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
k = 0.35 mn = 300 rpm50 kg

A flywheel of mass 50 kg has a radius of gyration of 0.35 m about its axis. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 50 kgk = 0.35 mn = 300 rpm
Ek = kJ
2.Easy
R = 0.2 mn = 1000 rpm240 kg

A flywheel is a uniform solid disc of mass 240 kg and radius 0.2 m. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.

M = 240 kgR = 0.2 mn = 1000 rpm
Ek = kJ
3.Medium
L = 1.9 mm = 18.5 kgα

A uniform slender rod of mass 18.5 kg and length 1.9 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 = 18.5 kgL = 1.9 mg = 9.81 m/s²
α = rad/s²
4.Medium
ω = ?L = 0.7 mm = 9 kg

A uniform slender rod of mass 9 kg and length 0.7 m is pinned at one end and released from rest in a horizontal position. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 9 kgL = 0.7 mg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 20°a

A solid cylinder rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 20°I = ½·m·r²g = 9.81 m/s²
μs =
6.Hard
disc: 5 kgring: 5 kgn1​ = 800 rpm

A uniform solid disc (mass 5 kg, radius 0.2 m) spins freely at 800 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. How much kinetic energy ΔE is lost in the process?

Mdisc = 5 kgMring = 5 kgR = 0.2 mn1 = 800 rpm
ΔE = J

Answer key

  1. 1. Ek = 3.023 kJ
  2. 2. Ek = 26.32 kJ
  3. 3. α = 7.745 rad/s²
  4. 4. ω = 6.484 rad/s
  5. 5. μs = 0.1213
  6. 6. ΔE = 233.9 J

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