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 m16 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 200 m at a constant 16 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 16 m/sr = 200 m
ac = m/s²
2.Easy
r = ?250 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?

v = 250 km/hamax = 2 m/s²
rmin = m
3.Medium
r = 30 mvmax​ = ?

A car takes a flat curve of radius 30 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 = 30 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 30 mvmax​ = ?

A car takes a flat curve of radius 30 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 = 30 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.5 mv = 5.5 m/s

A 1.1 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.5 mv = 5.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1 m10 m/svtop​ = ?

A 0.4 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.4 kgr = 1 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 1.28 m/s²
  2. 2. rmin = 2411 m
  3. 3. vmax = 14.35 m/s
  4. 4. vmax = 13.29 m/s
  5. 5. T = 77.34 N
  6. 6. Ttop = 20.38 N

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