula_80-axis when the objects are rotated around the x-axis, formula_290 denotes the moment of inertia around the formula_81-axis when the objects are rotated around the formula_80-axis, and so on. These quantities can be generalized to an object with distributed mass, described by a mass density function, in a similar fashion to the The distance formula_2 of a particle at formula_310 from the axis of rotation passing through the origin in the formula_311 direction is formula_312. By using the formula formula_313 (and some simple vector algebra) it can be seen that the moment of inertia of The use of the inertia matrix in Newton's second law assumes its components are computed relative to axes parallel to the inertial frame and not relative to a body-fixed reference frame. This means that as the body moves the components of the inertia matrix change with time. In contrast, the components of the inertia matrix measured in a body-fixed frame are constant. Let the body frame inertia matrix relative to the center of mass be denoted formula_318, and define the orientation of the body frame relative to the inertial frame by the rotation matrix Measured in the body frame the inertia matrix is a constant real symmetric matrix. A real symmetric matrix has the eigendecomposition into the product of a rotation matrix formula_326 and a diagonal matrix formula_327, given by where The columns of the rotation matrix formula_326 define the directions of the principal axes of the body, and the constants formula_331, formula_332, and formula_333 are called the principal moments of inertia. This result was first shown by J. J. Sylvester (1852), and is a form of Sylvester's law of inertia. The principal axis with the highest moment of inertia is sometimes called the figure axis or axis of figure. When all principal moments of inertia are distinct, the principal axes through center of mass are uniquely specified. If two principal moments are the same, the rigid body is called a symmetrical top and there is no unique choice for the The moment of inertia matrix in body-frame coordinates is a quadratic form that defines a surface in the body called Poinsot's ellipsoid. Let formula_327 be the inertia matrix relative to the center of mass aligned with the principal axes, then the surface or defines an ellipsoid in the body frame. Write this equation

The moment of inertia, otherwise known as the mass moment of inertia, angular mass or rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis; similar to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

en

83

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summarize: The drag coefficient formula_4 is defined as where: The reference area depends on what type of drag coefficient is being measured. For automobiles and many other objects, the reference area is the projected frontal area of the vehicle. This may not necessarily be the cross-sectional area of the vehicle, depending on where the cross-section is taken. For example, for a sphere formula_10 (note this is not the surface area = formula_11). For airfoils, the reference area is the nominal wing area. Since this tends to be large compared to the frontal area, the resulting drag coefficients tend to be low, much lower than for a car with the same drag, frontal area, and speed. Airships and some bodies of revolution use the volumetric drag coefficient, in which the reference area is the square of the cube root of the airship volume (volume to the two-thirds power). Submerged streamlined bodies use the wetted surface area. Two objects having the same reference area moving at the same speed through a fluid will experience a drag force proportional to their respective drag coefficients. Coefficients for unstreamlined objects can be 1 or more, for streamlined objects much less. It has been demonstrated that drag coefficient formula_12 is a function of Bejan number (formula_13), Reynolds number (formula_14) and the ratio between wet area formula_15and front area formula_16: formula_17 where formula_18is the Reynold Number related to fluid path length L. The drag equation is essentially a statement that the drag force on any object is proportional to the density of the fluid and proportional to the square of the relative flow speed between the object and the fluid. "C" is not a constant but varies as a function of flow speed, flow direction, object position, object size, fluid density and fluid viscosity. Speed, kinematic viscosity and a characteristic length scale of the object are incorporated into a dimensionless quantity called the Reynolds number formula_20. formula_1 is thus a function of formula_20. In a compressible flow, the speed of sound is relevant, and formula_1 is also a function of Mach number formula_24. For certain body shapes, the drag coefficient formula_1 only depends on the Reynolds number formula_20, Mach number formula_24 and the direction of the flow. For low Mach number formula_24, the drag coefficient is independent of Mach number. Also, the variation with Reynolds number formula_20 within a practical range of interest is usually small, while for cars at highway speed and aircraft at cruising speed, the incoming flow direction is also more-or-less the same. Therefore, the drag coefficient formula_1 can often be treated as a constant. For a streamlined body to achieve a low drag coefficient, the boundary layer around the body must remain attached to the surface of the body for as long as possible, causing the wake to be narrow. A high "form drag" results in a broad wake. The boundary layer will transition from laminar to turbulent if Reynolds number of the flow around the body is sufficiently great. Larger velocities, larger objects, and lower viscosities contribute to larger Reynolds numbers. For other objects, such as small particles, one can no longer consider that the drag coefficient formula_1 is constant, but certainly is a function of Reynolds number. At a low Reynolds number, the flow around the object does not transition to turbulent but remains laminar, even up to the point at which it separates from the surface of the object. At very low Reynolds numbers, without flow separation, the drag force formula_32 is proportional to formula_33 instead of formula_34; for a sphere this is known as Stokes law. The Reynolds number will be low for small objects, low velocities, and high viscosity fluids. A formula_1 equal to 1 would be obtained in a case where all of the fluid approaching the object is brought to rest, building up stagnation pressure over the whole front surface. The top figure shows a flat plate with the fluid coming from the right and stopping at the plate. The graph to the left of it shows equal pressure across the surface. In a real flat plate, the fluid must turn around the sides, and full stagnation pressure is found only at the center, dropping off toward the edges as in the lower figure and graph. Only considering the front side, the formula_1 of a real flat plate would be less than 1; except that there will be suction on the back side: a negative pressure (relative to ambient). The overall formula_1 of a real square flat plate perpendicular to the flow is often given as 1.17. Flow patterns and therefore formula_1 for some shapes can change with the Reynolds number and the roughness of the surfaces. In general, formula_4 is not an absolute constant for a given body shape. It varies with the speed of airflow (or more generally with Reynolds number formula_14). A smooth sphere, for example, has a formula_4 that varies from high values for laminar flow to 0.47 for turbulent flow. Although the drag coefficient decreases with increasing formula_14, the drag force increases. As noted above, aircraft use their wing area as the reference area when computing formula_4, while automobiles (and many other objects) use frontal cross sectional area; thus, coefficients are not directly comparable between these classes of vehicles. In the aerospace industry, the drag coefficient is sometimes expressed in drag counts where 1 drag count = 0.0001 of a formula_44. Drag, in the context of fluid dynamics, refers to forces that act on a solid object in the direction of the relative flow velocity (note that the diagram below shows the drag in the opposite direction to the flow). The aerodynamic forces on a body come primarily from differences in pressure and viscous shearing stresses. Thereby, the drag force on a body could be divided into two components, namely frictional drag (viscous drag) and pressure drag (form drag). The net drag force could be decomposed as follows: where: Therefore, when the drag is dominated by a frictional component, the body is called a streamlined body; whereas in the case of dominant pressure drag, the body is called a blunt body. Thus, the shape of the body and the angle of attack determine the type of drag. For example, an airfoil is considered as a body with a small angle of attack by the fluid flowing across it. This means that it has attached boundary layers, which produce much less pressure drag. The wake produced is very small and drag is dominated by the friction component. Therefore, such a body (here an airfoil) is described as streamlined, whereas for bodies with fluid flow at high angles of attack, boundary layer separation takes place. This mainly occurs due to adverse pressure gradients at the top and rear parts of an airfoil. Due to this, wake formation takes place, which consequently leads to eddy formation and pressure loss due to pressure drag. In such situations, the airfoil is stalled and has higher pressure drag than friction drag. In this case, the body is described as a blunt body. A streamlined body looks like a fish (Tuna), Oropesa, etc. or an airfoil with small angle of attack, whereas a blunt body looks like a brick, a cylinder or an airfoil with high angle of attack. For a given frontal area and velocity, a streamlined body will have lower resistance than a blunt body. Cylinders and spheres are taken as blunt bodies because the drag is dominated by the pressure component in the wake region at high Reynolds number. To reduce this drag, either the flow separation could be reduced or the surface area in contact with the fluid could be reduced (to reduce friction drag). This reduction is necessary in devices like cars, bicycle, etc. to avoid vibration and noise production. The aerodynamic design of cars has evolved from the 1920s to the end of the 20th century. This change in design from a blunt body to a more streamlined body reduced the drag coefficient from about 0.95 to 0.30. "Time history of cars' aerodynamic drag in comparison to change in geometry of streamlined bodies (blunt to streamline)."

In fluid dynamics, the drag coefficient (commonly denoted as: formula_1, formula_2 or formula_3) is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.

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summarize: In most flows of liquids, and of gases at low Mach number, the density of a fluid parcel can be considered to be constant, regardless of pressure variations in the flow. Therefore, the fluid can be considered to be incompressible and these flows are called incompressible flows. Bernoulli performed his experiments on liquids, so his equation in its original form is valid only for incompressible flow. A common form of Bernoulli's equation, valid at any arbitrary point along a streamline, is: where: The constant on the right-hand side of the equation depends only on the streamline chosen, whereas, and depend on the particular point on that streamline. The following assumptions must be met for this Bernoulli equation to apply: For conservative force fields (not limited to the gravitational field), Bernoulli's equation can be generalized as: where is the force potential at the point considered on the streamline. E.g. for the Earth's gravity. By multiplying with the fluid density, equation () can be rewritten as: or: where The constant in the Bernoulli equation can be normalised. A common approach is in terms of total head or energy head : The above equations suggest there is a flow speed at which pressure is zero, and at even higher speeds the pressure is negative. Most often, gases and liquids are not capable of negative absolute pressure, or even zero pressure, so clearly Bernoulli's equation ceases to be valid before zero pressure is reached. In liquids – when the pressure becomes too low – cavitation occurs. The above equations use a linear relationship between flow speed squared and pressure. At higher flow speeds in gases, or for sound waves in liquid, the changes in mass density become significant so that the assumption of constant density is invalid. In many applications of Bernoulli's equation, the change in the term along the streamline is so small compared with the other terms that it can be ignored. For example, in the case of aircraft in flight, the change in height along a streamline is so small the term can be omitted. This allows the above equation to be presented in the following simplified form: where is called "total pressure", and is "dynamic pressure". Many authors refer to the pressure as static pressure to distinguish it from total pressure and dynamic pressure. In "Aerodynamics", L.J. Clancy writes: "To distinguish it from the total and dynamic pressures, the actual pressure of the fluid, which is associated not with its motion but with its state, is often referred to as the static pressure, but where the term pressure alone is used it refers to this static pressure." The simplified form of Bernoulli's equation can be summarized in the following memorable word equation: Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure and dynamic pressure. Their sum is defined to be the total pressure. The significance of Bernoulli's principle can now be summarized as "total pressure is constant along a streamline". If the fluid flow is irrotational, the total pressure on every streamline is the same and Bernoulli's principle can be summarized as "total pressure is constant everywhere in the fluid flow". It is reasonable to assume that irrotational flow exists in any situation where a large body of fluid is flowing past a solid body. Examples are aircraft in flight, and ships moving in open bodies of water. However, it is important to remember that Bernoulli's principle does not apply in the boundary layer or in fluid flow through long pipes. If the fluid flow at some point along a streamline is brought to rest, this point is called a stagnation point, and at this point the total pressure is equal to the stagnation pressure. Bernoulli's equation is sometimes valid for the flow of gases: provided that there is no transfer of kinetic or potential energy from the gas flow to the compression or expansion of the gas. If both the gas pressure and volume change simultaneously, then work will be done on or by the gas. In this case, Bernoulli's equation – in its incompressible flow form – cannot be assumed to be valid. However, if the gas process is entirely isobaric, or isochoric, then no work is done on or by the gas, (so the simple energy balance is not upset). According to the gas law, an isobaric or isochoric process is ordinarily the only way to ensure constant density in a gas. Also the gas density will be proportional to the ratio of pressure and absolute temperature, however this ratio will vary upon compression or expansion, no matter what non-zero quantity of heat is added or removed. The only exception is if the net heat transfer is zero, as in a complete thermodynamic cycle, or in an individual isentropic (frictionless adiabatic) process, and even then this reversible process must be reversed, to restore the gas to the original pressure and specific volume, and thus density. Only then is the original, unmodified Bernoulli equation applicable. In this case the equation can be used if the flow speed of the gas is sufficiently below the speed of sound, such that the variation in density of the gas (due to this effect) along each streamline can be ignored. Adiabatic flow at less than Mach 0.3 is generally considered to be slow enough. The Bernoulli equation for unsteady potential flow is used in the theory of ocean surface waves and acoustics. For an irrotational flow, the flow velocity can be described as the gradient of a velocity potential. In that case, and for a constant density, the momentum equations of the Euler equations can be integrated to: which is a Bernoulli equation valid also for unsteady—or time dependent—flows. Here denotes the partial derivative of the velocity potential with respect to time, and is the flow speed. The function depends only on time and not on position in the fluid. As a result, the Bernoulli equation at some moment does not only apply along a certain streamline, but in the whole fluid domain. This is also true for the special case of a steady irrotational flow, in which case and are constants so equation () can be applied in every point of the fluid domain. Further can be made equal to zero by incorporating it into the velocity potential using the transformation resulting in Note that the relation of the potential to the flow velocity is unaffected by this transformation:. The Bernoulli equation for unsteady potential flow also appears to play a central role in Luke's variational principle, a variational description of free-surface flows using the Lagrangian (not to be confused with Lagrangian coordinates). Bernoulli developed his principle from his observations on liquids, and his equation is applicable only to incompressible fluids, and steady compressible fluids up to approximately Mach number 0.3. It is possible to use the fundamental principles of physics to develop similar equations applicable to compressible fluids. There are numerous equations, each tailored for a particular application, but all are analogous to Bernoulli's equation and all rely on nothing more than the fundamental principles of physics such as Newton's laws of motion or the first law of thermodynamics. For a compressible fluid, with a barotropic equation of state, and under the action of conservative forces, where: In engineering situations, elevations are generally small compared to the size of the Earth, and the time scales of fluid flow are small enough to consider the equation of state as adiabatic. In this case, the above equation for an ideal gas becomes: where, in addition to the terms listed above: In many applications of compressible flow, changes in elevation are negligible compared to the other terms, so the term can be omitted. A very useful form of the equation is then: where: The most general form of the equation, suitable for use in thermodynamics in case of (quasi) steady flow, is: Here is the enthalpy per unit mass (also known as specific enthalpy), which is also often written as (not to be confused with "head" or "height"). Note that formula_15 where formula_16 is the thermodynamic energy per unit mass, also known as the specific internal energy. So, for constant internal energy formula_16 the equation reduces to the incompressible-flow form. The constant on the right-hand side is often called the Bernoulli constant, and denoted. For steady inviscid adiabatic flow with no additional sources or sinks of energy, is constant along any given streamline. More generally, when may vary along streamlines, it still proves a useful parameter, related to the "head" of the fluid (see below). When the change in can be ignored, a very useful form of this equation is: where is total enthalpy. For a calorically perfect gas such as an ideal gas, the enthalpy is directly proportional to the temperature, and this leads to the concept of the total (or stagnation) temperature. When shock waves are present, in a reference frame in which the shock is stationary and the flow is steady, many of the parameters in the Bernoulli equation suffer abrupt changes in passing through the shock. The Bernoulli parameter itself, however, remains unaffected. An exception to this rule is radiative shocks, which violate the assumptions leading to the Bernoulli equation, namely the lack of additional sinks or sources of energy. For a compressible fluid, with a barotropic equation of state, the unsteady momentum conservation equation formula_19 With the irrotational assumption, namely, the flow velocity can be described as the gradient ∇"φ" of a velocity potential φ. The unsteady momentum conservation equation becomes formula_20 which leads to formula_21 In this case, the above equation for isentropic flow becomes: formula_22 In modern everyday life there are many observations that can be successfully explained by application of Bernoulli's principle, even though no real fluid is entirely inviscid and a small viscosity often has a large effect on the flow. Many explanations for the generation of lift (on airfoils, propeller blades, etc.) can be found; some of these explanations can be misleading, and some are false. There has been debate about whether lift is best introduced to students using Bernoulli's principle or Newton's laws of motion. Modern writings agree that both Bernoulli's principle and Newton's laws are relevant, and either can be used to correctly describe lift. Several of these explanations use the Bernoulli principle to connect the flow kinematics to the flow-induced pressures. In cases of incorrect (or partially correct) explanations relying on the Bernoulli principle, the errors generally occur in the assumptions on the flow kinematics and how these are produced. It is not the Bernoulli principle itself that is questioned, because this principle is well established (the airflow above the wing "is" faster, the question is "why" it is faster). There are several common classroom demonstrations that are sometimes incorrectly explained using Bernoulli's principle. One involves holding a piece of paper horizontally so that it droops downward and then blowing over the top of it. As the demonstrator blows over the paper, the paper rises. It is then asserted that this is because "faster moving air has lower pressure". One problem with this explanation can be seen by blowing along the bottom of the paper: were the deflection due simply to faster moving air one would expect the paper to deflect downward, but the paper deflects upward regardless of whether the faster moving air is on the top or the bottom. Another problem is that when the air leaves the demonstrator's mouth it has the "same" pressure as the surrounding air; the air does not have lower pressure just because it is moving; in the demonstration, the static pressure of the air leaving the demonstrator's mouth is "equal" to the pressure of the surrounding air. A third problem is that it is false to make a connection between the flow on the two sides of the paper using Bernoulli's equation since the air above and below are "different" flow fields and Bernoulli's principle only applies within a flow field. As the wording of the principle can change its implications, stating the principle correctly is important. What Bernoulli's principle actually says is that within a flow of constant energy, when fluid flows through a region of lower pressure it speeds up and vice versa. Thus, Bernoulli's principle concerns itself with "changes" in speed and "changes" in pressure "within" a flow field. It cannot be used to compare different flow fields. A correct explanation of why the paper rises would observe that the plume follows the curve of the paper and that a curved streamline will develop a pressure gradient perpendicular to the direction of flow, with the lower pressure on the inside of the curve. Bernoulli's principle predicts that the decrease in pressure is associated with an increase in speed, i.e. that as the air passes over the paper it speeds up and moves faster than it was moving when it left the demonstrator's mouth. But this is not apparent from the demonstration. Other common classroom demonstrations, such as blowing between two suspended spheres, inflating a large bag, or suspending a ball in an airstream are sometimes explained in a similarly misleading manner by saying "faster moving air has lower pressure".

