# Proving Rotational K.E. Formula?

by greswd
Tags: formula, proving, rotational
 P: 147 The total kinetic energy (as viewed from one inertial frame) of a free, rigid body is the sum of all the infinitesimal kinetic energies of the components that comprise the body. How do we prove that for a rotating body $$E_k=\frac{1}{2}\left(M_{T} v_{c}^{2} + I_{c} ω^{2}\right)$$