Moment of inertia for door hinges

[DanicaK]

How do we find out that the moment of inertia about the hinges of a door with a width w is I=M w²/3.
I find it like this in a book and also in table for the moments of inertia of homogeneous rigid objects with different geometries (about a long thin rod with rotation axis trough end).
Thank you.

 

[Doc Al]

If you understand how the moment of inertia of the thin rod is found, then just realize that the door can be treated like a bunch of rods. (Imagine the door sliced into thin slits.)

 

[DanicaK]

OK, but i don't understand neither how the moment of inertia of a thin rod is found. Can you explain me please

 

[Doc Al]

Take a look at these examples (click on the figures for details): Common Moments of Inertia