Definition:Moment of Inertia/Continuous

Definition
Let $B$ be a rigid body which is rotating in space about some axis $\LL$. Let each point in $B$ have:
 * a position vector $\mathbf r$ a given frame of reference.
 * a density $\map \rho {\mathbf r}$
 * a perpendicular distance $\map p {\mathbf r}$ from $\LL$

The moment of inertia of $B$ about $\LL$ is given by:
 * $I := \ds \int_B \paren {\map p {\mathbf r} }^2 \map \rho {\mathbf r} \rd v$

where $\d v$ is an infinitesimal volume element of $B$.