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 1800 kg car drives around a flat curve of radius 40 m at a constant 12 m/s. Find the inward (centripetal) force F_c needed.

m = 1800 kgv = 12 m/sr = 40 m

F_c = N

2.Easy

A 1700 kg car drives around a flat curve of radius 80 m at a constant 28 m/s. Find its centripetal acceleration a_c.

m = 1700 kgv = 28 m/sr = 80 m

a_c = m/s²

3.Medium

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3 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 mμ_s = 0.6g = 9.81 m/s²

ω = rad/s

4.Medium

A car takes a flat curve of radius 90 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 = 90 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.9 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.9 kgr = 0.9 mv = 8 m/sg = 9.81 m/s²

T = N

6.Hard

A 0.6 kg ball on a string 1.1 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 = 0.6 kgr = 1.1 mv = 3 m/sg = 9.81 m/s²

T = N

Answer key

1. F_c = 6480 N
2. a_c = 9.8 m/s²
3. ω = 2.335 rad/s
4. v_max = 26.58 m/s
5. T = 153.8 N
6. T = 10.8 N

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