In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book "Hydrodynamica" in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler who derived Bernoulli's equation in its usual form in 1752. The principle is only applicable for isentropic flows: when the effects of irreversible processes (like turbulence) and non-adiabatic processes (e.g. heat radiation) are small and can be neglected.

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summarize: "For a table of sovereign states and dependent territories in Africa with geographical data such as area, population, and population density, see Africa: territories and regions." Geologically, Africa is connected to Eurasia by the Isthmus of Suez and forms part of Afro-Eurasia. "For a table of sovereign states and dependent territories in Asia with geographical data such as area, population, and population density, see Asia: territories and regions." Geologically, Asia is part of Eurasia and due to the Isthmus of Suez forms part of Afro-Eurasia. "For a table of sovereign states and dependent territories in Europe with geographical data such as area, population, and population density, see Europe: political geography." Geologically, Europe is part of Eurasia and due to the Isthmus of Suez forms part of Afro-Eurasia. "For a table of sovereign states and dependent territories in North America with geographical data such as area, population, and population density, see North America: countries and territories." Geologically, North America is joined with South America by the Isthmus of Panama to form the Americas. "For a table of sovereign states and dependent territories in Oceania with geographical data such as area, population, and population density, see Oceania: territories and regions." "For a table of sovereign states and dependent territories in South America with geographical data such as area, population, and population density, see South America: demographics." Geologically, South America is joined with North America by the Isthmus of Panama to form the Americas. Antarctica is regulated by the Antarctic Treaty System, which defines it as all land and ice shelves south of 60°S, and has no government and belongs to no country. However, the following territorial claims in Antarctica have been made: The United States and Russia have reserved the right to claim territory on Antarctica. Unlike Antarctica itself, other nearby subantarctic island territories most commonly associated with the Antarctic continent, but lying north of 60°S, have had full sovereignty established over them by a governing state. The following dependent territories are situated within in the wider Antarctic Region, but are not directly part of the Antarctic Treaty System: In addition to the dependent territories listed above, the following islands are governed as a direct part of a controlling state. Thus they are fully and legally integrated within the governance structure of the respective state. They are similarly also not part of the Antarctic Treaty System.

This is a list of sovereign states and dependent territories of the world by continent, displayed with their respective national flags, including the following entities:

en

28

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summarize: The German name for Austria,, derives from the Old High German, which meant "eastern realm" and which first appeared in the "Ostarrîchi document" of 996. This word is probably a translation of Medieval Latin into a local (Bavarian) dialect. Another theory says that this The Central European land that is now Austria was settled in pre-Roman times by various Celtic tribes. The Celtic kingdom of Noricum was later claimed by the Roman Empire and made a province. Present-day Petronell-Carnuntum in eastern Austria was an important army camp turned capital city in what became known as the Upper Pannonia province. Carnuntum was home for 50,000 people for nearly 400 years. After the fall of the Roman Empire, the area was invaded by Bavarians, Slavs, and Avars. Charlemagne, King of the Franks, conquered the area in AD 788, encouraged colonization, and introduced Christianity. As part of Eastern Francia, the core areas that now encompass Austria were bequeathed to the house of Babenberg. The area was known as the "marchia Orientalis" and was given to Leopold of Babenberg in 976. The first record showing the name Austria is from 996, where it is written as "Ostarrîchi", referring to the territory of the Babenberg March. In 1156, the Privilegium Minus elevated Austria to the status of a duchy. In 1192, the Babenbergs also acquired the Duchy of Styria. With the death of Frederick II in 1246, the line of the Babenbergs was extinguished. As a result, Ottokar II of Bohemia effectively assumed control of the duchies of Austria, Styria, and Carinthia. His reign came to an end with his defeat at Dürnkrut at the hands of Rudolph I of Germany in 1278. Thereafter, until World War I, Austria's history was largely that of its ruling dynasty, the Habsburgs. In the 14th and 15th centuries, the Habsburgs began to accumulate other provinces in the vicinity of the Duchy of Austria. In 1438, Duke Albert V of Austria was chosen as the successor to his father-in-law, Emperor Sigismund. Although Albert himself only reigned for a year, henceforth every emperor of the Holy Roman Empire was a Habsburg, with only one exception. The Habsburgs began also to accumulate territory far from the hereditary lands. In 1477, Archduke Maximilian, only son of Emperor Frederick III, married the heiress Maria of Burgundy, During the long reign of Leopold I (1657–1705) and following the successful defence of Vienna against the Turks in 1683 (under the command of the King of Poland, John III Sobieski), a series of campaigns resulted in bringing most of Hungary to Austrian control by the Treaty of Karlowitz in 1699. Emperor Charles VI relinquished many Austria later became engaged in a war with Revolutionary France, at the beginning highly unsuccessfully, with successive defeats at the hands of Napoleon, meaning the end of the old Holy Roman Empire in 1806. Two years earlier, the Empire of Austria was founded. From 1792 to 1801, the Austrians had suffered 754,700 casualties. In 1814, Austria was part of the Allied forces that invaded France and brought to an end the Napoleonic Wars. It emerged from the Congress of Vienna in 1815 as one of the continent's four dominant powers and a recognised great power. The same year, the German Confederation () was founded under the presidency of Austria. As the Second Constitutional Era began in the Ottoman Empire, Austria-Hungary took the opportunity to annex Bosnia and Herzegovina in 1908. The assassination of Archduke Franz Ferdinand in Sarajevo in 1914 by Bosnian Serb Gavrilo Princip was used by leading Austrian politicians and generals to persuade the emperor to declare war on Serbia, thereby risking and prompting the outbreak of World War I, which eventually led to the dissolution of the Austro-Hungarian Empire. Over one million Austro-Hungarian soldiers died in World War I. On 21 October 1918, the elected German members of the "Reichsrat" (parliament of Imperial Austria) met After the war, inflation began to devalue the Krone, which was still Austria's currency. In autumn 1922, Austria was granted an international loan supervised by the League of Nations. The purpose of the loan was to avert bankruptcy, stabilise the currency, and improve Austria's general economic condition. The loan meant that Austria passed from an independent state to the control exercised by the League of Nations. In 1925, the "Schilling" was introduced, replacing the Krone at a rate of 10,000:1. Later, it was nicknamed the "Alpine dollar" due to its stability. From 1925 to 1929, the economy enjoyed a short high before nearly crashing after Black Tuesday. The First Austrian Republic lasted until 1933, when Chancellor Engelbert Dollfuss, using what he called "self-switch-off of Parliament", established an autocratic regime tending towards Italian fascism. The two big parties at this time, the Social Much like Germany, Austria was divided into American, British, French, and Soviet zones and governed by the Allied Commission for Austria. As forecast in the Moscow Declaration in 1943, a subtle difference was seen in the treatment of Austria by the Allies. The Austrian government, consisting of Social Democrats, Conservatives, and Communists (until 1947), and residing in Vienna, which was surrounded by the Soviet zone, was recognised by the Western Allies in October 1945 after some doubts that Renner could be Stalin's puppet. Thus, the creation of a separate Western Austrian government and the division of the country was avoided. Austria, in general, was treated as though it had been originally invaded by Germany and liberated by the Allies. On 15 May 1955, after talks which lasted for years and were influenced by the Cold War, Austria regained full independence by concluding the Austrian State Treaty with the Four Occupying Powers. On 26 October 1955, after all occupation troops had left, Austria declared its "permanent neutrality" by an act of parliament. This day is now Austria's National Day, a public holiday. The political system of the Second Republic is based on The Parliament of Austria is located in Vienna, the country's capital and most populous city. Austria became a federal, representative democratic republic through the Federal Constitution of 1920. The political system of the Second Republic with its nine states is based on the constitution of 1920, amended in 1929, which was reenacted on 1 May 1945. The head of state is the Federal President ("Bundespräsident"), who is directly elected by popular majority vote, with a run-off between the top-scoring candidates, if necessary. The head of the Federal Government is the Federal Chancellor ("Bundeskanzler"), who is selected by the President and tasked with forming a government based on the partisan composition of the lower house of parliament. The government can be removed from office by either a presidential decree or by vote of no confidence in the lower chamber of parliament, the Nationalrat. Voting for the Federal President and for the Parliament used to be compulsory in Austria, but this was abolished in steps from 1982 to 2004. Austria's parliament consists of two chambers. The composition of the Nationalrat (183 seats) is determined every five years (or whenever the Nationalrat has been dissolved by the federal president on a motion by the federal chancellor, or by Nationalrat itself) by a general election in which every citizen over the age of 16 has the right to vote. The voting age was lowered from 18 in 2007. While there is a general threshold of 4% of the vote for all parties in federal elections (Nationalratswahlen) to participate in the proportional allocation of seats, there remains the possibility of being elected to a seat directly in one of the 43 regional electoral districts (). The Nationalrat is the dominant chamber in the legislative process in Austria. However, the upper house of parliament, the Bundesrat, has a limited right of veto (the Nationalrat can—in almost all cases—ultimately pass the respective bill by voting a second time. This is referred to as "Beharrungsbeschluss", lit. "vote of persistence"). A constitutional convention, called the was convened on 30 June 2003 to consider reforms to the constitution, but failed to produce a proposal that would command a two-third majority in the Nationalrat, the margin necessary for constitutional amendments and/or reform. While the bicameral Parliament and the Government constitute the legislative and executive branches, respectively, the courts are the third branch of Austrian state powers. The Constitutional Court ("Verfassungsgerichtshof") exerts considerable influence on the political system because of its power to invalidate legislation and ordinances that are not in compliance with the constitution. Since 1995, the European Court of Justice may overrule Austrian decisions in all matters defined in laws of the European Union. Austria also implements the decisions of the European Court of Human Rights, since the European Convention on Human Rights is part of the Austrian constitution. Austria is a largely mountainous country because of its location in the Alps. The Central Eastern Alps, Northern Limestone Alps and Southern Limestone Alps are all partly in Austria. Of the total area of Austria (), only about a quarter can be considered low lying, and only 32% of the country is below. The Alps of western Austria give way somewhat into low lands and plains in the eastern part of the country. Austria lies between latitudes 46° and 49° N, and longitudes 9° and 18° E. It can be divided into five areas, the biggest being the Eastern Alps, which constitute 62% of the nation's total area. The Austrian foothills at the base of the Alps and the Carpathians account for around 12% and the foothills in the east and areas surrounding the periphery of the Pannoni low country amount to about 12% of the total landmass. The second greater mountain area (much lower than the Alps) is situated in the north. Known as the Austrian granite plateau, it is located in the central area of the Bohemian Mass and accounts for 10% of Austria. The Austrian portion of the Vienna basin makes up the remaining 4%. Phytogeographically, Austria belongs to the Central European province of the Circumboreal Region within the Boreal Kingdom. According to the WWF, the territory of Austria can be subdivided into four ecoregions: the Central European mixed forests, Pannonian mixed forests, Alps conifer and mixed forests and Western European broadleaf forests. The greater part of Austria lies in the cool/temperate climate zone, where humid westerly winds predominate. With nearly three-quarters of the country dominated by the Alps, the alpine climate is predominant. In the east—in the Pannonian Plain and along the Danube valley—the climate shows continental features with less rain than the alpine areas. Although Austria is cold in the winter (−10 to 0 °C), summer temperatures can be relatively high, with average temperatures in the mid-20s and a Austria consistently ranks high in terms of GDP per capita, due to its highly industrialized economy, and well-developed social market economy. Until the 1980s, many of Austria's largest industry firms were nationalised; in recent years, however, privatisation has reduced state holdings to a level comparable to other European economies. Labour movements are particularly influential, exercising large influence on labour politics and decisions related to the expansion of the economy. Next to a highly developed industry, international tourism is the most important part of the economy of Austria. Germany has historically been the main trading partner of Austria, making it vulnerable to rapid changes in the German economy. Since Austria became a member state of the European Union, it has gained closer ties to other EU economies, reducing its economic dependence on Germany. In addition, membership of the EU has drawn an influx of foreign investors attracted by Austria's access to the single European market and proximity to the aspiring economies of the European Union. Growth in GDP reached 3.3% in 2006. At least 67% of Austria's imports come from other European Union member states. Austria indicated on 16 November 2010 that it would withhold the December installment of its contribution to the EU bailout of Greece, citing the material worsening of the Greek debt situation and the apparent inability of Greece to collect the level of tax receipts it had previously promised. The Financial crisis of 2007–2008 dented the economy of Austria in other ways as well. It caused, for example, the Hypo Alpe-Adria-Bank International to be purchased in December 2009 by the government for 1 euro owing to credit difficulties, thus wiping out the €1.63bn of BayernLB., the HGAA situation was unresolved, causing Chancellor Werner Faymann to warn that its failure would be comparable to the 1931 Creditanstalt event. Since the fall of communism, Austrian companies have been quite active players and consolidators in Eastern Europe. Between 1995 and 2010, 4,868 mergers and acquisitions with a total known value of 163 bil. EUR with the involvement of Austrian firms have been announced. The largest transactions with involvement of Austrian companies have been: the acquisition of Bank Austria by Bayerische Hypo- und Vereinsbank for 7.8 billion EUR in 2000, the acquisition of Porsche Holding Salzburg by Volkswagen Group for 3.6 billion EUR in 2009, and the acquisition of Banca Comercială Română by Erste Group for 3.7 bil. EUR in 2005. Tourism in Austria accounts for almost 9% of its gross domestic product. In 2007, Austria ranked 9th worldwide in international tourism receipts, with 18.9 billion US$. In international tourist arrivals, Austria ranked 12th with 20.8 million tourists. Austria's population was estimated to be nearly 9 million (8.9) in 2020 by the Statistik Austria. The population of the capital, Vienna, exceeds 1.9 million (2.6 million, including the suburbs), representing about a quarter of the country's population. It is known for its cultural offerings and high standard of living. Vienna is by far the country's largest city. Graz is second in size, with 291,007 inhabitants, followed by Linz (206,604), Salzburg (155,031), Innsbruck (131,989), and Klagenfurt (101,303). All other cities have fewer than 100,000 inhabitants. According to Eurostat, in 2018 there were 1.69 million foreign-born residents in Austria, corresponding to 19.2% of the total population. Of these, 928,700 (10.5%) were born outside the EU and 762,000 (8.6%) were born in another EU Member State. There are more than 483,100 descendants of foreign-born immigrants. Turks form one of the largest ethnic groups in Austria, numbering around 350,000. 13,000 Turks were naturalised in 2003 and an unknown number have arrived in Austria at the same time. While 2,000 Turks left Austria in the same year, 10,000 immigrated to the country, confirming a strong trend of growth. Together, Serbs, Croats, Bosniaks and Slovenes make up about 5.1% of Austria's total population. The total fertility rate (TFR) in 2017 was estimated at 1.52 children born per woman, below the replacement rate of 2.1, it remains considerably below the high of 4.83 children born per woman in 1873. In 2015, 42.1% of births were to unmarried women. Austria subsequently has the 12th oldest population in the world, with the average age of 44.2 years. The life expectancy in 2016 was estimated at 81.5 years (78.9 years male, 84.3 years female). Statistics Austria estimates that nearly 10 million people will live in the country by 2080. Standard Austrian German is spoken in Austria, though used primarily just in education, publications, announcements and websites. It is mostly identical to the Standard German of Germany but with some vocabulary differences. This Standard German language is used in formal contexts across Germany, Austria, Switzerland and Liechtenstein, as well as among those with significant German-speaking minorities: Italy, Belgium and Denmark. However, the common spoken language of Austria is not the Standard German taught in schools but Austro-Bavarian: a group of Upper German local dialects with varying degrees of difficulty being understood by each other as well as by speakers of non-Austrian German dialects. Taken as a collective whole, German languages or dialects are thus spoken natively by 88.6% of the population, which includes the 2.5% German-born citizens who reside in Austria, followed by Turkish (2.28%), Serbian (2.21%), Croatian (1.63%), English (0.73%), Hungarian (0.51%), Bosnian (0.43%), Polish (0.35%), Albanian (0.35%), Slovenian (0.31%), Czech (0.22%), Arabic (0.22%), and Romanian (0.21%). The Austrian federal states of Carinthia and Styria are home to a significant indigenous Slovene-speaking minority while in the easternmost state, Burgenland (formerly part of the Hungarian portion of Austria–Hungary), there are Historically Austrians were regarded as ethnic Germans and viewed themselves as such, although this national identity was challenged by Austrian nationalism in the decades after the end of World War I and even more so after World War II. Austria was part of the Holy Roman Empire of the German Nation until its ending in 1806 and had been part of the German Confederation, a loose association of 39 separate German-speaking countries, until the Austro-Prussian war in 1866, which resulted in the exclusion of Austria from the German Confederation and the creation of the North German Confederation led by Prussia. In 1871, Germany was founded as a nation-state, Austria was not a part of it. After World In 2001, about 74% of Austria's population were registered as Roman Catholic, while about 5% considered themselves Protestants. Austrian Christians, both Catholic and Protestant, are obliged to pay a mandatory membership fee (calculated by income—about 1%) to their church; this payment is called "Kirchenbeitrag" ("Ecclesiastical/Church contribution"). Since the second half of the 20th century, the number of adherents and churchgoers has declined. Data for 2018 from the Austrian Roman Catholic Church list 5,050,000 members, or 56.9% of the total Austrian population. Sunday church Education in Austria is entrusted partly to the Austrian states (Bundesländer) and partly to the federal government. School attendance is compulsory for nine years, i.e. usually to the age of fifteen. Pre-school education (called "Kindergarten" in German), free in most states, is provided for all children between the ages of three and six years and, whilst optional, is considered a normal part of a child's education due to its high takeup rate. Maximum class size is around 30, each class normally being cared for by one qualified teacher and one assistant. Primary education, or Volksschule, lasts for four years, starting at age six. The maximum class size is 30, but may be as low as 15. It is generally expected Austria's past as a European power and its cultural environment generated a broad contribution to various forms of art, most notably among them music. Austria was the birthplace of many famous composers such as Joseph Haydn, Michael Haydn, Franz Liszt, Franz Schubert, Anton Bruckner, Johann Strauss, Sr. and Johann Strauss, Jr. as well as members of the Second Viennese School such as Arnold Schoenberg, Anton Webern and Alban Berg. Wolfgang Amadeus Mozart was born in Salzburg, then an independent Church Principality of the Holy Roman Empire, which later became part of Austria, and much of Mozart's career was spent in Vienna. Vienna was for a long time an important centre of musical innovation. 18th- Among Austrian Artists and architects one can find the painters Ferdinand Georg Waldmüller, Rudolf von Alt, Hans Makart, Gustav Klimt, Oskar Kokoschka, Egon Schiele, Carl Sascha Kolowrat was an Austrian pioneer of filmmaking. Billy Wilder, Fritz Lang, Josef von Sternberg, and Fred Zinnemann originally came from the Austrian Empire before establishing themselves as internationally relevant filmmakers. Willi Forst, Ernst Marischka, and Franz Antel enriched the popular cinema in German-speaking countries. Michael Haneke became internationally known for his disturbing cinematic studies, receiving a Golden Globe for his critically acclaimed film "The White Ribbon" (2010). Austria was the cradle of numerous scientists with international reputation. Among them are Ludwig Boltzmann, Ernst Mach, Victor Franz Hess and Christian Doppler, prominent scientists in the 19th century. In the 20th century, contributions by Lise Meitner, Erwin Schrödinger and Wolfgang Pauli to nuclear research and quantum mechanics were key to these areas' development during the 1920s and 1930s. A present-day quantum physicist is Anton Zeilinger, noted as the first scientist to demonstrate quantum teleportation. In addition to physicists, Austria was the birthplace of two of the most noteworthy philosophers of the 20th century, Ludwig Wittgenstein and Karl Popper. Complementing its status as a land of artists and scientists, Austria has always been a country of poets, writers, and novelists. It was the home of novelists Arthur Schnitzler, Austria's cuisine is derived from that of the Austro-Hungarian Empire. Austrian cuisine is mainly the tradition of Royal-Cuisine ("Hofküche") delivered over centuries. It is famous for its well-balanced variations of beef and pork and countless variations of vegetables. There is also the "Mehlspeisen" Bakery, which created particular delicacies such as Sachertorte, "Krapfen" which are doughnuts usually filled with apricot jam or custard, and "Strudel" such as "Apfelstrudel" filled with apple, "Topfenstrudel" filled with a type of cheese curd called "topfen", and "Millirahmstrudel" (milk-cream strudel). In addition to native regional traditions, the cuisine has been influenced by Hungarian, Czech, Polish, Jewish, Italian, Balkan and French cuisines, from which both dishes and methods of food preparation have often been borrowed. The Austrian cuisine is therefore one of the most multicultural and transcultural in Europe. Typical Austrian dishes include Wiener Schnitzel, Schweinsbraten, Kaiserschmarren, Knödel, Sachertorte and Tafelspitz. There are also Kärntner Kasnudeln, which are pockets of dough filled with Topfen, potatoes, herbs and peppermint which are boiled and served with a butter sauce. Kasnudeln are traditionally served with a salad. Eierschwammerl dishes are also popular. The sugar Due to the mountainous terrain, alpine skiing is a prominent sport in Austria and is extremely valuable in the promotion and economic growth of the country. Similar sports such as snowboarding or ski-jumping are also widely popular. Austrian athletes such as Annemarie Moser-Pröll, Franz Klammer, Hermann Maier, Toni Sailer, Benjamin Raich, Marlies Schild & Marcel Hirscher are widely regarded as some of the greatest alpine skiers of all time, Armin Kogler, Andreas Felder, Ernst Vettori, Andreas Goldberger, Andreas Widhölzl, Thomas Morgenstern & Gregor Schlierenzauer as some of the greatest ski jumpers of all time. Bobsleigh, luge, and skeleton are also popular events with a permanent track located in Igls, which hosted bobsleigh and luge competitions for the 1964 and 1976 Winter Olympics held in Innsbruck. The first Winter Youth Olympics in 2012 were held in Innsbruck as well. A popular team sport in Austria is football, which is governed by the Austrian Football Association. Austria was among the most successful football playing nations on the European continent placing 4th at the 1934 FIFA World Cup, 3rd at the 1954 FIFA World Cup and 7th at the 1978 FIFA World Cup. However, recently

