1. The problem statement, all variables and given/known data What must the ratio of height to radius of a cylinder be so that every axis is a principal axis (with the CM as the origin)? 2. Relevant equations Moment of inertia tensor. I need I_yy = [itex]\sum m *(x^2 + z^2)[/itex] 3. The attempt at a solution I calculated I_zz = MR^2 /12 . Now I change the principal axis to y-axis. I need to determine the moment of inertia tensor of it. Polar coordinates won't work. If I go for cartesian, I do not know the limits for the dx.