- #1
eprparadox
- 138
- 2
Homework Statement
Square lamina (of side a) of uniform density. Find I about a diagonal.
Homework Equations
I = ∫ dm*l^2
The Attempt at a Solution
So I drew a square and its diagonal and I imagine a differential mass drawn somewhere on the lamina. The distance squared to that differential mass from the diagonal axis is x^2 + y^2.
So I did the following integral:
[tex]
\rho \int_ \frac{-a}{2}^\frac{a}{2} \int_\frac{-a}{2}^\frac{a}{2} (x^2 + y^2) dx dy
[/tex]
thinking this would be the correct answer, however I get
[tex]
\frac{1}{6}Ma^{2}
[/tex]
which is wrong by a factor of [tex] \frac{1}{2} [/tex]
I don't know where I'm going wrong. Any help would be greatly appreciated. Thanks so much.