I am currently trying to calculate the moment and products of inertia of a ring rotating about the x axis at the moment the ring lies in the xy plane. The problem is that the notations I have from textbook are denoted for Cartesian coordinates. i.e. Ixx=∑i mi(yi2+zi2), and Ixy=∑imixiyi. How can I convert these to polar coordinates?
x=rcosθ, y=rsinθ, z=?
The Attempt at a Solution
I'd assume that the moment of inertia would become Ixx=∑mr2dθ.
but since the problem is for a ring with linear mass density, I am also wondering must I exclude certain coordinates?
thank you in advance.