Definition:Moment of Inertia/Discrete

Definition
Let $B$ be a rigid body which is rotating in space about some axis $\LL$. Let $B$ be composed of a countable number of particles $P_1, P_2, \ldots$ such that:
 * each $P_i$ has mass $m_i$
 * each $P_i$ has perpendicular distance $r_i$ from $\LL$.

The moment of inertia of $B$ about $\LL$ is given by:
 * $I := \ds \sum m_i {r_i}^2$