Proving Rotational K.E. Formula?

greswd

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

[tex]E_k=\frac{1}{2}\left(M_{T} v_{c}^{2} + I_{c} ω^{2}\right)[/tex]

greswd Recognitions: Gold Member	Proving Rotational K.E. Formula? Tweet 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 [tex]E_k=\frac{1}{2}\left(M_{T} v_{c}^{2} + I_{c} ω^{2}\right)[/tex]