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 = 140 m17 m/sac​ = ?

A 1800 kg car drives around a flat curve of radius 140 m at a constant 17 m/s. Find its centripetal acceleration ac.

m = 1800 kgv = 17 m/sr = 140 m
ac = m/s²
2.Easy
r = 50 m13 m/sac​ = ?

A 1700 kg car drives around a flat curve of radius 50 m at a constant 13 m/s. Find its centripetal acceleration ac.

m = 1700 kgv = 13 m/sr = 50 m
ac = m/s²
3.Medium
r = 145 mvmax​ = ?

A car takes a flat curve of radius 145 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 = 145 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 2.5 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.5 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.4. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.5 mμs = 0.4g = 9.81 m/s²
ω = rad/s
5.Hard
r = 0.8 m8 m/svtop​ = ?

A 1.7 kg ball on a light string 0.8 m long is swung in a vertical circle. At the lowest point its speed is 8 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.7 kgr = 0.8 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.9 mv = ?

A ball on a string 0.9 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 = 0.9 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 2.064 m/s²
  2. 2. ac = 3.38 m/s²
  3. 3. vmax = 31.55 m/s
  4. 4. ω = 3.132 rad/s
  5. 5. Ttop = 52.61 N
  6. 6. vmin = 2.971 m/s

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