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.

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1.Easy
k = 0.6 m900 → 2600 rpm180 kg

A flywheel of mass 180 kg with a radius of gyration of 0.6 m is accelerated uniformly from 900 rpm to 2600 rpm. The driving torque is a constant 640 N·m and friction can be ignored. How long t does this take?

m = 180 kgk = 0.6 mn1 = 900 rpmn2 = 2600 rpmT = 640 N·m
t = s
2.Easy
k = 0.4 mn = 900 rpm100 kg

A flywheel of mass 100 kg has a radius of gyration of 0.4 m about its axis. It spins at 900 rpm. Find its kinetic energy Ek in kJ.

M = 100 kgk = 0.4 mn = 900 rpm
Ek = kJ
3.Medium
L = 2.5 mm = 8 kgα

A uniform slender rod of mass 8 kg and length 2.5 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 8 kgL = 2.5 mg = 9.81 m/s²
α = rad/s²
4.Medium
0 → 1100 rpmI = 36.5 kg·m²

A motor brings a flywheel with a moment of inertia of 36.5 kg·m² from rest up to 1100 rpm in 34 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 36.5 kg·m²n = 1100 rpmt = 34 s
Pavg = kW
5.Hard
disc: 15 kgring: 18 kgn1​ = 450 rpm

A uniform solid disc (mass 15 kg, radius 0.2 m) spins freely at 450 rpm about a vertical frictionless shaft. A thin ring of mass 18 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 15 kgMring = 18 kgR = 0.2 mn1 = 450 rpm
n2 = rpm
6.Hard
3 m/sω

A solid cylinder of mass 8 kg rolls without slipping at 3 m/s. What percentage p of its total kinetic energy is rotational?

m = 8 kgv = 3 m/sI = ½·m·r²
p = %

Answer key

  1. 1. t = 18.02 s
  2. 2. Ek = 71.06 kJ
  3. 3. α = 5.886 rad/s²
  4. 4. Pavg = 7.122 kW
  5. 5. n2 = 132.4 rpm
  6. 6. p = 33.33 %

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