Calculating Inertia Tensor and Principal Moments for a Half Disk

[pandarean]

Homework Statement

Half disk, radius R, mass m. I need the inertia tensor about the center of mass and then find the Principal moments of inertia about another coordinate system. Struggling with the product of inertia.

https://dl-web.dropbox.com/get/Public/Captura%20de%20pantalla%20de%202014-11-24%2001%3A39%3A45.png?_subject_uid=1095356&w=AACECjyEV4pBdqLhSXXGSMtL5WXwAK8nETA8TGnww5IDfQ

Homework Equations

Concept question.

The Attempt at a Solution

I already have the mass products of inertia and the xy product of inertia (all about the center of mass) but my big problem is the product of inertia xz ¿How do I find it? ¿Is it zero?
Products of inertia hold information about the symmetry of the object, a bunch of zeros doesn't seem to be a good answer for this.

Thanks for your time.

 

[OldEngr63]

We need a figure to be sure of your coordinate directions.

Most of your problems will be most easily considered in a cylindrical coordinate system, centered at the center of the half disk. Moments and products of inertia can then be transferred to the CM by the parallel axis theorem (in 3 D).