Austria (, ; ), officially the Republic of Austria (, ), is a landlocked East Alpine country in the southern part of Central Europe. It is composed of nine federated states ("Bundeslände"r), one of which is Vienna, Austria's capital and its largest city. It is bordered by Germany to the northwest, Czech Republic to the north, Slovakia to the northeast, Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the west. Austria occupies an area of and has a population of nearly 9 million people. While German is the country's official language, many Austrians communicate informally in a variety of Bavarian dialects.

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summarize: A fluid flowing around the surface of an object applies a force against it. It makes no difference whether the fluid is flowing past a stationary body or the body is moving through a stationary volume of fluid. Lift is the component of this force that is perpendicular to the oncoming flow direction. Lift is always accompanied by a drag force, which is the component of the surface force parallel to the flow direction. Lift is mostly associated with the wings of fixed-wing aircraft, although it is more widely generated by many other streamlined bodies such as propellers, kites, helicopter rotors, racing car wings, maritime sails, and wind turbines in air, and by sailboat keels, ship's rudders, and hydrofoils An airfoil is a streamlined shape that is capable of generating significantly more lift than drag. A flat plate can generate lift, but not as much as a streamlined airfoil, and with somewhat higher drag. There are several ways to explain how an airfoil generates lift. Some are more complicated or more physically rigorous than others; some have been shown to be incorrect. For example, there are explanations based directly on Newton's laws of motion and explanations based on Bernoulli's principle. Either can be used to explain lift. An airfoil generates lift by exerting a downward force on the air as it flows past. According to Newton's third law, the air must exert an equal and opposite (upward) force on the airfoil, which is lift. The airflow changes direction as it passes the airfoil and follows a path that is curved downward. According to Newton's second law, this change in flow Bernoulli's principle states that there is a direct mathematical relationship between the pressure of a fluid and the speed of that fluid, so if one knows the speed at all points within the airflow one can calculate the pressure, and vice versa. For any airfoil generating lift, there must be a pressure imbalance, i.e. lower average air pressure on the top than on the bottom. Bernoulli's principle states that this pressure difference must be accompanied by a speed difference. Starting with the flow pattern observed in both theory and experiments, the increased flow speed over the upper surface can be explained in terms of streamtube pinching and conservation of mass. For incompressible flow, the rate of volume flow (e.g. volume units per minute) must be constant within each streamtube since matter is not created or destroyed. If a streamtube becomes narrower, the flow speed must increase in the narrower region to maintain the constant flow rate, to satisfy the principle of conservation of mass. The upper streamtubes constrict as they flow up and around the airfoil. Conservation of mass says that the flow speed must increase as the stream tube area decreases. Similarly, the lower streamtubes expand and their flowrate slows. From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower. This pressure difference creates a net aerodynamic force, pointing upward. As explained below under a more comprehensive physical explanation, producing a lift force requires maintaining pressure differences in both the vertical and horizontal directions, and thus requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. The simplified explanations given above are therefore incomplete because they define lift in terms of only one or the other. And depending on the details, they have other shortcomings as well. The explanation based on flow deflection and Newton's laws is correct but is incomplete. It does not explain how the airfoil can impart downward Many alternative explanations for the generation of lift by an airfoil have been put forward, most intended to explain the phenomenon of lift to a general audience. Although the explanations may share features in common with the explanations above, additional assumptions and simplifications may be introduced. Some explanations introduce assumptions which proved to be wrong, such as "equal transit-time", and some used controversial terminology, such as "Coandă effect". Basic or popular sources often describe the "equal transit-time" theory of lift, which incorrectly assumes that the parcels of air that divide at the leading edge of an airfoil must rejoin at the trailing edge, forcing the air traveling along the longer upper surface to go faster. Bernoulli's principle is then cited to conclude that since the air moves slower along the bottom of the In its original sense, the "Coandă effect" refers to the tendency of a fluid jet to stay attached to an adjacent surface that curves away from the flow, and the resultant entrainment of ambient air into the flow. The effect is named for Henri Coandă, the Romanian aerodynamicist who exploited it in many of his patents. More broadly, some consider the effect to include the tendency of any fluid boundary layer to adhere to a curved surface, not just the boundary layer accompanying a fluid jet. It is in this broader sense that the Coandă effect is used by some to explain why airflow remains attached to the top Lift is a result of pressure differences and depends on angle of attack, airfoil shape, air density, and airspeed. Pressure is the normal force per unit area exerted by the air on itself and on surfaces that it touches. The lift force is transmitted through the pressure, which acts perpendicular to the surface of the airfoil. Thus, the net force manifests itself as pressure differences. The direction of the net force implies that the average pressure on the upper surface of the airfoil is lower than the average pressure on the underside. These pressure differences arise in conjunction with the The angle of attack is the angle between the chord line of an airfoil and the oncoming airflow. A symmetrical airfoil will generate zero lift at zero angle of attack. But as the angle of attack increases, the air is deflected through a larger angle and the vertical component of the airstream The lift force depends on the shape of the airfoil, especially the amount of camber (curvature such that the upper surface is more convex than the lower surface, as illustrated at right). Increasing the camber generally increases lift. Cambered airfoils will The ambient flow conditions which affect lift include the fluid density, viscosity and Lift is proportional to the density of the air and approximately proportional to the square of the flow speed. Lift also depends on No matter how smooth the surface of an airfoil seems, any surface is rough on the scale of air molecules. Air molecules flying into the surface bounce off the rough surface in random directions relative to their original velocities. The result is that when the air is viewed as a continuous material, it is seen to be unable to slide along the surface, and the air's velocity relative to the airfoil decreases to nearly zero at the surface (i.e., the air molecules "stick" to the surface instead of sliding along it), something known as the no-slip condition. Because the air at the surface has near-zero velocity but the air An airfoil's maximum lift at a given airspeed is limited by boundary-layer separation. As the angle of attack is increased, a point is reached where the boundary layer can no longer remain attached to the upper surface. When the boundary layer separates, it leaves a region of recirculating flow above The flow around bluff bodies – i.e. without a streamlined shape, or stalling airfoils – may also generate lift, in addition to a strong drag force. This lift may be steady, or it may oscillate due to vortex shedding. Interaction of the object's flexibility with the vortex shedding may enhance the effects of fluctuating lift and cause vortex-induced vibrations. For instance, the flow around a circular cylinder generates a Kármán vortex street: vortices being shed in an alternating fashion from the cylinder's sides. The oscillatory nature of the flow produces a fluctuating lift force on the cylinder, even though the net (mean) As described above under "Simplified physical explanations of lift on an airfoil", there are two main popular explanations: one based on downward deflection of the flow (Newton's laws), and one based on pressure differences accompanied by changes in flow speed (Bernoulli's principle). Either of these, by itself, correctly identifies some aspects of the lifting flow but leaves other important aspects of the phenomenon unexplained. A more comprehensive explanation involves both downward deflection and pressure differences (including changes in flow speed associated with the pressure differences), and requires looking at the flow in more detail. The airfoil shape and angle of attack work together so that the airfoil exerts a downward force on the air as it flows past. According to Newton's third law, the air must then exert an equal and opposite (upward) force on the airfoil, which is the lift. The net force exerted by the air occurs as a pressure difference over the airfoil's surfaces. Pressure in a fluid is always positive in an absolute sense, so An airfoil affects the speed and direction of the flow over a wide area, producing a pattern called a "velocity field". When an airfoil produces lift, the flow ahead of the airfoil is deflected upward, the flow above and below the airfoil is deflected downward, and the flow behind the airfoil is deflected upward again, leaving the air far behind the airfoil in the same state as the oncoming flow far ahead. The flow above the upper surface is sped up, while the flow below the airfoil is slowed down. Together with the upward deflection of air in front and the downward The non-uniform pressure exerts forces on the air in the direction from higher pressure to lower pressure. The direction of the force is different at different locations around the airfoil, as indicated by the block arrows in the "pressure distribution with isobars" figure. Air above the airfoil is pushed toward the center of the low-pressure region, and air below the airfoil is pushed outward from the center of the high-pressure region. According to "Newton's second law", a force causes air to accelerate in the direction of the force. Thus the vertical arrows in the "pressure distribution with isobars" figure Producing a lift force requires both downward turning of the flow and changes in flow speed consistent with Bernoulli's principle. Each of the simplified explanations When the pressure distribution on the airfoil surface is known, determining the total lift requires adding up the contributions to the pressure force from local elements of the surface, each with its own local value of pressure. The total lift is thus the integral of the pressure, in the direction perpendicular to the farfield flow, over the airfoil surface. formula_2 where: Lift depends on the size of the wing, being approximately proportional to the wing area. It is often convenient to quantify the lift of a given airfoil by its "lift Mathematical theories of lift are based on continuum fluid mechanics, assuming that air flows as a continuous fluid. Lift is generated in accordance with the fundamental principles of physics, the most relevant being the following three principles: Because an airfoil affects the flow in a wide area around it, the conservation laws of mechanics are embodied in the form of partial differential equations combined with a set of boundary condition requirements which the flow has to satisfy at the airfoil surface and far away from the airfoil. To predict lift requires solving the equations for a particular airfoil shape and flow condition, which generally requires calculations that are so voluminous that they are practical only on a computer, through the methods of computational fluid dynamics (CFD). Determining the net aerodynamic force from a CFD solution requires "adding up" (integrating) the forces due to pressure and shear determined by the CFD over every surface element of the airfoil as described under "pressure integration". The Navier–Stokes equations (NS) provide the potentially most accurate theory of lift, but in practice, capturing the effects of turbulence in the boundary layer on the airfoil surface requires sacrificing some accuracy, and requires use of the Reynolds-averaged Navier–Stokes equations (RANS). Simpler but less accurate theories have also been developed. These equations represent conservation of mass, Newton's second law (conservation of momentum), conservation of energy, the Newtonian law for the action of viscosity, the Fourier heat conduction law, an equation of state relating density, temperature, and pressure, and formulas for the viscosity and thermal conductivity of the fluid. In principle, the NS equations, combined with boundary conditions of no through-flow and no slip at the airfoil surface, could be used to predict lift These are the NS equations with the turbulence motions averaged over time, and the effects of the turbulence on the time-averaged flow represented by turbulence modeling (an additional set of equations based on a combination of dimensional analysis and empirical information on how turbulence affects a boundary layer in a time-averaged average sense). A RANS solution consists of the time-averaged velocity vector, pressure, density, The Euler equations are the NS equations without the viscosity, heat conduction, and turbulence effects. As with a RANS solution, an Euler solution consists of the velocity vector, pressure, density, and temperature defined at a dense grid of points surrounding the airfoil. While the Euler equations are simpler than the NS equations, they do not lend themselves to exact analytic solutions. Further simplification is available through potential flow theory, which reduces the number of unknowns to be determined, and makes analytic solutions possible in some cases, as described below. Either Euler or potential-flow calculations predict This is potential-flow theory with the further assumptions that the airfoil is very thin and the angle of attack is small. The linearized theory predicts the general character of the When an airfoil generates lift, several components of the overall velocity field contribute to a net circulation of air around it: the upward flow ahead of the airfoil, the accelerated flow above, the decelerated flow below, and the downward flow behind. The circulation can be understood as the total amount of "spinning" (or vorticity) of an inviscid fluid around the airfoil. The Kutta–Joukowski theorem relates the lift per unit width of span of a two-dimensional airfoil to this circulation component of the flow. It is a key element in an explanation of lift that follows the development of the flow around an airfoil as the airfoil starts its motion from rest and a starting vortex is The flow around a three-dimensional wing involves significant additional issues, especially relating to the wing tips. For a wing of low aspect ratio, such as a typical delta wing, two-dimensional theories may provide a poor model and three-dimensional flow effects can dominate. Even for wings of high aspect ratio, the three-dimensional effects associated with finite span can affect the whole span, not just close to the tips. The vertical pressure gradient at the wing tips causes air to flow sideways, out from under the wing then up and back over the upper surface. This reduces the pressure gradient at the wing tip, therefore also reducing lift. The lift tends to decrease in the spanwise direction from root to tip, and the pressure distributions around the airfoil sections change accordingly in the spanwise direction. Pressure distributions in planes perpendicular to the flight direction tend to look like the illustration at right. This spanwise-varying pressure distribution is sustained by a mutual interaction with the velocity field. Flow below the wing is accelerated outboard, flow outboard of the tips is accelerated upward, and flow above The wingtip flow leaving the wing creates a tip vortex. As the main vortex sheet passes downstream from the trailing edge, it rolls up at its outer edges, merging with the tip vortices. The combination of the wingtip vortices and the vortex sheets feeding them is called the vortex wake. In addition to the vorticity in the trailing vortex wake there is vorticity in the wing's boundary layer, called 'bound vorticity', which connects the trailing sheets from the two sides of the wing into a vortex system in the general form of a horseshoe. The horseshoe form of the vortex system was recognized by the British aeronautical The flow around a lifting airfoil must satisfy Newton's second law regarding conservation of momentum, both locally at every point in the flow field, and in an integrated sense over any extended region of the flow. For an extended region, Newton's second law takes the form of the "momentum theorem for a control volume", where a control volume can be any region of the flow chosen for analysis. The momentum theorem states that the integrated force exerted at the boundaries of the control volume (a surface integral), is equal to the integrated time rate of change (material derivative) of the momentum of fluid parcels passing through the interior of the control volume. For a steady flow, this can be expressed in the form of the net surface integral of the flux of momentum through the boundary. The lifting flow around a 2D airfoil is usually analyzed in a control volume that completely surrounds the airfoil, so that the inner boundary of the control volume is the airfoil surface, where the downward force per unit span formula_12 is exerted on the fluid by the airfoil. The outer boundary is usually either a large circle An airfoil produces a pressure field in the surrounding air, as explained under "The wider flow around the airfoil" above. The pressure differences associated with this field die off gradually, becoming very small at large distances, but never disappearing altogether. Below the airplane, the pressure field persists as a positive pressure disturbance that reaches the ground, forming a pattern of slightly-higher-than-ambient pressure on the ground, as shown on the right. Although the pressure differences are very small far below the airplane, they

