# Reduced Mass

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## reduced mass

[ri′düst ′mas]*m*

_{1}and

*m*

_{2}exerting equal and opposite forces on each other and subject to no external forces, the reduced mass is the mass

*m*such that the motion of either particle, with respect to the other as origin, is the same as the motion with respect to a fixed origin of a single particle with mass

*m*acted on by the same force; it is given by

*m*=

*m*

_{1}

*m*

_{2}/(

*m*

_{1}+

*m*

_{2}).

## Reduced Mass

a coventional characterization of the distribution of mass in a mechanical or mixed (for example, electromechanical) system in motion. Reduced mass depends on such physical parameters of the system as mass, moment of inertia, and inductance, as well as on the law of the system’s motion. In the simplest cases, the reduced mass μ is defined by *T* = ½ μ*v*^{2}, where *T* is the kinetic energy of the system and v is the velocity of a certain characteristic point, to which the mass of the system is being reduced. For example, for a body in plane-parallel motion, μ = [1 + (ρ_{c}/*h*_{c})^{2}]*m* relative to the center of mass *C*, where *m* is the body’s mass, p_{c} is the radius of inertia relative to the axis perpendicular to the plane of motion through the point *C*, and *h _{c}* is the distance from the center of mass to the instantaneous axis of rotation, which as a rule is variable.