- #1
Bomberman334
- 5
- 0
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.
Attached is the my assignment, the ones I am referencing here are questions Three and Four.
Homework Equations
The components of the inertia tensor are
I_xx= ∭ (y^2+z^2 ) ρdv
I_yy= ∭ (x^2+z^2 ) ρdv
I_zz= ∭(x^2+y^2 ) ρdv
I_xy= I_yx= ∭xy ρdv
I_xz= I_zx= ∭xz ρdv
The Attempt at a Solution
I can't really start on the work until I know the limits...
However i know the limits of a filled sphere are
X= -R to R
Y = sqrt(R^2 -X^2)
Z = sqrt(R^2 -X^2-Y^2)
Attachments
Last edited: