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 = 70 m18 m/sF = ?

A 1800 kg car drives around a flat curve of radius 70 m at a constant 18 m/s. Find the inward (centripetal) force Fc needed.

m = 1800 kgv = 18 m/sr = 70 m
Fc = N
2.Easy
r = 0.7 mvmax​ = ?

A 0.3 kg stone is whirled in a horizontal circle of radius 0.7 m on a smooth, level table, held by a string that breaks at a tension of 10 N. Find the highest speed vmax the stone can have.

m = 0.3 kgr = 0.7 mTmax = 10 N
vmax = m/s
3.Medium
r = 110 mvmax​ = ?

A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 20 mvmax​ = ?

A car takes a flat curve of radius 20 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 20 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.7 mv = 6.5 m/s

A 1.7 kg ball on a string 0.7 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 = 0.7 mv = 6.5 m/sg = 9.81 m/s²
T = N
6.Hard
R = 7 mh = 34.3 m

A 1.5 kg cart is released from rest at a height of 34.3 m on a frictionless track and runs through a vertical loop of radius 7 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 1.5 kgh = 34.3 mR = 7 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. Fc = 8331 N
  2. 2. vmax = 4.83 m/s
  3. 3. vmax = 29.38 m/s
  4. 4. vmax = 12.53 m/s
  5. 5. T = 119.3 N
  6. 6. Nbottom = 158.9 N

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