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 1400 kg car drives around a flat curve of radius 60 m at a constant 29 m/s. Find its centripetal acceleration a_c.

m = 1400 kgv = 29 m/sr = 60 m

a_c = m/s²

2.Easy

A small object sits 80 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find the speed v of the object.

n = 300 rpmr = 0.8 m

v = m/s

3.Medium

A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 130 mμ_s = 0.5g = 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 1.5 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 = 1.5 mμ_s = 0.7g = 9.81 m/s²

ω = rad/s

5.Hard

A ball on a string 0.6 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 = 0.6 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 1.1 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 8.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.7 mv = 8.5 m/sg = 9.81 m/s²

T = N

Answer key

1. a_c = 14.02 m/s²
2. v = 25.13 m/s
3. v_max = 25.25 m/s
4. ω = 3.057 rad/s
5. v_min = 2.426 m/s
6. T = 124.3 N

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