# Difference Between Centrifugal and Centripetal Force

## Main Difference – Centrifugal vs. Centripetal Force

There are forces acting on any object that is travelling on a circular path. Depending on the type of frame of reference from which the object is observed, forces may appear to act on the object differently. The main difference between centrifugal and centripetal force is that centripetal force acts on the object towards the centre of the circular path. In contrast, centrifugal force is an apparent force that acts on the object in a direction pointing away from the centre of the circle. An observer in an inertial frame of reference does not perceive a centrifugal force. Only an observer in a rotating frame of reference who rotates along with the object in circular motion perceives a centrifugal force.

## What is Centripetal Force

An object accelerates whenever its velocity changes. Since velocity is a vector quantity, it can be changed by either changing its size (speed) or the direction of motion. Any object travelling in a circular path is constantly changing direction, which means it is constantly accelerating. According to Newton’s second law, since the object is accelerating it should have a resultant force acting on it. By considering the vector representation of the velocity of an object travelling in a circular path, and then applying Newton’s second law to this acceleration, we found that the centripetal force on an object travelling in a circular path always acts towards the centre of the circle, and that this centripetal force $F$ could be given by:

$F=\frac{mv^2}{r}$

where $m$ is the mass and $v$ is the velocity of the object, and $r$ is the radius of the object’s circular path.

## What is Centrifugal Force

Consider the man about to do a “hammer throw” shown below:

A hammer thrower

As the hammer thrower rotates the hammer, he is also rotating along with the hammer. In other words, he and the hammer are in a rotating frame of reference. When he looks at the hammer, he sees (with respect to himself) that the hammer is stationary. He feels a tension in the handle and so he knows hat the hammer is pulling the handle away from him. With Newton’s third law, he concludes that the handle must be pulling the hammer towards him.

However, the hammer thrower thinks that the hammer is at rest. He also knows that the hammer is being pulled towards him, so according to Newton’s first law, he concludes that there must be another force acting on the hammer, pulling it directly away from him. This force is centrifugal: the word “centrifugal” here means that this perceived force is attempting to pull the object away from the centre of the object’s circular path (of course, the hammer thrower does not know that the hammer is moving in a circular path, but if he were to later explain the forces he perceived to someone else who had observed the hammer thrower from an inertial reference frame, that person would identify that the “centrifugal” force pointed away from the centre of the circular path).

The hammer is not at rest in an inertial frame of reference. An observer looking at the hammer from an inertial frame of reference will see the hammer travelling in a circular path and they will not find a centrifugal force. In fact, if you view the hammer from an inertial frame of reference, you would identify two forces acting on the hammer, the tension along the handle and the hammer’s weight:

Forces acting on the hammer

The tension acts along the handle of the hammer, pulling the hammer in towards the circle while gravity attempts to pull the hammer down. Centripetal force is the resultant force towards the centre. For instance, if the hammer thrower is rotating the hammer in a horizontal circle at the time, then the resultant force towards the centre of the circle would be $T\:\mathrm{sin\:}\theta$.

The video below also discusses the difference between “centripetal” and “centrifugal” forces for objects moving in circular paths:

Centrifugal force is often viewed as a “fictitious” force because it cannot be observed from an inertial frame of reference and also because there is no real “interaction” that one could point to, in order to explain its origin. However, at times, it is useful to imagine centrifugal forces as though they were real, especially if you are designing things that are going to become a part of a rotating system!

## Difference Between Centrifugal and Centripetal Force

### Real or Fictitious

Centripetal force is a real force that is a result of a physical interaction.

Centrifugal force is a fictitious force which appears to be present when a rotating object is viewed from a frame of reference which is also rotating along with the object.

### Direction

Centripetal force acts towards the centre of the circular path.

Centrifugal force appears to act in a direction pointing away from the centre of the circular path.

### Appearance in Inertial Frames of Reference

Centripetal force can be observed from an inertial frame of reference.

Centrifugal force cannot be observed from an inertial frame of reference.

Image Courtesy

“Throwing the Hammer – Dornoch Highland Gathering 2007” by John Haslam (Own work) [CC BY 2.0], via flickr