# Centripetal Force: Definition, Examples & Problems

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• 0:02 What is a Centripetal Force?
• 1:56 The Mystery Force
• 2:43 Equation
• 3:23 Example Calculation
• 4:29 Lesson Summary

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you should be able to explain what centripetal force is, identify the centripetal force in a particular situation, and solve problems using the centripetal force equation. A short quiz will follow.

## What Is a Centripetal Force?

How many examples can you think of where an object moves in a circle? A car can drive in a circle. A lasso can be whirled around your head in a circle. And even planets orbit each other in circles. But what is it that keeps them moving in that circle?

What would you have to do to make the car move in a circle? You would have to push it - you would have to apply a force. A centripetal force is a force directed towards the center of a circle that keeps an object moving in a circle.

But hold on a minute. Imagine you're in a car, and that car takes a sharp right turn. What force do you feel? Which way are you pushed? It feels like you're pushed, not inwards, but outwards - towards the outside of the circle. Or if you've ever been on a fairground ride that spins and holds you against the outside wall, it's the same effect. This feeling of being pushed out is called the centriFUgal force, or cenTRIFugal force, a force pointing away from the center of a circle.

But the centrifugal force you feel is a fictitious force - it isn't real. The only force that applies to you is the centripetal one that keeps you in the circle. So why do you feel like you're being pushed out?

Well, when you sit in a car moving in a straight line, your body, like any object, wants to keep moving in a straight line. Newton's First Law says that a body in motion stays in motion, a body at rest stays at rest, unless acted upon by an unbalanced force. The car tries to turn the corner, but your body wants to keep going straight, so you get pushed towards the outside of the car as your body tries to continue in a straight line. If it wasn't for the centripetal force provided by the friction between you and the car seat and the seat belt, and the normal force the side of the car applies to you, you would indeed just... keep going.

## The Mystery Force

The centripetal force is nothing mysterious, but it sounds kind of like it is. People will often make the terrible mistake of drawing Fc for centripetal force on a free-body force diagram. Never, ever do this. The centripetal force in a given situation is always created by a specific, real-life force. A satellite is kept in orbit by gravity - gravity, Fg, is the centripetal force. A ball whirled on a string over your head is held in place by tension, FT. And the car moves in a circle because of friction, Ff. There is always a specific force that plays the role of the centripetal force - you just have to figure out what it is!

## Equation

The equation for centripetal force says that the centripetal force, Fc, measured in newtons, is equal to the mass of the object moving in a circle, m, measured in kilograms, multiplied by the velocity of the object as it goes around the circle, v, measured in meters per second, squared (it's just the velocity that's squared), divided by the radius of the circle, measured in meters.

Fc = mv^2 / r

So for example, if gravity is the centripetal force, because we're looking at a satellite in orbit, then you could say that the force of gravity (given by the equation F = mg or Fg) is equal to mv-squared over r.

Fg = mv^2 / r

## Example Calculation

Okay, let's go through an example of how to use the equation.

Imagine you're spinning that lasso, but this time you attach a mass to the end of it. If the spinning lasso is 2 meters long, and the mass of the... mass, is 0.1 kilograms, and the mass is moving around the circular path at a speed of 3 m/s, what is the force of tension in the lasso?

The first step, as always, is to write down what we know. We have the length of the string, which in this case is the radius of the circle, so r equals 2 meters (r = 2 meters). And we have the mass of 0.1 kilograms (m = 0.1 kilograms). And we have the velocity of 3 m/s (v = 3 m/s). And we want the force of tension, FT.

Since the mass is moving in a circle, the force of tension is acting as our centripetal force.

Fc = mv^2 / r, which means for this situation, FT = mv^2 / r.

.1 (3) ^2 / 2 = 0.45 newtons

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