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
L = 2.7 mGOd = 1.1 mm = 7 kg

A uniform slender rod of mass 7 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 1.1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7 kgL = 2.7 md = 1.1 m
IO = kg·m²
2.Easy
k = 0.55 m200 → 1600 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.55 m is accelerated uniformly from 200 rpm to 1600 rpm. The driving torque is a constant 210 N·m and friction can be ignored. How long t does this take?

m = 120 kgk = 0.55 mn1 = 200 rpmn2 = 1600 rpmT = 210 N·m
t = s
3.Medium
v = ?L = 2.3 mm = 8.5 kg

A uniform slender rod of mass 8.5 kg and length 2.3 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 = 8.5 kgL = 2.3 mg = 9.81 m/s²
v = m/s
4.Medium
v = ?2.5 kgL = 1.2 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 1.2 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2.5 kg is fixed to its free end. 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 = 2.5 kgL = 1.2 mmball = 2.5 kgg = 9.81 m/s²
v = m/s
5.Hard
1 m/sω

A solid sphere of mass 1.5 kg rolls without slipping at 1 m/s. What percentage p of its total kinetic energy is rotational?

m = 1.5 kgv = 1 m/sI = (2/5)·m·r²
p = %
6.Hard
disc: 29 kgring: 19 kgn1​ = 800 rpm

A uniform solid disc (mass 29 kg, radius 0.5 m) spins freely at 800 rpm about a vertical frictionless shaft. A thin ring of mass 19 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. How much kinetic energy ΔE is lost in the process?

Mdisc = 29 kgMring = 19 kgR = 0.5 mn1 = 800 rpm
ΔE = J

Answer key

  1. 1. IO = 12.72 kg·m²
  2. 2. t = 25.34 s
  3. 3. v = 8.227 m/s
  4. 4. v = 5.147 m/s
  5. 5. p = 28.57 %
  6. 6. ΔE = 7215 J

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