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 1 kg stone is whirled in a horizontal circle of radius 0.3 m on a smooth, level table, held by a string that breaks at a tension of 180 N. Find the highest speed v_max the stone can have.

m = 1 kgr = 0.3 mT_max = 180 N

v_max = m/s

2.Easy

A 1100 kg car drives around a flat curve of radius 100 m at a constant 24 m/s. Find its centripetal acceleration a_c.

m = 1100 kgv = 24 m/sr = 100 m

a_c = m/s²

3.Medium

A curve of radius 230 m is banked at 8°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 230 mθ = 8°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 85 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 = 85 mμ_s = 0.3g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1.5 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 = 1.5 mg = 9.81 m/s²

v_min = m/s

6.Hard

A 0.5 kg cart is released from rest at a height of 6 m on a frictionless track and runs through a vertical loop of radius 2 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 = 0.5 kgh = 6 mR = 2 mg = 9.81 m/s²

N_top = N

Answer key

1. v_max = 7.348 m/s
2. a_c = 5.76 m/s²
3. v = 17.81 m/s
4. v_max = 15.82 m/s
5. v_min = 3.836 m/s
6. N_top = 4.905 N

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