You have probably experienced driving down the highway, when suddenly the road curves left and it feels like you are being pushed out towards the right, in the opposite direction of the curve. This is a common example of what many people think of as and call a "centrifugal force." This "force" is mistakenly called the centrifugal force, but in fact there is no such thing!

## There is No Such Thing as Centrifugal Acceleration

Objects moving in a uniform circular motion experience forces which keep the object in perfect circular motion, meaning the sum of the forces is directed inward toward the center. A single force such as tension in a string is an example of centripetal force, but other forces can fill this role too. The tension in the string results in a centripetal force, which causes the uniform circular motion. Likely, this is what you want to calculate.

Let's first go through what centripetal acceleration is and how to calculate it, as well as how to calculate centripetal forces. Then, we will be able to understand why there is no centrifugal force.

#### Tips

There is no centrifugal force; if there was there would be no circular motion. You can see this easily if you create a centrifugal force diagram that also includes the centripetal force. Centripetal forces cause circular motion, and are directed towards the center of the motion.

## A Quick Recap

To understand centripetal force and acceleration, it may be helpful to remember some vocabulary. First, velocity is a vector that describes the speed and direction of motion for an object. Next, if the velocity is changing, or in other words the speed or the direction of the object is changing as a function of time, it also has an acceleration.

A particular case of two-dimensional motion is uniform circular motion, in which an object is moving with constant angular speed around a central, stationary point.

Notice we say that the object has a constant *speed*, but not *velocity*, because the object continuously changes directions. Therefore, the object has two components of acceleration: the tangential acceleration which is parallel to the object’s direction of motion, and the centripetal acceleration which is perpendicular.

If the motion is uniform, the magnitude of the tangential acceleration is zero, and the centripetal acceleration has a constant, non-zero magnitude. The force (or forces) that cause the centripetal acceleration is the centripetal force, which also points inwards towards the center.

This force, from the Greek meaning “seeking the center," is responsible for the rotation of the object in a uniform circular path around the center.

## Calculating Centripetal Acceleration and Forces

The centripetal acceleration of an object is given by

where *v* is the speed of the object and *R* is the radius at which it is rotating. However, it turns out that the quantity

is not really a force, but can be used to help you relate the force or forces which give rise to the circular motion, to the centripetal acceleration.

## So Why Is There No Centrifugal Force?

Let's pretend that there was such a thing as a centrifugal force, or a force that is equal and opposite to the centripetal force. If that were the case, the two forces would cancel each other out, meaning that the object would not move in a circular path. Any other forces present might push the object in some other direction or in a straight line, but if there was always an equal and opposite centrifugal force, there would be no circular motion.

So what about the sensation you feel when you go around a curve on the road and in other centrifugal force examples? This "force" is actually a result of inertia: you body keeps moving in a straight line, and the car actually pushes you around the curve, so it feels like we are getting pressed into the car in the opposite direction of the curve.

## What a Centrifugal Force Calculator Really Does

A centrifugal force calculator basically takes the formula for centripetal acceleration (which describes a real phenomenon) and reverses the direction of the force, to describe the apparent (but ultimately fictitious) centrifugal force. There is really no need to do this in most cases, because it doesn't describe the reality of the physical situation, only the apparent situation in a non-inertial reference frame (i,e. from the perspective of someone inside the turning car).

References

- Young, H. D., Freedman, R. A., (2012) University Physics. San Francisco, CA: Addison-Wesley.
- Britannica: Centrifugal Force

Tips

- Remember not to confuse centripetal and centrifugal. Remember, the centripetal force is a real force; the centrifugal force is an apparent force.

About the Author

Lipi Gupta is currently pursuing her Ph. D. in physics at the University of Chicago. She earned her Bachelor of Arts in physics with a minor in mathematics at Cornell University in 2015, where she was a tutor for engineering students, and was a resident advisor in a first-year dorm for three years. With this experience, when not working on her Ph. D. research, Gupta participates in STEM outreach activities to promote young women and minorities to pursue science careers.

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