Linear Momentum of the Center of Mass

Consider a system of point-masses , each traveling with vector velocity , and not necessarily rigidly attached to each other. Then the total momentum of the system is

where denotes the total mass, and is the velocity of the center of mass.

Thus, the momentum of any collection of masses (including rigid bodies) equals the total mass times the velocity of the center-of-mass.

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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.