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Kinetic energy (also called vis viva, or living force) is energy possessed by a body by virtue of its motion. The kinetic energy of a body is equal to the amount of work needed to establish its velocity and rotation, starting from rest.1 Equations
1.1 Definition
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In words the above equation states that the kinetic energy (Ek) is equal to the integral of the dot product of the velocity (v) of a body and the infinitesimal of the body's momentum (p).
1.2 Newtonian mechanics
For non-relativistic mechanics, the total kinetic energy of a body can be considered as the sum of the body's translational kinetic energy and its rotational energy, or angular kinetic energy:
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where:
- Ek is the total kinetic energy
- Et is the translational kinetic energy
- Er is the rotational kinetic energy
For the translational kinetic energy of a body with mass m, whose centre of mass is moving in a straight line with linear velocity v, we can use the Newtonian approximation:
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Thus, for a speed of 10 m/s the kinetic energy is 50 J/kg, for a speed of 100 m/s it is 5 kJ/kg, etc.
If a body is rotating, its rotational kinetic energy or angular kinetic energy is calculated from:
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where:
1.3 Relativistic mechanics
In Einstein's relativistic mechanics, (used especially for near-light velocities) the kinetic energy of a body is:
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- Ek is the kinetic energy of the body
- v is the velocity of the body
- m is its rest mass
- c is the speed of light in a vacuum.
- γmc2 is the total energy of the body
- mc2 is the rest mass energy (90 petaThis article describes the SI prefix peta . For other meanings, see Peta (disambiguation In physics and mathematics, peta (symbol: P is a prefix in the SI system of units denoting 1015, or 1,000,000,000,000,000. For example: 1 petametre 1015 metres 1 petajoule/kg)
It is an edifying exercise to show that the ratio of this relativistic kinetic energy to the Newtonian kinetic energy given by (1/2)mv2 approaches 1 as v approaches 0, i.e.,
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This can be done by the techniques of first-year calculus.
Relativity theory states that the kinetic energy of an object grows towards infinity as its velocity approaches the speed of light, and thus that it is impossible to accelerate an object to this boundary.
Where gravity is weak, and objects move at much slower velocities than light (e.g. in everyday phenomena on Earth), Newton's formula is an excellent approximation of relativistic kinetic energy.
The next term in the approximation is 0.375 mv4/cē, e.g. for a speed of 10 km/s this is 0.04 J/kg, for a speed of 100 km/s it is 40 J/kg, etc.
2 Heat as kinetic energy
HeatCommonly, heat is estrus, a period of increased sexual drive in female mammals. For the National Basketball Association team, see Miami Heat. For the movie, see Heat (movie). Heat (abbreviated Q also called heat change is the transfer of thermal energy be is a form of energy due to the total kinetic energy of moleculeIn science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. A molecule consists of multiple atoms joined by shared pairs of electrons in a covalent bond''. It may consist of atoms and atomFor alternative meanings see atom (disambiguation). An atom is a microscopic structure found in all ordinary matter around us. Atoms are composed of 3 types of subatomic particles: electrons, which have a negative charge; protons, which have a positive chs of matter. The relationship between heat, temperatureTemperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter. General description The formal properties of temperature are studied in thermodynamics. and kinetic energy of atoms and molecules is the subject of statistical mechanics. Heat is more akin to work in that it represents a change in internal energy. The energy that heat represents specifically refers to the energy associated with the random translational motion of atoms and molecules in some identifiable matter within a system. The conservation of heat and mechanical work form the first law of thermodynamics.
See Boltzmann constant and heat capacity.
