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 = 170 m27 m/sF = ?

A 1100 kg car drives around a flat curve of radius 170 m at a constant 27 m/s. Find the inward (centripetal) force Fc needed.

m = 1100 kgv = 27 m/sr = 170 m
Fc = N
2.Easy
r = 150 m13 m/sF = ?

A 1200 kg car drives around a flat curve of radius 150 m at a constant 13 m/s. Find the inward (centripetal) force Fc needed.

m = 1200 kgv = 13 m/sr = 150 m
Fc = N
3.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 0.5. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.7 mμs = 0.5g = 9.81 m/s²
n = rpm
4.Medium
r = 40 mvmax​ = ?

A car takes a flat curve of radius 40 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 = 40 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.2 mv = 6.5 m/s

A 1.7 kg ball on a string 1.2 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 = 1.7 kgr = 1.2 mv = 6.5 m/sg = 9.81 m/s²
T = N
6.Hard
θ = 12°to centrevmax​ = ?

A curve of radius 60 m is banked at 12°, and the coefficient of static friction between tyres and road is 0.2. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 60 mθ = 12°μs = 0.2g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. Fc = 4717 N
  2. 2. Fc = 1352 N
  3. 3. n = 25.74 rpm
  4. 4. vmax = 12.53 m/s
  5. 5. T = 76.53 N
  6. 6. vmax = 15.93 m/s

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