Practice Circular Motion in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

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

Example 2

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

Example 3

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

Example 4

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)?

Example 5

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

Example 6

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

Example 7

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 8

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

Example 9

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

Example 10

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 11

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

Example 12

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 13

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

Example 14

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

Example 15

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 16

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 17

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 18

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

Example 19

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 20

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?
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