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 = 40 m16 m/sac​ = ?

A 1800 kg car drives around a flat curve of radius 40 m at a constant 16 m/s. Find its centripetal acceleration ac.

m = 1800 kgv = 16 m/sr = 40 m
ac = m/s²
2.Easy
r = 1.3 mvmax​ = ?

A 0.5 kg stone is whirled in a horizontal circle of radius 1.3 m on a smooth, level table, held by a string that breaks at a tension of 100 N. Find the highest speed vmax the stone can have.

m = 0.5 kgr = 1.3 mTmax = 100 N
vmax = m/s
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 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 105 mvmax​ = ?

A car takes a flat curve of radius 105 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 = 105 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.9 mv = 5.5 m/s

A 1.1 kg ball on a string 0.9 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 = 0.9 mv = 5.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.3 m9 m/svtop​ = ?

A 0.8 kg ball on a light string 1.3 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.8 kgr = 1.3 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 6.4 m/s²
  2. 2. vmax = 16.12 m/s
  3. 3. vmax = 25.45 m/s
  4. 4. vmax = 24.86 m/s
  5. 5. T = 47.76 N
  6. 6. Ttop = 10.61 N

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