Kinetic energy is energy associated to motion. The kinetic energy of a mechanical system is the work required to bring the system from its `rest' state to a `moving' state. When exactly a system is considered to be `at rest' depends on the context: a stone is usually considered to be at rest when its centre of mass is fixed, but in situations where, for example, the stone undergoes a change in temperature the movement of the individual particles will play a role in the energetic description of the stone.
Kinetic energy is commonly denoted by various symbols, such as
,
,
, or
(the latter is the convention in Lagrangian
mechanics). The SI unit of kinetic energy, like that of all sorts of energy, is the joule (J), which is the same as
in SI base units.
Energy associated to motion in a straight line is called translational kinetic energy. For a particle or rigid body
with mass
and velocity
, the translational kinetic energy is
Kinetic energy associated to rotation of a rigid body is called rotational kinetic energy. It depends on the moment of inertia
In special relativity, the total energy of an object
of mass
moving in a straight line with speed
is
where
In particular, the rest energy of this object (obtained by setting
For values of
Substituting this into the expression for the kinetic energy gives the following expansion:
When
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