A closed cylindrical canister with central axis coincident with the Z axis has a height H and a radius R. It is suspended by a rod coincident with the Y axis that passes through the canister, transecting its central axis at a height h above the bottom surface of the canister with h > 0.5H.
A volume V of a uniform fluid with density d is placed in the canister (V ≤ 0.2∏R^2H). Derive the equation describing the locus in the XZ plane of the center of mass of the fluid as the cylinder pivots around the rod such that the axis of the cylinder with respect to the Z axis varies from -80 to +80 degrees.
For other equations see http://mathworld.wolfram.com/CylindricalWedge.html
The Attempt at a Solution
I have been working on this for a week and cannot seem to conceptualize a method for solving the problem. I would greatly appreciate any help and/or suggestions.