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 = 1.5 mGOd = 0.7 mm = 11 kg

A uniform slender rod of mass 11 kg and length 1.5 m rotates about an axis O perpendicular to the rod, 0.7 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11 kgL = 1.5 md = 0.7 m
IO = kg·m²
2.Easy
k = 0.5 m0 → 900 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 900 rpm. The driving torque is a constant 220 N·m and friction can be ignored. How long t does this take?

m = 120 kgk = 0.5 mn1 = 0 rpmn2 = 900 rpmT = 220 N·m
t = s
3.Medium
L = 1.2 mm = 9 kgα

A uniform slender rod of mass 9 kg and length 1.2 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 9 kgL = 1.2 mg = 9.81 m/s²
atip = m/s²
4.Medium
n = 2900 rpmTb​ = 195 N·mI = 35.5 kg·m²

A flywheel with a moment of inertia of 35.5 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 195 N·m. How many revolutions N does the flywheel make before it stops?

I = 35.5 kg·m²n = 2900 rpmTb = 195 N·m
N = rev
5.Hard
disc: 5 kgring: 8 kgn1​ = 1100 rpm

A uniform solid disc (mass 5 kg, radius 0.5 m) spins freely at 1100 rpm about a vertical frictionless shaft. A thin ring of mass 8 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 = 5 kgMring = 8 kgR = 0.5 mn1 = 1100 rpm
n2 = rpm
6.Hard
θ = 30°a

A thin hoop rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 30°I = m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 7.452 kg·m²
  2. 2. t = 12.85 s
  3. 3. atip = 14.71 m/s²
  4. 4. N = 1336 rev
  5. 5. n2 = 261.9 rpm
  6. 6. a = 2.452 m/s²

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