Moment of inertia for a door help

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Homework Help Overview

The discussion revolves around determining the moment of inertia for a door, specifically a 19kg door that is 2.5m high and 1.1m wide, hinged along its long side. The problem involves understanding how to apply the concept of moment of inertia to a two-dimensional object, which presents challenges for the original poster.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses uncertainty about how to approach the problem, particularly in relation to calculating the mass element (dm) and its dependence on the distance (R). Some participants suggest breaking the door into thin vertical slices to facilitate the calculation, while others reference the integral provided by the original poster as a means to derive the moment of inertia analytically.

Discussion Status

The discussion indicates that the original poster is struggling to grasp the concepts involved, with requests for examples or further clarification. While some guidance has been offered regarding the approach to take, there is no explicit consensus or resolution reached among participants.

Contextual Notes

The original poster mentions a lack of familiarity with calculating moments for two-dimensional objects, as their textbook primarily covers cylindrical shapes and rods. This context highlights the potential gaps in understanding that are influencing the discussion.

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Homework Statement


Determine the moment of inertia of a 19kg door that is 2.5m high and 1.1m wide and is hinged along long side. Ignore the thickness of the door


Homework Equations



I=[tex]\int[/tex] (R^2 dm)

The Attempt at a Solution


I really don't know where to start with this problem. My book only shows me how to do moments for cylindrically shaped objects and rods, so i don't know how to deal with 2d objects. I'm having particular trouble with coming up with a dm that is reliant on R.
 
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The general definition of moment of intertia is to consider a small part of the object with mass dm at a distance r and sum the product of r*r dm.
So for the door, imagine splitting the door into thin vertical slices, then calculate the mass of the slice and the square of the distance from the hinge.
If you know calculus you can do this analytically and come up with an equation - that's what the integral you have given calculates
 
i still have absolutely no clue how to do this. can you point to an example or something?
 
never mind...
 

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