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 1
Homework Statement
Find the moment of inertia tensor of the plate attached below
Homework Equations
σ = area density
The Attempt at a Solution
So the main problem I'm having is solving for Ixx and Iyy:
1) Ixx = σ∫∫(y^2 + z^2)dydz, since there are no dz components, I don't see how you end up with 1/3Ma^2. But iIf you approach it like this:
2) Ixx = σ∫∫(y^2 + z^2)dA = (M/a^2)∫(y^2 + z^2)(ady) = 1/3Ma^2, you get the right answer (where after integration you fill in z=0), and it makes sense, but is there a way to get there from 1)?
Also, my prof seemed really confused about how the moment of inertia tensor components translate to rotations about different axes. I had a hunch that Ixx would translate to the rotation about the xaxis, Iyy about the yaxis, Izz about the zaxis, Ixy about some diagonal rotation in the xyplane, Ixz about some diagonal rotation in the xzplane, etc. Is there any truth to this? My prof said it doesn't translate that way, but didn't seem sure. I want some closure.
Thanks,
Ari
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