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derrickb
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Homework Statement
A triangular prism (like a box of toblerone) of mass M, whose ends are equilateral triangles parallel to the xy plane with side 2a, is centered on the origin with its axis along the z axis. Find its moment of inertia for rotation about the z axis. Without doing any integrals write down and explain its two products of inertia for rotation about the z axis.
Homework Equations
I=∫r2dm
ρ=M/V
r2=x2+y2
The Attempt at a Solution
ρ=M/(.5bhH);H is total length along z-axis
ρdV=dM=.5ρdxdydz
I=∫∫∫x2+y2dxdydz
I evaluated this with integration limits
for x: 0 to a
for y: 0 to √3a/2
for z: 0 to h/2
after doing it all out and substituting M/V back in for ρ, I got an answer of 7Ma2/96. I muliplied by 2 since that integral was only for half of the object, so my final answer would be 7Ma2/48. I have an intuition that this is incorrect. Can anyone point me in the right direction? Are my limits of integration correct? Any help would be much appreciated. Thank you