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 = 120 m25 m/sF = ?

An 800 kg car drives around a flat curve of radius 120 m at a constant 25 m/s. Find the inward (centripetal) force Fc needed.

m = 800 kgv = 25 m/sr = 120 m
Fc = N
2.Easy
r = ?250 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?

v = 250 km/hamax = 1.5 m/s²
rmin = m
3.Medium
r = 115 mvmax​ = ?

A car takes a flat curve of radius 115 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 = 115 mμs = 0.3g = 9.81 m/s²
vmax = m/s
4.Medium
L = 0.9 m30°

A small ball on a string of length 0.9 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 0.9 mθ = 30°g = 9.81 m/s²
T = s
5.Hard
r = 1 m11 m/svtop​ = ?

A 2 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 11 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 2 kgr = 1 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.9 m10.5 m/svtop​ = ?

A 1.2 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 10.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.2 kgr = 0.9 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 4167 N
  2. 2. rmin = 3215 m
  3. 3. vmax = 18.4 m/s
  4. 4. T = 1.771 s
  5. 5. Ttop = 143.9 N
  6. 6. Ttop = 88.14 N

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