[UPSC CSE 2011] Rigid Body Dynamics (Q216, 10M)

Imagine that a rigid body is rotating about a fixed point with angular velocity \vec{\omega}. Assuming that the coordinate axes coincide with the principal axes, if T stands for kinetic energy and G for external torque acting on the body, show that \frac{dT}{dt}=\vec{G}\cdot\vec{\omega}