For a particle that has no rotation, the
kinetic energy is simply,
T = 1/2 m v^{2}
This equation can be applied to every particle that makes up a rigid
body,
However, if the particle is a rigid body with dimensions, then the velocity needs to be written as
where G is the center of gravity. The second terms models the rotation of the object. Substituting v_{i} into the kinetic equation and noting that a magnitude of v_{i/G} = r_{i/G} ω gives

T = 1/2 m v_{G}^{2} + 1/2
I_{G} ω^{2}


If the rigid body has a fixed point, then the equation becomes
T = 1/2 I_{o} ω^{2}
where I_{o} is moment of inertia about the fixed point. 