Calc III Ch14 Notes_Part11

# Calc III Ch14 Notes_Part11 - 14.4 — Center of Mass and...

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Unformatted text preview: 14.4 — Center of Mass and Moments of Inertia In Calc 2 we studied laminas with constant density, but what if the density isn’t'constant throughout the lamina? If p is the density function of a lamina corresponding to a region, R, in the xy—plane,' then the mass is Basically we are treatmg t is like the density is the “height” when ﬁnding a volume. 1’ 511‘ F" Ex: Find the mass of a triangular lamina with vertices (0,0), (1, 0), and (0,2) 1f the; density function is p(x, y)— - l + 3x + y. ﬂ? Ex: Using polars, ﬁnd the mass of the semi—circular lamina where the density is mappi‘tinnal to the distance from the center of the circle. KK frhrr Mid 00 0 / 3a (ﬂak £349 {kg " 3 o ...
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