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 = 0.3 mvmax​ = ?

A 0.7 kg stone is whirled in a horizontal circle of radius 0.3 m on a smooth, level table, held by a string that breaks at a tension of 190 N. Find the highest speed vmax the stone can have.

m = 0.7 kgr = 0.3 mTmax = 190 N
vmax = m/s
2.Easy
r = 100 m29 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 100 m at a constant 29 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 29 m/sr = 100 m
ac = m/s²
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 = 150 mvmax​ = ?

A car takes a flat curve of radius 150 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 150 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.5 mv = 6 m/s

A 0.7 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.7 kgr = 0.5 mv = 6 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.2 mv = 8 m/s

A 1.7 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.7 kgr = 1.2 mv = 8 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. vmax = 9.024 m/s
  2. 2. ac = 8.41 m/s²
  3. 3. vmax = 27.48 m/s
  4. 4. vmax = 24.26 m/s
  5. 5. T = 57.27 N
  6. 6. T = 107.3 N

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