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 1300 kg car drives around a flat curve of radius 100 m at a constant 9 m/s. Find the inward (centripetal) force F_c needed.

m = 1300 kgv = 9 m/sr = 100 m

F_c = N

2.Easy

A small object sits 45 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find its centripetal acceleration a_c.

n = 30 rpmr = 0.45 m

a_c = m/s²

3.Medium

A 1600 kg car drives over the top of a hump in the road at 5 m/s. The top of the hump is a circular arc of radius 65 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1600 kgv = 5 m/sr = 65 mg = 9.81 m/s²

N = N

4.Medium

An 800 kg car drives over the top of a hump in the road at 17 m/s. The top of the hump is a circular arc of radius 70 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 800 kgv = 17 m/sr = 70 mg = 9.81 m/s²

N = N

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 40 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.15. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

r = 40 mθ = 25°μ_s = 0.15g = 9.81 m/s²

v_min = m/s

Answer key

1. F_c = 1053 N
2. a_c = 4.441 m/s²
3. N = 15081 N
4. N = 4545 N
5. v_min = 2.426 m/s
6. v_min = 10.77 m/s

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