centripetal force and centrifugal force, action-reaction force pair associated with circular motion. According to Newton's first law of motion, a moving body travels along a straight path with constant speed (i.e., has constant velocity) unless it is acted on by an outside force. For circular motion to occur there must be a constant force acting on a body, pushing it toward the center of the circular path. This force is the centripetal ("center-seeking") force. For a planet orbiting the sun, the force is gravitational; for an object twirled on a string, the force is mechanical; for an electron orbiting an atom, it is electrical. The magnitude F of the centripetal force is equal to the mass m of the body times its velocity squared v ² divided by the radius r of its path: F=mv²/r. According to Newton's third law of motion, for every action there is an equal and opposite reaction. The centripetal force, the action, is balanced by a reaction force, the centrifugal ("center-fleeing") force. The two forces are equal in magnitude and opposite in direction. The centrifugal force does not act on the body in motion; the only force acting on the body in motion is the centripetal force. The centrifugal force acts on the source of the centripetal force to displace it radially from the center of the path. Thus, in twirling a mass on a string, the centripetal force transmitted by the string pulls in on the mass to keep it in its circular path, while the centrifugal force transmitted by the string pulls outward on its point of attachment at the center of the path. The centrifugal force is often mistakenly thought to cause a body to fly out of its circular path when it is released; rather, it is the removal of the centripetal force that allows the body to travel in a straight line as required by Newton's first law. If there were in fact a force acting to force the body out of its circular path, its path when released would not be the straight tangential course that is always observed.

Machine for moving liquids and gases. Its two major parts are the impeller (a wheel with vanes) and the circular pump casing around it. In the most common type, called the volute centrifugal pump, fluid enters the pump at high speed near the centre of the rotating impeller and is thrown against the casing by the vanes. The centrifugal pressure forces the fluid through an opening in the casing; this outlet widens progressively in a spiral fashion, which reduces the speed of the fluid and thereby increases pressure. Centrifugal pumps are used for many purposes, such as pumping liquids for water supply, irrigation, and sewage disposal systems. They are also used as gas compressors.

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Fictitious force, peculiar to circular motion, that is equal but opposite to the centripetal force that keeps a particle on a circular path (see centripetal acceleration). For example, a stone attached to a string and whirling in a horizontal circular path is accelerated toward the centre of its path by the tension in the string, the only force acting on the string. However, in a reference frame at rest with the stone, another force—the centrifugal force—must be introduced for Newton's laws of motion to apply. Centrifugal force is a useful concept in analyzing behaviour in rotating systems.

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