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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. In recent years, experts have debated the validity of the term "centrifugal force" as conceptualized by Newton, in favor of the view that there is no such force but only inertia that is overcome by a centripetal (center seeking) force. This article summarizes several related but distinct concepts representing different ideas of centrifugal force.
Historically, the concept of "centrifugal force" was pioneered by Sir Isaac Newton. According to Newton's third law of "action and reaction", when a centripetal force acts on an object, pushing it into a curved path, 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 in a rotating reference frame is a fictitious force that acts on any mass in a (non-inertial) rotating reference frame. According to the planetary orbital equation first conceived by Gottfried Leibniz, the centrifugal force in planetary orbits is an inverse cube law force of repulsion which acts in tandem with gravity to produce hyperbolic, parabolic, or elliptical orbits.
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 while the centripetal force acts on one object, the centrifugal force provides an equal and opposite reaction on the object causing the centripetal force. Others argue that the Newton model is refuted by other models, such as planetary orbital models, and that "centrifugal force" is only a fictitious force invented to explain a property of inertia in rotational motion.
Reactive vs. fictitious force
The table below compares the various facets of the competing "reactive force" and "fictitious force" models of centrifugal force.
| Reactive centrifugal force | Fictitious centrifugal force | |
|---|---|---|
| Reference frame |
Any | Only rotating frames |
| Exerted by |
Bodies moving in circular paths |
Acts as if emanating from the rotation axis, but no real source |
| Exerted upon |
The object(s) causing the curved motion, not upon the body in curved motion |
All bodies, moving or not; if moving, Coriolis force also is present |
| Direction | Opposite to the centripetal force causing curved path |
Away from rotation axis, regardless of path of body |
| Analysis | Kinematic: related to centripetal force |
Kinetic: included as force in Newton's laws of motion |
Reactive centrifugal force
Main article: Reactive centrifugal forceThe 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. Nelkon & Parker's Advanced Level Physics is one example of a textbook which used this approach until the 1960s and then dropped it. In the 1961 edition of this textbook, centrifugal force is introduced and explained according to 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.
Fictitious force in a rotating reference frame
Main article: Centrifugal force (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 body's mass and 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.
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
- Linton, Christopher. From Exodus to Einstein. Cambridge: University Press, 2004, p. 285. ISBN 0521827507
- Swetz, Frank et al. Learn from the Masters! Mathematical Association of America, 1997, p. 269. ISBN 0883857030