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 = 0.6 mn = 2400 rpm210 kg

A flywheel of mass 210 kg has a radius of gyration of 0.6 m about its axis. It spins at 2400 rpm. Find its kinetic energy Ek in kJ.

M = 210 kgk = 0.6 mn = 2400 rpm
Ek = kJ
2.Easy
L = 0.4 mGOd = 0.1 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 0.4 m rotates about an axis O perpendicular to the rod, 0.1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4.5 kgL = 0.4 md = 0.1 m
IO = kg·m²
3.Medium
n = 500 rpmTb​ = 85 N·mI = 25.5 kg·m²

A flywheel with a moment of inertia of 25.5 kg·m² spins at 500 rpm. A brake applies a constant friction torque of 85 N·m. How long t does it take to stop?

I = 25.5 kg·m²n = 500 rpmTb = 85 N·m
t = s
4.Medium
0 → 1800 rpmI = 28.5 kg·m²

A motor brings a flywheel with a moment of inertia of 28.5 kg·m² from rest up to 1800 rpm in 59 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 28.5 kg·m²n = 1800 rpmt = 59 s
Pavg = kW
5.Hard
1.5 m/sω

A solid cylinder of mass 16.5 kg rolls without slipping at 1.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 16.5 kgv = 1.5 m/sI = ½·m·r²
p = %
6.Hard
θ = 35°a

A thin hoop rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 35°I = m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. Ek = 2388 kJ
  2. 2. IO = 0.105 kg·m²
  3. 3. t = 15.71 s
  4. 4. Pavg = 8.582 kW
  5. 5. p = 33.33 %
  6. 6. μs = 0.3501

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