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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

v = 250 km/ha_max = 2 m/s²

r_min = m

2.Easy

A small object sits 145 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find its centripetal acceleration a_c.

n = 90 rpmr = 1.45 m

a_c = m/s²

3.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 35° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.7 mθ = 35°g = 9.81 m/s²

v = m/s

4.Medium

A small ball on a string of length 1.3 m moves in a horizontal circle so that the string makes a constant angle of 25° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.3 mθ = 25°g = 9.81 m/s²

T = s

5.Hard

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²

v_min = m/s

6.Hard

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²

v_min = m/s

Answer key

1. r_min = 2411 m
2. a_c = 128.8 m/s²
3. v = 1.661 m/s
4. T = 2.177 s
5. v_min = 2.62 m/s
6. v_min = 2.971 m/s

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