Moment of Inertia

Definition: Moment of Inertia of a Point Mass

The moment of inertia $I$ of a point mass $m$ which is a distance $r$ from a given axis is defined as

$$I\stackrel{\text{def}}{=}m{r}^2$$

Definition: Moment of Inertia of a Physical System

The moment of inertia $I$ of a physical system around a given axis is the sum of the moments of inertia $I_1,I_2\cdots$ around that axis of all its components.

$$I\stackrel{\text{def}}{=}\sum _k{I}_k=\sum _k{m}_k{r}_k^2$$

NOTE

The moment of inertia serves as an analogue to mass in many laws of rotational motion.