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Homework Statement
Calculate the moment of inertia of a straight homogenous plate with mass m shaped like a square where the axis of rotation goes through the diagonal of the plate.
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Homework Equations
Moment of inertia [tex]I=\int r^{2}dm[/tex]
Perpendicular axis theorem [tex]I_{z}=I_{x}+I_{y}[/tex]
The Attempt at a Solution
This is what I've come up with, but I don't know if I'm right.
Being this a square, I've concluded that [tex]I_{x}=I_{y}[/tex]
Using a Perpendicular axis theorem I have [tex]I_{z}=2I_{x}[/tex]
I need [tex]I_{x}=0.5I_{z}[/tex]
I have [tex]I_{z}=\frac{m*\left(a^{2}+a^{2}\right)}{12}=\frac{m*\left(a^{2}\right)}{6}[/tex]
And then I just put it in [tex]I_{x}=0.5I_{z}[/tex] and get [tex]I_{x}=\frac{m*a^{2}}{12}[/tex]
But somehow, I think I'm wrong