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 1500 kg car drives around a flat curve of radius 140 m at a constant 12 m/s. Find its centripetal acceleration a_c.

m = 1500 kgv = 12 m/sr = 140 m

a_c = m/s²

2.Easy

A 700 kg car drives around a flat curve of radius 20 m at a constant 17 m/s. Find its centripetal acceleration a_c.

m = 700 kgv = 17 m/sr = 20 m

a_c = m/s²

3.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

4.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.7 mμ_s = 0.6g = 9.81 m/s²

ω = rad/s

5.Hard

A 0.6 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.6 kgr = 1 mv = 3.5 m/sg = 9.81 m/s²

T = N

6.Hard

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²

v_min = m/s

Answer key

1. a_c = 1.029 m/s²
2. a_c = 14.45 m/s²
3. v_max = 16.57 m/s
4. ω = 2.102 rad/s
5. T = 13.24 N
6. v_min = 2.62 m/s

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