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 = 140 m30 m/sac​ = ?

A 1100 kg car drives around a flat curve of radius 140 m at a constant 30 m/s. Find its centripetal acceleration ac.

m = 1100 kgv = 30 m/sr = 140 m
ac = m/s²
2.Easy
r = 180 m13 m/sF = ?

A 1000 kg car drives around a flat curve of radius 180 m at a constant 13 m/s. Find the inward (centripetal) force Fc needed.

m = 1000 kgv = 13 m/sr = 180 m
Fc = N
3.Medium
r = 3.7 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 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 angular speed ω in rad/s.

r = 3.7 mμs = 0.3g = 9.81 m/s²
ω = rad/s
4.Medium
r = 120 mvmax​ = ?

A car takes a flat curve of radius 120 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 = 120 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.5 mv = 8.5 m/s

A 0.7 kg ball on a string 1.5 m long is swung in a vertical circle. At the lowest point it moves at 8.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.7 kgr = 1.5 mv = 8.5 m/sg = 9.81 m/s²
T = N
6.Hard
R = 6.5 mh = 18.2 m

A 0.5 kg cart is released from rest at a height of 18.2 m on a frictionless track and runs through a vertical loop of radius 6.5 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 = 0.5 kgh = 18.2 mR = 6.5 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. ac = 6.429 m/s²
  2. 2. Fc = 938.9 N
  3. 3. ω = 2.973 rad/s
  4. 4. vmax = 30.69 m/s
  5. 5. T = 40.58 N
  6. 6. Ntop = 2.943 N

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