Re: Moment of inertia
※ 引述《gs86137 (小飛魚)》之銘言：
: A lamina has the shape of a closed region bounded by the graphs x^2 + y^2 = 4
: and x + y = 2 , and has density ρ(x,y) = xy .
: Write the iterated integral for the moment of inertia about the y-axis.
Moment of inertia about the y-axis : ∫r^2 dm
又 密度ρ(x,y) = xy = dm / dA
∫X^2 dm = ∫∫X^2 ρ(x,y)dydx
= ∫∫X^3 ydydx ( y = 2- x ~ y = √4-x^2 x= 0~ 1)
應該就可以解出來了 (轉極座標好像也蠻複雜的)
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