# centrifugal force

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## centrifugal force

## Centrifugal force

A fictitious or pseudo outward force on a particle rotating about an axis which by Newton's third law is equal and opposite to the centripetal force. Like all such action-reaction pairs of forces, they are equal and opposite but do not act on the same body and so do not cancel each other. Consider a mass *M* tied by a string of length *R* to a pin at the center of a smooth horizontal table and whirling around the pin with an angular velocity of ω radians per second. The mass rotates in a circular path because of the centripetal force *F*_{C} = *M*ω^{2}*R* which is exerted on the mass by the string. The reaction force exerted by the rotating mass *M*, the so-called centrifugal force, is *M*ω^{2}*R* in a direction away from the center of rotation. *See* Centripetal force

From another point of view, consider an experimenter in a windowless, circular laboratory that is rotating smoothly about a centrally located vetical axis. No object remains at rest on a smooth surface; all such objects move outward toward the wall of the laboratory as though an outward, centrifugal force were acting. To the experimenter partaking in the rotation, in a rotating frame of reference, the centrifugal force is real. An outside observer would realize that the inward force which the experimenter in the rotating laboratory must exert to keep the object at rest does not keep it at rest, but furnishes the centripetal force required to keep the object moving in a circular path. The concept of an outward, centrifugal force explains the action of a centrifuge.

## centrifugal force

(sen-**trif**-ŭ-găl, -yŭ-găl) See centripetal force.

## Centrifugal Force

the force exerted by a moving mass point on a body or constraint that restricts the free motion of the point and that compels the point to move in a curvilinear manner. Quantitatively, a centrifugal force is equal to *mv*^{2}/ρ, where *m* is the mass of the point, *v* is its velocity, and ρ is the radius of curvature of the point’s trajectory. Such a force is exerted along the principal normal to the trajectory from the center of curvature, or—if the point moves in a circle—from the center of the circle.

Centrifugal and centripetal forces are numerically equal and are exerted in opposite directions along the same line. However, they act on different bodies—as the forces of action and reaction. For example, when a mass tied to a string rotates in the horizontal plane, a centripetal force is exerted on the mass by the string, causing the mass to move in a circle. At the same time, a centrifugal force is exerted on the string by the mass, stretching the string and, at a sufficiently high velocity, possibly breaking it.

When D’Alembert’s principle is used to solve problems of dynamics, a different meaning is sometimes assigned to the term “centrifugal force.” In this case, the component of a mass point’s inertial force that is exerted along the principal normal to the trajectory is called the centrifugal force. Occasionally, when equations of relative motion are formulated, the normal component of the vehicle force of inertia also is called the centrifugal force.