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In physics, kinetic energy (or vis vis, "living force") is energy possessed by a body by virtue of its motion. In Newtonian mechanics, a body with mass m, moving in a straight line with velocity v, has a translational kinetic energy of

${\displaystyle E_{k}={\frac {1}{2}}mv^{2}}$.

If a body is rotating, its rotational kinetic energy equals

${\displaystyle E_{rotation}={\frac {1}{2}}I\omega ^{2}}$,

where I is its moment of inertia and ω its angular velocity.

In Einstein's relativistic mechanics, the kinetic energy of a body is

${\displaystyle E_{k}=\gamma mc^{2}-mc^{2}=\left({\frac {1}{\sqrt {1-v^{2}/c^{2}}}}-1\right)mc^{2}}$

where m is its mass (i.e. rest mass), and c is the speed of light in vacuum. 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.

See also:

• momentum
• recoil