Moment of inertia for a cylinder at a distance from rotation axis

AI Thread Summary
The discussion focuses on calculating the inertia tensor for a cylinder with respect to different rotational axes, specifically the x and y axes. The inertia tensor for a cylinder is acknowledged, with the understanding that the bottom right element remains constant for rotation around the z-axis. The user expresses uncertainty about how to adjust the inertia tensor matrix for rotations about the x and y axes while maintaining its diagonal form. There is a consideration of how to incorporate the distance from the rotation axis into the calculations. The conversation highlights the complexity of inertia tensors and the need for clarity in applying the principles to different rotational scenarios.
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Homework Statement


I have a cylinder, for which i want to find the inertia tensor.
http://www.mip.sdu.dk/~pino/inertiacyl.JPG
Where the rotational axis are either the x (red) or y (green).


Homework Equations


I know that the inertia tensor for a cylinder is of the form
http://www.mip.sdu.dk/~pino/inertiamoment-cylinder.jpg
Then I believe that the bottom right element stays the same, since this describes the rotation around the z-axis.
The tricky part for me is the rest of the matrix. I am no expert, and do not understand inertia tensors fully, so I would like some pointers.


The Attempt at a Solution


My immediate idea is that the matrix should remain in its diagonal form, the zeros will remain zeros, is this correct?

I know that for complex forms i can split up the moments of inertia, so i have the moment of inertia for the blank space d, which is 0. and then i can add the moment of inertia of the cylinder, but how do i calculate this, when the rotational axis is x-axis for example?
 
Physics news on Phys.org
I had a sudden struck of enlightment...
Is it really as simple as just taking d+h and and using as h in the matrix?
 

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