A fluid flowing around the surface of an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow.

en

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summarize: The word "viscosity" is derived from the Latin In materials science and engineering, one is often interested in understanding the forces, or stresses, involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law, which says that the force experienced by a spring is proportional to the distance displaced from equilibrium. Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses. In other materials, stresses are present which can be attributed to the rate of change In very general terms, the viscous stresses in a fluid are defined as those resulting from the relative velocity of different fluid particles. As such, the viscous stresses must depend on spatial gradients of the flow velocity. If the velocity gradients are small, then to a first approximation the viscous stresses depend only on the first derivatives of the velocity. (For Newtonian fluids, this is also a linear dependence.) In Cartesian coordinates, the general relationship can then be written as where formula_23 is a viscosity tensor that maps the velocity gradient tensor formula_24 onto the viscous stress tensor formula_25. Since the indices in this expression can vary from 1 to 3, there are 81 "viscosity coefficients" formula_26 in total. However, assuming that the viscosity rank-4 tensor is isotropic reduces these 81 coefficients to three independent parameters formula_27, formula_28, formula_29: and furthermore, it is assumed that no viscous In fluid dynamics, it is common to work in terms of the "kinematic viscosity" (also called "momentum diffusivity"), defined as the ratio of the viscosity to the density Transport theory provides an alternative interpretation of viscosity in terms of momentum transport: viscosity is the material property which characterizes momentum transport within a fluid, just as thermal conductivity characterizes heat transport, and (mass) diffusivity characterizes mass transport. To see this, note that in Newton's law of viscosity, formula_48, the shear stress formula_49 has units equivalent to a momentum flux, i.e. momentum per unit time per unit area. Thus, formula_49 can be interpreted as specifying the flow of momentum in the formula_8 direction from one fluid layer to the next. Per Newton's law of viscosity, this momentum flow occurs across a velocity gradient, and the magnitude of Newton's law of viscosity is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law, Fick's law, and Ohm's law) which serves to define the viscosity formula_10. Its form is motivated by experiments which show that for a wide range of fluids, formula_10 is independent of strain rate. Such fluids are called Newtonian. Gases, water, and many common liquids can be considered Newtonian in ordinary conditions and contexts. The viscous forces that arise during fluid flow must not be confused with the elastic forces that arise in a solid in response to shear, compression or extension stresses. While in the latter the stress is proportional to the "amount" of shear deformation, in a fluid it is proportional to the "rate" of deformation over time. (For this reason, Maxwell used the term "fugitive elasticity" for fluid viscosity.) However, many liquids (including water) will briefly react Viscosity is measured with various types of viscometers and rheometers. A rheometer is used for those fluids that cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. Close temperature control of the fluid is essential to acquire accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. For some fluids, the viscosity is constant over a wide range of shear rates (Newtonian fluids). The fluids without a constant viscosity (non-Newtonian fluids) cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate. One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer. In coating industries, viscosity may be measured with a cup in which the The SI unit of dynamic viscosity is the pascal-second (Pa·s), or equivalently kilogram per meter per second (kg·m·s). The CGS unit is the poise (P, or g·cm·s = 0.1 Pa·s), named after Jean Léonard Marie Poiseuille. It is commonly expressed, particularly in ASTM standards, as "centipoise" (cP) since the latter is equal to the SI multiple millipascal seconds (mPa·s). The SI unit of kinematic viscosity is square meter per second (m/s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm·s = 0.0001 m·s), named after Sir George Gabriel Stokes. In U.S. usage, "stoke" is sometimes used In general, the viscosity of a system depends in detail on how the molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the "transient time correlation function" expressions derived by Evans and Morriss in 1988. Although these expressions are each exact, calculating the viscosity of a dense fluid using these relations currently requires the use of molecular dynamics computer simulations. On the other hand, much more progress can be made for a dilute gas. Even elementary assumptions about how gas molecules move and interact lead to a basic understanding of the molecular origins of viscosity. More sophisticated treatments can be constructed by systematically coarse-graining the equations of motion of the gas molecules. An example of such a treatment is Chapman–Enskog theory, which derives expressions for the viscosity of a dilute gas from the Boltzmann equation. Momentum transport in gases is generally mediated by discrete molecular collisions, and in liquids by attractive forces which bind molecules close together. Because of this, the dynamic viscosities of liquids are typically much larger than those of gases. Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. An elementary calculation for a dilute gas at temperature formula_62 and density formula_53 gives where formula_65 is the Boltzmann constant, formula_66 the molecular mass, and formula_27 a numerical constant on the order of formula_68. The quantity formula_69, the mean free path, measures the average distance a molecule travels between collisions. Even without "a priori" knowledge of formula_27, this expression has interesting implications. In particular, since formula_69 is typically inversely proportional A technique developed by Sydney Chapman and David Enskog in the early 1900s allows a more refined calculation of formula_10. It is based on the Boltzmann equation, which provides a systematic statistical description of a dilute gas in terms of intermolecular interactions. As such, their technique allows accurate calculation of formula_10 for more realistic molecular models, such as those incorporating intermolecular attraction rather than just hard-core repulsion. It turns out that a more realistic modeling of interactions is essential for accurate prediction of the temperature dependence of formula_10, which experiments show increases more rapidly than the formula_82 trend predicted for rigid elastic spheres. Indeed, the Chapman–Enskog analysis shows that the predicted temperature dependence can be tuned by varying the parameters in various molecular models. A simple example is the Sutherland model, which describes rigid elastic spheres with "weak" mutual In the kinetic-molecular picture, a non-zero bulk viscosity arises in gases whenever there are non-negligible relaxational timescales governing the exchange of energy between the translational energy of molecules and their internal energy, e.g. rotational and vibrational. As such, the bulk viscosity is formula_2 for a monatomic ideal gas, in which the internal energy of molecules in negligible, but is nonzero for a gas like carbon dioxide, whose molecules possess both rotational and vibrational energy. In contrast with gases, there is no simple yet accurate picture for the molecular origins of viscosity in liquids. At the simplest level of description, the relative motion of adjacent layers in a liquid is opposed primarily by attractive molecular forces acting across the layer boundary. In this picture, one (correctly) expects viscosity to decrease with increasing temperature. This is because increasing temperature increases the random thermal motion of the molecules, which makes it easier for them to overcome their attractive interactions. Building on this visualization, a simple theory can be constructed in analogy with the discrete structure of a solid: groups of molecules in a liquid are visualized as forming "cages" which surround and enclose single molecules. These cages can be occupied or unoccupied, and stronger molecular attraction corresponds to stronger cages. Due to random thermal motion, a molecule "hops" between cages at a rate which varies inversely with the strength of molecular attractions. In equilibrium these "hops" are not biased in any direction. On the other hand, in The same molecular-kinetic picture of a single component gas can also be applied to a gaseous mixture. For instance, in the Chapman–Enskog approach the viscosity formula_101 of a binary mixture of gases can be written in terms of the individual component viscosities formula_102, their respective volume fractions, and the intermolecular As for pure liquids, the viscosity of a blend of liquids is difficult to predict from molecular principles. One method is to extend the molecular "cage" theory presented above for a pure liquid. This can be done with varying levels of sophistication. One useful expression resulting from such an analysis is the Lederer–Roegiers equation for a binary mixture: where formula_27 is an empirical parameter, and formula_107 and formula_102 are the respective mole fractions and viscosities of the component liquids. Since blending is an important process in the lubricating and oil industries, a variety of empirical and propriety equations exist for predicting the viscosity of a blend, besides those stemming directly from molecular theory. Depending on the solute and range of concentration, an aqueous electrolyte solution can have either a larger or smaller viscosity compared with pure water at the same temperature and pressure. For instance, a 20% saline (sodium chloride) solution has viscosity over 1.5 times that of pure water, whereas a 20% potassium iodide solution has viscosity about 0.91 times that of pure water. An idealized model of dilute electrolytic solutions leads to the following prediction for In a suspension of solid particles (e.g. micron-size spheres suspended in oil), an effective viscosity formula_119 can be defined in terms of stress and strain components which are averaged over a volume large compared with the distance between the suspended particles, but small with respect to macroscopic dimensions. Such suspensions generally exhibit non-Newtonian behavior. However, for dilute systems in steady flows, the behavior is Newtonian and expressions for formula_119 can be derived directly from the particle dynamics. In a very dilute system, with volume fraction formula_121, interactions between the suspended particles can be ignored. In such a case one can explicitly calculate the flow field around each particle independently, and combine the results to obtain formula_122. For spheres, this results in the Einstein equation: where formula_87 is the viscosity of the suspending liquid. The linear dependence on formula_125 In the high and low temperature limits, viscous flow in amorphous materials (e.g. in glasses and melts) has the Arrhenius form: where is a relevant activation energy, given in terms of molecular parameters; is temperature; is the molar gas constant; and is approximately a constant. The activation energy takes a different value depending on whether the high or low temperature limit is being considered: it changes from a high value at low temperatures (in the glassy state) to a low value at high temperatures (in the liquid state). For intermediate temperatures, formula_139 varies nontrivially with temperature and the simple Arrhenius form fails. On the other hand, the two-exponential equation where formula_7, formula_100, formula_117, formula_56 are all constants, provides a good fit to experimental data over the entire range of temperatures, while at the same time reducing to the correct Arrhenius form in the low and high temperature limits. Besides being a convenient fit to data, the expression can also be derived In the study of turbulence in fluids, a common practical strategy is to ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an "effective" Observed values of viscosity vary over several orders of magnitude, even for common substances (see the order of magnitude table below). For instance, a 70% sucrose (sugar) solution has a viscosity over 400 times that of water, and 26000 times that of air. More dramatically, pitch has been estimated to have a viscosity 230 billion times that of water. The dynamic viscosity formula_10 of water is about 0.89 mPa·s at room temperature (25 °C). As a function of temperature in kelvins, the viscosity Under standard atmospheric conditions (25 °C and pressure of 1 bar), the dynamic viscosity of air is 18.5 μPa·s, roughly 50 times smaller than the viscosity of water at the same temperature. Except at very high pressure, the The following table illustrates the range of viscosity values observed in common substances. Unless otherwise noted, a temperature of 25 °C and

The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.

