# Inertial Force

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## inertial force

[i′nər·shəl ′fȯrs]## Inertial Force

a vector quantity equal in magnitude to the product of the mass *m* of a mass point and the acceleration *w* of the mass point. The inertial force is opposite in direction to the acceleration. In the case of curvilinear motion, the inertial force can be resolved into a tangential component J_{τ} opposite in direction to the tangential acceleration w_{τ} and a normal, or centrifugal, component J* _{n}* directed away from the center of curvature along the principal normal to the trajectory of the mass point. Numerically,

*J*

_{τ}=

*mw*, and

_{τ}*J*=

_{n}*mv*

^{2}ρ, where

*v*is the velocity of the point and ρ is the radius of curvature of the trajectory. When motion with respect to an inertial frame of reference is studied, the inertial force is introduced in order to have the formal possibility of expressing equations of dynamics in the form of the simpler equations of statics.

The concept of inertial force is also used in the study of relative motion. In this case, when the “vehicle” force *J*_{veh} and the Coriolis forces *J*_{Cor} are added to the forces of interaction (with other bodies) acting on the mass point, the equations of motion of the point in a moving, or noninertial, frame of reference can be written in the same form as in an inertial frame (*see*RELATIVE MOTION and CORIOLIS FORCE).

S. M. TARG