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## Homework Statement

Starting from the sum: I=Ʃ m

_{α}*ρ

_{α}

^{2}and replacing it by the appropriate integral, find the moment of inertia of a uniform thin square with side length 2*b, lying in the x-y plane, rotated about the x-axis. Calculate its moment of inertia.

## Homework Equations

The integral form turns to I=∫ρ(

**r**)*r

^{2}dV

## The Attempt at a Solution

I rotated it around the z-axis, giving me a cylinder with radius 2b and height 2b. I know the volume of this cylinder is 2*∏*r

^{2}*h. And that ρ=mass/volume. I need help in setting up and evaluating the integral because what I got seems wrong.

I used cylindrical coordinates, claiming that:

θ goes from 0 to 2∏

r goes from 0 to 2b

z goes from 0 to 2b

and my volume element dV=r*dr*dz*dθ. I end up with mass*b

^{2}, and I do not believe this is correct. Help please?