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 1200 kg car drives around a flat curve of radius 140 m at a constant 27 m/s. Find the inward (centripetal) force F_c needed.

m = 1200 kgv = 27 m/sr = 140 m

F_c = N

2.Easy

A 0.2 kg stone is whirled in a horizontal circle of radius 0.8 m on a smooth, level table, held by a string that breaks at a tension of 200 N. Find the highest speed v_max the stone can have.

m = 0.2 kgr = 0.8 mT_max = 200 N

v_max = m/s

3.Medium

A car takes a flat curve of radius 70 m. The coefficient of static friction between tyres and road is 0.4. 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 = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 30 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 = 30 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.3 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 = 1.3 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.9 kg ball on a string 1.2 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 = 0.9 kgr = 1.2 mv = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 6249 N
2. v_max = 28.28 m/s
3. v_max = 16.57 m/s
4. v_max = 15.34 m/s
5. v_min = 3.571 m/s
6. T = 51.02 N

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