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 = 3 mGOd = 0.75 mm = 10 kg

A uniform slender rod of mass 10 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.75 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10 kgL = 3 md = 0.75 m
IO = kg·m²
2.Easy
k = 0.4 m0 → 400 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.4 m is accelerated uniformly from rest to 400 rpm. This takes 12 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.4 mn1 = 0 rpmn2 = 400 rpmt = 12 s
T = N·m
3.Medium
8 kgaαM = 4 kgR = 0.35 m

An 8 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4 kg and radius 0.35 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 = 8 kgM = 4 kgR = 0.35 mg = 9.81 m/s²
a = m/s²
4.Medium
n = 3000 rpmTb​ = 115 N·mI = 39.5 kg·m²

A flywheel with a moment of inertia of 39.5 kg·m² spins at 3000 rpm. A brake applies a constant friction torque of 115 N·m. How long t does it take to stop?

I = 39.5 kg·m²n = 3000 rpmTb = 115 N·m
t = s
5.Hard
disc: 35 kgring: 14 kgn1​ = 150 rpm

A uniform solid disc (mass 35 kg, radius 0.3 m) spins freely at 150 rpm about a vertical frictionless shaft. A thin ring of mass 14 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 = 14 kgR = 0.3 mn1 = 150 rpm
n2 = rpm
6.Hard
θ = 40°a

A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 40°I = (2/5)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 13.13 kg·m²
  2. 2. T = 67.02 N·m
  3. 3. a = 7.848 m/s²
  4. 4. t = 107.9 s
  5. 5. n2 = 83.33 rpm
  6. 6. a = 4.504 m/s²

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