Problem — Moment of inertia of a solid sphere

Problem

Calculate the moment of inertia of a homogeneous solid sphere of mass $M = 3{,}0\;\mathrm{kg}$ and radius $R = 0{,}30\;\mathrm{m}$ about an axis through its centre, knowing that for a solid sphere $I = \tfrac{2}{5}MR^2$.

Solution

Direct application of the formula: $I = \tfrac{2}{5}MR^2 = \tfrac{2}{5}\cdot 3{,}0\cdot (0{,}30)^2 = \tfrac{2}{5}\cdot 3{,}0\cdot 0{,}09$ $\ev{I \approx 0{,}11\;\mathrm{kg\,m^2}}$

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Topics: Dinamica rotazionale Concepts: Momento d’inerzia