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 mGOd = 0.25 mm = 11.5 kg

A uniform slender rod of mass 11.5 kg and length 2 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11.5 kgL = 2 md = 0.25 m
IO = kg·m²
2.Easy
Or = 0.15 mL = 1.5 m1.65 m3.5 kg7 kg

A pendulum is made of a uniform slender rod (3.5 kg, 1.5 m long) pivoted at its top end O, with a solid sphere of mass 7 kg and radius 0.15 m fixed to its lower end. The centre of the sphere is 1.65 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 1.5 mmsphere = 7 kgr = 0.15 md = 1.65 m
IO = kg·m²
3.Medium
n = 2900 rpmTb​ = 95 N·mI = 16.5 kg·m²

A flywheel with a moment of inertia of 16.5 kg·m² spins at 2900 rpm. A brake applies a constant friction torque of 95 N·m. How many revolutions N does the flywheel make before it stops?

I = 16.5 kg·m²n = 2900 rpmTb = 95 N·m
N = rev
4.Medium
n = 1400 rpmTb​ = 35 N·mI = 35.5 kg·m²

A flywheel with a moment of inertia of 35.5 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 35 N·m. How many revolutions N does the flywheel make before it stops?

I = 35.5 kg·m²n = 1400 rpmTb = 35 N·m
N = rev
5.Hard
θ = 10°as = 2.5 m

A solid sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2.5 m down the slope?

θ = 10°I = (2/5)·m·r²g = 9.81 m/s²s = 2.5 m
t = s
6.Hard
disc: 4 kgring: 15 kgn1​ = 850 rpm

A uniform solid disc (mass 4 kg, radius 0.25 m) spins freely at 850 rpm about a vertical frictionless shaft. A thin ring of mass 15 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 = 4 kgMring = 15 kgR = 0.25 mn1 = 850 rpm
ΔE = J

Answer key

  1. 1. IO = 4.552 kg·m²
  2. 2. IO = 21.75 kg·m²
  3. 3. N = 1275 rev
  4. 4. N = 1735 rev
  5. 5. t = 2.027 s
  6. 6. ΔE = 436.9 J

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