Practice Applying Circular Motion Formulas

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  • 0:00 Circular Motion Overview
  • 0:33 Calculating Velocity
  • 1:57 Calculating Acceleration
  • 2:42 Calculating Force
  • 3:38 Calculating Force in a…
  • 4:47 Lesson Summary
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Lesson Transcript
Instructor: Laura Foist

Laura has a Masters of Science in Food Science and Human Nutrition and has taught college Science.

We can calculate velocity, acceleration, and force when traveling in a circle. In this lesson, we'll look at some sample problems using the formulas to calculate velocity, acceleration, and force of an object traveling in a circle.

Circular Motion Overview

Imagine that you and a friend are looking at a carousel at an amusement park and wondering what the difference in force and speed would be between a center seat and an outside seat. This could be difficult to determine because you are traveling in a circle. Also, if you're traveling at the same speed for a given period of time, how would you experience any acceleration in order to experience force? We can use the formulas for circular motion to answer these questions.

Calculating Velocity

First, let's learn how to calculate velocity using this formula, where r is the radius of a circle and t is the period, or average time needed to complete one rotation.

The main formulas are:


Let's say that the carousel has a radius of 4 meters on the outside and a radius of 3 meters on the inside. When you time a single rotation, you find that it takes 20 seconds, whether you're sitting on the inside or the outside of the carousel.

We can plug this information into the formula to calculate the velocity of the carousel. First, let's calculate the velocity when sitting on an outside seat. Using the formula, we find that the velocity is:

velocity outside

So, the carousel moves at a speed of 1.3 m/s when you're riding on one of the outside horses. Now, let's calculate the speed of an inside horse. Using the same formula, we find that:

Velocity inside

This means that you're traveling quite a bit slower on an inside horse. It's important to note that this speed is constant, but the direction changes as the carousel turns. And because velocity is speed and direction, this means that the velocity changes as we go around the carousel.

Calculating Acceleration

It's important to understand that velocity changes the carousel turns because if the velocity was constant, we would have no acceleration. Because velocity does change, we must have acceleration, even though the speed stays the same.

To calculate acceleration, we use this formula, where acceleration equals velocity squared divided by the radius of the circle:

Acceleration outside

Let's figure out the acceleration of the carousel while riding on an outside horse. Plugging the values into the formula, we find that acceleration on an outside horse is 0.4 m/s 2.

Now, for the acceleration for an inside horse.

Acceleration inside

Using the formula, we find that the inside horse is accelerating at a rate of 0.3 m/s 2.

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