Welcome to PF forums! If you haven't looked around yet, I believe you will find many interesting & information discussions around the forum. There are also helpful folks who can aim you in a successful direction, when you have questions. Particularly on homework, it is a good idea to look at some of the examples in this
thread to get an idea on how to construct a question.
A poorly constructed question, will get little response.
I don't know too much about proofs. But I have had calc3 and can get you started on understanding cylindrical & spherical coordinates.
All three systems may be converted from one to another. The Cartesian system, with 3 dimensions (x,y,z)
The
cylindrical coordinate system, is like using polar coordinates in one plane (r,\theta) and extending into the third dimension with displacement z. So a point in space may be specified by (r,\theta,z)
With
spherical coordiates: a point in space is given with two angular directions and one radial distance. The radial distance
r is like you use for polar coordinates (distance from the origin), \theta is the angular displacement taken in the horizontal plane, as you do with polar coordinates, and \phi is the angular displacement from the z-axis (from straight up).
So you have (r,\theta,\phi)
For moments of inertia, if you don't already have this part explained, you might investigate the concept at
hyperphysics website. They give examples of common moments of inertia.