Area Moment of Inertia

The *area moment of inertia* is the second moment of an area
around a given axis:

where denotes a differential element of the area (summing to ), and denotes its distance from the axis of rotation.

Comparing with the definition of *mass moment of inertia* in
§B.4.4 above, we see that mass is replaced by area in
the area moment of inertia.

In a planar mass distribution with total mass
uniformly
distributed over an area
(*i.e.*, a constant mass density of
), the mass moment of inertia
is given by the area
moment of inertia
times mass-density
:

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University