# Transforming Cartesian to Polar Coordinates

1. Nov 19, 2015

### shanepitts

1. The problem statement, all variables and given/known data
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?

2. Relevant equations
x=rcosθ, y=rsinθ, z=?

3. 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?

2. Nov 19, 2015

### Staff: Mentor

You can find descriptions of how to calculate such moments of inertia at http://hyperphysics.phy-astr.gsu.edu/hbase/ihoop.html
Be careful that for continuous objects, not point masses, you have to use density instead of masses and integrals instead of sums.

For symmetry reasons, you have that Ixy = 0, Ixz = 0, etc., and also Ixx = Iyy.