Moment of Inertia

I = Σmr² for discrete; ∫r²dm continuous.

Concept

Moment of Inertia is a foundational idea in this chapter. The defining relationship is:

$I = \int r^2\,dm$

Standard I values: rod about centre ML²/12; ring MR²; disc MR²/2; sphere 2MR²/5.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $I = \int r^2\,dm$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.