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 :

---

Previous: Stretch Rule
Next: Radius of Gyration

Order a Hardcopy of Physical Audio Signal Processing

---

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.