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 = 50 m21 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 50 m at a constant 21 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 21 m/sr = 50 m
ac = m/s²
2.Easy
r = 0.55 mv120 rpm

A small object sits 55 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration ac.

n = 120 rpmr = 0.55 m
ac = m/s²
3.Medium
r = 2.4 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.4 mμs = 0.6g = 9.81 m/s²
ω = rad/s
4.Medium
r = 2.7 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.7 mμs = 0.6g = 9.81 m/s²
n = rpm
5.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 200 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.4. 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 = 200 mθ = 30°μs = 0.4g = 9.81 m/s²
vmin = m/s
6.Hard
r = 1 mv = 6.5 m/s

A 1.5 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.5 kgr = 1 mv = 6.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. ac = 8.82 m/s²
  2. 2. ac = 86.85 m/s²
  3. 3. ω = 2.61 rad/s
  4. 4. n = 23.5 rpm
  5. 5. vmin = 16.81 m/s
  6. 6. T = 78.09 N

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