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
r = ?200 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?

v = 200 km/hamax = 1 m/s²
rmin = m
2.Easy
r = 160 m29 m/sF = ?

A 700 kg car drives around a flat curve of radius 160 m at a constant 29 m/s. Find the inward (centripetal) force Fc needed.

m = 700 kgv = 29 m/sr = 160 m
Fc = N
3.Medium
r = 110 mvmax​ = ?

A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 55 mvmax​ = ?

A car takes a flat curve of radius 55 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 55 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
R = 8 mh = 32.8 m

A 2.5 kg cart is released from rest at a height of 32.8 m on a frictionless track and runs through a vertical loop of radius 8 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 2.5 kgh = 32.8 mR = 8 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 0.8 mv = 3 m/s

A 0.6 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.6 kgr = 0.8 mv = 3 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. rmin = 3086 m
  2. 2. Fc = 3679 N
  3. 3. vmax = 27.48 m/s
  4. 4. vmax = 19.43 m/s
  5. 5. Nbottom = 225.6 N
  6. 6. T = 12.64 N

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