Mass Moment of Inertia

The mass moment of inertia (or moment of inertia) plays the role of mass in angular momentum. Thus, while is the linear momentum associated with mass and velocity , the angular momentum associated with rotational speed is .

The mass moment of inertia is given by summing all mass points times the square of their distance from the center of rotation. Thus, for a point mass orbiting along a circle of radius , the moment of inertia is . For a set of point masses orbiting along circles of radii , , the moment of inertia for the ensemble of masses is

For a continuous mass distribution, the moment of inertia is given by integrating the contribution of each differential mass element:

where is the distance from the point of rotation to the mass element .

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Subsections

• Circular Disk
• Parallel Axis Theorem

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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.