Computing a Region's Moment of Inertia 

Compute the moment of inertia of a region for any axis of rotation.

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X inertialMoment[reg_?RegionQ, axis_InfiniteLine] := Module[{df = RegionDistance[axis]}, Integrate[df[{x, y, z}], {x, y, z} \[Element] reg]]

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X mr = ConvexHullMesh[RandomReal[1, {30, 3}]]; axis = InfiniteLine[{1, 0, 0}, {1, 2, 3}]; Show[Graphics3D[{Red, Thick, axis}, Boxed -> False], mr]

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The moment of inertia around the axis illustrated.

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X inertialMoment[mr, axis]

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