Moment of inertia for door hinges

AI Thread Summary
The moment of inertia for a door about its hinges is expressed as I = M w^2/3, where M is the mass and w is the width of the door. This formula is derived from the moment of inertia of a thin rod with the rotation axis at one end. To understand this, one can visualize the door as composed of multiple thin rods stacked together. The discussion emphasizes the importance of recognizing the geometry of the object when calculating its moment of inertia. A deeper understanding of the thin rod's moment of inertia is necessary for applying this concept to doors.
DanicaK
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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.
 
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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.)
 
OK, but i don't understand neither how the moment of inertia of a thin rod is found. Can you explain me please
 

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