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 = 0.35 mv = ?300 rpm

A small object sits 35 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find the speed v of the object.

n = 300 rpmr = 0.35 m
v = m/s
2.Easy
r = 120 m9 m/sac​ = ?

A 1800 kg car drives around a flat curve of radius 120 m at a constant 9 m/s. Find its centripetal acceleration ac.

m = 1800 kgv = 9 m/sr = 120 m
ac = m/s²
3.Medium
L = 1.5 m50°

A small ball on a string of length 1.5 m moves in a horizontal circle so that the string makes a constant angle of 50° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

L = 1.5 mθ = 50°g = 9.81 m/s²
T = s
4.Medium
r = 115 m18 m/s

A 1100 kg car drives over the top of a hump in the road at 18 m/s. The top of the hump is a circular arc of radius 115 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1100 kgv = 18 m/sr = 115 mg = 9.81 m/s²
N = N
5.Hard
r = 0.6 m8.5 m/svtop​ = ?

A 1 kg ball on a light string 0.6 m long is swung in a vertical circle. At the lowest point its speed is 8.5 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 kgr = 0.6 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
θ = 20°to centrevmin​ = ?

A curve of radius 240 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 = 240 mθ = 20°μs = 0.15g = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. v = 11 m/s
  2. 2. ac = 0.675 m/s²
  3. 3. T = 1.97 s
  4. 4. N = 7692 N
  5. 5. Ttop = 71.37 N
  6. 6. vmin = 21.86 m/s

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