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 m0 → 400 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.25 m is accelerated uniformly from rest to 400 rpm. This takes 25 s. Ignoring friction, find the constant torque T needed.

m = 150 kgk = 0.25 mn1 = 0 rpmn2 = 400 rpmt = 25 s
T = N·m
2.Easy
Or = 0.25 mL = 1.5 m1.75 m3.5 kg10 kg

A pendulum is made of a uniform slender rod (3.5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 10 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 1.75 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 1.5 mmsphere = 10 kgr = 0.25 md = 1.75 m
IO = kg·m²
3.Medium
0 → 2900 rpmI = 30.5 kg·m²

A motor brings a flywheel with a moment of inertia of 30.5 kg·m² from rest up to 2900 rpm in 24 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 30.5 kg·m²n = 2900 rpmt = 24 s
Pavg = kW
4.Medium
n = 2800 rpmTb​ = 45 N·mI = 18.5 kg·m²

A flywheel with a moment of inertia of 18.5 kg·m² spins at 2800 rpm. A brake applies a constant friction torque of 45 N·m. How long t does it take to stop?

I = 18.5 kg·m²n = 2800 rpmTb = 45 N·m
t = s
5.Hard
θ = 15°a

A solid sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 15°I = (2/5)·m·r²g = 9.81 m/s²
μs =
6.Hard
9 m/sω

A solid cylinder of mass 4.5 kg rolls without slipping at 9 m/s. Find its rotational kinetic energy Erot.

m = 4.5 kgv = 9 m/sI = ½·m·r²
Erot = J

Answer key

  1. 1. T = 15.71 N·m
  2. 2. IO = 33.5 kg·m²
  3. 3. Pavg = 58.6 kW
  4. 4. t = 120.5 s
  5. 5. μs = 0.07656
  6. 6. Erot = 91.13 J

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