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 = 1.1 mv200 rpm

A small object sits 110 cm from the axis of a disc that turns at a steady 200 revolutions per minute. Find its centripetal acceleration ac.

n = 200 rpmr = 1.1 m
ac = m/s²
2.Easy
r = ?200 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 200 km/h?

v = 200 km/hamax = 1 m/s²
rmin = m
3.Medium
L = 1.7 m25°

A small ball on a string of length 1.7 m moves in a horizontal circle so that the string makes a constant angle of 25° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.7 mθ = 25°g = 9.81 m/s²
T = s
4.Medium
r = 145 mvmax​ = ?

A car takes a flat curve of radius 145 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 = 145 mμs = 0.7g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.8 m9 m/svtop​ = ?

A 1.7 kg ball on a light string 0.8 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.7 kgr = 0.8 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 1.4 m11.5 m/svtop​ = ?

A 1.1 kg ball on a light string 1.4 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 = 1.1 kgr = 1.4 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 482.5 m/s²
  2. 2. rmin = 3086 m
  3. 3. T = 2.49 s
  4. 4. vmax = 31.55 m/s
  5. 5. Ttop = 88.74 N
  6. 6. Ttop = 49.96 N

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