# centripetal force

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Related to centripetal force: centripetal acceleration

## centripetal force

## Centripetal force

The inward force required to keep a particle or an object moving in a circular path. It can be shown that a particle moving in a circular path has an acceleration toward the center of the circle along a radius. *See* Acceleration

This radial acceleration, called the centripetal acceleration, is such that, if a particle has a linear or tangential velocity *v* when moving in a circular path of radius *R*, the centripetal acceleration is *v*^{2}/*R*. If the particle undergoing the centripetal acceleration has a mass *M*, then by Newton's second law of motion the centripetal force *F*_{C} is in the direction of the acceleration. This is expressed by the equation below,

*v*/

*R*. From Newton's laws of motion it follows that the natural motion of an object is one with constant speed in a straight line, and that a force is necessary if the object is to depart from this type of motion. Whenever an object moves in a curve, a centripetal force is necessary. In circular motion the tangential speed is constant but is changing direction at the constant rate of ω, so the centripetal force along the radius is the only force involved.

## centripetal force

A force, such as gravitation, that causes a body to deviate from motion in a straight line to motion along a curved path, the force being directed toward the center of curvature of the body's motion. The force reacting against this constraint, i.e. the force equal in magnitude but opposite in direction, is the*centrifugal force*. The centrifugal force results from the inertia of all solid bodies, i.e. their resistance to acceleration, and unlike gravitational or electrical forces, cannot be considered a real force. The centripetal force is equal to the product of the mass of the body and its

*centripetal acceleration*. The latter is the acceleration toward the center, and for a body moving in a circle at a constant angular velocity ω it is given by ω

^{2}

*r*, where

*r*is the radius.

## Centripetal Force

the force that acts on a mass point in the direction of the principal normal to the point’s trajectory and is directed toward the center of curvature. If the point moves in a circle, the centripetal force is directed toward the center of the circle. Numerically, the centripetal force that acts on a point of mass *m* moving with a velocity *v* is equal to *mv*^{2}/ρ, where ρ is the radius of curvature of the point’s trajectory. Under the action of a centripetal force, the motion of a free mass point is curvilinear. During rectilinear motion, the centripetal force is equal to zero.