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 small object sits 130 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find the speed v of the object.

n = 300 rpmr = 1.3 m

v = m/s

2.Easy

A small object sits 25 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find the speed v of the object.

n = 78 rpmr = 0.25 m

v = m/s

3.Medium

A car takes a flat curve of radius 90 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 = 90 mμ_s = 0.8g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 150 m at 120 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 150 mv = 120 km/hg = 9.81 m/s²

θ = °

5.Hard

A 1.4 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 7.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 1.3 mv = 7.5 m/sg = 9.81 m/s²

T = N

6.Hard

A 4.5 kg cart is released from rest at a height of 43.2 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 = 4.5 kgh = 43.2 mR = 9 mg = 9.81 m/s²

N_top = N

Answer key

1. v = 40.84 m/s
2. v = 2.042 m/s
3. v_max = 26.58 m/s
4. θ = 37.06 °
5. T = 74.31 N
6. N_top = 203.1 N

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