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 m25 m/sF = ?

A 1400 kg car drives around a flat curve of radius 130 m at a constant 25 m/s. Find the inward (centripetal) force Fc needed.

m = 1400 kgv = 25 m/sr = 130 m
Fc = N
2.Easy
r = 200 m27 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 200 m at a constant 27 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 27 m/sr = 200 m
ac = m/s²
3.Medium
r = 25 mvmax​ = ?

A car takes a flat curve of radius 25 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 = 25 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 2.9 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.9 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 = 2.9 mμs = 0.6g = 9.81 m/s²
n = rpm
5.Hard
r = 1.2 mv = 7 m/s

A 0.4 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.4 kgr = 1.2 mv = 7 m/sg = 9.81 m/s²
T = N
6.Hard
θ = 20°to centrevmax​ = ?

A curve of radius 130 m is banked at 20°, and 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 a car can take the curve without sliding up and out.

r = 130 mθ = 20°μs = 0.4g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. Fc = 6731 N
  2. 2. ac = 3.645 m/s²
  3. 3. vmax = 13.1 m/s
  4. 4. n = 22.67 rpm
  5. 5. T = 20.26 N
  6. 6. vmax = 33.77 m/s

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