Hollow Sphere Inertia in Cartesian Coordinates

[colemc20]

Homework Statement

How do you calculate the rotational inertia of a hollow sphere in cartesian (x,y) coordinates?

Relevant Equations

I=Mr^2

Problem Statement: How do you calculate the rotational inertia of a hollow sphere in cartesian (x,y) coordinates?
Relevant Equations: I=Mr^2

My physics teacher said its his goal to figure this out before he dies. He has personally solved all objects inertias in cartesian coordinates but can't figure out a hollow sphere's. He said if anyone in the class can help he'd forever be in debt to them and I just genuinely want to help. Do any of you know how to do this?

 

[berkeman]

That's a sad story. The calculation does seem awkward to do in Cartesian coordinates, but not too difficult. How would you set up the integral yourself? And what constraints are there on the hollow sphere? What is the thickness of the sphere wall compared to the radius?

 

[berkeman]

Problem Statement: How do you calculate the rotational inertia of a hollow sphere in cartesian (x,y) coordinates?
Relevant Equations: I=Mr^2

And just to be clear, you mean (x,y,z) coordinates for the sphere, correct?

 

[colemc20]

And just to be clear, you mean (x,y,z) coordinates for the sphere, correct?

Haha yes!

 

[colemc20]

And just to be clear, you mean (x,y,z) coordinates for the sphere, correct?

Honestly I myself am not entirely sure how to do it. I’ll ask him in school tomorrow for extra information. I am not sure what he wants the thickness. I’m also not sure if he cares I think he just wants to know how to do it in general.