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 = 100 m18 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 100 m at a constant 18 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 18 m/sr = 100 m
ac = m/s²
2.Easy
r = 0.1 mv30 rpm

A small object sits 10 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find its centripetal acceleration ac.

n = 30 rpmr = 0.1 m
ac = m/s²
3.Medium
r = 95 mvmax​ = ?

A car takes a flat curve of radius 95 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 95 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.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
5.Hard
r = 0.9 m12 m/svtop​ = ?

A 1.8 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 12 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.8 kgr = 0.9 mvbottom = 12 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 25°to centrevmax​ = ?

A curve of radius 110 m is banked at 25°, and 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 a car can take the curve without sliding up and out.

r = 110 mθ = 25°μs = 0.3g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. ac = 3.24 m/s²
  2. 2. ac = 0.987 m/s²
  3. 3. vmax = 25.54 m/s
  4. 4. vmax = 17.99 m/s
  5. 5. Ttop = 199.7 N
  6. 6. vmax = 31.01 m/s

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