en

43

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summarize: Electric energy is most often measured either in joules (J), or in watt hours (W·h) representing a constant power over a period of time. Electric and electronic devices consume electric energy to generate desired output (i.e., light, heat, motion, etc.). During operation, some part of the energy—depending on the electrical efficiency—is consumed in unintended output, such as waste heat. Electricity has been generated in power stations since 1882. The invention of the steam turbine in 1883 to drive the electric generator started a strong increase of world electricity consumption. In 2008, the world total of electricity production was 20.279 petawatt-hours (PWh). This number corresponds to an average power of 2.31 TW continuously during the year. The total primary energy used in a thermal power station to produce this power is roughly a factor 2 to 3 higher because the efficiency of electricity generation is roughly 30–50% (see also energy conversion efficiency). The primary energy consumption to generate electric power is thus in the order of 5 TW. This is approximately a third of the total energy consumption of 15 TW ("see world energy consumption"). In 2005, the primary energy used to generate electricity was. This was compounded of Coal, Natural (fossil) gas, Petroleum, Nuclear electric power, Renewable energy respectively. The gross generation of electricity in that year was ; the difference of was conversion losses. Among all electricity, was used in residential area, used in commercial, used in industrial and used in transportation. 1 Quad = 1 Quadrillion BTU = 1 x 10 BTU = 293 TWh During the year 16,816 TWh (83%) of electric energy was consumed by final users. The difference of 3,464 TWh (17%) was consumed in the process of generating power and lost in transmission to end users. A sensitivity analysis on an adaptive neuro-fuzzy network model for electric demand estimation shows that employment is the most critical factor influencing electrical consumption. The study used six parameters as input data, employment, GDP, dwelling, population, heating degree day and cooling degree day, with electricity demand as output variable. At the world level, energy consumption was cut down by 1.5% during 2009, for the first time since World War II. Except in Asia and Middle East, consumptions were reduced in all the world regions. In OECD countries, accounting for 53% of the total, electricity demand scaled down by more than 4.5% in both Europe and North America while it shrank by above 7% in Japan. Electricity demand also dropped by more than 4.5% in CIS countries, driven by a large cut in Russian consumption. Conversely, in China and India (22% of the world's consumption), electricity consumption continued to rise at a strong pace (+6-7%) to meet energy demand related to high economic growth. In Middle East, growth rate was softened but remained high, just below 4%. The table lists the top 37 electricity consuming countries, which use 19,000 TWh/a. i.e. 90% of the consumption of all more than 190 countries. The total consumption (including the amount consumed by the power plants) and the energy sources to generate this electricity is given per country. The data is from 2012. Total consumption (2nd column) divided by number of inhabitants (last column) gives a country's consumption per head. In W-Europe this is between 5 and 8 MWh/a. (1 MWh equals 1000 kWh.) In Scandinavia, USA, Canada, Taiwan and South Korea it is much more, in developing countries much less. The worlds average is 3 MWh/a. A very low consumption per head, as in Indonesia, means that many inhabitants are not connected to the electricity grid, and this is the reason that the world's 7th and 8th most populous countries—Nigeria (177M) and Bangladesh (156M)—do not appear in the table. From 2012 to 2014 worldwide electricity consumption increased 5%. Nuclear and fossil generated electricity rose 3%, renewable electricity 12%. A small part of the renewables, solar and wind electricity, increased much more, 46% in line with the strong growth since 1990. In Brazil, wind power increased 140%, in China not only solar and wind increased fast, 81%, but also nuclear, 36%. Listed countries are top 20 populous countries and/or top 20 GDP (PPP) countries and Saudi Arabia as of CIA World Factbook 2009. 30 countries (exclude EU/IEA) in this table represent 77% of world population, 84% of world GDP, 83% of world electricity generation. Productivity per Electricity generation (concept similar to Energy intensity) can be measured by dividing GDP amount by the electricity generated. World average was $3.5 production/kWh. Electricity generation include Final consumption, in process consumption, and losses. About 17% of total electricity production is consumed by in-processes, such as self-consumption of power plants, grid losses and storage losses. In 2008, total electricity generation accounted for 20,261 TWh (20.26 PWh), while 3,464 TWh (3.46 PWh) were self-consumption and losses and 16,816 TWh (16.82 PWh) went to final consumption. In the consumption rate in Industry, China is highest with 67.8%, South Korea is 51.0% (7th), Germany 46.1% (11th), Japan 31.5% (26th), USA 24.0% (28th) In the Commercial and Public Service, Japan is highest with 36.4%, USA 35.6% (3rd), China 5.4% (29th). For Domestic usage, Saudi Arabia is highest with 56.9%, USA 36.2% (8th), Japan 29.8% (16th), China 15.5% (29th), Korea 13.8% (30th). Definition Electric energy consumption per inhabitant by primary energy source in some countries and areas in 2008 is in the table. For the OECD with 8 991 kWh/yr/person: 1.026 watt/person. In a recent report, the IEA reported a total worlds electric energy consumption in 2017 of 21,372 TWh, which is an increase of 2.6% in comparison to 2016. The electric energy consumption of the OECD countries in 2017 was 9,518 TWh and thus about 0.2% higher than in 2016. This compares to a power production in the OECD countries of 11,051 TWh in 2017, and to 11,173 TWh in 2018. The electric power consumption of the non-OECD countries in 2017 amounts to 11,854 TWh. An increase of 4.6% over the year 2016. The share of the gross electric production by source is summarized in the following table for the available assessment in the years 2017 or 2018. In all scenarios, increasing efficiency will result in less electricity needed for a given demand of power and light. But demand will increase strongly on account of As transport and heating become more climate-friendly, the environmental effect of energy consumption will be more determined by electricity. This is mainly supplied by burning fossil fuel which disturbs the natural carbon cycle. The scenarios arrive at very different results for the environment. The International Energy Agency expects revision of subsidy for fossil fuel which amounted to 550 billion dollar in 2013, more than four times renewable energy subsidy. In this scenario almost half of the increase in 2040 of electricity consumption is covered by more than 80% growth of renewable energy. Many new nuclear plants will be constructed, mainly to replace old ones. The nuclear part of electricity generation will increase from 11 to 12%. The renewable part goes up much, from 21 to 33%. The IEA warns that in order to restrict global warming to 2 °C, the carbon dioxide emission must not exceed 1000 gigaton (Gt) from 2014. This limit is reached in 2040 and emissions will not drop to zero ever. The World Energy Council sees world electricity consumption increasing to more than 40,000 TWh/a in 2040. The fossil part of generation depends on energy policy. It can stay around 70% in the so-called Jazz scenario where countries rather independently "improvise" but it can also decrease to around 40% in the Symphony scenario if countries work "orchestrated" for more climate friendly policy. Carbon dioxide emission, 32 Gt/a in 2012, will increase to 46 Gt/a in Jazz but decrease to 26 Gt/a in Symphony. Accordingly, until 2040 the renewable part of generation will stay at about 20% in Jazz but increase to about 45% in Symphony.

Electric energy consumption is the form of energy consumption that uses electric energy. Electric energy consumption is the actual energy demand made on existing electricity supply.

en

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summarize: There are various types of potential energy, each associated with a particular type of force. For example, the work of an elastic force is called elastic potential energy; work of the gravitational force is called gravitational potential energy; work of the Coulomb force is called electric potential energy; work of the strong nuclear force or weak nuclear force acting on the baryon charge is called nuclear potential energy; work of intermolecular forces is called intermolecular potential energy. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of configurations of electrons and nuclei in atoms and molecules. Thermal energy usually has two components: the kinetic energy of random motions of particles and the potential energy of their configuration. Forces derivable from a potential are also called conservative forces. The work done by a conservative force is where formula_2 is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, while work done by the force field decreases potential energy. Common notations for potential energy are "PE", "U", "V", and "E". Potential energy is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as a spring or the force of gravity. The action of stretching a spring or lifting a mass is performed by an external force that works against the force field of the potential. This work is stored in the force field, which is said to be stored as potential energy. If the external force is removed the force field acts on the body to perform the work as it moves the body back to the initial position, reducing the stretch of the spring or causing a body to fall. Consider a ball whose mass is m and whose height is h. The acceleration g of free fall is approximately constant, so the weight force of the ball mg is constant. Force × displacement gives the work done, which is equal to the gravitational potential energy, thus The more formal definition is that potential energy is the energy difference between the energy of an object in a given position and its energy at a reference position. Potential energy is closely linked with forces. If the work done by a force on a body that moves from "A" to "B" does not depend on the path between these points (if the work is done by a conservative force), then the work of this force measured from "A" assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for an applied force is independent of the path, then the work done by the force is evaluated at the start and end of the trajectory of the point of application. This means that there is a function "U"(x), called a "potential," that can be evaluated at the two points x and x to obtain the work over any trajectory between these two points. It is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is where "C" is the trajectory taken from A to B. Because the work done is independent of the path taken, then this expression is true for any trajectory, "C", from A to B. The function "U"(x) is called the potential energy associated with the applied force. Examples of forces that have potential energies are gravity and spring forces. In this section the relationship between work and potential energy is presented in more detail. The line integral that defines work along curve "C" takes a special form if the force F is related to a scalar field φ(x) so that In this case, work along the curve is given by which can be evaluated using the gradient theorem to obtain This shows that when forces are derivable from a scalar field, the work of those forces along a curve "C" is computed by evaluating the scalar field at the start point "A" and the end point "B" of the curve. This means the work integral does not depend on the path between "A" and "B" and is said to be independent of the path. Potential energy "U"=-φ(x) is traditionally defined as the negative of this scalar field so that work by the force field decreases potential energy, that is In this case, the application of the del operator to the work function yields, and the force F is said to be "derivable from a potential." This also necessarily implies that F must be a conservative vector field. The potential "U" defines a force F at every point x in space, so the set of forces is called a force field. Given a force field F(x), evaluation of the work integral using the gradient theorem can be used to find the scalar function associated with potential energy. This is done by introducing a parameterized curve γ(t)=r(t) from γ(a)=A to γ(b)=B, and computing, For the force field F, let v= dr/dt, then the gradient theorem yields, The power applied to a body by a force field is obtained from the gradient of the work, or potential, in the direction of the velocity v of the point of application, that is Examples of work that can be computed from potential functions are gravity and spring forces. For small height changes, gravitational potential energy can be computed using where m is the mass in kg, g is the local gravitational field (9.8 metres per second squared on earth), h is the height above a reference level in metres, and U is the energy in joules. In classical physics, gravity exerts a constant downward force F=(0, 0, "F") on the center of mass of a body moving near the surface of the Earth. The work of gravity on a body moving along a trajectory r(t) = ("x"(t), "y"(t), "z"(t)), such as the track of a roller coaster is calculated using its velocity, v=("v", "v", "v"), to obtain where the integral of the vertical component of velocity is the vertical distance. The work of gravity depends only on the vertical movement of the curve r(t). A horizontal spring exerts a force F = (−"kx", 0, 0) that is proportional to its deformation in the axial or "x" direction. The work of this spring on a body moving along the space curve s("t") = ("x"("t"), "y"("t"), "z"("t")), is calculated using its velocity, v = ("v", "v", "v"), to obtain For convenience, consider contact with the spring occurs at "t" = 0, then the integral of the product of the distance "x" and the "x"-velocity, "xv", is "x"/2. The function is called the potential energy of a linear spring. Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology). It arises as a consequence of a force that tries to restore the object to its original shape, which is most often the electromagnetic force between the atoms and molecules that constitute the object. If the stretch is released, the energy is transformed into kinetic energy. The gravitational potential function, also known as gravitational potential energy, is: The negative sign follows the convention that work is gained from a loss of potential energy. The gravitational force between two bodies of mass "M" and "m" separated by a distance "r" is given by Newton's law where formula_19 is a vector of length 1 pointing from "M" to "m" and "G" is the gravitational constant. Let the mass "m" move at the velocity v then the work of gravity on this mass as it moves from position r(t) to r(t) is given by The position and velocity of the mass "m" are given by where e and e are the radial and tangential unit vectors directed relative to the vector from "M" to "m". Use this to simplify the formula for work of gravity to, This calculation uses the fact that The electrostatic force exerted by a charge "Q" on another charge "q" separated by a distance "r" is given by Coulomb's Law where formula_19 is a vector of length 1 pointing from "Q" to "q" and "ε" is the vacuum permittivity. This may also be written using Coulomb constant. The work "W" required to move "q" from "A" to any point "B" in the electrostatic force field is given by the potential function The potential energy is a function of the state a system is in, and is defined relative to that for a particular state. This reference state is not always a real state; it may also be a limit, such as with the distances between all bodies tending to infinity, provided that the energy involved in tending to that limit is finite, such as in the case of inverse-square law forces. Any arbitrary reference state could be used; therefore it can be chosen based on convenience. Typically the potential energy of a system depends on the "relative" positions of its components only, so the reference state can also be expressed in terms of relative positions. Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth's gravity. The potential energy due to elevated positions is called gravitational potential energy, and is evidenced by water in an elevated reservoir or kept behind a dam. If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. Consider a book placed on top of a table. As the book is raised from the floor to the table, some external force works against the gravitational force. If the book falls back to the floor, the "falling" energy the book receives is provided by the gravitational force. Thus, if the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy. When the book hits the floor this kinetic energy is converted into heat, deformation, and sound by the impact. The factors that affect an object's gravitational potential energy are its height relative to some reference point, its mass, and the strength of the gravitational field it is in. Thus, a book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard and less gravitational potential energy than a heavier book lying on the same table. An object at a certain height above the Moon's surface has less gravitational potential energy than at the same height above the Earth's surface because the Moon's gravity is weaker. "Height" in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. The following sections provide more detail. The strength of a gravitational field varies with location. However, when the change of distance is small in relation to the distances from the center of the source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is constant. Near the surface of the Earth, for example, we assume that the acceleration due to gravity is a constant ("standard gravity"). In this case, a simple expression for gravitational potential energy can be derived using the "W" = "Fd" equation for work, and the equation The amount of gravitational potential energy held by an elevated object is equal to the work done against gravity in lifting it. The work done equals the force required to move it upward multiplied with the vertical distance it is moved (remember "W = Fd"). The upward force required while moving at a constant velocity is equal to the weight, "mg", of an object, so the work done in lifting it through a height "h" is the product "mgh". Thus, when accounting only for mass, gravity, and altitude, the equation is: where "U" is the potential energy of the object relative to its being on the Earth's surface, "m" is the mass of the object, "g" is the acceleration due to gravity, and "h" is the altitude of the object. If "m" is expressed in kilograms, "g" in m/s and "h" in metres then "U" will be calculated in joules. Hence, the potential difference is However, over large variations in distance, the approximation that "g" is constant is no longer valid, and we have to use calculus and the general mathematical definition of work to determine gravitational potential energy. For the computation of the potential energy, we can integrate the gravitational force, whose magnitude is given by Newton's law of gravitation, with respect to the distance "r" between the two bodies. Using that definition, the gravitational potential energy of a system of masses "m" and "M" at a distance "r" using gravitational constant "G" is where "K" is an arbitrary constant dependent on the choice of datum from which potential is measured. Choosing the convention that "K"=0 (i.e. in relation to a point at infinity) makes calculations simpler, albeit at the cost of making "U" negative; for why this is physically reasonable, see below. Given this formula for "U", the total potential energy of a system of "n" bodies is found by summing, for all formula_31 pairs of two bodies, the potential energy of the system of those two bodies. Considering the system of bodies as the combined set of small particles the bodies consist of, and applying the previous on the particle level we get the negative gravitational binding energy. This potential energy is more strongly negative than the total potential energy of the system of bodies as such since it also includes the negative gravitational binding energy of each body. The potential energy of the system of bodies as such is the negative of the energy needed to separate the bodies from each other to infinity, while the gravitational binding energy is the energy needed to separate all particles from each other to infinity. therefore, As with all potential energies, only differences in gravitational potential energy matter for most physical purposes, and the choice of zero point is arbitrary. Given that there is no reasonable criterion for preferring one particular finite "r" over another, there seem to be only two reasonable choices for the distance at which "U" becomes zero: formula_34 and formula_35. The choice of formula_36 at infinity may seem peculiar, and the consequence that gravitational energy is always negative may seem counterintuitive, but this choice allows gravitational potential energy values to be finite, albeit negative. The singularity at formula_34 in the formula for gravitational potential energy means that the only other apparently reasonable alternative choice of convention, with formula_36 for formula_34, would result in potential energy being positive, but infinitely large for all nonzero values of "r", and would make calculations involving sums or differences of potential energies beyond what is possible with the real number system. Since physicists abhor infinities in their calculations, and "r" is always non-zero in practice, the choice of formula_36 at infinity is by far the more preferable choice, even if the idea of negative energy in a gravity well appears to be peculiar at first. The negative value for gravitational energy also has deeper implications that make it seem more reasonable in cosmological calculations where the total energy of the universe can meaningfully be considered; see inflation theory for more on this. Gravitational potential energy has a number of practical uses, notably the generation of pumped-storage hydroelectricity. For example, in Dinorwig, Wales, there are two lakes, one at a higher elevation than the other. At times when surplus electricity is not required (and so is comparatively cheap), water is pumped up to the higher lake, thus converting the electrical energy (running the pump) to gravitational potential energy. At times of peak demand for electricity, the water flows back down through electrical generator turbines, converting the potential energy into kinetic energy and then back into electricity. The process is not completely efficient and some of the original energy from the surplus electricity is in fact lost to friction. Gravitational potential energy is also used to power clocks in which falling weights operate the mechanism. It's also used by counterweights for lifting up an elevator, crane, or sash window. Roller coasters are an entertaining way to utilize potential energy – chains are used to move a car up an incline (building up gravitational potential energy), to then have that energy converted into kinetic energy as it falls. Another practical use is utilizing gravitational potential energy to descend (perhaps coast) downhill in transportation such as the descent of an automobile, truck, railroad train, bicycle, airplane, or fluid in a pipeline. In some cases the kinetic energy obtained from the potential energy of descent may be used to start ascending the next grade such as what happens when a road is undulating and has frequent dips. The commercialization of stored energy (in the form of rail cars raised to higher elevations) that is then converted to electrical energy when needed by an electrical grid, is being undertaken in the United States in a system called Advanced Rail Energy Storage (ARES). Chemical potential energy is a form of potential energy related to the structural arrangement of atoms or molecules. This arrangement may be the result of chemical bonds within a molecule or otherwise. Chemical energy of a chemical substance can be transformed to other forms of energy by a chemical reaction. As an example, when a fuel is burned the chemical energy is converted to heat, same is the case with digestion of food metabolized in a biological organism. Green plants transform solar energy to chemical energy through the process known as photosynthesis, and electrical energy can be converted to chemical energy through electrochemical reactions. The similar term chemical potential is used to indicate the potential of a substance to undergo a change of configuration, be it in the form of a chemical reaction, spatial transport, particle exchange with a reservoir, etc. An object can have potential energy by virtue of its electric charge and several forces related to their presence. There are two main types of this kind of potential energy: electrostatic potential energy, electrodynamic potential energy (also sometimes called magnetic potential energy). Electrostatic potential energy between two bodies in space is obtained from the force exerted by a charge "Q" on another charge "q" which is given by where formula_19 is a vector of length 1 pointing from "Q" to "q" and "ε" is the vacuum permittivity. This may also be written using Coulomb's constant. If the electric charge of an object can be assumed to be at rest, then it has potential energy due to its position relative to other charged objects. The electrostatic potential energy is the energy of an electrically charged particle (at rest) in an electric field. It is defined as the work that must be done to move it from an infinite distance away to its present location, adjusted for non-electrical forces on the object. This energy will generally be non-zero if there is another electrically charged object nearby. The work "W" required to move "q" from "A" to any point "B" in the electrostatic force field is given by typically given in "J" for Joules. A related quantity called "electric potential" (commonly denoted with a "V" for voltage) is equal to the electric potential energy per unit charge. The energy of a magnetic moment formula_44 in an externally produced magnetic B-field has potential energy The magnetization in a field is where the integral can be over all space or, equivalently, where is nonzero. Magnetic potential energy is the form of energy related not only to the distance between magnetic materials, but also to the orientation, or alignment, of those materials within the field. For example, the needle of a compass has the lowest magnetic potential energy when it is aligned with the north and south poles of the Earth's magnetic field. If the needle is moved by an outside force, torque is exerted on the magnetic dipole of the needle by the Earth's magnetic field, causing it to move back into alignment. The magnetic potential energy of the needle is highest when its field is in the same direction as the Earth's magnetic field. Two magnets will have potential energy in relation to each other and the distance between them, but this also depends on their orientation. If the opposite poles are held apart, the potential energy will be higher the further they are apart and lower the closer they are. Conversely, like poles will have the highest potential energy when forced together, and the lowest when they spring apart. Nuclear potential energy is the potential energy of the particles inside an atomic nucleus. The nuclear particles are bound together by the strong nuclear force. Weak nuclear forces provide the potential energy for certain kinds of radioactive decay, such as beta decay. Nuclear particles like protons and neutrons are not destroyed in fission and fusion processes, but collections of them can have less mass than if they were individually free, in which case this mass difference can be liberated as heat and radiation in nuclear reactions (the heat and radiation have the missing mass, but it often escapes from the system, where it is not measured). The energy from the Sun is an example of this form of energy conversion. In the Sun, the process of hydrogen fusion converts about 4 million tonnes of solar matter per second into electromagnetic energy, which is radiated into space. Potential energy is closely linked with forces. If the work done by a force on a body that moves from "A" to "B" does not depend on the path between these points, then the work of this force measured from "A" assigns a scalar value to every other point in space and defines a scalar potential field. In this case, the force can be defined as the negative of the vector gradient of the potential field. For example, gravity is a conservative force. The associated potential is the gravitational potential, often denoted by formula_47 or formula_48, corresponding to the energy per unit mass as a function of position. The gravitational potential energy of two particles of mass "M" and "m" separated by a distance "r" is The gravitational potential (specific energy) of the two bodies is where formula_51 is the reduced mass. The work done against gravity by moving an infinitesimal mass from point A with formula_52 to point B with formula_53 is formula_54 and the work done going back the other way is formula_55 so that the total work done in moving from A to B and returning to A is If the potential is redefined at A to be formula_57 and the potential at B to be formula_58, where formula_59 is a constant (i.e. formula_59 can be any number, positive or negative, but it must be the same at A as it is at B) then the work done going from A to B is as before. In practical terms, this means that one can set the zero of formula_62 and formula_47 anywhere one likes. One may set it to be zero at the surface of the Earth, or may find it more convenient to set zero at infinity (as in the expressions given earlier in this section). A conservative force can be expressed in the language of differential geometry as a closed form. As Euclidean space is contractible, its de Rham cohomology vanishes, so every closed form is also an exact form, and can be expressed as the gradient of a scalar field. This gives a mathematical justification of the fact that all conservative forces are gradients of a potential field.

