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 = 50 m20 m/sF = ?

A 1700 kg car drives around a flat curve of radius 50 m at a constant 20 m/s. Find the inward (centripetal) force Fc needed.

m = 1700 kgv = 20 m/sr = 50 m
Fc = N
2.Easy
r = ?160 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?

v = 160 km/hamax = 0.8 m/s²
rmin = m
3.Medium
r = 90 mvmax​ = ?

A car takes a flat curve of radius 90 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 90 mμs = 0.3g = 9.81 m/s²
vmax = m/s
4.Medium
r = 70 mvmax​ = ?

A car takes a flat curve of radius 70 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 70 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
R = 9.5 mh = 38.95 m

A 2.5 kg cart is released from rest at a height of 38.95 m on a frictionless track and runs through a vertical loop of radius 9.5 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 = 38.95 mR = 9.5 mg = 9.81 m/s²
Nbottom = N
6.Hard
r = 1.1 m11 m/svtop​ = ?

A 0.2 kg ball on a light string 1.1 m long is swung in a vertical circle. At the lowest point its speed is 11 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.2 kgr = 1.1 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 13600 N
  2. 2. rmin = 2469 m
  3. 3. vmax = 16.27 m/s
  4. 4. vmax = 18.53 m/s
  5. 5. Nbottom = 225.6 N
  6. 6. Ttop = 12.19 N

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