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 = 110 m9 m/sF = ?

A 600 kg car drives around a flat curve of radius 110 m at a constant 9 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 9 m/sr = 110 m
Fc = N
2.Easy
r = 110 m13 m/sac​ = ?

A 1500 kg car drives around a flat curve of radius 110 m at a constant 13 m/s. Find its centripetal acceleration ac.

m = 1500 kgv = 13 m/sr = 110 m
ac = m/s²
3.Medium
r = 90 mvmax​ = ?

A car takes a flat curve of radius 90 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 90 mμs = 0.3g = 9.81 m/s²
vmax = m/s
4.Medium
r = 3.9 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.9 mμs = 0.3g = 9.81 m/s²
n = rpm
5.Hard
r = 1.3 mv = 9 m/s

A 0.2 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 1.3 mv = 9 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.8 mv = 8 m/s

A 1.5 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.5 kgr = 0.8 mv = 8 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 441.8 N
  2. 2. ac = 1.536 m/s²
  3. 3. vmax = 16.27 m/s
  4. 4. n = 27.65 rpm
  5. 5. T = 14.42 N
  6. 6. T = 134.7 N

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