Part of JME-04 — Rotational Motion & Moment of Inertia

Standard MOI Table

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BodyAxisMOI
Thin rod (M, L)Centre, perp.ML2ML^2/12
Thin rodEnd, perp.ML2ML^2/3
Ring (M, R)Central axisMR2MR^2
RingDiameterMR2MR^2/2
Disc (M, R)Central axisMR2MR^2/2
DiscDiameterMR2MR^2/4
Solid sphere (M, R)Diameter\frac{2}{5}$$MR^2
Hollow sphere (M, R)Diameter\frac{2}{3}$$MR^2
Solid cylinder (M, R)Central axisMR2MR^2/2

Memory trick: Ring > Hollow sphere > Disc = Solid cylinder > Solid sphere (for same M, R about natural axis). The more mass is concentrated far from the axis, the larger the MOI.

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