How Do You Apply the Parallel Axis Theorem to Calculate Moment of Inertia?

[mayaitagaki]

Hi everyone,
I've got stuck on this prove problem
Please help me!

Let S be a rectangular sheet with sides a and b and uniform density, and total
mass M.

(a) Show that the moment of inertia of S about an axis L that is perpendicular to S,
meeting S through its center, is

I =1/12*M(a^2 + b^2)

(b) Use the Parallel Axis Theorem in combination with part (a) to show that the moment of inertia of S about an axis L' that is perpendicular to S, meeting S through one of its corner, is

I =1/3*M(a^2 + b^2)

Please see the attachment.
Theorem and an example!

Thank you,
Maya

 

[vela]

You need to show some work first so we can see where you're getting stuck.

 

[mayaitagaki]

Ok, sorry about that! :shy:

I think I kind of got the part a. Then, I don't know how to go from there...

Thank you,

 

[vela]

In the parallel-axis theorem, h is the distance from the center of mass of the object to the new axis. In your case, it would be the distance from the center of the slab to the corner. What is that in terms of a and b?