Symmetric object prove principle axis goes through CM

[m0nk3y]

Homework Statement

c) For such a "symmetric" object, prove that any axis going through the center of mass is a principal axis.

Homework Equations

The Attempt at a Solution

I am not sure how they want me to prove this. I was looking at the Displacement Axis Thm but I am not sure how to use it, or appropriate for this problem.

Thanks in advance.

 

[Meir Achuz]

The tensor of inertial you have is a sum of that for a stick and that for a disk.
Each of these has all principal axes through the center.

 

[m0nk3y]

Thank you for your reply,

Is there a way to prove this with math?