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 = 170 m26 m/sac​ = ?

A 1200 kg car drives around a flat curve of radius 170 m at a constant 26 m/s. Find its centripetal acceleration ac.

m = 1200 kgv = 26 m/sr = 170 m
ac = m/s²
2.Easy
r = ?250 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?

v = 250 km/hamax = 2 m/s²
rmin = m
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 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.3g = 9.81 m/s²
vmax = m/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 = 0.8 mv = 4.5 m/s

A 1.3 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 4.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 0.8 mv = 4.5 m/sg = 9.81 m/s²
T = N
6.Hard
θ = 18°to centrevmax​ = ?

A curve of radius 260 m is banked at 18°, and the coefficient of static friction between tyres and road is 0.25. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 260 mθ = 18°μs = 0.25g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. ac = 3.976 m/s²
  2. 2. rmin = 2411 m
  3. 3. vmax = 17.99 m/s
  4. 4. vmax = 30.69 m/s
  5. 5. T = 45.66 N
  6. 6. vmax = 39.95 m/s

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