Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A 600 kg car drives around a flat curve of radius 40 m at a constant 11 m/s. Find its centripetal acceleration a_c.

m = 600 kgv = 11 m/sr = 40 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 120 km/h?

v = 120 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A 1100 kg car drives over the top of a hump in the road at 13 m/s. The top of the hump is a circular arc of radius 55 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1100 kgv = 13 m/sr = 55 mg = 9.81 m/s²

N = N

4.Medium

A car takes a flat curve of radius 50 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 50 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A curve of radius 220 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 220 mθ = 25°μ_s = 0.15g = 9.81 m/s²

v_min = m/s

6.Hard

A ball on a string 1 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?

r = 1 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 3.025 m/s²
2. r_min = 925.9 m
3. N = 7411 N
4. v_max = 15.66 m/s
5. v_min = 25.26 m/s
6. v_min = 3.132 m/s

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