# Centripetal Force

**Centripetal force** causes an object in motion to continue in a curved path rather than a linear one. If this force stops, the object will continue in a tangential linear path. An example of **centripetal force** is how planets rotate around the sun. In this case gravity is a **centripetal force** because it keeps the planets on curved paths and we say that *centripetal acceleration = velocity^2 /radius* while *centripetal force = mass x velocity^2 / radius*.

Centripetal force we all have felt the centripetal force anytime you've been in a bus or your car and you've taken a tight turn especially at a high speed you may have had to grab the rail so you didn't slide into the wall or into the side of your car right. Well that's a very natural feeling we can all relate to what a centripetal force is, but what is it really? Well it's the force that is pushing you to the center and that forces causes to you move in a circular path because remember a velocity is a direction and a speed a speed and a direction and if you're going on a circular path your velocity is always going to be tangent to the center of that circle. So your velocity is always changing okay, well the force that allows for that change in velocity is a centripetal force okay.

And that force is the acceleration of that force we can describe as the velocity squared divided by the radius r. So the radius is going to be again this distance right here okay. So that's the acceleration due to the centripetal force which allows that change in velocity okay. The force itself remember a force is mass times acceleration, so now we need to multiply the mass of the object times the velocity squared and divide by the radius and that will tell us what that centripetal force is that is allowing that object to change direction as it continues to revolve around the center of the circle okay.

Let's look at an example of how you could calculate centripetal force okay so I've got a 2 kilogram object and it's swinging from a 0.5 meters string okay and it's moving at 3 meters per second okay. What's the centripetal force on that object okay? So again this is a force so it's the acceleration velocity squared over the radius times the mass okay. Well let's plug those numbers in okay. So our mass is 2 kilograms, okay our velocity 3 meters per second squared okay. This is tricky meters per second squared that really is going to equal 9 meters per second meters squared over second squared okay. So don't be confused when you have drive unit and you got a square. You got to square both of those units okay.

And the radius here we said was 0.5 meters okay well let's go ahead and just crunch these numbers okay, so 9 meters per second squared times 2 is 18 okay and let's keep our units there 18 kilograms okay times meters squared over second squared okay over 0.5 meters. Okay another thing students often times gets tripped up is I've got this unit up here and this unit up here and I've got a unit down here how do I solve for that right, well remember this unit can actually come down here okay and then our meters squared will just become meters we can cancel that meter and we're going to get 36 I'm sorry I'll keep my units before I jump to Newtons 36 times kilograms times meters over seconds squared. And remember kilograms times meters seconds squared is a easy way to simplify that into 36 Newtons we're back at the Newtons which is the unit of force.

Okay so this is how we can calculate a centripetal force on an object and just moving in a circular orbit.

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