Rigid Body Rotation

Rotational Kinetic Energy

For rotation about a principal axis,

$$T=\frac{1}{2}I\omega^2.$$

In three dimensions, the inertia tensor relates angular momentum to angular velocity:

$$\mathbf L = I\boldsymbol\omega.$$

Torque Equation

The rotational equation of motion is

$$\boldsymbol\tau = \frac{d\mathbf L}{dt}.$$

This is the rotational analogue of Newton’s second law.