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 = 2.8 mGOd = 1.4 mm = 3.5 kg

A uniform slender rod of mass 3.5 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 = 3.5 kgL = 2.8 md = 1.4 m
IO = kg·m²
2.Easy
k = 0.35 m700 → 1200 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.35 m is accelerated uniformly from 700 rpm to 1200 rpm. The driving torque is a constant 9.2 N·m and friction can be ignored. How long t does this take?

m = 40 kgk = 0.35 mn1 = 700 rpmn2 = 1200 rpmT = 9.2 N·m
t = s
3.Medium
v = ?L = 1.4 mm = 8 kg

A uniform slender rod of mass 8 kg and length 1.4 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 8 kgL = 1.4 mg = 9.81 m/s²
v = m/s
4.Medium
ω = ?3 kgL = 2.3 mm = 4 kg

A uniform slender rod of mass 4 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 4 kgL = 2.3 mmball = 3 kgg = 9.81 m/s²
ω = rad/s
5.Hard
1.5 m/sω

A solid sphere of mass 12 kg rolls without slipping at 1.5 m/s. Find its rotational kinetic energy Erot.

m = 12 kgv = 1.5 m/sI = (2/5)·m·r²
Erot = J
6.Hard
θ = 20°a

A thin hoop rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 20°I = m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. IO = 9.147 kg·m²
  2. 2. t = 27.89 s
  3. 3. v = 6.419 m/s
  4. 4. ω = 3.137 rad/s
  5. 5. Erot = 5.4 J
  6. 6. μs = 0.182

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