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 = 130 m27 m/sF = ?

A 600 kg car drives around a flat curve of radius 130 m at a constant 27 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 27 m/sr = 130 m
Fc = N
2.Easy
r = 70 m12 m/sac​ = ?

A 1200 kg car drives around a flat curve of radius 70 m at a constant 12 m/s. Find its centripetal acceleration ac.

m = 1200 kgv = 12 m/sr = 70 m
ac = m/s²
3.Medium
r = 140 mvmax​ = ?

A car takes a flat curve of radius 140 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 = 140 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 2.7 mω = ?

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 0.5. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.7 mμs = 0.5g = 9.81 m/s²
ω = rad/s
5.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 110 m is banked at 30°, 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 = 110 mθ = 30°μs = 0.1g = 9.81 m/s²
vmin = m/s
6.Hard
r = 0.8 mv = 4 m/s

A 0.5 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.5 kgr = 0.8 mv = 4 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 3365 N
  2. 2. ac = 2.057 m/s²
  3. 3. vmax = 28.71 m/s
  4. 4. ω = 2.696 rad/s
  5. 5. vmin = 22.07 m/s
  6. 6. T = 14.91 N

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