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## Homework Statement

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. I

_{xx}=∑

_{i}m

_{i}(y

_{i}

^{2}+z

_{i}

^{2}), and I

_{xy}=∑

_{i}m

_{i}x

_{i}y

_{i}. How can I convert these to polar coordinates?

## Homework Equations

x=rcosθ, y=rsinθ, z=?

## The Attempt at a Solution

I'd assume that the moment of inertia would become I

_{xx}=∑mr

^{2}dθ.

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.