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 = 1.2 mGOd = 0.15 mm = 5 kg

A uniform slender rod of mass 5 kg and length 1.2 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5 kgL = 1.2 md = 0.15 m
IO = kg·m²
2.Easy
k = 0.45 m200 → 400 rpm10 kg

A flywheel of mass 10 kg with a radius of gyration of 0.45 m is accelerated uniformly from 200 rpm to 400 rpm. This takes 22 s. Ignoring friction, find the constant torque T needed.

m = 10 kgk = 0.45 mn1 = 200 rpmn2 = 400 rpmt = 22 s
T = N·m
3.Medium
ω = ?L = 0.5 mm = 6 kg

A uniform slender rod of mass 6 kg and length 0.5 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 = 6 kgL = 0.5 mg = 9.81 m/s²
ω = rad/s
4.Medium
ω = ?1.5 kgL = 0.8 mm = 8 kg

A uniform slender rod of mass 8 kg and length 0.8 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 kg is fixed to its free end. 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 = 8 kgL = 0.8 mmball = 1.5 kgg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 25°vs = 9 m

A hollow sphere starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.25 m. Find its angular velocity ω after it has rolled 9 m along the slope.

θ = 25°s = 9 mI = (2/3)·m·r²g = 9.81 m/s²r = 0.25 m
ω = rad/s
6.Hard
disc: 13 kgring: 14 kgn1​ = 400 rpm

A uniform solid disc (mass 13 kg, radius 0.25 m) spins freely at 400 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. How much kinetic energy ΔE is lost in the process?

Mdisc = 13 kgMring = 14 kgR = 0.25 mn1 = 400 rpm
ΔE = J

Answer key

  1. 1. IO = 0.7125 kg·m²
  2. 2. T = 1.928 N·m
  3. 3. ω = 7.672 rad/s
  4. 4. ω = 5.69 rad/s
  5. 5. ω = 26.77 rad/s
  6. 6. ΔE = 243.4 J

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