Practice · 12 problems · Paper

Printable Worksheet

Twelve problems to work by hand, from particles and integration to composite bodies, the inertia tensor, a wobbling disk and principal axes. Print it, show your work in the space provided, then check your final answers here.

Mass Moments of Inertia · Worksheet

12 problems · Parts A–C
Name Course / section Date

Show your work in the space provided. Use SI units and give answers to 4 significant figures. Products of inertia are defined as \(I_{xy} = \int xy\,dm\) and enter the inertia tensor with a minus sign. You may use the Formula Sheet.

Answer sheet: final answers only.

How to use this worksheet

  1. Print it, or save it as a PDF. Each problem gets a dotted work space. It fits on about five Letter or A4 pages.
  2. Work on paper. Part A is moments of inertia, Part B is products of inertia and the inertia tensor, and Part C is any axis and principal axes. Each problem names the lesson to review if you get stuck.
  3. Check your final answers with Show answer under each problem, or show them all at once. Only final answers are given here.

Part A · Moments of inertia

Problems 1–5 · Basic to challenge · Lessons 1–4

Part B · Products of inertia and the inertia tensor

Problems 6–9 · Basic to challenge · Lessons 5–6

Part C · Any axis and principal axes

Problems 10–12 · Basic to challenge · Lessons 7–8