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 1700 kg car drives around a flat curve of radius 20 m at a constant 14 m/s. Find the inward (centripetal) force F_c needed.

m = 1700 kgv = 14 m/sr = 20 m

F_c = N

2.Easy

A 1100 kg car drives around a flat curve of radius 200 m at a constant 27 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 27 m/sr = 200 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 150 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 = 150 mμ_s = 0.5g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 105 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A 3.5 kg cart is released from rest at a height of 31.5 m on a frictionless track and runs through a vertical loop of radius 9 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 = 3.5 kgh = 31.5 mR = 9 mg = 9.81 m/s²

N_top = N

6.Hard

A ball on a string 1 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 = 1 mg = 9.81 m/s²

v_min = m/s

Answer key

1. F_c = 16660 N
2. a_c = 3.645 m/s²
3. v_max = 27.12 m/s
4. v_max = 17.58 m/s
5. N_top = 68.67 N
6. v_min = 3.132 m/s

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