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 small object sits 5 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration a_c.

n = 200 rpmr = 0.05 m

a_c = m/s²

2.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 120 km/h?

v = 120 km/ha_max = 0.5 m/s²

r_min = m

3.Medium

A road engineer wants cars to take a curve of radius 230 m at 40 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 230 mv = 40 km/hg = 9.81 m/s²

θ = °

4.Medium

A small ball on a string of length 0.7 m moves in a horizontal circle so that the string makes a constant angle of 40° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.7 mθ = 40°g = 9.81 m/s²

T = s

5.Hard

A 0.2 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 1.3 mv = 4 m/sg = 9.81 m/s²

T = N

6.Hard

A curve of radius 50 m is banked at 8°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 50 mθ = 8°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

Answer key

1. a_c = 21.93 m/s²
2. r_min = 2222 m
3. θ = 3.132 °
4. T = 1.469 s
5. T = 4.424 N
6. v_max = 12.07 m/s

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