Circular Motion

Introduction

So far we've learned about the motion of objects that move left and right, up and down, and anything in between. But what about things that move around in a circle? Think of a car driving around a circular race track, a person riding on a carousel or a Ferris wheel, the moon orbiting the Earth or the planets orbiting the sun (most orbits follow an ellipse, but we'll treat them as circles for now).

Technically, circular motion would be considered 2D motion. But in this lesson, we're going to describe how an object moves around the circumference of a circle. Instead of describing the x and y motion of the object, imagine we take the x axis and we wrap it around in a circle. The object can only move clockwise and counterclockwise, so we only need one number to describe its position along that path.

Once we understand how to describe position, we'll learn about displacement, tangential velocity and tangential acceleration. We call this the tangential description of motion because the object's instantaneous motion points in a direction that is tangent to the circular path.

We'll also touch on uniform circular motion where an object travels in a circle at a constant speed due to a centripetal acceleration. Centripetal force will be covered later in the course.

We'll learn about rotational motion in the next lesson. After that, we'll explain how circular and rotational motion are related and how to convert between them.

Lesson

Circular Motion: Using the Tangential Description of Motion (19:03)
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What is circular motion?

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Linear motion review

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Position and displacement

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Tangential velocity

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Tangential acceleration

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Summary
Study Guide

Study guide for circular motion kinematic equations and variables
Study guide for the equations for converting between circular and rotational motion
Study guide for uniform circular motion, frequency and period
Study guide for centripetal acceleration variables, equations and vectors
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Example Problems

Circular Motion Example Problems (18:10)
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Problem 1: Displacement

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Problem 2: Tangential velocity

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Problem 3: Tangential acceleration

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Problem 4: Constant acceleration equation 1

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Problem 5: Constant acceleration equation 2
Practice Problems

Tangential Position and Displacement
Circular motion practice problem 1
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Circular motion practice problem answer 1Circular motion practice problem 2
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Circular motion practice problem answer 2Circular motion practice problem 3
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Circular motion practice problem answer 3Circular motion practice problem 4
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Circular motion practice problem answer 14Circular motion practice problem 15
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Circular motion practice problem answer 15Circular motion practice problem 16
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Circular motion practice problem answer 16
Tangential Velocity
Circular motion practice problem 17
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Circular motion practice problem answer 17Circular motion practice problem 18
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Circular motion practice problem answer 18Circular motion practice problem 19
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Circular motion practice problem answer 27Circular motion practice problem 28
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Circular motion practice problem answer 28
Tangential Acceleration
Circular motion practice problem 29
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Circular motion practice problem answer 29Circular motion practice problem 30
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Circular motion practice problem answer 30Circular motion practice problem 31
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Circular motion practice problem answer 37Circular motion practice problem 38
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Circular motion practice problem answer 39Circular motion practice problem 40
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Circular motion practice problem answer 42Circular motion practice problem 43
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Circular motion practice problem answer 44Circular motion practice problem 45
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Circular motion practice problem answer 45
Version 3
AP®-Style Questions

Multiple-Choice Questions

Answers

Version 4

Free-Response Questions

Circular motion

  • 2024 Q1 - - Block sliding on a track with loops, forces, FBDs, circular motion, energy
  • 2023 Q3 - - Block and spring rotating about axle, circular motion, centripetal force, FBDs
  • 2018 Q1 - - Spacecraft in circular orbit, circular motion, forces, FBDs, law of gravitation
Other Resources

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