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 1100 kg car drives around a flat curve of radius 170 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

m = 1100 kgv = 17 m/sr = 170 m

F_c = N

2.Easy

A 900 kg car drives around a flat curve of radius 120 m at a constant 9 m/s. Find the inward (centripetal) force F_c needed.

m = 900 kgv = 9 m/sr = 120 m

F_c = N

3.Medium

A car takes a flat curve of radius 115 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 = 115 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 30 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 30 mμ_s = 0.4g = 9.81 m/s²

v_max = m/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 curve of radius 270 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 270 mθ = 12°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

Answer key

1. F_c = 1870 N
2. F_c = 607.5 N
3. v_max = 18.4 m/s
4. v_max = 10.85 m/s
5. v_min = 2.426 m/s
6. v_max = 31.49 m/s

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