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 small object sits 15 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find the speed v of the object.

n = 78 rpmr = 0.15 m

v = m/s

2.Easy

An 800 kg car drives around a flat curve of radius 40 m at a constant 9 m/s. Find the inward (centripetal) force F_c needed.

m = 800 kgv = 9 m/sr = 40 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 0.3. 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 = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.3 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.3 mμ_s = 0.8g = 9.81 m/s²

n = rpm

5.Hard

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.8 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.8 kgr = 1 mv = 3 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 1.225 m/s
2. F_c = 1620 N
3. v_max = 14.35 m/s
4. n = 18.41 rpm
5. v_min = 2.971 m/s
6. T = 33.86 N

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