Moment of inertia for door hinges

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Homework Help Overview

The discussion revolves around understanding the moment of inertia for a door, specifically how it relates to the hinges and the width of the door. The original poster references a formula found in a book and seeks clarification on its derivation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the idea of treating the door as a collection of thin rods to understand the moment of inertia. There is a request for clarification on the derivation of the moment of inertia for a thin rod, indicating a gap in understanding.

Discussion Status

The discussion is ongoing, with participants questioning the foundational concepts of moment of inertia. Some guidance has been offered regarding the treatment of the door as multiple rods, but there is no consensus on the understanding of the thin rod's moment of inertia.

Contextual Notes

Participants express a lack of understanding regarding the derivation of the moment of inertia for both the door and the thin rod, indicating a need for further exploration of these concepts.

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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