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 = 0.7 mvmax​ = ?

A 0.9 kg stone is whirled in a horizontal circle of radius 0.7 m on a smooth, level table, held by a string that breaks at a tension of 20 N. Find the highest speed vmax the stone can have.

m = 0.9 kgr = 0.7 mTmax = 20 N
vmax = m/s
2.Easy
r = 0.4 mvmax​ = ?

A 1.4 kg stone is whirled in a horizontal circle of radius 0.4 m on a smooth, level table, held by a string that breaks at a tension of 90 N. Find the highest speed vmax the stone can have.

m = 1.4 kgr = 0.4 mTmax = 90 N
vmax = m/s
3.Medium
r = 2.3 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.3 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.3 mμs = 0.6g = 9.81 m/s²
ω = rad/s
4.Medium
r = 20 mvmax​ = ?

A car takes a flat curve of radius 20 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 = 20 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.9 m10 m/svtop​ = ?

A 0.9 kg ball on a light string 0.9 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 = 0.9 kgr = 0.9 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 20°to centrevmin​ = ?

A curve of radius 150 m is banked at 20°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 150 mθ = 20°μs = 0.1g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. vmax = 3.944 m/s
  2. 2. vmax = 5.071 m/s
  3. 3. ω = 2.666 rad/s
  4. 4. vmax = 7.672 m/s
  5. 5. Ttop = 55.85 N
  6. 6. vmin = 19.36 m/s

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