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 = 160 m26 m/sF = ?

A 1400 kg car drives around a flat curve of radius 160 m at a constant 26 m/s. Find the inward (centripetal) force Fc needed.

m = 1400 kgv = 26 m/sr = 160 m
Fc = N
2.Easy
r = 90 m18 m/sac​ = ?

A 900 kg car drives around a flat curve of radius 90 m at a constant 18 m/s. Find its centripetal acceleration ac.

m = 900 kgv = 18 m/sr = 90 m
ac = m/s²
3.Medium
r = 3.8 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.8 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.8 mμs = 0.3g = 9.81 m/s²
ω = rad/s
4.Medium
r = 35 mvmax​ = ?

A car takes a flat curve of radius 35 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 = 35 mμs = 0.8g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.5 m9.5 m/svtop​ = ?

A 1.8 kg ball on a light string 1.5 m long is swung in a vertical circle. At the lowest point its speed is 9.5 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 = 1.5 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.6 mv = ?

A ball on a string 0.6 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 = 0.6 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. Fc = 5915 N
  2. 2. ac = 3.6 m/s²
  3. 3. ω = 2.933 rad/s
  4. 4. vmax = 16.57 m/s
  5. 5. Ttop = 20.01 N
  6. 6. vmin = 2.426 m/s

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