Circular Motion Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Circular Motion.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept Recap

Motion of an object along a circular path where the speed may be constant but the velocity is continuously changing direction, requiring a centripetal acceleration directed toward the centre of the circle.

A car on a circular track at constant speed is still accelerating—toward the center.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Changing direction requires acceleration even if speed is constant.

Common stuck point: The acceleration points toward the center, not along the motion.

Sense of Study hint: When solving a circular motion problem, first identify the radius of the path and the speed (or period) of the object. Then calculate the centripetal acceleration using a_c = v^2/r. Finally, identify which real force (gravity, tension, friction, normal force) provides the centripetal force and set it equal to mv^2/r.

Worked Examples

Example 1

easy
A car drives around a circular track of radius 50 \text{ m} at a constant speed of 10 \text{ m/s}. What is the centripetal acceleration?

Solution

  1. 1
    Centripetal acceleration is directed toward the center of the circle: a_c = \frac{v^2}{r}.
  2. 2
    a_c = \frac{10^2}{50} = \frac{100}{50} = 2 \text{ m/s}^2
  3. 3
    This acceleration changes the direction of velocity, not its magnitude.

Answer

a_c = 2 \text{ m/s}^2 \text{ toward center}
In circular motion, even at constant speed, the velocity direction changes continuously. This requires a centripetal (center-seeking) acceleration, which is always directed toward the center of the circle.

Example 2

medium
A satellite orbits Earth at a radius of 6.8 \times 10^6 \text{ m} with a period of 5400 \text{ s}. What is its orbital speed and centripetal acceleration?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium
A point on the rim of a bicycle wheel (r = 0.35 \text{ m}) moves at 5 \text{ m/s}. What is the period of rotation and the centripetal acceleration?

Example 2

hard
A ball on a 0.8 \text{ m} string is swung in a vertical circle. What minimum speed must it have at the top of the circle so the string remains taut? Use g = 9.8 \text{ m/s}^2.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

accelerationvelocity