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.

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: Circular Motion starts by naming what changes, over what time interval, and whether direction matters.

Common stuck point: Students often know a formula related to circular motion but skip the recognition step: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I describing motion over time with position, distance, direction, speed, velocity, or acceleration clearly separated?

Worked Examples

Example 1

easy
A car drives around a circular track of radius 50 m50 \text{ m} at a constant speed of 10 m/s10 \text{ m/s}. What is the centripetal acceleration?

Answer

ac=2 m/s2 toward centera_c = 2 \text{ m/s}^2 \text{ toward center}

First step

1
Centripetal acceleration is directed toward the center of the circle: ac=v2ra_c = \frac{v^2}{r}.

Full solution

  1. 2
    ac=10250=10050=2 m/s2a_c = \frac{10^2}{50} = \frac{100}{50} = 2 \text{ m/s}^2
  2. 3
    This acceleration changes the direction of velocity, not its magnitude.
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 6.8×106 m6.8 \times 10^6 \text{ m} with a period of 5400 s5400 \text{ s}. What is its orbital speed and centripetal acceleration?

Example 3

medium
A car travels around a circular track of radius 50 m at 20 m/s. Find the centripetal acceleration.

Example 4

medium
A 2 kg2 \text{ kg} ball on a 1.5 m1.5 \text{ m} string moves in a horizontal circle at 4 m/s4 \text{ m/s}. Find the centripetal force.

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 mr = 0.35 \text{ m}) moves at 5 m/s5 \text{ m/s}. What is the period of rotation and the centripetal acceleration?

Example 2

hard
A ball on a 0.8 m0.8 \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 m/s2g = 9.8 \text{ m/s}^2.

Example 3

easy
An object moves at 44 m/s in a circle of radius 22 m. Find its centripetal acceleration.

Example 4

easy
A car rounds a circular track at constant speed. Is it accelerating?

Example 5

easy
In which direction does centripetal acceleration point?

Example 6

easy
An object completes a circle of radius 33 m. What distance does one revolution cover?

Example 7

easy
Period T=4T=4 s for one revolution. What is the frequency?

Example 8

easy
An object speeds around a circle of radius 55 m at 1010 m/s. Centripetal acceleration?

Example 9

easy
A wheel spins so a point goes around in 22 s. How many revolutions in 1010 s?

Example 10

easy
At constant speed on a circle, is the speed changing?

Example 11

medium
A ball on a string moves in a circle of radius 0.50.5 m, completing a revolution in 11 s. Find its speed.

Example 12

medium
A satellite circles at v=8v=8 km/s, radius r=8000r=8000 km. Find the centripetal acceleration in m/s2^2.

Example 13

medium
A point at radius rr and one at radius 2r2r on the same rigid wheel. Compare their speeds.

Example 14

medium
An object needs centripetal acceleration 1818 m/s2^2 on a radius 22 m. Find its speed.

Example 15

medium
A car rounds a curve of radius 5050 m at 2020 m/s. Find the centripetal acceleration.

Example 16

medium
A fan blade tip is at radius 0.30.3 m spinning so a point completes 55 revolutions per second. Find the tip speed.

Example 17

challenge
A ball on a 11 m string is whirled so its centripetal acceleration equals g=9.8g=9.8 m/s2^2. Find the period of revolution.

Example 18

challenge
A coin sits 0.10.1 m from the center of a turntable. If max static friction gives a=2a=2 m/s2^2, find the maximum frequency before it slips.

Example 19

challenge
Two objects orbit the same center: A at radius rr, speed vv; B at radius 4r4r, speed 2v2v. Compare their centripetal accelerations.

Example 20

medium
A car rounds a curve of radius 2020 m at 1010 m/s. Find the centripetal acceleration.

Example 21

medium
A point moves in a circle of radius 44 m, completing a revolution in 88 s. Find its speed.

Example 22

medium
An object on a circle of radius 33 m has centripetal acceleration 1212 m/s2^2. Find its speed.

Example 23

easy
A ball moves at 6 m/s6 \text{ m/s} on a circle of radius 3 m3 \text{ m}. Find its centripetal acceleration.

Example 24

easy
A turntable rotates at 22 Hz. What is its period?

Example 25

easy
An object moves at constant v=8 m/sv = 8 \text{ m/s} on a circle of radius r=4 mr = 4 \text{ m}. Find the centripetal acceleration.

Example 26

easy
A wheel completes 44 revolutions in 22 seconds. Find the frequency.

Example 27

easy
A particle moves on a circle of radius 0.50.5 m at 44 m/s. Find the centripetal acceleration.

Example 28

medium
A car on a curve of radius 40 m40\text{ m} has ac=4 m/s2a_c = 4 \text{ m/s}^2. Find its speed.

Example 29

medium
A wheel of radius 0.50.5 m rotates with period T=1T = 1 s. Find the speed of a point on its rim.

Example 30

medium
A car drives at 2020 m/s around a curve. To halve its centripetal acceleration, by what factor should the radius change?

Example 31

medium
A point on a wheel of radius 0.2 m0.2 \text{ m} rotates at f=3 Hzf = 3 \text{ Hz}. Find its speed.

Example 32

medium
A 0.1 kg0.1 \text{ kg} ball on a 0.4 m0.4 \text{ m} string is whirled at 3 m/s3 \text{ m/s}. Find the tension.

Example 33

medium
A satellite orbits at constant v=7000 m/sv = 7000 \text{ m/s} at radius 7×106 m7 \times 10^6 \text{ m}. Find the centripetal acceleration.

Example 34

hard
A 1000 kg1000 \text{ kg} car on a 50 m50 \text{ m} curve has μs=0.4\mu_s = 0.4. Find the maximum speed (use g=9.8g = 9.8).

Example 35

hard
A ball on a 1 m1 \text{ m} string swings in a vertical circle. At the top, gravity provides all the centripetal force. Find the minimum speed (use g=9.8g = 9.8).

Example 36

hard
A point on a 0.25 m0.25 \text{ m} wheel rotates at f=4 Hzf = 4 \text{ Hz}. Find its centripetal acceleration.

Example 37

hard
A conical pendulum: a 0.5 kg0.5 \text{ kg} ball on a 1 m1 \text{ m} string makes a 30°30° angle with vertical. Find the speed (use g=9.8g = 9.8, sin⁡30°=0.5\sin 30° = 0.5, cos⁡30°≈0.866\cos 30° \approx 0.866).

Example 38

hard
A 1500 kg1500 \text{ kg} car on a banked curve (angle 20°20°, radius 60 m60 \text{ m}, no friction). Find the design speed (use g=9.8g = 9.8, tan⁡20°≈0.364\tan 20° \approx 0.364).

Example 39

medium
A coin on a turntable is 0.15 m0.15 \text{ m} from the center, rotating at f=1.5 Hzf = 1.5 \text{ Hz}. Find the required centripetal acceleration.

Example 40

challenge
Earth orbits the Sun at radius 1.5×1011 m1.5 \times 10^{11} \text{ m} with period T=3.16×107 sT = 3.16 \times 10^7 \text{ s}. Find the centripetal acceleration.

Example 41

medium
A wheel turns through one revolution in 0.50.5 s, radius 0.40.4 m. Find the tip speed.

Example 42

challenge
A roller-coaster loop of radius 88 m. What minimum speed at the top guarantees riders stay seated (use g=9.8g = 9.8)?
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Background Knowledge

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

accelerationvelocity