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Inertia
An object in space has a moment of inertia about each coordinate axis. Intuitively, the moment of inertia about an axis is the analogue of mass for rotations about the axis. DEFINITION If an object in space fills a region E and has continuous density ρ(x, y, z), its moments of inertia about the coordinate axes are
JUSTIFICATION A point mass in has a moment of inertia about the x-axis of Ix = (y2 + z2)m. On an element of volume ΔE, the object has moment of inertia ΔIx ≈ (y2 + z2) Δm ≈ (y2 + z2)ρ(x, y, z) ΔV (compared to ΔV). The triple integral for Ix follows by the Infinite Sum Theorem.
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Last Update: 2010-11-25