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
L = 0.4 mGOd = 0.1 mm = 6.5 kg

A uniform slender rod of mass 6.5 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 = 6.5 kgL = 0.4 md = 0.1 m
IO = kg·m²
2.Easy
L = 0.6 mGOd = 0.25 mm = 12 kg

A uniform slender rod of mass 12 kg and length 0.6 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 12 kgL = 0.6 md = 0.25 m
IO = kg·m²
3.Medium
n = 1100 rpmTb​ = 90 N·mI = 36.5 kg·m²

A flywheel with a moment of inertia of 36.5 kg·m² spins at 1100 rpm. A brake applies a constant friction torque of 90 N·m. How long t does it take to stop?

I = 36.5 kg·m²n = 1100 rpmTb = 90 N·m
t = s
4.Medium
n = 2200 rpmTb​ = 195 N·mI = 18 kg·m²

A flywheel with a moment of inertia of 18 kg·m² spins at 2200 rpm. A brake applies a constant friction torque of 195 N·m. How long t does it take to stop?

I = 18 kg·m²n = 2200 rpmTb = 195 N·m
t = s
5.Hard
3.5 m/sω

A solid sphere of mass 2 kg rolls without slipping at 3.5 m/s. Find its total kinetic energy Ek.

m = 2 kgv = 3.5 m/sI = (2/5)·m·r²
Ek = J
6.Hard
θ = 20°a

A solid sphere rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 20°I = (2/5)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 0.1517 kg·m²
  2. 2. IO = 1.11 kg·m²
  3. 3. t = 46.72 s
  4. 4. t = 21.27 s
  5. 5. Ek = 17.15 J
  6. 6. a = 2.397 m/s²

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