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 = 180 m11 m/sac​ = ?

A 1800 kg car drives around a flat curve of radius 180 m at a constant 11 m/s. Find its centripetal acceleration ac.

m = 1800 kgv = 11 m/sr = 180 m
ac = m/s²
2.Easy
r = 60 m22 m/sac​ = ?

A 1700 kg car drives around a flat curve of radius 60 m at a constant 22 m/s. Find its centripetal acceleration ac.

m = 1700 kgv = 22 m/sr = 60 m
ac = m/s²
3.Medium
r = 45 mvmax​ = ?

A car takes a flat curve of radius 45 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 = 45 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
θ = ?to centre80 km/h

A road engineer wants cars to take a curve of radius 80 m at 80 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 80 mv = 80 km/hg = 9.81 m/s²
θ = °
5.Hard
r = 1.4 mv = 9 m/s

A 1.6 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.6 kgr = 1.4 mv = 9 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.7 mv = ?

A ball on a string 0.7 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?

r = 0.7 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 0.6722 m/s²
  2. 2. ac = 8.067 m/s²
  3. 3. vmax = 17.58 m/s
  4. 4. θ = 32.18 °
  5. 5. T = 108.3 N
  6. 6. vmin = 2.62 m/s

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