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 = 1.2 mv300 rpm

A small object sits 120 cm from the axis of a disc that turns at a steady 300 revolutions per minute. Find its centripetal acceleration ac.

n = 300 rpmr = 1.2 m
ac = m/s²
2.Easy
r = 0.4 mv120 rpm

A small object sits 40 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration ac.

n = 120 rpmr = 0.4 m
ac = m/s²
3.Medium
L = 1 m25°

A small ball on a string of length 1 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 speed v of the ball.

L = 1 mθ = 25°g = 9.81 m/s²
v = m/s
4.Medium
r = 3.9 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.4. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.9 mμs = 0.4g = 9.81 m/s²
ω = rad/s
5.Hard
r = 1.4 m10 m/svtop​ = ?

A 0.2 kg ball on a light string 1.4 m long is swung in a vertical circle. At the lowest point its speed is 10 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.2 kgr = 1.4 mvbottom = 10 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 0.7 m10.5 m/svtop​ = ?

A 0.2 kg ball on a light string 0.7 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 = 0.2 kgr = 0.7 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 1184 m/s²
  2. 2. ac = 63.17 m/s²
  3. 3. v = 1.39 m/s
  4. 4. ω = 2.508 rad/s
  5. 5. Ttop = 4.476 N
  6. 6. Ttop = 21.69 N

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