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 200 km/h?

v = 200 km/ha_max = 2 m/s²

r_min = m

2.Easy

A 700 kg car drives around a flat curve of radius 160 m at a constant 19 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 19 m/sr = 160 m

a_c = m/s²

3.Medium

A small ball on a string of length 0.6 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.6 mθ = 20°g = 9.81 m/s²

T = s

4.Medium

A car takes a flat curve of radius 70 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 70 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 1 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1.3 mv = 7.5 m/sg = 9.81 m/s²

T = N

6.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 7 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 7 mv₀ = 0

h_min = m

Answer key

1. r_min = 1543 m
2. a_c = 2.256 m/s²
3. T = 1.506 s
4. v_max = 23.44 m/s
5. T = 53.08 N
6. h_min = 17.5 m

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