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Embedded SystemsFPGAElectronics

Physical Audio Signal Processing
    Elementary Physics, Mechanics, and Acoustics
       Rigid-Body Dynamics
          Mass Moment of Inertia
             Circular Disk Rotating in Its Own Plane

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Circular Disk Rotating in Its Own Plane

For example, the moment of inertia for a uniform circular disk of total mass $ M$ and radius $ R$, rotating in its own plane about a rotation axis piercing its center, is given by

$\displaystyle I = \frac{M}{\pi R^2}\int_{-\pi}^\pi \int_0^R r^2\, r\,dr\,d\thet... ...c{2M}{R^2}\int_0^R r^3 dr = \frac{2M}{R^2}\frac{1}{4} R^4 = \frac{1}{2} M R^2. $

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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.


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