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 1.5 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 1.5 m/s²

r_min = m

2.Easy

A 1200 kg car drives around a flat curve of radius 70 m at a constant 26 m/s. Find its centripetal acceleration a_c.

m = 1200 kgv = 26 m/sr = 70 m

a_c = m/s²

3.Medium

A road engineer wants cars to take a curve of radius 390 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 390 mv = 90 km/hg = 9.81 m/s²

θ = °

4.Medium

A car takes a flat curve of radius 35 m. The coefficient of static friction between tyres and road is 0.7. 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 = 0.7g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 2 kg cart is released from rest at a height of 21 m on a frictionless track and runs through a vertical loop of radius 6 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 = 2 kgh = 21 mR = 6 mg = 9.81 m/s²

N_top = N

Answer key

1. r_min = 4630 m
2. a_c = 9.657 m/s²
3. θ = 9.278 °
4. v_max = 15.5 m/s
5. v_min = 2.971 m/s
6. N_top = 39.24 N

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