I figured out a way to do it without the triple integral but I want to let you know that I feel like you didn't understand what I was saying.
I couldn't show any calculations since all of my calculations would rely on the having upper and lower bounds to work with. Since I couldn't find said...
I figured out how to do the rod one using the formula for a solid cylinder, but I am still stuck on the hollow sphere. Could I just take the integral of a sphere radius r and then compare it to an integral where I use the term r-1 instead of r in the limits?
I.E.
X = -sqrt((r^2)-(z^2)-(y^2))...
So are you saying I should do triple integrals for the sphere with radius Ro and Radius Ri, or is there some other method?
Sorry I'm being forced to do this for my Calculus Project with absolutely no knowledge of Inertia Tensors, I've pretty much tried to learn this in two weeks with nothing...
Homework Statement
I need to find the Inertia Tensor of a Hollow Sphere and of a Slender Rod with center of mass set at the origin for my calculus 2 final project. I know how to do the triple integrals I am just having trouble figuring out what the limits should be for each of these shapes...