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 = 130 m14 m/sF = ?

A 1100 kg car drives around a flat curve of radius 130 m at a constant 14 m/s. Find the inward (centripetal) force Fc needed.

m = 1100 kgv = 14 m/sr = 130 m
Fc = N
2.Easy
r = ?160 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?

v = 160 km/hamax = 1.5 m/s²
rmin = m
3.Medium
r = 60 mvmax​ = ?

A car takes a flat curve of radius 60 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 = 60 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 95 mvmax​ = ?

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 95 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.5 mv = 7.5 m/s

A 1.3 kg ball on a string 0.5 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 = 1.3 kgr = 0.5 mv = 7.5 m/sg = 9.81 m/s²
T = N
6.Hard
R = 3 mh = 13.5 m

A 1.5 kg cart is released from rest at a height of 13.5 m on a frictionless track and runs through a vertical loop of radius 3 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 1.5 kgh = 13.5 mR = 3 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. Fc = 1658 N
  2. 2. rmin = 1317 m
  3. 3. vmax = 20.3 m/s
  4. 4. vmax = 23.65 m/s
  5. 5. T = 159 N
  6. 6. Ntop = 58.86 N

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