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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:

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:

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 push or pull, 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.

Ball swung on rope requires centripetal force to keep ball from flying away

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

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 = mv2/F

where

Circular motion from centripetal 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 = mv2/F.


Work beyond your abilities


Resources and references

Ron Kurtus' Credentials

Websites

The Centripetal Force Requirement - Physics Classroom

Centripetal Force - The Real Force - Good animations

Centripetal force - Wikipedia

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)

Top-rated books on Physics of Force


Questions and comments

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.


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