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 1 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 1 m/s²

r_min = m

2.Easy

A 1700 kg car drives around a flat curve of radius 200 m at a constant 8 m/s. Find its centripetal acceleration a_c.

m = 1700 kgv = 8 m/sr = 200 m

a_c = m/s²

3.Medium

A 1100 kg car drives over the top of a hump in the road at 16 m/s. The top of the hump is a circular arc of radius 75 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1100 kgv = 16 m/sr = 75 mg = 9.81 m/s²

N = N

4.Medium

A small ball on a string of length 1 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 time T for one revolution.

L = 1 mθ = 35°g = 9.81 m/s²

T = s

5.Hard

A ball on a string 1.4 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 = 1.4 mg = 9.81 m/s²

v_min = m/s

6.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 4.5 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 = 4.5 mv₀ = 0

h_min = m

Answer key

1. r_min = 6944 m
2. a_c = 0.32 m/s²
3. N = 7036 N
4. T = 1.816 s
5. v_min = 3.706 m/s
6. h_min = 11.25 m

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