Parallel Axis Theorem

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For an area whose centroidal axis is displaced from the axis of rotation along , the moment of inertia about the axis is given by

$\displaystyle I_x(d) = I_x(0) + Md^2$

where

denotes the total rotating mass, and

is defined as the moment of inertia of area

about its centroidal axis parallel to the

axis. Thus, the added inertia due to displacement by

meters from the centroidal axis is equal to that of a point mass

rotating a distance

from the center of rotation.

written by 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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