Kinetic energy due to rotation is defined as

A. $\frac{1}{2} m (v_g)^2$
B. $\frac{1}{2} m (v_g)^2 + \frac{1}{2} I_g \omega ^2$
C. $\frac{1}{2} I_g \omega ^2$
D. $I_g \omega ^2$