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 = 2.4 mGOd = 0.95 mm = 3.5 kg

A uniform slender rod of mass 3.5 kg and length 2.4 m rotates about an axis O perpendicular to the rod, 0.95 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3.5 kgL = 2.4 md = 0.95 m
IO = kg·m²
2.Easy
k = 0.6 m1000 → 2400 rpm40 kg

A flywheel of mass 40 kg with a radius of gyration of 0.6 m is accelerated uniformly from 1000 rpm to 2400 rpm. The driving torque is a constant 120 N·m and friction can be ignored. How long t does this take?

m = 40 kgk = 0.6 mn1 = 1000 rpmn2 = 2400 rpmT = 120 N·m
t = s
3.Medium
L = 1.5 mm = 2 kgα

A uniform slender rod of mass 2 kg and length 1.5 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 = 2 kgL = 1.5 mg = 9.81 m/s²
α = rad/s²
4.Medium
2.5 kgaαM = 10.5 kgR = 0.25 m

A 2.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 10.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 2.5 kgM = 10.5 kgR = 0.25 mg = 9.81 m/s²
a = m/s²
5.Hard
disc: 15 kgring: 5 kgn1​ = 150 rpm

A uniform solid disc (mass 15 kg, radius 0.45 m) spins freely at 150 rpm about a vertical frictionless shaft. A thin ring of mass 5 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 = 5 kgR = 0.45 mn1 = 150 rpm
n2 = rpm
6.Hard
disc: 35 kgring: 7 kgn1​ = 1050 rpm

A uniform solid disc (mass 35 kg, radius 0.25 m) spins freely at 1050 rpm about a vertical frictionless shaft. A thin ring of mass 7 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 = 35 kgMring = 7 kgR = 0.25 mn1 = 1050 rpm
n2 = rpm

Answer key

  1. 1. IO = 4.839 kg·m²
  2. 2. t = 17.59 s
  3. 3. α = 9.81 rad/s²
  4. 4. a = 3.165 m/s²
  5. 5. n2 = 90 rpm
  6. 6. n2 = 750 rpm

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