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 = 130 m22 m/sF = ?

A 1700 kg car drives around a flat curve of radius 130 m at a constant 22 m/s. Find the inward (centripetal) force Fc needed.

m = 1700 kgv = 22 m/sr = 130 m
Fc = N
2.Easy
r = 0.8 mvmax​ = ?

A 0.5 kg stone is whirled in a horizontal circle of radius 0.8 m on a smooth, level table, held by a string that breaks at a tension of 200 N. Find the highest speed vmax the stone can have.

m = 0.5 kgr = 0.8 mTmax = 200 N
vmax = m/s
3.Medium
r = 2.5 mn = ?

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 0.8. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 2.5 mμs = 0.8g = 9.81 m/s²
n = rpm
4.Medium
r = 1.5 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.5 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 1.5 mμs = 0.7g = 9.81 m/s²
n = rpm
5.Hard
θ = 15°to centrevmax​ = ?

A curve of radius 190 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.15. 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 = 190 mθ = 15°μs = 0.15g = 9.81 m/s²
vmax = m/s
6.Hard
r = 0.6 m11.5 m/svtop​ = ?

A 0.7 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 11.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.7 kgr = 0.6 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 6329 N
  2. 2. vmax = 17.89 m/s
  3. 3. n = 21.15 rpm
  4. 4. n = 29.19 rpm
  5. 5. vmax = 28.49 m/s
  6. 6. Ttop = 120 N

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