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 1300 kg car drives around a flat curve of radius 130 m at a constant 11 m/s. Find its centripetal acceleration a_c.

m = 1300 kgv = 11 m/sr = 130 m

a_c = m/s²

2.Easy

A 1600 kg car drives around a flat curve of radius 30 m at a constant 13 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 13 m/sr = 30 m

F_c = N

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.2 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.2 mμ_s = 0.7g = 9.81 m/s²

n = rpm

4.Medium

A car takes a flat curve of radius 30 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 = 30 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.3 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 0.7 mv = 4.5 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 1 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 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 0.9308 m/s²
2. F_c = 9013 N
3. n = 24.1 rpm
4. v_max = 13.29 m/s
5. T = 50.36 N
6. v_min = 3.132 m/s

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