In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

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summarize: The adjective "kinetic" has its roots in the Greek word κίνησις "kinesis", meaning "motion". The dichotomy between kinetic energy and potential energy can be traced back to Aristotle's concepts of actuality and potentiality. The principle in classical mechanics that "E ∝ mv" was first developed by Gottfried Leibniz and Johann Bernoulli, who described kinetic energy as the "living force", "vis viva". Willem's Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Willem's Gravesande determined that their penetration depth was proportional to the square of their impact speed. Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms "kinetic energy" and "work" in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled "Du Calcul de l'Effet des Machines" outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term "kinetic energy" c. 1849–51. Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two main classes: potential energy and kinetic energy. Kinetic energy is the movement energy of an object. Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to and from other forms of energy. For example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance and friction. The chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms. For example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely been converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling. The energy is not destroyed; it has only been converted to another form by friction. Alternatively, the cyclist could connect a dynamo to one of the wheels and generate some electrical energy on the descent. The bicycle would be traveling slower at the bottom of the hill than without the generator because some of the energy has been diverted into electrical energy. Another possibility would be for the cyclist to apply the brakes, in which case the kinetic energy would be dissipated through friction as heat. Like any physical quantity that is a function of velocity, the kinetic energy of an object depends on the relationship between the object and the observer's frame of reference. Thus, the kinetic energy of an object is not invariant. Spacecraft use chemical energy to launch and gain considerable kinetic energy to reach orbital velocity. In an entirely circular orbit, this kinetic energy remains constant because there is almost no friction in near-earth space. However, it becomes apparent at re-entry when some of the kinetic energy is converted to heat. If the orbit is elliptical or hyperbolic, then throughout the orbit kinetic and potential energy are exchanged; kinetic energy is greatest and potential energy lowest at closest approach to the earth or other massive body, while potential energy is greatest and kinetic energy the lowest at maximum distance. Without loss or gain, however, the sum of the kinetic and potential energy remains constant. Kinetic energy can be passed from one object to another. In the game of billiards, the player imposes kinetic energy on the cue ball by striking it with the cue stick. If the cue ball collides with another ball, it slows down dramatically, and the ball it hit accelerates its speed as the kinetic energy is passed on to it. Collisions in billiards are effectively elastic collisions, in which kinetic energy is preserved. In inelastic collisions, kinetic energy is dissipated in various forms of energy, such as heat, sound, binding energy (breaking bound structures). Flywheels have been developed as a method of energy storage. This illustrates that kinetic energy is also stored in rotational motion. Several mathematical descriptions of kinetic energy exist that describe it in the appropriate physical situation. For objects and processes in common human experience, the formula 1⁄2mv2 given by Newtonian (classical) mechanics is suitable. However, if the speed of the object is comparable to the speed of light, relativistic effects become significant and the relativistic formula is used. If the object is on the atomic or sub-atomic scale, quantum mechanical effects are significant, and a quantum mechanical model must be employed. In classical mechanics, the kinetic energy of a "point object" (an object so small that its mass can be assumed to exist at one point), or a non-rotating rigid body depends on the mass of the body as well as its speed. The kinetic energy is equal to 1/2 the product of the mass and the square of the speed. In formula form: where formula_2 is the mass and formula_3 is the speed (or the velocity) of the body. In SI units, mass is measured in kilograms, speed in metres per second, and the resulting kinetic energy is in joules. For example, one would calculate the kinetic energy of an 80 kg mass (about 180 lbs) traveling at 18 metres per second (about 40 mph, or 65 km/h) as When a person throws a ball, the person does work on it to give it speed as it leaves the hand. The moving ball can then hit something and push it, doing work on what it hits. The kinetic energy of a moving object is equal to the work required to bring it from rest to that speed, or the work the object can do while being brought to rest: net force × displacement = kinetic energy, i.e., Since the kinetic energy increases with the square of the speed, an object doubling its speed has four times as much kinetic energy. For example, a car traveling twice as fast as another requires four times as much distance to stop, assuming a constant braking force. As a consequence of this quadrupling, it takes four times the work to double the speed. The kinetic energy of an object is related to its momentum by the equation: where: For the "translational kinetic energy," that is the kinetic energy associated with rectilinear motion, of a rigid body with constant mass formula_8, whose center of mass is moving in a straight line with speed formula_10, as seen above is equal to where: The kinetic energy of any entity depends on the reference frame in which it is measured. However the total energy of an isolated system, i.e. one in which energy can neither enter nor leave, does not change over time in the reference frame in which it is measured. Thus, the chemical energy converted to kinetic energy by a rocket engine is divided differently between the rocket ship and its exhaust stream depending upon the chosen reference frame. This is called the Oberth effect. But the total energy of the system, including kinetic energy, fuel chemical energy, heat, etc., is conserved over time, regardless of the choice of reference frame. Different observers moving with different reference frames would however disagree on the value of this conserved energy. The kinetic energy of such systems depends on the choice of reference frame: the reference frame that gives the minimum value of that energy is the center of momentum frame, i.e. the reference frame in which the total momentum of the system is zero. This minimum kinetic energy contributes to the invariant mass of the system as a whole. The work done in accelerating a particle with mass "m" during the infinitesimal time interval "dt" is given by the dot product of "force" F and the infinitesimal "displacement "dx" where we have assumed the relationship p = "m" v and the validity of Newton's Second Law. (However, also see the special relativistic derivation below.) Applying the product rule we see that: Therefore, (assuming constant mass so that "dm" = 0), we have, Since this is a total differential (that is, it only depends on the final state, not how the particle got there), we can integrate it and call the result kinetic energy. Assuming the object was at rest at time 0, we integrate from time 0 to time t because the work done by the force to bring the object from rest to velocity "v" is equal to the work necessary to do the reverse: This equation states that the kinetic energy ("E") is equal to the integral of the dot product of the velocity (v) of a body and the infinitesimal change of the body's momentum (p). It is assumed that the body starts with no kinetic energy when it is at rest (motionless). If a rigid body Q is rotating about any line through the center of mass then it has "rotational kinetic energy" (formula_18) which is simply the sum of the kinetic energies of its moving parts, and is thus given by: where: (In this equation the moment of inertia must be taken about an axis through the center of mass and the rotation measured by ω must be around that axis; more general equations exist for systems where the object is subject to wobble due to its eccentric shape). A system of bodies may have internal kinetic energy due to the relative motion of the bodies in the system. For example, in the Solar System the planets and planetoids are orbiting the Sun. In a tank of gas, the molecules are moving in all directions. The kinetic energy of the system is the sum of the kinetic energies of the bodies it contains. A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin. These all contribute to the body's mass, as provided by the special theory of relativity. When discussing movements of a macroscopic body, the kinetic energy referred to is usually that of the macroscopic movement only. However all internal energies of all types contribute to body's mass, inertia, and total energy. In fluid dynamics, the kinetic energy per unit volume at each point in an incompressible fluid flow field is called the dynamic pressure at that point. Dividing by V, the unit of volume: where formula_24 is the dynamic pressure, and ρ is the density of the incompressible fluid. The speed, and thus the kinetic energy of a single object is frame-dependent (relative): it can take any non-negative value, by choosing a suitable inertial frame of reference. For example, a bullet passing an observer has kinetic energy in the reference frame of this observer. The same bullet is stationary to an observer moving with the same velocity as the bullet, and so has zero kinetic energy. By contrast, the total kinetic energy of a system of objects cannot be reduced to zero by a suitable choice of the inertial reference frame, unless all the objects have the same velocity. In any other case, the total kinetic energy has a non-zero minimum, as no inertial reference frame can be chosen in which all the objects are stationary. This minimum kinetic energy contributes to the system's invariant mass, which is independent of the reference frame. The total kinetic energy of a system depends on the inertial frame of reference: it is the sum of the total kinetic energy in a center of momentum frame and the kinetic energy the total mass would have if it were concentrated in the center of mass. This may be simply shown: let formula_25 be the relative velocity of the center of mass frame "i" in the frame "k". Since Then, However, let formula_28 the kinetic energy in the center of mass frame, formula_29 would be simply the total momentum that is by definition zero in the center of mass frame, and let the total mass: formula_30. Substituting, we get: Thus the kinetic energy of a system is lowest to center of momentum reference frames, i.e., frames of reference in which the center of mass is stationary (either the center of mass frame or any other center of momentum frame). In any different frame of reference, there is additional kinetic energy corresponding to the total mass moving at the speed of the center of mass. The kinetic energy of the system in the center of momentum frame is a quantity that is invariant (all observers see it to be the same). It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass (rotational energy): where: Thus the kinetic energy of a tennis ball in flight is the kinetic energy due to its rotation, plus the kinetic energy due to its translation. If a body's speed is a significant fraction of the speed of light, it is necessary to use relativistic mechanics to calculate its kinetic energy. In special relativity theory, the expression for linear momentum is modified. With "m" being an object's rest mass, v and "v" its velocity and speed, and "c" the speed of light in vacuum, we use the expression for linear momentum formula_33, where formula_34. Integrating by parts yields Since formula_36, formula_38 is a constant of integration for the indefinite integral. Simplifying the expression we obtain formula_38 is found by observing that when formula_41 and formula_42, giving resulting in the formula This formula shows that the work expended accelerating an object from rest approaches infinity as the velocity approaches the speed of light. Thus it is impossible to accelerate an object across this boundary. The mathematical by-product of this calculation is the mass-energy equivalence formula—the body at rest must have energy content At a low speed ("v" ≪ "c"), the relativistic kinetic energy is approximated well by the classical kinetic energy. This is done by binomial approximation or by taking the first two terms of the Taylor expansion for the reciprocal square root: So, the total energy formula_47 can be partitioned into the rest mass energy plus the Newtonian kinetic energy at low speeds. When objects move at a speed much slower than light (e.g. in everyday phenomena on Earth), the first two terms of the series predominate. The next term in the Taylor series approximation is small for low speeds. For example, for a speed of the correction to the Newtonian kinetic energy is 0.0417 J/kg (on a Newtonian kinetic energy of 50 MJ/kg) and for a speed of 100 km/s it is 417 J/kg (on a Newtonian kinetic energy of 5 GJ/kg). The relativistic relation between kinetic energy and momentum is given by This can also be expanded as a Taylor series, the first term of which is the simple expression from Newtonian mechanics: This suggests that the formulae for energy and momentum are not special and axiomatic, but concepts emerging from the equivalence of mass and energy and the principles of relativity. Using the convention that where the four-velocity of a particle is and formula_53 is the proper time of the particle, there is also an expression for the kinetic energy of the particle in general relativity. If the particle has momentum as it passes by an observer with four-velocity "u", then the expression for total energy of the particle as observed (measured in a local inertial frame) is and the kinetic energy can be expressed as the total energy minus the rest energy: Consider the case of a metric that is diagonal and spatially isotropic ("g", "g", "g", "g"). Since where "v" is the ordinary velocity measured w.r.t. the coordinate system, we get Solving for "u" gives Thus for a stationary observer ("v" = 0) and thus the kinetic energy takes the form Factoring out the rest energy gives: This expression reduces to the special relativistic case for the flat-space metric where In the Newtonian approximation to general relativity where Φ is the Newtonian gravitational potential. This means clocks run slower and measuring rods are shorter near massive bodies. In quantum mechanics, observables like kinetic energy are represented as operators. For one particle of mass "m", the kinetic energy operator appears as a term in the Hamiltonian and is defined in terms of the more fundamental momentum operator formula_65. The kinetic energy operator in the non-relativistic case can be written as Notice that this can be obtained by replacing formula_67 by formula_65 in the classical expression for kinetic energy in terms of momentum, In the Schrödinger picture, formula_65 takes the form formula_71 where the derivative is taken with respect to position coordinates and hence The expectation value of the electron kinetic energy, formula_73, for a system of "N" electrons described by the wavefunction formula_74 is a sum of 1-electron operator expectation values: where formula_76 is the mass of the electron and formula_77 is the Laplacian operator acting upon the coordinates of the "i" electron and the summation runs over all electrons. The density functional formalism of quantum mechanics requires knowledge of the electron density "only", i.e., it formally does not require knowledge of the wavefunction. Given an electron density formula_78, the exact N-electron kinetic energy functional is unknown; however, for the specific case of a 1-electron system, the kinetic energy can be written as where formula_80 is known as the von Weizsäcker kinetic energy functional.

