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For the pseudoforce that appears with a noninertial, rotating frame of reference see centrifugal force (fictitious)

A reactive centrifugal force refers to a force which is generated by a rotation and acts away from the axis of rotation. It is the reaction force to a centripetal force.

A mass undergoing circular motion constantly accelerates toward the center of the circle. This centripetal acceleration is caused by a centripetal force, which is applied to the mass by some other object. In accordance with Newton's Third Law of Motion, the mass exerts an equal and opposite force on the object. This is the real or "reactive" centrifugal force: it is directed away from the center of rotation, and is exerted by the rotating mass on the object which imposes the centripetal acceleration. Although this sense was used by Isaac Newton, it is only occasionally used in modern discussions.

Reactive centrifugal force

A car with a passenger inside driving around a curve provides an example of the reactive centrifugal force. Viewed from an inertial frame of reference, the passenger's inertia resists acceleration, keeping the passenger moving with constant speed and direction as the car begins to turn. From this point of view, the passenger does not gravitate toward the outside of the path which the car follows; instead, the car's path curves to meet the passenger.

Once the car contacts the passenger, it then applies a sideways force to accelerate him or her around the turn with the car. This force is called a centripetal ("center seeking") force because its vector changes direction to continue to point toward the center (precisely, the center of curvature) of the car's arc as the car traverses it.

If the car is acting upon the passenger, then the passenger must be acting upon the car with an equal and opposite force. Being opposite, this reaction force is directed away from the center, therefore centrifugal. It is critical to realize that this centrifugal force acts upon the car, not the passenger.

The centrifugal reaction force with which the passenger pushes back against the door of the car is given by:

${\displaystyle \mathbf {F} _{\mathrm {centrifugal} }\,}$	${\displaystyle =-m\mathbf {a} _{\mathrm {centripetal} }\,}$
	${\displaystyle =m\omega ^{2}\mathbf {r} _{\perp }\,}$

where ${\displaystyle m}$ is the mass of the rotating object, ${\displaystyle \omega }$ the rotational speed (in radians per unit time), and ${\displaystyle r}$ the radius from the center of curvature.

The reactive centrifugal force is a real force, but the term is rarely used in modern discussions.

Confusion and misconceptions

Centrifugal force can be a confusing term because it is used (or misused) in more than one instance, and because sloppy labelling can obscure which forces are acting upon which objects in a system. When diagramming forces in a system, one must describe each object separately, attaching only those forces acting upon it (not forces that it exerts upon other objects).

Real versus fictional forces

• As already discussed a mass undergoing circular motion constantly accelerates toward the center of the circle. This centripetal acceleration is caused by a centripetal force, which is applied to the mass by some other object. In accordance with Newton's Third Law of Motion, the mass exerts an equal and opposite force on the object. This is the real or "reactive" centrifugal force: it is directed away from the center of curvature, and is exerted by the rotating mass on the object which imposes the centripetal acceleration. Although this sense was used by Isaac Newton, it is only occasionally used in modern discussions.

• An inertial (also known as fictitious or pseudo) centrifugal force appears when a rotating reference frame is used for analysis. To make Newton's laws of motion valid in such a frame, any true force on a mass must be supplemented by a (fictitious) centrifugal force that is directed away from the axis of rotation and a coriolis force that bends a moving objects path.

Referring back to the earlier example, in the reference frame that is rotating together with the car (a model which those inside the car will often find natural), it looks as if a 'magical' force is pushing the passenger away from the center of the bend. In a rotating frame this is ascribed to the fictitious forces—but it is not actual forces exerted by any other object- in reality it is inertia. The effect occurs when the reference frame is following the car, because that hides the car's acceleration. Nevertheless physicists sometimes treat these types of forces much as if they were real forces, as it makes some kinds of calculations simpler and gives correct results, but these forces do not appear in inertial frames of reference that most students would normally use to do their calculations.

See also

• Circular motion
• Coriolis force
• Centripetal force
• Rotational motion

References

1. Gravity book 2
2. Comparison of Bearings
3. High Technology Gyroplane
4. Hitachi News
5. http://physnet.org/modules/pdf_modules/m17.pdf ACCELERATION AND FORCE IN CIRCULAR MOTION by Peter Signell
6. Book I, Section II: Of the Invention of Centripetal Forces
7. http://www.infoplease.com/ce6/sci/A0811114.html
8. Microsoft Word - Comparison of Bearings.doc
9. High Tech Gyro, AHS 2000 on CarterAviationTechnologies.com
10. Gravity book 2
11. Comparison of Bearings
12. High Technology Gyroplane
13. Hitachi News
14. http://physnet.org/modules/pdf_modules/m17.pdf ACCELERATION AND FORCE IN CIRCULAR MOTION by Peter Signell

• Newton's description in Principia
• Centrifugal reaction force - Columbia electronic encyclopedia
• M. Alonso and E.J. Finn, Fundamental university physics, Addison-Wesley
• Centripetal force vs. Centrifugal force - from an online Regents Exam physics tutorial by the Oswego City School District
• Centrifugal force acts inwards near a black hole

External links

• Centripetal and Centrifugal Forces at MathPages
• Centrifugal Force at h2g2

• Force
• Mechanics