Circular Motion Examples: 46 Problems with Answers

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 \text{ m}

at a constant speed of

10 \text{ m/s}

. What is the centripetal acceleration?

Answer

a_{c} = 2 {m/s}^{2} toward center

First step

Centripetal acceleration is directed toward the center of the circle:

a_c = \frac{v^2}{r}

Full solution

2
$a_{c} = \frac{10^{2}}{50} = \frac{100}{50} = 2 {m/s}^{2}$
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 \times 10^6 \text{ m}

with a period of

5400 \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

2 \text{ kg}

ball on a

1.5 \text{ m}

string moves in a horizontal circle at

4 \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 \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

Example 3

easy

An object moves at

4

m/s in a circle of radius

2

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

3

m. What distance does one revolution cover?

Example 7

easy

Period

T=4

s for one revolution. What is the frequency?

Example 8

easy

An object speeds around a circle of radius

5

m at

10

m/s. Centripetal acceleration?

Example 9

easy

A wheel spins so a point goes around in

2

s. How many revolutions in

10

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

0.5

m, completing a revolution in

1

s. Find its speed.

Example 12

medium

A satellite circles at

v=8

km/s, radius

r=8000

km. Find the centripetal acceleration in m/s

^2

Example 13

medium

A point at radius

r

and one at radius

2r

on the same rigid wheel. Compare their speeds.

Same angular speed: outer point at r

Example 14

medium

An object needs centripetal acceleration

18

m/s

^2

on a radius

2

m. Find its speed.

Example 15

medium

A car rounds a curve of radius

50

m at

20

m/s. Find the centripetal acceleration.

Example 16

medium

A fan blade tip is at radius

0.3

m spinning so a point completes

5

revolutions per second. Find the tip speed.

Example 17

challenge

A ball on a

1

m string is whirled so its centripetal acceleration equals

g=9.8

m/s

^2

. Find the period of revolution.

Example 18

challenge

A coin sits

0.1

m from the center of a turntable. If max static friction gives

a=2

m/s

^2

, find the maximum frequency before it slips.

Example 19

challenge

Two objects orbit the same center: A at radius

r

, speed

v

; B at radius

4r

, speed

2v

. Compare their centripetal accelerations.

Objects A (r, v) and B (4r, 2v) — compare centripetal accelerations

Example 20

medium

A car rounds a curve of radius

20

m at

10

m/s. Find the centripetal acceleration.

Example 21

medium

A point moves in a circle of radius

4

m, completing a revolution in

8

s. Find its speed.

Example 22

medium

An object on a circle of radius

3

m has centripetal acceleration

12

m/s

^2

. Find its speed.

Example 23

easy

A ball moves at

6 \text{ m/s}

on a circle of radius

3 \text{ m}

. Find its centripetal acceleration.

Example 24

easy

A turntable rotates at

2

Hz. What is its period?

Example 25

easy

An object moves at constant

v = 8 \text{ m/s}

on a circle of radius

r = 4 \text{ m}

. Find the centripetal acceleration.

Example 26

easy

A wheel completes

4

revolutions in

2

seconds. Find the frequency.

Example 27

easy

A particle moves on a circle of radius

0.5

m at

4

m/s. Find the centripetal acceleration.

Example 28

medium

A car on a curve of radius

40\text{ m}

has

a_c = 4 \text{ m/s}^2

. Find its speed.

Example 29

medium

A wheel of radius

0.5

m rotates with period

T = 1

s. Find the speed of a point on its rim.

Example 30

medium

A car drives at

20

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 \text{ m}

rotates at

f = 3 \text{ Hz}

. Find its speed.

Example 32

medium

0.1 \text{ kg}

ball on a

0.4 \text{ m}

string is whirled at

3 \text{ m/s}

. Find the tension.

Example 33

medium

A satellite orbits at constant

v = 7000 \text{ m/s}

at radius

7 \times 10^6 \text{ m}

. Find the centripetal acceleration.

Example 34

hard

1000 \text{ kg}

car on a

50 \text{ m}

curve has

\mu_s = 0.4

. Find the maximum speed (use

g = 9.8

Example 35

hard

A ball on a

1 \text{ m}

string swings in a vertical circle. At the top, gravity provides all the centripetal force. Find the minimum speed (use

g = 9.8

Example 36

hard

A point on a

0.25 \text{ m}

wheel rotates at

f = 4 \text{ Hz}

. Find its centripetal acceleration.

Example 37

hard

A conical pendulum: a

0.5 \text{ kg}

ball on a

1 \text{ m}

string makes a

30°

angle with vertical. Find the speed (use

g = 9.8

\sin 30° = 0.5

\cos 30° \approx 0.866

Example 38

hard

1500 \text{ kg}

car on a banked curve (angle

20°

, radius

60 \text{ m}

, no friction). Find the design speed (use

g = 9.8

\tan 20° \approx 0.364

Banked curve at 20°, r

Example 39

medium

A coin on a turntable is

0.15 \text{ m}

from the center, rotating at

f = 1.5 \text{ Hz}

. Find the required centripetal acceleration.

Example 40

challenge

Earth orbits the Sun at radius

1.5 \times 10^{11} \text{ m}

with period

T = 3.16 \times 10^7 \text{ s}

. Find the centripetal acceleration.

Example 41

medium

A wheel turns through one revolution in

0.5

s, radius

0.4

m. Find the tip speed.

Example 42

challenge

A roller-coaster loop of radius

8

m. What minimum speed at the top guarantees riders stay seated (use

g = 9.8

Roller-coaster loop r

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Related Concepts

Acceleration Velocity Centripetal Force Angular Velocity

Background Knowledge

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

accelerationvelocity