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 = 80 m29 m/sF = ?

A 1100 kg car drives around a flat curve of radius 80 m at a constant 29 m/s. Find the inward (centripetal) force Fc needed.

m = 1100 kgv = 29 m/sr = 80 m
Fc = N
2.Easy
r = 1.3 mvmax​ = ?

A 1.9 kg stone is whirled in a horizontal circle of radius 1.3 m on a smooth, level table, held by a string that breaks at a tension of 40 N. Find the highest speed vmax the stone can have.

m = 1.9 kgr = 1.3 mTmax = 40 N
vmax = m/s
3.Medium
r = 90 m22 m/s

A 1700 kg car drives over the top of a hump in the road at 22 m/s. The top of the hump is a circular arc of radius 90 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1700 kgv = 22 m/sr = 90 mg = 9.81 m/s²
N = N
4.Medium
r = 140 mvmax​ = ?

A car takes a flat curve of radius 140 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 = 140 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 20°to centrevmin​ = ?

A curve of radius 200 m is banked at 20°, and the coefficient of static friction between tyres and road is 0.15. 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 = 200 mθ = 20°μs = 0.15g = 9.81 m/s²
vmin = m/s
6.Hard
r = 0.5 mv = 5 m/s

A 1.1 kg ball on a string 0.5 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.5 mv = 5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 11564 N
  2. 2. vmax = 5.231 m/s
  3. 3. N = 7535 N
  4. 4. vmax = 31.01 m/s
  5. 5. vmin = 19.95 m/s
  6. 6. T = 65.79 N

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