Solid Mass Properties Library
Center of gravity and mass moments of inertia for the homogeneous solids — with orientation handled properly: you choose which coordinate axis carries the axis of symmetry, and the library reports the full inertia set about the centroid and about the useful offset axes (base, end, apex, rim) by the parallel-axis theorem.
Solid
Two ideas run this entire table. Mass far from the axis costs the square of its distance — so the thin ring (all mass at r) carries mr², the disk (mass spread inward) only ½mr², and the sphere (mass crowding the axis in 3-D) just ⅖mr². And the parallel-axis theorem, I = Ī + md², converts every centroidal value into the value about any parallel axis you actually need — a rod swung from its end resists 4× what it does about its middle.