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 1500 kg car drives around a flat curve of radius 200 m at a constant 29 m/s. Find its centripetal acceleration a_c.

m = 1500 kgv = 29 m/sr = 200 m

a_c = m/s²

2.Easy

A small object sits 75 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find the speed v of the object.

n = 33 rpmr = 0.75 m

v = m/s

3.Medium

A curve of radius 80 m is banked at 10°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 80 mθ = 10°g = 9.81 m/s²

v = m/s

4.Medium

A car takes a flat curve of radius 50 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 = 50 mμ_s = 0.7g = 9.81 m/s²

v_max = m/s

5.Hard

A 1.7 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 6.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 1.7 kgr = 0.6 mv_bottom = 6.5 m/sg = 9.81 m/s²

T_top = N

6.Hard

A 5 kg cart is released from rest at a height of 36 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_bottom of the track on the cart at the bottom of the loop.

m = 5 kgh = 36 mR = 9 mg = 9.81 m/s²

N_bottom = N

Answer key

1. a_c = 4.205 m/s²
2. v = 2.592 m/s
3. v = 11.76 m/s
4. v_max = 18.53 m/s
5. T_top = 36.32 N
6. N_bottom = 441.5 N

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