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# Centrifugal Force Caused by Inertia

by Ron Kurtus (revised 19 March 2018)

When you swing an object around on a string or rope, the object will pull outward on the string. The force you feel is called the centrifugal force and is caused by the inertia of the object, where it seeks to follow a straight-line path. It is also called an inertial force or pseudo force.

According to Newton's Third Law or Action-Reaction Law, the centrifugal force is equal to and opposite the centripetal force that acts on the object and causes it to move in a curved line.

Applications of centrifugal force include a rotating disk, amusement park rides, and water in a swinging bucket. The equation for the centrifugal force is similar to that for centripetal force.

Note: You can remember

When the subject of circular motion is discussed, it is not uncommon to hear mention of the word centrifugalCentrifugal, not to be confused with centripetal, means away from the center or outward.

Questions you may have include:

• What causes centrifugal forces?
• What are some examples of centrifugal force?
• What is centrifugal force equation?

This lesson will answer those questions. Useful tool: Units Conversion

## Cause of centrifugal force

The cause of a centrifugal force is related to the centripetal force on an object.

### Centripetal force

According to Newton's First Law or Law of Inertia, an object in motion tends to follow a straight line.

However, by applying a continuous sideways force on the object can overcome the inertia and cause the object to take a curved path, for as long as that force is applied. That applied force is called a centripetal force. A common example is swinging an object around on a rope.

### Centrifugal force

Newton's Third Law or Action-Reaction Law states that for every applied force, there is an equal and opposite force.

In other words, when you apply a force on a rope in swinging an object around you, the rope pulls on the object with that force, and the object provides an equal and opposite force on the rope. You will then feel that equal and opposite force pulling the rope and the object away from you. This force is the centrifugal force.

Note: Many Physics sources say that centrifugal force is a fictitious or pseudo (false) force. This is contrary to the fact the you can feel the force.

Also, they seem to have forgotten Newton's Third Law. If they would have applied the Law, they would have seen that the centrifugal force is equal and opposite the centripetal force.

Centrifugal force is an inertial force that resists changing the direction or velocity of the object.

## Examples of centrifugal force

There are various examples of applications of the centrifugal force.

### Spinning disk

If you place an object on a disk and start it spinning, the friction holding the object on the disk is the centripetal force causing the object to move in a curved path.

Once the disk spins fast enough, the centrifugal inertial force can become greater than the centripetal friction force holding the object in place. The object will then fly off in a straight line.

Ball flies off spinning disk in straight line
due to centrifugal force overcoming friction

### Round-Up ride

A related example is the amusement park ride, Round-Up, which consists of a circular platform that has a vertical cage-like wall around the edge.

Centrifugal force holds people on walls in carnival ride

When the platform spins at a high enough rate, the centrifugal inertial force pushes the riders against the wall, holding them in place as the platform changes directions.

Although the riders feel a force pushing them against the wall, there is no real force or agent that is doing the pushing. It is simply an effect of inertia.

### Roller coaster ride

Another amusement park ride that shows the centrifugal force is the roller coaster. When the roller coaster goes over the curved top of the tracks, you feel the centrifugal force pulling you upward. Likewise, at the lower curved part of the tracks, you feel the force pushing you downward.

### Water stays in swinging bucket

There is also a trick where you take a pail half-full of water and swing it on a rope in a vertical circle, such that the water stays in the bucket, even when directly above you by centrifugal force.

## Equation for centrifugal force

The equation for the outward or centrifugal force due to inertia of an object following a curved path is:

F = mv2/R

where

• F is the centrifugal force pulling object away from center
• m is the mass of the object
• v is the straight line velocity of the object
• R is the radius of curvature caused by the centripetal force
This equation is similar to that of the centripetal force causing an object to follow a curved path, except that the force is in the opposite direction.

Centrifugal force is in the opposite direction
of centripetal force

Thus, if the centripetal force causing an object to go in a circular path is 25 newtons, the centrifugal force felt will be 25 newtons.

## Summary

A centrifugal force is the outward inertial force on an object moving along a curved path. An object will move in a curved path, provided a centripetal force prevents it from moving in a straight line.

Newton's Third Law or Action-Reaction Law states that for every applied force, there is an equal and opposite force. Thus, the centrifugal force is in the opposite direction than the centripetal force, but they are equal in magnitude.

The equation for the centrifugal inertial force, as a function of mass, velocity and radius is:

F = mv2/R.

Work beyond your abilities

## Resources and references

Ron Kurtus' Credentials

### Websites

Centrifugal Force - Wikipedia

Centrifugal Force - Physics Classroom

Centrifugal Force - HowStuffWorks

Physics Resources

### Books

The Science of Forces by Steve Parker; Heinemann (2005) \$29.29 - Projects with experiments with forces and machines

Glencoe Science: Motion, Forces, and Energy, by McGraw-Hill; Glencoe/McGraw-Hill (2001) \$19.32 - Student edition (Hardcover)

## Questions and comments

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www.school-for-champions.com/science/
force_centrifugal.htm

Please include it as a link on your website or as a reference in your report, document, or thesis.

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