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

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 200 km/h?

v = 200 km/ha_max = 1.2 m/s²

r_min = m

2.Easy

A 600 kg car drives around a flat curve of radius 30 m at a constant 14 m/s. Find its centripetal acceleration a_c.

m = 600 kgv = 14 m/sr = 30 m

a_c = m/s²

3.Medium

A curve of radius 110 m is banked at 15°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 110 mθ = 15°g = 9.81 m/s²

v = m/s

4.Medium

A 1500 kg car drives over the top of a hump in the road at 12 m/s. The top of the hump is a circular arc of radius 120 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1500 kgv = 12 m/sr = 120 mg = 9.81 m/s²

N = N

5.Hard

A 4.5 kg cart is released from rest at a height of 36.1 m on a frictionless track and runs through a vertical loop of radius 9.5 m. Use g = 9.81 m/s². Find the normal force N_top of the track on the cart at the top of the loop.

m = 4.5 kgh = 36.1 mR = 9.5 mg = 9.81 m/s²

N_top = N

6.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

Answer key

1. r_min = 2572 m
2. a_c = 6.533 m/s²
3. v = 17 m/s
4. N = 12915 N
5. N_top = 114.8 N
6. v_min = 2.426 m/s

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