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stateofdogma
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Homework Statement
I found the moment of inertia of a rectangle, with the axis perpendicular and going through the center using double integration. But I also used what i thought to be an equivalent method, but it didn't work.
Homework Equations
[tex]dI=r^2dm[/tex]
[tex]\int dI [/tex]
The Attempt at a Solution
I was able to solve the double integration of the problem. But before that I tried using the double integrals, I used this method [tex]4((\int^\frac{a}{2}_0\frac{b^2}{4}+x^2)dx + (\int^\frac{b^2}{2}_0\frac{a^2}{4}+y^2))dy[/tex]
As you can imagine I toke the integral of the equation [tex] x^2+y^2[/tex] by one of the length like b/2 as constant and integrating over the width a, from a/2 to -a/2 and because its an even function it be taken from a/2 to 0 and you can take a 2 out. And lastly add another to for the symmetry, do the same for the same for the onther side.
You don't get the correct answer which is [tex]M\frac{a^2+b^2}{12}[/tex] and I don't understand why?
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