Quick spherical coordinate question

[Shaybay92]

So I have the following shape for which I want to calculate the inertia matrix. Basically I just want to know what limits of integration I should use if I am using spherical coordinates. Assume the convention that phi is the angle from x to y in the xy plane and theta is from z to the xy plane. Thus the limits I chose were [theta, -pi/2,pi/2] and [phi,0,pi/2]. Do you agree with these? The reason I ask is I am getting zero for my calculation of Izz.

Thanks in advance.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[cragar]

if your defining theta from the positive z axis then i think theta should go from 0 to pi/2
and i think phi is from 0 to pi .

 

[Shaybay92]

Thanks so much! I just wasn't visualizing it properly, and I used those values and it seems to be working :D

 

[cragar]

no problem