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# Centrifugal Force Caused by Inertia

by Ron Kurtus (revised 1 September 2014)

When you swing an object around on a string or rope, you will *feel a force* pulling the object outward. This 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 called a resistive force or an inertial force.

Objects will move on a curved path if a centripetal force is applied to the object at an angle to the straight-line motion. The centrifugal force acts in the opposite direction of the centripetal force and is equal in magnitude. Although some sources call centrifugal force a virtual or false force, it certainly seems real to the person holding the rope.

There are various examples of the centrifugal force, which use the same equation as for centripetal force.

Questions you may have include:

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

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

## Centrifugal force is resistive

When an object is following a curved path due to a *centripetal force*, it exhibits an equal force in the opposite direction.

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, you will feel an equal and opposite force pulling the object away from you. This 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 canfeelthe 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 a resistive or inertial force in that it resists changing the direction or velocity of the object.

## Examples of centrifugal force

There are various examples of applications of centrifugal inertial 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.

### 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 centrifugal force is the same as that for the centripetal force causing an object to follow a curved path is:

F = mv^{2}/r

where

**F**is the 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 cause by the force

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. Objects move on a curved path if a centripetal force is applied to the object, and centrifugal force acts in the opposite direction of the centripetal force.

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

F = mv^{2}/r.

Work beyond your abilities

## Resources and references

### Websites

### Books

**Forces In Nature** by Liz Sonneborn Rosen; Publishing Group (2004) $25.25 - Understanding gravitational, electrical and magnetic force

**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)

**Top-rated books on Physics of Force**

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## Centrifugal Force Caused by Inertia