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 = 2.6 mGOd = 0.55 mm = 7 kg

A uniform slender rod of mass 7 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7 kgL = 2.6 md = 0.55 m
IO = kg·m²
2.Easy
k = 0.35 m100 → 1600 rpm160 kg

A flywheel of mass 160 kg with a radius of gyration of 0.35 m is accelerated uniformly from 100 rpm to 1600 rpm. This takes 7 s. Ignoring friction, find the constant torque T needed.

m = 160 kgk = 0.35 mn1 = 100 rpmn2 = 1600 rpmt = 7 s
T = N·m
3.Medium
0 → 2300 rpmI = 28.5 kg·m²

A motor brings a flywheel with a moment of inertia of 28.5 kg·m² from rest up to 2300 rpm in 45 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 28.5 kg·m²n = 2300 rpmt = 45 s
Pavg = kW
4.Medium
L = 1.1 mm = 11.5 kgα

A uniform slender rod of mass 11.5 kg and length 1.1 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 = 11.5 kgL = 1.1 mg = 9.81 m/s²
α = rad/s²
5.Hard
380 m/s35 g1.09 mL = 1.6 m5.5 kg

A uniform slender rod of mass 5.5 kg and length 1.6 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 380 m/s hits the rod 1.09 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 5.5 kgL = 1.6 mm = 35 gv = 380 m/sd = 1.09 m
ω = rad/s
6.Hard
disc: 9 kgring: 14 kgn1​ = 700 rpm

A uniform solid disc (mass 9 kg, radius 0.5 m) spins freely at 700 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 = 9 kgMring = 14 kgR = 0.5 mn1 = 700 rpm
ΔE = J

Answer key

  1. 1. IO = 6.061 kg·m²
  2. 2. T = 439.8 N·m
  3. 3. Pavg = 18.37 kW
  4. 4. α = 13.38 rad/s²
  5. 5. ω = 3.062 rad/s
  6. 6. ΔE = 2287 J

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