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Kinetic energy

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Kinetic energy (also called vis vis, or living force) is energy possessed by a body by virtue of its motion.


Equations

E k = ∫ v ⋅ d p {\displaystyle E_{k}=\int \mathbf {v} \cdot \mathrm {d} \mathbf {p} }


In words the equation hereabove says 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).

For the non-relativistic translational kinetic energy for a body with mass m, moving in a straight line with velocity v, we can use the Newtonian approximation:

E k = 1 2 m v 2 {\displaystyle E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}}


  • Ek is kinetic energy
  • m is mass of the body
  • v is velocity of the body

If a body is rotating, its rotational kinetic energy equals

E r o t a t i o n = 1 2 I ω 2 {\displaystyle E_{rotation}={\begin{matrix}{\frac {1}{2}}\end{matrix}}I\omega ^{2}} ,

In Einstein's relativistic mechanics, (used especially for near-light velocities) the kinetic energy of a body is:

E k = m c 2 ( γ − 1 ) = γ m c 2 − m c 2 {\displaystyle E_{k}=mc^{2}(\gamma -1)=\gamma mc^{2}-mc^{2}\;\!}
γ = 1 1 − ( v / c ) 2 {\displaystyle \gamma ={\frac {1}{\sqrt {1-(v/c)^{2}}}}}
E k = γ m c 2 − m c 2 = ( 1 1 − v 2 / c 2 − 1 ) m c 2 {\displaystyle E_{k}=\gamma mc^{2}-mc^{2}=\left({\frac {1}{\sqrt {1-v^{2}/c^{2}}}}-1\right)mc^{2}}
  • v is the velocity of the body
  • m is its rest mass
  • c is the speed of light in a vacuum.
  • γmc is the total energy of the body
  • mc is the rest mass energy.

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.

Types

Heat

Heat is a form of energy due to the total kinetic energy of molecules and atoms of matter. 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 work form the first law of thermodynamics.

See also