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 m8 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 130 m at a constant 8 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 8 m/sr = 130 m
ac = m/s²
2.Easy
r = 160 m16 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 160 m at a constant 16 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 16 m/sr = 160 m
ac = m/s²
3.Medium
r = 105 mvmax​ = ?

A car takes a flat curve of radius 105 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 = 105 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 95 mvmax​ = ?

A car takes a flat curve of radius 95 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 = 95 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
R = 6 mh = 18.6 m

A 4.5 kg cart is released from rest at a height of 18.6 m on a frictionless track and runs through a vertical loop of radius 6 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 4.5 kgh = 18.6 mR = 6 mg = 9.81 m/s²
Ntop = N
6.Hard
R = 3 mh = 11.1 m

A 5 kg cart is released from rest at a height of 11.1 m on a frictionless track and runs through a vertical loop of radius 3 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 = 5 kgh = 11.1 mR = 3 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. ac = 0.4923 m/s²
  2. 2. ac = 1.6 m/s²
  3. 3. vmax = 28.71 m/s
  4. 4. vmax = 25.54 m/s
  5. 5. Ntop = 52.97 N
  6. 6. Nbottom = 412 N

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