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 $\mathbf r$ with respect to 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 $B$.

Also see

• Results about moment of inertia can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): moment of inertia