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 1800 kg car drives around a flat curve of radius 160 m at a constant 24 m/s. Find the inward (centripetal) force F_c needed.

m = 1800 kgv = 24 m/sr = 160 m

F_c = N

2.Easy

A 1200 kg car drives around a flat curve of radius 100 m at a constant 19 m/s. Find its centripetal acceleration a_c.

m = 1200 kgv = 19 m/sr = 100 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 80 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 = 80 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 110 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.2 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.2 kgr = 0.6 mv = 3 m/sg = 9.81 m/s²

T = N

6.Hard

A 2 kg cart is released from rest at a height of 26.4 m on a frictionless track and runs through a vertical loop of radius 5.5 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 = 2 kgh = 26.4 mR = 5.5 mg = 9.81 m/s²

N_top = N

Answer key

1. F_c = 6480 N
2. a_c = 3.61 m/s²
3. v_max = 23.44 m/s
4. v_max = 25.45 m/s
5. T = 29.77 N
6. N_top = 90.25 N

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