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

[pinodk]

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?

 

[pinodk]

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?

 

[m2003]

I would suggest first clarifying the problem by defining the dimensions and orientation of the cylinder. Is it a solid cylinder or a hollow one? Is it oriented along the x or y axis? This will help in determining the appropriate formula for calculating the moment of inertia.

Once the dimensions and orientation are clear, you can use the formula for the moment of inertia of a cylinder, which is dependent on the mass and dimensions of the object. This formula can then be used to calculate the moments of inertia for each axis, taking into account the distance from the rotation axis.

For the x-axis, the moment of inertia will be calculated by considering the rotation of the cylinder around the y-axis. Similarly, for the y-axis, the moment of inertia will be calculated by considering the rotation around the x-axis.

In summary, to calculate the moment of inertia for a cylinder at a distance from the rotation axis, you will need to know the dimensions and orientation of the cylinder, and then use the appropriate formula for the moment of inertia, taking into account the distance from the rotation axis.