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 900 kg car drives around a flat curve of radius 50 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

m = 900 kgv = 17 m/sr = 50 m

F_c = N

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 160 km/h?

v = 160 km/ha_max = 1.2 m/s²

r_min = m

3.Medium

A 1000 kg car drives over the top of a hump in the road at 24 m/s. The top of the hump is a circular arc of radius 95 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1000 kgv = 24 m/sr = 95 mg = 9.81 m/s²

N = N

4.Medium

A car takes a flat curve of radius 75 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 = 75 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.2 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 = 1.2 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.7 kg ball on a light string 1.5 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.7 kgr = 1.5 mv_bottom = 10 m/sg = 9.81 m/s²

T_top = N

Answer key

1. F_c = 5202 N
2. r_min = 1646 m
3. N = 3747 N
4. v_max = 24.26 m/s
5. v_min = 3.431 m/s
6. T_top = 12.33 N

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