In physics, the kinetic energy (KE) of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest.

en

86

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summarize: A continuity equation is useful when a "flux" can be defined. To define flux, first there must be a quantity which can flow or move, such as mass, energy, electric charge, momentum, number of molecules, etc. Let be the volume density of this quantity, that is, the amount of per unit volume. The way that this quantity is flowing is described by its flux. The flux of is a vector field, which we denote as j. Here are some examples and properties of flux: The integral form of the continuity equation states that: Mathematically, the integral form of the continuity equation expressing the rate of increase of within a volume is: where In a simple example, could be a building, and could be the number of people in the building. The surface would consist of the walls, doors, roof, and foundation of the building. Then the continuity equation states that the number of people in the building increases when people enter the building (an inward flux through the surface), decreases when people exit the building (an outward flux through the surface), increases when someone in the building gives birth (a source, ), and decreases when someone in the building dies (a sink, ). By the divergence theorem, a general continuity equation can also be written in a "differential form": where This general equation may be used to derive any continuity equation, ranging from as simple as the volume continuity equation to as complicated as the Navier–Stokes equations. This equation also generalizes the advection equation. Other equations in physics, such as Gauss's law of the electric field and Gauss's law for gravity, have a similar mathematical form to the continuity equation, but are not usually referred to by the term "continuity equation", because in those cases does not represent the flow of a real physical quantity. In the case that is a conserved quantity that cannot be created or destroyed (such as energy), and the equations become: In electromagnetic theory, the continuity equation is an empirical law expressing (local) charge conservation. Mathematically it is an automatic consequence of Maxwell's equations, although charge conservation is more fundamental than Maxwell's equations. It states that the divergence of the current density (in amperes per square metre) is equal to the negative rate of change of the charge density (in coulombs per cubic metre), Current is the movement of charge. The continuity equation says that if charge is moving out of a differential volume (i.e. divergence of current density is positive) then the amount of charge within that volume is going to decrease, so the rate of change of charge density is negative. Therefore, the continuity equation amounts to a conservation of charge. If magnetic monopoles exist, there would be a continuity equation for monopole currents as well, see the monopole article for background and the duality between electric and magnetic currents. In fluid dynamics, the continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system plus the accumulation of mass within the system. The differential form of the continuity equation is: where The time derivative can be understood as the accumulation (or loss) of mass in the system, while the divergence term represents the difference in flow in versus flow out. In this context, this equation is also one of the Euler equations (fluid dynamics). The Navier–Stokes equations form a vector continuity equation describing the conservation of linear momentum. If the fluid is incompressible ( is constant, independent of space and time), the mass continuity equation simplifies to a volume continuity equation: which means that the divergence of the velocity field is zero everywhere. Physically, this is equivalent to saying that the local volume dilation rate is zero, hence a flow of water through a converging pipe will adjust solely by increasing its velocity as water is largely incompressible. Conservation of energy says that energy cannot be created or destroyed. (See below for the nuances associated with general relativity.) Therefore, there is a continuity equation for energy flow: where An important practical example is the flow of heat. When heat flows inside a solid, the continuity equation can be combined with Fourier's law (heat flux is proportional to temperature gradient) to arrive at the heat equation. The equation of heat flow may also have source terms: Although "energy" cannot be created or destroyed, "heat" can be created from other types of energy, for example via friction or joule heating. If there is a quantity that moves continuously according to a stochastic (random) process, like the location of a single dissolved molecule with Brownian motion, then there is a continuity equation for its probability distribution. The flux in this case is the probability per unit area per unit time that the particle passes through a surface. According to the continuity equation, the negative divergence of this flux equals the rate of change of the probability density. The continuity equation reflects the fact that the molecule is always somewhere—the integral of its probability distribution is always equal to 1—and that it moves by a continuous motion (no teleporting). Quantum mechanics is another domain where there is a continuity equation related to "conservation of probability". The terms in the equation require the following definitions, and are slightly less obvious than the other examples above, so they are outlined here: With these definitions the continuity equation reads: Either form may be quoted. Intuitively, the above quantities indicate this represents the flow of probability. The "chance" of finding the particle at some position and time flows like a fluid; hence the term "probability current", a vector field. The particle itself does "not" flow deterministically in this vector field. The notation and tools of special relativity, especially 4-vectors and 4-gradients, offer a convenient way to write any continuity equation. The density of a quantity and its current can be combined into a 4-vector called a 4-current: where is the speed of light. The 4-divergence of this current is: where is the 4-gradient and is an index labelling the spacetime dimension. Then the continuity equation is: in the usual case where there are no sources or sinks, that is, for perfectly conserved quantities like energy or charge. This continuity equation is manifestly ("obviously") Lorentz invariant. Examples of continuity equations often written in this form include electric charge conservation where is the electric 4-current; and energy-momentum conservation where is the stress-energy tensor. In general relativity, where spacetime is curved, the continuity equation (in differential form) for energy, charge, or other conserved quantities involves the "covariant" divergence instead of the ordinary divergence. For example, the stress–energy tensor is a second-order tensor field containing energy–momentum densities, energy–momentum fluxes, and shear stresses, of a mass-energy distribution. The differential form of energy-momentum conservation in general relativity states that the "covariant" divergence of the stress-energy tensor is zero: This is an important constraint on the form the Einstein field equations take in general relativity. However, the "ordinary" divergence of the stress-energy tensor does "not" necessarily vanish: The right-hand side strictly vanishes for a flat geometry only. As a consequence, the "integral" form of the continuity equation is difficult to define and not necessarily valid for a region within which spacetime is significantly curved (e.g. around a black hole, or across the whole universe). Quarks and gluons have "color charge", which is always conserved like electric charge, and there is a continuity equation for such color charge currents (explicit expressions for currents are given at gluon field strength tensor). There are many other quantities in particle physics which are often or always conserved: baryon number (proportional to the number of quarks minus the number of antiquarks), electron number, mu number, tau number, isospin, and others. Each of these has a corresponding continuity equation, possibly including source / sink terms. One reason that conservation equations frequently occur in physics is Noether's theorem. This states that whenever the laws of physics have a continuous symmetry, there is a continuity equation for some conserved physical quantity. The three most famous examples are: See Noether's theorem for proofs and details.

A continuity equation in physics is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations.

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summarize: The word "lever" entered English about 1300 from Old French, in which the word was "levier". This sprang from the stem of the verb "lever", meaning "to raise". The verb, in turn, goes back to the Latin "levare", itself from the adjective "levis", meaning "light" (as in "not heavy"). The word's primary origin is the Proto-Indo-European (PIE) stem "legwh-", meaning "light", "easy" or "nimble", among other things. The PIE stem also gave rise to the English word "light". The earliest evidence of the lever mechanism dates back to the ancient Near East circa 5000 BC, when it was first used in a simple balance scale. In ancient Egypt circa 4400 BC, a foot pedal was used for the earliest horizontal frame loom. In Mesopotamia (modern Iraq) circa 3000 BC, the shadouf, a crane-like device that uses a lever mechanism, was invented. In ancient Egypt technology, workmen used the lever to move and uplift obelisks weighing more than 100 tons. This is evident from the recesses in the large blocks and the handling bosses which could not be used for any purpose other than for levers. The earliest remaining writings regarding levers date from the 3rd century BCE and were provided by Archimedes. He stated, 'Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.' A lever is a beam connected to ground by a hinge, or pivot, called a fulcrum. The ideal lever does not dissipate or store energy, which means there is no friction in the hinge or bending in the beam. In this case, the power into the lever equals the power out, and the ratio of output to input force is given by the ratio of the distances from the fulcrum to the points of application of these forces. This is known as the "law of the lever." The mechanical advantage of a lever can be determined by considering the balance of moments or torque, "T", about the fulcrum. If the distance traveled is greater, then the output force is lessened. where F is the input force to the lever and F is the output force. The distances "a" and "b" are the perpendicular distances between the forces and the fulcrum. Since the moments of torque must be balanced, formula_3. So, formula_4. The mechanical advantage of the lever is the ratio of output force to input force, This relationship shows that the mechanical advantage can be computed from ratio of the distances from the fulcrum to where the input and output forces are applied to the lever, assuming no losses due to friction, flexibility or wear. This remains true even though the "horizontal" distance (perpendicular to the pull of gravity) of both "a" and "b" change (diminish) as the lever changes to any position away from the horizontal. Levers are classified by the relative positions of the fulcrum, effort and resistance (or load). It is common to call the input force "the effort" and the output force "the load" or "the resistance." This allows the identification of three classes of levers by the relative locations of the fulcrum, the resistance and the effort: These cases are described by the mnemonic "fre 123" where the "f" fulcrum is between "r" and "e" for the 1st class lever, the "r" resistance is between "f" and "e" for the 2nd class lever, and the "e" effort is between "f" and "r" for the 3rd class lever. A compound lever comprises several levers acting in series: the resistance from one lever in a system of levers acts as effort for the next, and thus the applied force is transferred from one lever to the next. Examples of compound levers include scales, nail clippers and piano keys. The lever is a movable bar that pivots on a fulcrum attached to a fixed point. The lever operates by applying forces at different distances from the fulcrum, or a pivot. Assuming the lever does not dissipate or store energy, the power into the lever must equal the power out of the lever. As the lever rotates around the fulcrum, points farther from this pivot move faster than points closer to the pivot. Therefore, a force applied to a point farther from the pivot must be less than the force located at a point closer in, because power is the product of force and velocity. If "a" and "b" are distances from the fulcrum to points "A" and "B" and the force "F" applied to "A" is the input and the force "F" applied at "B" is the output, the ratio of the velocities of points "A" and "B" is given by "a/b", so we have the ratio of the output force to the input force, or mechanical advantage, is given by This is the "law of the lever", which was proven by Archimedes using geometric reasoning. It shows that if the distance "a" from the fulcrum to where the input force is applied (point "A") is greater than the distance "b" from fulcrum to where the output force is applied (point "B"), then the lever amplifies the input force. On the other hand, if the distance "a" from the fulcrum to the input force is less than the distance "b" from the fulcrum to the output force, then the lever reduces the input force. The use of velocity in the static analysis of a lever is an application of the principle of virtual work. A lever is modeled as a rigid bar connected to a ground frame by a hinged joint called a fulcrum. The lever is operated by applying an input force F at a point "A" located by the coordinate vector r on the bar. The lever then exerts an output force F at the point "B" located by r. The rotation of the lever about the fulcrum "P" is defined by the rotation angle "θ" in radians. Let the coordinate vector of the point "P" that defines the fulcrum be r, and introduce the lengths which are the distances from the fulcrum to the input point "A" and to the output point "B", respectively. Now introduce the unit vectors e and e from the fulcrum to the point "A" and "B", so The velocity of the points "A" and "B" are obtained as where e and e are unit vectors perpendicular to e and e, respectively. The angle "θ" is the generalized coordinate that defines the configuration of the lever, and the generalized force associated with this coordinate is given by where "F" and "F" are components of the forces that are perpendicular to the radial segments "PA" and "PB". The principle of virtual work states that at equilibrium the generalized force is zero, that is Thus, the ratio of the output force "F" to the input force "F" is obtained as which is the mechanical advantage of the lever. This equation shows that if the distance "a" from the fulcrum to the point "A" where the input force is applied is greater than the distance "b" from fulcrum to the point "B" where the output force is applied, then the lever amplifies the input force. If the opposite is true that the distance from the fulcrum to the input point "A" is less than from the fulcrum to the output point "B", then the lever reduces the magnitude of the input force.

A lever ( or ) is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or fulcrum. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is divided into three types. It is one of the six simple machines identified by Renaissance scientists. A lever amplifies an input force to provide a greater output force, which is said to provide leverage. The ratio of the output force to the input force is the mechanical advantage of the lever. As such, the lever is a mechanical advantage device, trading off force against movement.

