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 = 60 m26 m/sac​ = ?

A 1600 kg car drives around a flat curve of radius 60 m at a constant 26 m/s. Find its centripetal acceleration ac.

m = 1600 kgv = 26 m/sr = 60 m
ac = m/s²
2.Easy
r = 160 m30 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 160 m at a constant 30 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 30 m/sr = 160 m
ac = m/s²
3.Medium
r = 35 mvmax​ = ?

A car takes a flat curve of radius 35 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 = 35 mμs = 0.4g = 9.81 m/s²
vmax = m/s
4.Medium
r = 130 mvmax​ = ?

A car takes a flat curve of radius 130 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 = 130 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.5 m10.5 m/svtop​ = ?

A 1.8 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 10.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.8 kgr = 0.5 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 10°to centrevmin​ = ?

A curve of radius 180 m is banked at 10°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 180 mθ = 10°μs = 0.1g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 11.27 m/s²
  2. 2. ac = 5.625 m/s²
  3. 3. vmax = 11.72 m/s
  4. 4. vmax = 27.66 m/s
  5. 5. Ttop = 308.6 N
  6. 6. vmin = 11.51 m/s

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