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 = 150 m11 m/sF = ?

A 1800 kg car drives around a flat curve of radius 150 m at a constant 11 m/s. Find the inward (centripetal) force Fc needed.

m = 1800 kgv = 11 m/sr = 150 m
Fc = N
2.Easy
r = 100 m22 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 100 m at a constant 22 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 22 m/sr = 100 m
ac = m/s²
3.Medium
L = 0.3 m25°

A small ball on a string of length 0.3 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 = 0.3 mθ = 25°g = 9.81 m/s²
T = s
4.Medium
r = 3.7 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 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 = 3.7 mμs = 0.4g = 9.81 m/s²
ω = rad/s
5.Hard
r = 1.2 mv = 8 m/s

A 0.2 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.2 kgr = 1.2 mv = 8 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1.4 m9 m/svtop​ = ?

A 1.5 kg ball on a light string 1.4 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 = 1.5 kgr = 1.4 mvbottom = 9 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 1452 N
  2. 2. ac = 4.84 m/s²
  3. 3. T = 1.046 s
  4. 4. ω = 2.575 rad/s
  5. 5. T = 12.63 N
  6. 6. Ttop = 13.21 N

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