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 = ?200 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 200 km/h?

v = 200 km/hamax = 0.5 m/s²
rmin = m
2.Easy
r = 110 m16 m/sac​ = ?

An 800 kg car drives around a flat curve of radius 110 m at a constant 16 m/s. Find its centripetal acceleration ac.

m = 800 kgv = 16 m/sr = 110 m
ac = m/s²
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 = 125 mvmax​ = ?

A car takes a flat curve of radius 125 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 = 125 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.3 mv = 9 m/s

A 1.7 kg ball on a string 1.3 m long is swung in a vertical circle. At the lowest point it moves at 9 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.7 kgr = 1.3 mv = 9 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.5 m10 m/svtop​ = ?

A 1.5 kg ball on a light string 1.5 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.5 kgr = 1.5 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. rmin = 6173 m
  2. 2. ac = 2.327 m/s²
  3. 3. vmax = 22.69 m/s
  4. 4. vmax = 19.18 m/s
  5. 5. T = 122.6 N
  6. 6. Ttop = 26.43 N

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