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
R = 0.55 mn = 2300 rpm300 kg

A flywheel is a uniform solid disc of mass 300 kg and radius 0.55 m. It spins at 2300 rpm. Find its kinetic energy Ek in kJ.

M = 300 kgR = 0.55 mn = 2300 rpm
Ek = kJ
2.Easy
L = 2.9 mGOd = 1.2 mm = 3 kg

A uniform slender rod of mass 3 kg and length 2.9 m rotates about an axis O perpendicular to the rod, 1.2 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3 kgL = 2.9 md = 1.2 m
IO = kg·m²
3.Medium
0 → 1500 rpmI = 4.5 kg·m²

A motor brings a flywheel with a moment of inertia of 4.5 kg·m² from rest up to 1500 rpm in 53 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 4.5 kg·m²n = 1500 rpmt = 53 s
Pavg = kW
4.Medium
n = 2600 rpmTb​ = 110 N·mI = 12 kg·m²

A flywheel with a moment of inertia of 12 kg·m² spins at 2600 rpm. A brake applies a constant friction torque of 110 N·m. How long t does it take to stop?

I = 12 kg·m²n = 2600 rpmTb = 110 N·m
t = s
5.Hard
1.5 m/sω

A solid cylinder of mass 5.5 kg rolls without slipping at 1.5 m/s. Find its total kinetic energy Ek.

m = 5.5 kgv = 1.5 m/sI = ½·m·r²
Ek = J
6.Hard
θ = 10°a

A hollow sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 10°I = (2/3)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. Ek = 1316 kJ
  2. 2. IO = 6.422 kg·m²
  3. 3. Pavg = 1.047 kW
  4. 4. t = 29.7 s
  5. 5. Ek = 9.281 J
  6. 6. a = 1.022 m/s²

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