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 1400 kg car drives around a flat curve of radius 90 m at a constant 26 m/s. Find the inward (centripetal) force F_c needed.

m = 1400 kgv = 26 m/sr = 90 m

F_c = N

2.Easy

A 1500 kg car drives around a flat curve of radius 180 m at a constant 8 m/s. Find the inward (centripetal) force F_c needed.

m = 1500 kgv = 8 m/sr = 180 m

F_c = N

3.Medium

A car takes a flat curve of radius 150 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 = 150 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 95 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.6 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.6 kgr = 0.9 mv = 7 m/sg = 9.81 m/s²

T = N

6.Hard

A 5 kg cart is released from rest at a height of 22.55 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_bottom of the track on the cart at the bottom of the loop.

m = 5 kgh = 22.55 mR = 5.5 mg = 9.81 m/s²

N_bottom = N

Answer key

1. F_c = 10516 N
2. F_c = 533.3 N
3. v_max = 29.71 m/s
4. v_max = 27.3 m/s
5. T = 38.55 N
6. N_bottom = 451.3 N

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