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 10 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find the speed v of the object.

n = 90 rpmr = 0.1 m

v = m/s

2.Easy

A 1400 kg car drives around a flat curve of radius 110 m at a constant 16 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 16 m/sr = 110 m

F_c = N

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.6 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 angular speed ω in rad/s.

r = 2.6 mμ_s = 0.7g = 9.81 m/s²

ω = rad/s

4.Medium

A car takes a flat curve of radius 35 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 = 35 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 2 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 2 kgr = 1.3 mv = 5.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.7 kg ball on a string 0.6 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 = 1.7 kgr = 0.6 mv = 7.5 m/sg = 9.81 m/s²

T = N

Answer key

1. v = 0.9425 m/s
2. F_c = 3258 N
3. ω = 2.322 rad/s
4. v_max = 16.57 m/s
5. T = 66.16 N
6. T = 176.1 N

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