# Centripetal Force

by Ron Kurtus (revised 22 September 2016)

A * centripetal force* is an applied force acting on a moving object that will cause it to move in a curved path. While the

*inertia*of an object causes it to move in a straight line, a force applied at an angle to the straight-line motion will overcome the object's inertia.

For example, when you swing an object around on a rope, you are applying a centripetal force on the rope that prevents the object from flying off away from you due to its inertia.

The radius of curvature depends on the mass, linear velocity, and force applied on the object.

Questions you may have include:

- What direction should centripetal force be with respect to the motion?
- What are some examples of centripetal force?
- What is the centripetal force equation?

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

## Centripetal force overcomes inertia

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

If a force is applied to an object at an angle to the direction of motion, that force will overcome the object's inertia, such that it will follow a curved path, depending on the amount of the force and how long it is applied.

### Curved paths

Depending on the mass and linear velocity of the object and the amount and angle of the applied force, the object can follow various conic section curved paths:

- Circle
- Ellipse
- Parabola
- Hyperbola

If the force is applied perpendicular to the line of motion, the object can follow a circular path. The equation later in this lesson can show the radius of curvature.

### Centrifugal force

According to Newton's *Third Law* or *Action-Reaction Law*, for every applied force, there is an equal and opposite force. Opposite of the centripetal force is the *centrifugal force*, which is the force *you feel* on the rope as the object swings around you.

(

See Centrifugal Force Caused by Inertia for more information on that subject.)

The terms centripetal and centrifugal can be confused. The way to keep them straight is the "**p**" in *centripetal* stands for a **p**ush or **p**ull, causing the curved motion.

## Examples of centripetal force

An object being swung around on a rope, the motion of the Moon around the Earth and an automobile going around a curve are examples of a centripetal force being applied.

### Swing object on rope

When you swing a ball around on a rope, you must hold onto the rope and pull on it with some force. Otherwise the ball and rope will fly off according the *Law of Inertia*, which wants to have an object move in a straight line. The force you are pulling on the rope is the centripetal force.

A ball swung on rope requires centripetal force

to keep ball from flying away

### Space satellites

Space satellites are kept in circular or elliptical orbits due to the force of gravity, which acts as a centripetal force.

### Motion of Moon around Earth

The Moon is kept in orbit around the Earth through centripetal force caused by the constant pull of the gravitational force between the Moon and the Earth.

If the gravitational force would suddenly vanish, the Moon would shoot off in a straight line, tangent to its previous orbit around the Earth.

### Car going around a curve

When an automobile moves along a road, it will tend to move on a straight line, due to its inertia. However, if it comes to a curve in the road, the driver turns the steering wheel to aim the front wheels in a direction following the curve in the road.

Tires provide centripetal force for car going around a curve

The friction between the front tires and the road create a force that is perpendicular to the direction of motion. That friction force is the centripetal force, causing the automobile to go on a curved path.

## Centripetal force equation

The equation for the radius of curvature due to a centripetal force perpendicular to the line of motion is:

R = mv^{2}/F

where

**F**is the perpendicular force required to cause curved motion of the object**m**is the mass of the object**v**is the straight line velocity of the object, tangent to the curve**R**is the radius of curvature caused by the force

Circular motion from centripetal force

## Summary

Centripetal force is a force acting on a moving object causing it to move in a curved path. While the *inertia* of an object causes it to move in a straight line, a force applied at an angle to the straight-line motion will overcome the object's inertia.

For example, when you swing an object around on a rope, you are applying a centripetal force on the rope that prevents the object from flying off away from you due to its inertia.

The radius of curvature depends on the mass, linear velocity, and force applied on the object.

Centripetal force is perpendicular to the motion of an object over a period of time, causing the object to move in a curve path. That path may be a slight curve, a circle or curved path. The centrifugal inertia force is equal and opposite to the centripetal force. There are various possible applications to the centripetal force.

The equation for the radius of curvature due to the centripetal force is: **R = mv ^{2}/F**.

Work beyond your abilities

## Resources and references

### Websites

**The Centripetal Force Requirement** - Physics Classroom

**Centripetal Force - The Real Force** - Good animations

**Centripetal force** - Wikipedia

### 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)

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

## Questions and comments

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## Where are you now?

## Centripetal Force