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 = 1.8 mGOd = 0.85 mm = 5 kg

A uniform slender rod of mass 5 kg and length 1.8 m rotates about an axis O perpendicular to the rod, 0.85 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5 kgL = 1.8 md = 0.85 m
IO = kg·m²
2.Easy
k = 0.55 m0 → 600 rpm50 kg

A flywheel of mass 50 kg with a radius of gyration of 0.55 m is accelerated uniformly from rest to 600 rpm. This takes 28 s. Ignoring friction, find the constant torque T needed.

m = 50 kgk = 0.55 mn1 = 0 rpmn2 = 600 rpmt = 28 s
T = N·m
3.Medium
0 → 2100 rpmI = 20 kg·m²

A motor brings a flywheel with a moment of inertia of 20 kg·m² from rest up to 2100 rpm in 16 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 20 kg·m²n = 2100 rpmt = 16 s
Pavg = kW
4.Medium
12.5 kgaαM = 17.5 kgR = 0.4 m

A 12.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 17.5 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 12.5 kgM = 17.5 kgR = 0.4 mg = 9.81 m/s²
a = m/s²
5.Hard
4 m/sω

A solid cylinder of mass 19.5 kg rolls without slipping at 4 m/s. Find its total kinetic energy Ek.

m = 19.5 kgv = 4 m/sI = ½·m·r²
Ek = J
6.Hard
disc: 37 kgring: 18 kgn1​ = 800 rpm

A uniform solid disc (mass 37 kg, radius 0.2 m) spins freely at 800 rpm about a vertical frictionless shaft. A thin ring of mass 18 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 = 37 kgMring = 18 kgR = 0.2 mn1 = 800 rpm
ΔE = J

Answer key

  1. 1. IO = 4.962 kg·m²
  2. 2. T = 33.94 N·m
  3. 3. Pavg = 30.23 kW
  4. 4. a = 5.771 m/s²
  5. 5. Ek = 234 J
  6. 6. ΔE = 1281 J

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