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 30 m at a constant 11 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 11 m/sr = 30 m

a_c = m/s²

2.Easy

A 1000 kg car drives around a flat curve of radius 200 m at a constant 22 m/s. Find its centripetal acceleration a_c.

m = 1000 kgv = 22 m/sr = 200 m

a_c = m/s²

3.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 50 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 50 mg = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 135 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 135 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

5.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 3 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 3 mv₀ = 0

h_min = m

6.Hard

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 3.5 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 3.5 mv₀ = 0

h_min = m

Answer key

1. a_c = 4.033 m/s²
2. a_c = 2.42 m/s²
3. v_max = 22.15 m/s
4. v_max = 25.73 m/s
5. h_min = 7.5 m
6. h_min = 8.75 m

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