Circular Disk Rotating About Its Diameter

Chapter Contents:

Search Physical Audio Signal Processing

Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

The moment of inertia for the same circular disk rotating about an axis in the plane of the disk, passing through its center, is given by

$\displaystyle I = \frac{M}{\pi R^2}\cdot 4\int_0^{\pi/2} \int_0^R [r\cos(\theta)]^2\, r\,dr\,d\theta = \frac{1}{4}MR^2$

Thus, the uniform disk's moment of inertia in its own plane is twice that about its diameter.

Previous: Circular Disk Rotating in Its Own Plane
Next: Perpendicular Axis Theorem

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.

Sign in