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Moment
An object in space has a moment about each coordinate plane. DEFINITION If an object in space fills a region E and has continuous density ρ(x, y, z) its moments about the coordinate planes are
The center of mass of the object is the point (x, y, z), where m is mass and
JUSTIFICATION A point mass m has moment Mxy = mz about the (x, y) plane (Figure 12.6.9). In an element of volume ΔE, the object has moment ΔMxy ≈ z Δm ≈ zρ(x, y, z) ΔV (compared to ΔV).
Figure 12.6.9 By the Infinite Sum Theorem,
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Last Update: 2010-11-25