The physics
The parallel axes rule works for any body. Start from I about an axle through the centre of mass. Move the axle a distance d, and keep it parallel. Then add Md².
I = Icm + M d²
The perpendicular axes rule works for flat bodies only. Two axles lie in the plane, at right angles. A third one stands at right angles to the plane. All three meet at one point.
Iz = Ix + Iy disc on a diameter: ¼MR²
For joined parts, find each part's I about the same axle and add them. For a hole, take away the missing piece's I, moved to the axle.
I = Σ Iparts I = Ifull − Ipiece
The test rig: a 0.5 kg weight on a cord round a 10 cm drum drops 1 m. A bigger I spins up slower, so the drop takes longer.