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
R = 0.35 mn = 2900 rpm50 kg

A flywheel is a uniform solid disc of mass 50 kg and radius 0.35 m. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 50 kgR = 0.35 mn = 2900 rpm
Ek = kJ
2.Easy
R = 0.65 mn = 300 rpm250 kg

A flywheel is a uniform solid disc of mass 250 kg and radius 0.65 m. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 250 kgR = 0.65 mn = 300 rpm
Ek = kJ
3.Medium
n = 1400 rpmTb​ = 115 N·mI = 32 kg·m²

A flywheel with a moment of inertia of 32 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 115 N·m. How many revolutions N does the flywheel make before it stops?

I = 32 kg·m²n = 1400 rpmTb = 115 N·m
N = rev
4.Medium
L = 2.6 mm = 6.5 kgα

A uniform slender rod of mass 6.5 kg and length 2.6 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 = 6.5 kgL = 2.6 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 15°a

A solid sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 15°I = (2/5)·m·r²g = 9.81 m/s²
μs =
6.Hard
disc: 8 kgring: 19 kgn1​ = 600 rpm

A uniform solid disc (mass 8 kg, radius 0.3 m) spins freely at 600 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 = 8 kgMring = 19 kgR = 0.3 mn1 = 600 rpm
ΔE = J

Answer key

  1. 1. Ek = 141.2 kJ
  2. 2. Ek = 26.06 kJ
  3. 3. N = 475.9 rev
  4. 4. atip = 14.71 m/s²
  5. 5. μs = 0.07656
  6. 6. ΔE = 587 J

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