en

129

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summarize: Examples of drag include the component of the net aerodynamic or hydrodynamic force acting opposite to the direction of movement of a solid object such as cars, aircraft and boat hulls; or acting in the same geographical direction of motion as the solid, as for sails attached to a down wind sail boat, or in intermediate directions on a sail depending on points of sail. In the case of viscous drag of fluid in a pipe, drag force on the immobile pipe decreases fluid velocity relative to the pipe. In the physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. Types of drag are generally divided into the following categories: The phrase "parasitic drag" is mainly used in aerodynamics, since for lifting wings, drag is generally small compared to lift. For flow around bluff bodies, form drag and skin friction drag dominate, and then the qualifier "parasitic" is meaningless. Further, lift-induced drag is only relevant when wings or a lifting body are present, and is therefore usually discussed either in aviation or in the design of semi-planing or planing hulls. Wave drag occurs either when a solid object is moving through a gas at or near the speed of sound or when a solid object is moving along a fluid boundary, as in surface waves. Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation: where The drag coefficient depends on the shape of the object and on the Reynolds number where "formula_8" is some characteristic diameter or linear dimension and formula_9 is the kinematic viscosity of the fluid (equal to the viscosity formula_10 divided by the density formula_11). At low formula_12, formula_6 is asymptotically proportional to formula_14, which means that the drag is linearly proportional to the speed. At high formula_12, formula_6 is more or less constant and drag will vary as the square of the speed. The graph to the right shows how formula_6 varies with formula_12 for the case of a sphere. Since the power needed to overcome the drag force is the product of the force times speed, the power needed to overcome drag will vary as the square of the speed at low Reynolds numbers and as the cube of the speed at high numbers. It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the Bejan number. Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of drag force it has been obtained: formula_19 and consequently allows expressing the drag coefficient formula_6as a function of Bejan number and the ratio between wet area formula_21and front area formula_22: formula_23 where formula_24is the Reynold Number related to fluid path length L. As mentioned, the drag equation with a constant drag coefficient gives the force experienced by an object moving through a fluid at relatively large velocity (i.e. high Reynolds number, Re > ~1000). This is also called "quadratic drag". The equation is attributed to Lord Rayleigh, who originally used "L" in place of "A" ("L" being some length). The reference area "A" is often orthographic projection of the object (frontal area)—on a plane perpendicular to the direction of motion—e.g. for objects with a simple shape, such as a sphere, this is the cross sectional area. Sometimes a body is a composite of different parts, each with a different reference areas, in which case a drag coefficient corresponding to each of those different areas must be determined. In the case of a wing the reference areas are the same and the drag force is in the same ratio to the lift force as the ratio of drag coefficient to lift coefficient. Therefore, the reference for a wing is often the lifting area ("wing area") rather than the frontal area. For an object with a smooth surface, and non-fixed separation points—like a sphere or circular cylinder—the drag coefficient may vary with Reynolds number "R", even up to very high values ("R" of the order 10). For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for "R" > 3,500. Further the drag coefficient "C" is, in general, a function of the orientation of the flow with respect to the object (apart from symmetrical objects like a sphere). Under the assumption that the fluid is not moving relative to the currently used reference system, the power required to overcome the aerodynamic drag is given by: Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at may require only to overcome aerodynamic drag, but that same car at requires. With a doubling of speed the drag (force) quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, 4 times the work done in half the time requires 8 times the power. When the fluid is moving relative to the reference system (e.g. a car driving into headwind) the power required to overcome the aerodynamic drag is given by: Where formula_28 is the wind speed and formula_29 is the object speed (both relative to ground). The velocity as a function of time for an object falling through a non-dense medium, and released at zero relative-velocity "v" = 0 at time "t" = 0, is roughly given by a function involving a hyperbolic tangent (tanh): The hyperbolic tangent has a limit value of one, for large time "t". In other words, velocity asymptotically approaches a maximum value called the terminal velocity "v": For an object falling and released at relative-velocity "v" = v at time "t" = 0, with v ≤ v, is also defined in terms of the hyperbolic tangent function: Actually, this function is defined by the solution of the following differential equation: Or, more generically (where F(v) are the forces acting on the object beyond drag): For a potato-shaped object of average diameter "d" and of density "ρ", terminal velocity is about For objects of water-like density (raindrops, hail, live objects—mammals, birds, insects, etc.) falling in air near Earth's surface at sea level, the terminal velocity is roughly equal to with "d" in metre and "v" in m/s. For example, for a human body (formula_37 ~ 0.6 m) formula_38 ~ 70 m/s, for a small animal like a cat (formula_37 ~ 0.2 m) formula_38 ~ 40 m/s, for a small bird (formula_37 ~ 0.05 m) formula_38 ~ 20 m/s, for an insect (formula_37 ~ 0.01 m) formula_38 ~ 9 m/s, and so on. Terminal velocity for very small objects (pollen, etc.) at low Reynolds numbers is determined by Stokes law. Terminal velocity is higher for larger creatures, and thus potentially more deadly. A creature such as a mouse falling at its terminal velocity is much more likely to survive impact with the ground than a human falling at its terminal velocity. A small animal such as a cricket impacting at its terminal velocity will probably be unharmed. This, combined with the relative ratio of limb cross-sectional area vs. body mass (commonly referred to as the Square-cube law), explains why very small animals can fall from a large height and not be harmed. The equation for viscous resistance or linear drag is appropriate for objects or particles moving through a fluid at relatively slow speeds where there is no turbulence (i.e. low Reynolds number, formula_45). Note that purely laminar flow only exists up to Re = 0.1 under this definition. In this case, the force of drag is approximately proportional to velocity. The equation for viscous resistance is: where: When an object falls from rest, its velocity will be which asymptotically approaches the terminal velocity formula_50. For a given formula_47, heavier objects fall more quickly. For the special case of small spherical objects moving slowly through a viscous fluid (and thus at small Reynolds number), George Gabriel Stokes derived an expression for the drag constant: where: The resulting expression for the drag is known as Stokes' drag: For example, consider a small sphere with radius formula_53 = 0.5 micrometre (diameter = 1.0 μm) moving through water at a velocity formula_57 of 10 μm/s. Using 10 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water. In aerodynamics, aerodynamic drag is the fluid drag force that acts on any moving solid body in the direction of the fluid freestream flow. From the body's perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized formula_58, and forces due to skin friction, which is a result of viscosity, denoted formula_59. Alternatively, calculated from the flowfield perspective (far-field approach), the drag force results from three natural phenomena: shock waves, vortex sheet, and viscosity. The pressure distribution acting on a body's surface exerts normal forces on the body. Those forces can be summed and the component of that force that acts downstream represents the drag force, formula_58, due to pressure distribution acting on the body. The nature of these normal forces combines shock wave effects, vortex system generation effects, and wake viscous mechanisms. The viscosity of the fluid has a major effect on drag. In the absence of viscosity, the pressure forces acting to retard the vehicle are canceled by a pressure force further aft that acts to push the vehicle forward; this is called pressure recovery and the result is that the drag is zero. That is to say, the work the body does on the airflow, is reversible and is recovered as there are no frictional effects to convert the flow energy into heat. Pressure recovery acts even in the case of viscous flow. Viscosity, however results in pressure drag and it is the dominant component of drag in the case of vehicles with regions of separated flow, in which the pressure recovery is fairly ineffective. The friction drag force, which is a tangential force on the aircraft surface, depends substantially on boundary layer configuration and viscosity. The net friction drag, formula_61, is calculated as the downstream projection of the viscous forces evaluated over the body's surface. The sum of friction drag and pressure (form) drag is called viscous drag. This drag component is due to viscosity. In a thermodynamic perspective, viscous effects represent irreversible phenomena and, therefore, they create entropy. The calculated viscous drag formula_62 use entropy changes to accurately predict the drag force. When the airplane produces lift, another drag component results. Induced drag, symbolized formula_63, is due to a modification of the pressure distribution due to the trailing vortex system that accompanies the lift production. An alternative perspective on lift and drag is gained from considering the change of momentum of the airflow. The wing intercepts the airflow and forces the flow to move downward. This results in an equal and opposite force acting upward on the wing which is the lift force. The change of momentum of the airflow downward results in a reduction of the rearward momentum of the flow which is the result of a force acting forward on the airflow and applied by the wing to the air flow; an equal but opposite force acts on the wing rearward which is the induced drag. Induced drag tends to be the most important component for airplanes during take-off or landing flight. Another drag component, namely wave drag, formula_64, results from shock waves in transonic and supersonic flight speeds. The shock waves induce changes in the boundary layer and pressure distribution over the body surface. The idea that a moving body passing through air or another fluid encounters resistance had been known since the time of Aristotle. Louis Charles Breguet's paper of 1922 began efforts to reduce drag by streamlining. Breguet went on to put his ideas into practice by designing several record-breaking aircraft in the 1920s and 1930s. Ludwig Prandtl's boundary layer theory in the 1920s provided the impetus to minimise skin friction. A further major call for streamlining was made by Sir Melvill Jones who provided the theoretical concepts to demonstrate emphatically the importance of streamlining in aircraft design. In 1929 his paper ‘The Streamline Airplane’ presented to the Royal Aeronautical Society was seminal. He proposed an ideal aircraft that would have minimal drag which led to the concepts of a 'clean' monoplane and retractable undercarriage. The aspect of Jones's paper that most shocked the designers of the time was his plot of the horse power required versus velocity, for an actual and an ideal plane. By looking at a data point for a given aircraft and extrapolating it horizontally to the ideal curve, the velocity gain for the same power can be seen. When Jones finished his presentation, a member of the audience described the results as being of the same level of importance as the Carnot cycle in thermodynamics. Lift-induced drag (also called induced drag) is drag which occurs as the result of the creation of lift on a three-dimensional lifting body, such as the wing or fuselage of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices (vortex drag); and the presence of additional viscous drag (lift-induced viscous drag) that is not present when lift is zero. The trailing vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air from above and below the body which flows in slightly different directions as a consequence of creation of lift. With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. This means that as the wing's angle of attack increases (up to a maximum called the stalling angle), the lift coefficient also increases, and so too does the lift-induced drag. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow in the wake behind the body. Parasitic drag is drag caused by moving a solid object through a fluid. Parasitic drag is made up of multiple components including viscous pressure drag (form drag), and drag due to surface roughness (skin friction drag). Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag, which is sometimes described as a component of parasitic drag. In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the angle of attack can be reduced and the induced drag decreases. Parasitic drag, however, increases because the fluid is flowing more quickly around protruding objects increasing friction or drag. At even higher speeds (transonic), wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance (minimum fuel consumption), or maximize gliding range in the event of an engine failure. The interaction of parasitic and induced drag "vs." airspeed can be plotted as a characteristic curve, illustrated here. In aviation, this is often referred to as the "power curve", and is important to pilots because it shows that, below a certain airspeed, maintaining airspeed counterintuitively requires "more" thrust as speed decreases, rather than less. The consequences of being "behind the curve" in flight are important and are taught as part of pilot training. At the subsonic airspeeds where the "U" shape of this curve is significant, wave drag has not yet become a factor, and so it is not shown in the curve. Wave drag (also called compressibility drag) is drag that is created when a body moves in a compressible fluid and at speeds that are close to the speed of sound in that fluid. In aerodynamics, wave drag consists of multiple components depending on the speed regime of the flight. In transonic flight (Mach numbers greater than about 0.8 and less than about 1.4), wave drag is the result of the formation of shockwaves in the fluid, formed when local areas of supersonic (Mach number greater than 1.0) flow are created. In practice, supersonic flow occurs on bodies traveling well below the speed of sound, as the local speed of air increases as it accelerates over the body to speeds above Mach 1.0. However, full supersonic flow over the vehicle will not develop until well past Mach 1.0. Aircraft flying at transonic speed often incur wave drag through the normal course of operation. In transonic flight, wave drag is commonly referred to as transonic compressibility drag. Transonic compressibility drag increases significantly as the speed of flight increases towards Mach 1.0, dominating other forms of drag at those speeds. In supersonic flight (Mach numbers greater than 1.0), wave drag is the result of shockwaves present in the fluid and attached to the body, typically oblique shockwaves formed at the leading and trailing edges of the body. In highly supersonic flows, or in bodies with turning angles sufficiently large, unattached shockwaves, or bow waves will instead form. Additionally, local areas of transonic flow behind the initial shockwave may occur at lower supersonic speeds, and can lead to the development of additional, smaller shockwaves present on the surfaces of other lifting bodies, similar to those found in transonic flows. In supersonic flow regimes, wave drag is commonly separated into two components, supersonic lift-dependent wave drag and supersonic volume-dependent wave drag. The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the Sears-Haack Distribution. Similarly, for a fixed volume, the shape for minimum wave drag is the Von Karman Ogive. The Busemann biplane is not, in principle, subject to wave drag when operated at its design speed, but is incapable of generating lift in this condition. In 1752 d'Alembert proved that potential flow, the 18th century state-of-the-art inviscid flow theory amenable to mathematical solutions, resulted in the prediction of zero drag. This was in contradiction with experimental evidence, and became known as d'Alembert's paradox. In the 19th century the Navier–Stokes equations for the description of viscous flow were developed by Saint-Venant, Navier and Stokes. Stokes derived the drag around a sphere at very low Reynolds numbers, the result of which is called Stokes' law. In the limit of high Reynolds numbers, the Navier–Stokes equations approach the inviscid Euler equations, of which the potential-flow solutions considered by d'Alembert are solutions. However, all experiments at high Reynolds numbers showed there is drag. Attempts to construct inviscid steady flow solutions to the Euler equations, other than the potential flow solutions, did not result in realistic results. The notion of boundary layers—introduced by Prandtl in 1904, founded on both theory and experiments—explained the causes of drag at high Reynolds numbers. The boundary layer is the thin layer of fluid close to the object's boundary, where viscous effects remain important even when the viscosity is very small (or equivalently the Reynolds number is very large).

In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity. Drag force is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity.

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summarize: The Halaf culture of 6500–5100 BCE has been credited with the earliest depiction of a wheeled vehicle, but this is doubtful as there is no evidence of Halafians using either wheeled vehicles or even pottery wheels. One of the first applications of the wheel to appear was the potter's wheel, used by prehistoric cultures to fabricate clay pots. The earliest type, known as "tournettes" or "slow wheels", were known in the Middle East by the 5th millennium BCE. One of the earliest examples was discovered at Tepe Pardis, Iran, and dated to 5200–4700 BCE. These were made of stone or clay and secured to the ground with a peg in the center, but required significant effort to turn. True potter's wheels, which are freely-spinning and have a wheel and axle mechanism, were developed in Mesopotamia (Iraq) by 4200–4000 BCE. The oldest surviving example, which was found in Ur (modern day Iraq), dates to approximately 3100 BCE. Evidence of wheeled vehicles appeared by the late 4th millennium BCE. Depictions of wheeled wagons found on clay tablet pictographs at the Eanna district of Uruk, in the Sumerian civilization of Mesopotamia, are dated between 3700–3500 BCE. In the second half of the 4th millennium BCE, evidence of wheeled vehicles appeared near-simultaneously in the Northern Caucasus (Maykop culture) and Eastern Europe (Cucuteni–Trypillian culture). Depictions of a wheeled vehicle appeared between 3500 and 3350 BCE in the Bronocice clay pot excavated in a Funnelbeaker culture settlement in southern Poland. In nearby Olszanica, a 2.2 m wide door was constructed (2.2 wide doors were constructed) for wagon entry; this barn was 40 m long and had 3 doors. Surviving evidence of a wheel–axle combination, from Stare Gmajne near Ljubljana in Slovenia (Ljubljana Marshes Wooden Wheel), is dated within two standard deviations to 3340–3030 BCE, the axle to 3360–3045 BCE. Two types of early Neolithic European wheel and axle are known; a circumalpine type of wagon construction (the wheel and axle rotate together, as in Ljubljana Marshes Wheel), and that of the Baden culture in Hungary (axle does not rotate). They both are dated to c. 3200–3000 BCE. Historians believe that there was a diffusion of the wheeled vehicle from the Near East to Europe around the mid-4th millennium BCE. An early example of a wooden wheel and its axle was found in 2002 at the Ljubljana Marshes some 20 km south of Ljubljana, the capital of Slovenia. According to radiocarbon dating, it is between 5,100 and 5,350 years old. The wheel was made of ash and oak and had a radius of 70 cm and the axle was 120 cm long and made of oak. In Roman Egypt, Hero of Alexandria identified the wheel and axle as one of the simple machines used to lift weights. This is thought to have been in the form of the windlass which consists of a crank or pulley connected to a cylindrical barrel that provides mechanical advantage to wind up a rope and lift a load such as a bucket from the well. The wheel and axle was identified as one of six simple machines by Renaissance scientists, drawing from Greek texts on technology. The simple machine called a "wheel and axle" refers to the assembly formed by two disks, or cylinders, of different diameters mounted so they rotate together around the same axis.The thin rod which needs to be turned is called the axle and the wider object fixed to the axle, on which we apply force is called the wheel. A tangential force applied to the periphery of the large disk can exert a larger force on a load attached to the axle, achieving mechanical advantage. When used as the wheel of a wheeled vehicle the smaller cylinder is the axle of the wheel, but when used in a windlass, winch, and other similar applications (see medieval mining lift to right) the smaller cylinder may be separate from the axle mounted in the bearings. It cannot be used separately. Assuming the wheel and axle does not dissipate or store energy, that is it has no friction or elasticity, the power input by the force applied to the wheel must equal the power output at the axle. As the wheel and axle system rotates around its bearings, points on the circumference, or edge, of the wheel move faster than points on the circumference, or edge, of the axle. Therefore, a force applied to the edge of the wheel must be less than the force applied to the edge of the axle, because power is the product of force and velocity. Let "a" and "b" be the distances from the center of the bearing to the edges of the wheel "A" and the axle "B." If the input force "F" is applied to the edge of the wheel "A" and the force "F" at the edge of the axle "B" is the output, then the ratio of the velocities of points "A" and "B" is given by "a/b", so the ratio of the output force to the input force, or mechanical advantage, is given by The mechanical advantage of a simple machine like the wheel and axle is computed as the ratio of the resistance to the effort. The larger the ratio the greater the multiplication of force (torque) created or distance achieved. By varying the radii of the axle and/or wheel, any amount of mechanical advantage may be gained. In this manner, the size of the wheel may be increased to an inconvenient extent. In this case a system or combination of wheels (often toothed, that is, gears) are used. As a wheel and axle is a type of lever, a system of wheels and axles is like a compound lever. The mechanical advantage of a wheel and axle with no friction is called the ideal mechanical advantage (IMA). It is calculated with the following formula: All actual wheels have friction, which dissipates some of the power as heat. The actual mechanical advantage (AMA) of a wheel and axle is calculated with the following formula: where Basic Machines and How They Work, United States. Bureau of Naval Personnel, Courier Dover Publications 1965, pp. 3–1 and following preview online

The wheel and axle is a machine consisting of a wheel attached to a smaller axle so that these two parts rotate together in which a force is transferred from one to the other. A hinge or bearing supports the axle, allowing rotation. It can amplify force; a small force applied to the periphery of the large wheel can move a larger load attached to the axle.

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summarize: Perhaps the first example of a wedge is the hand axe, also see biface and Olorgesailie. Wedges have existed for thousands of years, they were first made of simple stone. A hand axe is made by chipping stone, generally flint, to form a bifacial edge, or wedge. A wedge is a simple machine that transforms lateral force and movement of the tool into a transverse splitting force and movement of the workpiece. The available power is limited by the effort of the person using the tool, but because power is the product of force and movement, the wedge amplifies the force by reducing the movement. This amplification, or mechanical advantage is the ratio of the input speed to output speed. For a wedge this is given by 1/tanα, where α is the tip angle. The faces of a wedge are modeled as straight lines to form a sliding or prismatic joint. The origin of the wedge is not known. In ancient Egyptian quarries, bronze wedges were used to break away blocks of stone used in construction. Wooden wedges that swelled after being saturated with water, were also used. Some indigenous peoples of the Americas used antler wedges for splitting and working wood to make canoes, dwellings and other objects. Wedges are used to lift heavy objects, separating them from the surface upon which they rest. Consider a block that is to be lifted by a wedge. As the wedge slides under the block, the block slides up the sloped side of a wedge. This lifts the weight "F" of the block. The horizontal force "F" needed to lift the block is obtained by considering the velocity of the wedge "v" and the velocity of the block "v". If we assume the wedge does not dissipate or store energy, then the power into the wedge equals the power out. or The velocity of the block is related to the velocity of the wedge by the slope of the side of the wedge. If the angle of the wedge is "α" then which means that the mechanical advantage Thus, the smaller the angle "α" the greater the ratio of the lifting force to the applied force on the wedge. This is the mechanical advantage of the wedge. This formula for mechanical advantage applies to cutting edges and splitting operations as well as to lifting. They can also be used to separate objects, such as blocks of cut stone. Splitting mauls and splitting wedges are used to split wood along the grain. A narrow wedge with a relatively long taper used to finely adjust the distance between objects is called a shim, and is commonly used in carpentry. The tips of forks and nails are also wedges, as they split and separate the material into which they are pushed or driven; the shafts may then hold fast due to friction. The blade is a compound inclined plane, consisting of two inclined planes placed so that the planes meet at one edge. When the edge where the two planes meet is pushed into a solid or fluid substance it overcomes the resistance of materials to separate by transferring the force exerted against the material into two opposing forces normal to the faces of the blade. The blade's first known use by humans was the sharp edge of a flint stone that was used to cleave or split animal tissue, e.g. cutting meat. The use of iron or other metals led to the development of knives for those kinds of tasks. The blade of the knife allowed humans to cut meat, fibers, and other plant and animal materials with much less force than it would take to tear them apart by simply pulling with their hands. Other examples are plows, which separate soil particles, scissors which separate fabric, axes which separate wood fibers, and chisels and planes which separate wood. Wedges, saws and chisels can separate thick and hard materials, such as wood, solid stone and hard metals and they do so with much less force, waste of material, and with more precision, than crushing, which is the application of the same force over a wider area of the material to be separated. Other examples of wedges are found in drill bits, which produce circular holes in solids. The two edges of a drill bit are sharpened, at opposing angles, into a point and that edge is wound around the shaft of the drill bit. When the drill bit spins on its axis of rotation, the wedges are forced into the material to be separated. The resulting cut in the material is in the direction of rotation of the drill bit while the helical shape of a bit allows the removal of the cut material. Wedges can also be used to hold objects in place, such as engine parts (poppet valves), bicycle parts (stems and eccentric bottom brackets), and doors. A wedge-type door stop (door wedge) functions largely because of the friction generated between the bottom of the door and the wedge, and the wedge and the floor (or other surface). The mechanical advantage of a wedge can be calculated by dividing the height of the wedge by the wedge's width: The more acute, or narrow, the angle of a wedge, the greater the ratio of the length of its slope to its width, and thus the more mechanical advantage it will yield. A wedge will bind when the wedge included angle is less than the arctangent of the coefficient of friction between the wedge and the material. Therefore, in an elastic material such as wood, friction may bind a narrow wedge more easily than a wide one. This is why the head of a splitting maul has a much wider angle than that of an axe.

A wedge is a triangular shaped tool, and is a portable inclined plane, and one of the six classical simple machines. It can be used to separate two objects or portions of an object, lift up an object, or hold an object in place. It functions by converting a force applied to its blunt end into forces perpendicular (normal) to its inclined surfaces. The mechanical advantage of a wedge is given by the ratio of the length of its slope to its width. Although a short wedge with a wide angle may do a job faster, it requires more force than a long wedge with a narrow angle.

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120

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