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 m16 m/sF = ?

A 600 kg car drives around a flat curve of radius 120 m at a constant 16 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 16 m/sr = 120 m
Fc = N
2.Easy
r = 1.3 mvmax​ = ?

A 0.2 kg stone is whirled in a horizontal circle of radius 1.3 m on a smooth, level table, held by a string that breaks at a tension of 180 N. Find the highest speed vmax the stone can have.

m = 0.2 kgr = 1.3 mTmax = 180 N
vmax = m/s
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 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 105 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 130 mvmax​ = ?

A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 130 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
R = 1.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 1.5 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 1.5 mv₀ = 0
hmin = m
6.Hard
r = 1.2 mv = 6 m/s

A 1.5 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.5 kgr = 1.2 mv = 6 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 1280 N
  2. 2. vmax = 34.21 m/s
  3. 3. vmax = 22.69 m/s
  4. 4. vmax = 22.59 m/s
  5. 5. hmin = 3.75 m
  6. 6. T = 59.72 N

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