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 900 kg car drives around a flat curve of radius 170 m at a constant 11 m/s. Find its centripetal acceleration a_c.

m = 900 kgv = 11 m/sr = 170 m

a_c = m/s²

2.Easy

A 1800 kg car drives around a flat curve of radius 120 m at a constant 23 m/s. Find its centripetal acceleration a_c.

m = 1800 kgv = 23 m/sr = 120 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 140 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 140 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 55 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 55 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A 0.5 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 1.1 mv = 6 m/sg = 9.81 m/s²

T = N

6.Hard

A 1.5 kg cart is released from rest at a height of 33 m on a frictionless track and runs through a vertical loop of radius 7.5 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 = 1.5 kgh = 33 mR = 7.5 mg = 9.81 m/s²

N_top = N

Answer key

1. a_c = 0.7118 m/s²
2. a_c = 4.408 m/s²
3. v_max = 23.44 m/s
4. v_max = 14.69 m/s
5. T = 21.27 N
6. N_top = 55.92 N

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