# Uniform Circular Motion and Centripetal Force

It’s professor Dave, let’s discuss uniform circular motion. We’ve examined a lot of linear motion up to this point, whether horizontal, vertical or at some angle, but there are a lot of objects that follow circular paths of motion. This type of motion is accompanied by an entirely different set of equations, so we have to learn these if we want to approximate the motion of the planets, as well as a wide variety of earthbound objects. Consider a ferris wheel. As the wheel turns the cars exhibit circular motion because they revolve around a single axis of rotation which runs through the center of the wheel perpendicular to the plane that contains it. The cars move around this axis with a constant radius so they trace a circle as they move, since a circle is the set of all points equidistant from some central point. To describe the speed of the car it is common to discuss the tangential speed because the inertia of an object causes it to try to maintain a straight line path. This is the speed of the car along the tangent line at a particular instant. If this tangential speed is constant we will call this uniform circular motion. The tangential speed will depend on the distance of the car from the axis of rotation. If you place a sticker on the wheel very close to the center it will complete one revolution in the same amount of time as one of the cars. But the sticker will travel just a short distance that you could trace with your finger, while the car travels much farther, all the way along the edge of the wheel. Since speed is distance over time, a shorter distance covered in the same amount of time must mean a slower tangential speed. This seems counterintuitive, since the wheel is one object, but that’s why we can also discuss angular velocity, which we will learn about later. The uniform circular motion of the car happens because of a constant centripetal acceleration towards the center of the wheel. At any given moment the car has a velocity vector that is tangent to the wheel and while the magnitude of this velocity will not change, the direction is constantly changing, and any such change in velocity can only happen due to some acceleration. The centripetal acceleration will always point towards the center of the wheel, which will in turn continually pull the direction of the velocity vector towards the center of the wheel. This is what produces the circular motion, as though the car is always trying to move towards the center of the circle but never makes it there because of its tangential speed. Centripetal acceleration is given by tangential speed squared over the radius of the path, so this value would increase if the car were to move faster and if it were to sit closer to the center. We know from Newton’s second law that if an acceleration occurs there must be some force present to produce it, and centripetal acceleration is generated by the centripetal force. Centripetal force is simply centripetal acceleration times the mass of the object, since F equals ma. So we can describe centripetal force by simply adding the subscript C on force and acceleration or it can be given by m times tangential speed squared over the radius of the path. This represents the force that must be applied to produce the circular motion, like the amount of force that must be applied to spin a ball on a string in a circle around your head. If this centripetal force that points towards the center perpendicular to the tangential velocity were to suddenly vanish, in the event that you were to let go of the string, then the object would simply move along the tangent line at the precise moment of release, since there would no longer be any force pulling the object towards the axis of rotation. So centripetal force is the force pulling an object inwards towards the axis of rotation during circular motion, and it can take the form of tension from a string, gravity exerted by massive objects, or static friction from the road when a car navigates a curve. But when you are on a rotating object like a merry-go-round, you feel yourself getting pushed outwards. This is often referred to as the centrifugal force, implying that it is the reactionary force to the centripetal force, but in actuality this is not a real force. The sensation that is produced on the merry-go-round is simply due to the inertia of your body attempting to maintain a straight line path of motion. Inertia is not a force, it is just a result of Newton’s first law. You are not physically part of the merry-go-round, but if you hold on tight enough, the resulting frictional force will cause you to follow the same circular path without any problem. If you are seeking a thrill and decide to let go, inertia will outweigh the centripetal force and you will fly off the side hopefully onto some soft grass. Let’s check comprehension. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always feel free to email me:

## 45 Replies to “Uniform Circular Motion and Centripetal Force”

Thanks Mr.Dave, it helped a lot!

Right now, your videos are the favorite shows for me(Youtube/TV)….every now and then I check whether you have uploaded a video or not…..Thank you so much for making science so easy to comprehend!

sir, can you make a video on non inertial frames

professor Dave has helped me a lot

I got into an argument on the internet which prompted me to read the noether theorems, can you explain how energy is not conserved in an expanding universe?

Thank you proff Dave !!!

Have you considered doing a short Electricity series ?

I have nothing to say for now!!!!!!!!

The answer is 1.25

very, very good explanation.

Good graphics and Good way of explaining

please speak slowly and understandable language

First of all, thanks for all the help! I never thought I would be able to understand physics LOL!

This chapter was really hard for me and I don't feel like you get so much into it in this video. Is there anyother video about this out there that you've posted? I had big problems with equations and the formula K=1/2 * Mv^2 + 1/2 * Iw^2

super

Professor Dave, thank you very much.

sir pls upload a video on dimension and units tricks for engineering students.

Professor Dave is really great

Wait for the equation how come you didnt divide the distance by 2 for radius?

Thank you professor Dave

god bless you mannnn

Ur one of the reasons why I'm passing ap physics right now

amazing u r

Thanks to him, I passed my research paper. Thanks GOAT!

Any uniform circular motion example, like earth which doesn't stop, which is constant in speed any other example

I do not understand why any will click the dislike button on videos like these

Sir plzz cover and explain some topics of alternating current

Very nice, likes and subscribed.

Is Change in momentum = centripetal force ?

What is change in momentum conceptual based?

momentum is centrifugal force?

Thanks sir give ans please not clearly understand sir

good explanation

Dave sir u have helped me a lot.pls make vedios with more animation.This time my boards exam is there pls

Hello St. Henry people

Listen to the intro at 2x speed.

why the force will pull the object inwards?

does not derive the centripetal acc. formula

Awesome teaching… Made the whole chapter easy! Thank you so much

I only learned the meanings of the topic and the rest nothing, maybe Im just dumb.

* khan academy has left the chat *

Your 6 minute video summarized what my teacher was trying to explain for two hours!

Extremely helpful thanks!

Thank u alot sir..

this video is so simple but well-made… i'm studying for finals and when i started struggling with centripetal acceleration i had to come back to this specific video to remember it again. thank you professor dave!!

i love the way he teaches..way better than the professor i have in uni

I have fallen in 😍 with your channel Dave. It's a perfect balance of thoroughness and brevity.

Love this one!

good stuff my dude !

Listen to the intro at .25 speed lmfao

Your explanation is just amazing professor 👨🏫👨🏫👨🏫