Centripetal Acceleration: Definition, Formula & Example

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  • 0:00 What Is Centripetal…
  • 1:48 Equation
  • 2:21 Example
  • 3:01 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.

In this lesson, you will learn the meaning of the term centripetal acceleration, an equation to calculate it, and an example of how to use the equation. A short quiz will follow.

What Is Centripetal Acceleration?

If you whirl a ball on a string over your head, the ball is undergoing centripetal acceleration. If you drive your car around in a circle, your car is undergoing centripetal acceleration. And, a satellite orbiting the Earth also has a centripetal acceleration.

Centripetal acceleration is the idea that any object moving in a circle, in something called circular motion, will have an acceleration vector pointed towards the center of that circle. This is true even if the object is moving around the circle at a constant speed. Centripetal means towards the center.

An acceleration is a change in velocity. So, how can something moving at a constant speed in a circle have an acceleration? Well, speed and velocity are not quite the same thing. Speed is just how fast you're going. It is a scalar because it doesn't have a direction. Velocity, on the other hand, is your speed and direction. It is a vector because it does have a direction. For example, 3 miles per hour is a speed, but 3 miles per hour south is a velocity.

Since an object moving in a circle is constantly changing direction, its velocity is constantly changing. And whenever something's velocity is changing - even if only its direction, not its speed - that object must be accelerating.

A force always causes the centripetal acceleration. For a swingball (or tetherball) game, it is the tension in the string. For a satellite, it is the force of gravity. For a car moving around a corner, it is the frictional force between the car and the road. If you remove that force, you remove the centripetal acceleration, and if you remove the centripetal acceleration, the object will continue in a straight line tangent to the circle.

Equation

Acceleration is measured in meters per second per second. This is because it is the number of meters per second by which your velocity changes... each second. For an object moving in circular motion, we can calculate it using the following equation:

In this equation:

a is the centripetal acceleration, measured in meters per second per second (m/s/s)
v is the numerical velocity of the object, measured in meters per second (m/s)
r is the radius of the circle, measured in meters (m)

Example

Let's say you're driving down the street at 50 meters per second, when suddenly you take a corner sharply without slowing down at all. Assuming you manage to stay on the road without hurting yourself, and if the radius of the corner was 5 meters, what was your centripetal acceleration?

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