Calculus › Section O · Multiple integrals › Topic O.4
Centre of mass and moments of inertia
Where should you put your finger to balance a flat plate of uneven thickness, and how hard is it to spin? Both answers are double integrals, and both come from one idea: distance weighted by mass.
In this topic
- Questions you can ask a flat plate
- Mass from density
- Moments and the balance point
- Worked example: a plate with varying density
- Centroids and the symmetry shortcut
- Worked example: a centroid between parabolas
- Moments of inertia
- The polar moment and radius of gyration
- Worked example: inertia of a uniform disk
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP