Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
k = 0.25 mn = 2000 rpm70 kg

A flywheel of mass 70 kg has a radius of gyration of 0.25 m about its axis. It spins at 2000 rpm. Find its kinetic energy Ek in kJ.

M = 70 kgk = 0.25 mn = 2000 rpm
Ek = kJ
2.Easy
L = 2.8 mGOd = 1.4 mm = 9.5 kg

A uniform slender rod of mass 9.5 kg and length 2.8 m rotates about an axis O perpendicular to the rod, 1.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9.5 kgL = 2.8 md = 1.4 m
IO = kg·m²
3.Medium
L = 1.5 mm = 5.5 kgα

A uniform slender rod of mass 5.5 kg and length 1.5 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 5.5 kgL = 1.5 mg = 9.81 m/s²
α = rad/s²
4.Medium
4.5 kgaαM = 10.5 kgR = 0.2 m

A 4.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10.5 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 4.5 kgM = 10.5 kgR = 0.2 mg = 9.81 m/s²
α = rad/s²
5.Hard
θ = 40°a

A thin hoop rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 40°I = m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 20°vs = 6.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 6.5 m along the slope.

θ = 20°s = 6.5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s

Answer key

  1. 1. Ek = 95.95 kJ
  2. 2. IO = 24.83 kg·m²
  3. 3. α = 9.81 rad/s²
  4. 4. α = 22.64 rad/s²
  5. 5. μs = 0.4195
  6. 6. ω = 18.61 rad/s

Full step-by-step solutions: practise this topic on examproblems.com.