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In everyday understanding, centrifugal force (from Latin centrum "center" and fugere "to flee") represents the effects of inertia that arise in curved motion and are experienced as an outward force away from the center of curvature of the path or away from a center of rotation. Centrifugal force is not restricted to circular motion, however.

This article summarizes several related but distinct concepts related to the general idea of centrifugal force.

• Reactive centrifugal force – according to Newton's third law of "action and reaction", the reaction force upon the object supplying a centripetal force is the reactive centrifugal force, the outward force felt by that object when it is pulling or pushing another object into a curved path.

• Centrifugal force (rotating reference frame) – a fictitious force that acts on any mass in a (non-inertial) rotating reference frame.

• In planetary orbits, the centrifugal force is an inverse cube law force of repulsion which acts in tandem with gravity to produce hyperbolic, parabolic, or elliptical orbits. The planetary orbital equation was first conceived by Gottfried Leibniz

The fictitious centrifugal force and the reactive centrifugal force are compared in the table.

Reactive centrifugal force

The concept of reactive centrifugal force originated with Isaac Newton in the 17th century. From his third law of motion, Newton concluded that the centripetal force which acts on an object must be balanced by an equal and opposite centrifugal force. This approach to centrifugal force appeared in high school textbooks up until the 1960's. One example of a textbook which used this approach and then dropped it is Nelkon & Parker 'Advanced Level Physics'. In the 1961 edition of this textbook, centrifugal force is introduced and explained exactly as per Isaac Newton's action-reaction approach. In the same section, the centrifuge machine is explained using centrifugal force as a real force. However, in the 1971 revision of the same textbook, the centrifugal force section has disappeared and the centrifuge machine is explained using some kind of compound negative centripetal force.

In recent years, it has become common to teach circular motion using only the concept of inward acting centripetal force without any mention of centrifugal force. The inward centripetal force will cause an object that would otherwise have been moving in a straight line, to move in a circular path. The matter has become somewhat controversial with some physicists arguing that the centripetal force still needs to have an equal and opposite reaction. Some physicists further argue that while the centripetal force acts on one object, the centrifugal force acts on the object that causes the centripetal force. This argument cannot however be used in the case of planetary orbits since both the centrifugal force and the centripetal force act on the same body.

Fictitious force in a rotating reference frame

From the viewpoint of an observer in a rotating reference frame, centrifugal force is an apparent, or fictitious, or inertial, or pseudo force that seems to push a body away from the axis of rotation of the frame and is a consequence of the frame's angular rate of rotation. It is zero when the rate of rotation of the reference frame is zero, independent of the motions of objects in the frame.

Centrifugal force in planetary orbits

Gottfried Leibniz conceived of centrifugal force as a real outward force which is induced by the circulation of the body upon which the force acts. Leibniz showed that the centrifugal force obeys the inverse cube law. . Leibniz's method is used nowadays to solve the planetary orbital problem. The outward inverse cube law centrifugal force appears in a second order differential equation in the radial length alongside the inward inverse square law of gravity. The solution to this equation is a conic section which can be either a hyperbola, a parabola, or an ellipse.

There is evidence that Sir Isaac Newton originally conceived of a similar approach to centrifugal force as Leibniz. However, he seems to have changed his position at some point. In later years, Newton conceived of centrifugal force as being an equal and opposite reaction to centripetal force. see here.

Other topics

The concept of centrifugal force in its more technical aspects introduces several additional topics:

• Reference frames, which compare observations by observers in different states of motion. Among the many possible reference frames the inertial frame of reference are singled out as the frames where physical laws take their simplest form. In this context, physical forces are divided into two groups: real forces that originate in real sources, like electrical force originates in charges, and

• Fictitious forces that do not so originate, but originate instead in the motion of the observer. Naturally, forces that originate in the motion of the observer vary with the motion of the observer, and in particular vanish for some observers, namely those in inertial frames of reference.

Centrifugal force has played a key role in debates over relative versus absolute rotation. These historic arguments are found in the articles:

• Bucket argument: The historic example proposing that explanations of the observed curvature of the surface of water in a rotating bucket are different for different observers, allowing identification of the relative rotation of the observer. In particular, rotating observers must invoke centrifugal force as part of their explanation, while stationary observers do not.

• Rotating spheres: The historic example proposing that the explanation of the the tension in a rope joining two spheres rotating about their center of gravity are different for different observers, allowing identification of the relative rotation of the observer. In particular, rotating observers must invoke centrifugal force as part of their explanation of the tension, while stationary observers do not.

References

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• Fictitious forces
• Force
• Mechanics
• Rotation