Moment of Inertia

The moment of inertia (or rotational inertia) of a rigid body, $I$, measures the body's resistance to changes in its state of rotational motion. It is the rotational analogue of mass.

For a single particle rotating about an axis with distance $r$,

$$I = mr^2$$

For a system of discrete masses, the rotational inertia is the sum of the rotational inertiae of the individual passes.:

$$I = \Sigma mr^2 = m_{1}r_{1}^2 + m_{2}r_{2}^2 + \dots + m_{n}r_{n}^2 $$

Unlike mass, rotational inertia is dependent on the shape of the object, specifically the distribution of mass at the edges of the object.

$$ [I] = [m][r^2] = kgm^2 $$

Rotational inertiae of common geometries