Use the following formulas for the moments of inertia about the coordinate axes of a surface lamina of density ρ.

Verify that the moment of inertia of a spherical shell of uniform density about its diameter is 2/3ma², where m is the mass and a is the radius.

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I₂ = I, 1₁ = Į₂ N ff (y² + z²)p(x, y, z) ds SS₁ [√(x² + s. (x² + z²)p(x, y, z) ds = SS₁ (x² + y²)p(x, y, z) ds