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 = 120 m11 m/sac​ = ?

A 1600 kg car drives around a flat curve of radius 120 m at a constant 11 m/s. Find its centripetal acceleration ac.

m = 1600 kgv = 11 m/sr = 120 m
ac = m/s²
2.Easy
r = 60 m11 m/sF = ?

An 800 kg car drives around a flat curve of radius 60 m at a constant 11 m/s. Find the inward (centripetal) force Fc needed.

m = 800 kgv = 11 m/sr = 60 m
Fc = N
3.Medium
r = 90 m22 m/s

A 1800 kg car drives over the top of a hump in the road at 22 m/s. The top of the hump is a circular arc of radius 90 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1800 kgv = 22 m/sr = 90 mg = 9.81 m/s²
N = N
4.Medium
r = 30 mvmax​ = ?

A car takes a flat curve of radius 30 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 30 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
R = 3 mh = 9.9 m

A 4 kg cart is released from rest at a height of 9.9 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 Ntop of the track on the cart at the top of the loop.

m = 4 kgh = 9.9 mR = 3 mg = 9.81 m/s²
Ntop = N
6.Hard
R = 5 mh = 21.5 m

A 5 kg cart is released from rest at a height of 21.5 m on a frictionless track and runs through a vertical loop of radius 5 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 = 5 kgh = 21.5 mR = 5 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. ac = 1.008 m/s²
  2. 2. Fc = 1613 N
  3. 3. N = 7978 N
  4. 4. vmax = 13.29 m/s
  5. 5. Ntop = 62.78 N
  6. 6. Ntop = 176.6 N

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