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 = 1.9 mvmax​ = ?

A 0.5 kg stone is whirled in a horizontal circle of radius 1.9 m on a smooth, level table, held by a string that breaks at a tension of 80 N. Find the highest speed vmax the stone can have.

m = 0.5 kgr = 1.9 mTmax = 80 N
vmax = m/s
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 = 55 m16 m/s

A 900 kg car drives over the top of a hump in the road at 16 m/s. The top of the hump is a circular arc of radius 55 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 900 kgv = 16 m/sr = 55 mg = 9.81 m/s²
N = N
4.Medium
r = 105 mvmax​ = ?

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 105 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.6 m11.5 m/svtop​ = ?

A 1.2 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 = 1.2 kgr = 0.6 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 25°to centrevmin​ = ?

A curve of radius 110 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.25. 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 = 110 mθ = 25°μs = 0.25g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. vmax = 17.44 m/s
  2. 2. rmin = 3215 m
  3. 3. N = 4640 N
  4. 4. vmax = 24.86 m/s
  5. 5. Ttop = 205.6 N
  6. 6. vmin = 14.46 m/s

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