Describe the rotational kinetic energy of a rigid system in terms of the rotational inertia and angular velocity of that rigid system.

The rotational kinetic energy of an object or rigid system is related to the rotational inertia and angular velocity of the rigid system and is given by the equation \[\begin{equation} KE = \dfrac{1}{2} I \omega^2 \end{equation}\]

The rotational inertia of an object about a fixed axis can be used to show that the rotational kinetic energy of that object is equivalent to its translational kinetic energy, which is its total kinetic energy

The total kinetic energy of a rigid system is the sum of its rotational kinetic energy due to its rotation about its center of mass and the translational kinetic energy due to the linear motion of its center of mass.

A rigid system can have rotational kinetic energy while its center of mass is at rest due to the individual points within the rigid system having linear speed and, therefore, kinetic energy.

Rotational kinetic energy is a scalar quantity