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 = ?250 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?

v = 250 km/hamax = 1.2 m/s²
rmin = m
2.Easy
r = 120 m17 m/sF = ?

A 1700 kg car drives around a flat curve of radius 120 m at a constant 17 m/s. Find the inward (centripetal) force Fc needed.

m = 1700 kgv = 17 m/sr = 120 m
Fc = N
3.Medium
L = 0.7 m15°

A small ball on a string of length 0.7 m moves in a horizontal circle so that the string makes a constant angle of 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.7 mθ = 15°g = 9.81 m/s²
T = s
4.Medium
r = 110 mvmax​ = ?

A car takes a flat curve of radius 110 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 110 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 18°to centrevmax​ = ?

A curve of radius 50 m is banked at 18°, 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 = 50 mθ = 18°μs = 0.15g = 9.81 m/s²
vmax = m/s
6.Hard
r = 1.2 m8 m/svtop​ = ?

A 1.4 kg ball on a light string 1.2 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 = 1.4 kgr = 1.2 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. rmin = 4019 m
  2. 2. Fc = 4094 N
  3. 3. T = 1.65 s
  4. 4. vmax = 20.78 m/s
  5. 5. vmax = 15.65 m/s
  6. 6. Ttop = 5.997 N

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