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 600 kg car drives around a flat curve of radius 100 m at a constant 9 m/s. Find its centripetal acceleration a_c.

m = 600 kgv = 9 m/sr = 100 m

a_c = m/s²

2.Easy

A 1400 kg car drives around a flat curve of radius 140 m at a constant 11 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 11 m/sr = 140 m

F_c = N

3.Medium

A car takes a flat curve of radius 70 m. The coefficient of static friction between tyres and road is 0.7. 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 = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 35 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 35 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.8 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.8 kgr = 0.7 mv = 9 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.2 kg ball on a light string 0.8 m long is swung in a vertical circle. At the lowest point its speed is 11.5 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 = 1.2 kgr = 0.8 mv_bottom = 11.5 m/sg = 9.81 m/s²

T_top = N

Answer key

1. a_c = 0.81 m/s²
2. F_c = 1210 N
3. v_max = 21.92 m/s
4. v_max = 14.35 m/s
5. T = 225.9 N
6. T_top = 139.5 N

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