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Student

I don't understand how to calculate the moment of inertia for this cylinder.

Alexander

I can help with that. Instead of giving you the exact formula, let's think through the intuition first.

Open Chapter 7, Page 214 on the right — it's already there. Notice how the radius affects mass distribution. What do you think happens to the inertia if we double the radius?

↳ Socratic method · directing to textbook reference

Student

Physics: Rotational Dynamics Chapter 7 · Page 214 · Halliday & Resnick, 10th Ed.

Alexander Reference Active

Chapter 7 · Rotational Motion

7.4 Moment of Inertia of Rigid Bodies

The moment of inertia (I) quantifies an object's resistance to angular acceleration. Unlike linear mass, it depends on how mass is spatially distributed relative to the rotation axis — making geometry as important as total mass.

General form: I = ∫ r² dm
Solid cylinder about central axis: I = ½ MR²

Fig 7.4 — Solid cylinder rotating about its central symmetry axis

Since R appears squared, doubling the radius quadruples the moment of inertia — even if total mass M is unchanged. Mass distributed further from the axis contributes disproportionately to rotational inertia.

Compare this to a hollow cylinder (I = MR²) — all mass at the outer radius maximises inertia. This is why flywheels are rim-weighted.

Referenced by Alexander

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