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 = 1.7 mvmax​ = ?

A 0.8 kg stone is whirled in a horizontal circle of radius 1.7 m on a smooth, level table, held by a string that breaks at a tension of 170 N. Find the highest speed vmax the stone can have.

m = 0.8 kgr = 1.7 mTmax = 170 N
vmax = m/s
2.Easy
r = ?120 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?

v = 120 km/hamax = 0.5 m/s²
rmin = m
3.Medium
r = 95 m17 m/s

A 1100 kg car drives over the top of a hump in the road at 17 m/s. The top of the hump is a circular arc of radius 95 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1100 kgv = 17 m/sr = 95 mg = 9.81 m/s²
N = N
4.Medium
r = 65 mvmax​ = ?

A car takes a flat curve of radius 65 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 = 65 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1 mv = ?

A ball on a string 1 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?

r = 1 mg = 9.81 m/s²
vmin = m/s
6.Hard
θ = 25°to centrevmax​ = ?

A curve of radius 120 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.15. 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 = 120 mθ = 25°μs = 0.15g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. vmax = 19.01 m/s
  2. 2. rmin = 2222 m
  3. 3. N = 7445 N
  4. 4. vmax = 22.59 m/s
  5. 5. vmin = 3.132 m/s
  6. 6. vmax = 27.93 m/s

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