Solving Moment of Inertia Homework: Deriving Disk Formula

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Homework Help Overview

The discussion revolves around deriving the moment of inertia for a uniform disk rotating about a central axis. The original poster expresses confusion after receiving explanations from their teacher and various online sources regarding the derivation process, which involves parameters such as radius, thickness, mass, and density.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the integral \(\int r^2 dm\) as a method to derive the moment of inertia. There are attempts to express mass in terms of density and dimensions, and questions arise about how to handle the differential mass element "dm" in the context of the integral.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the integral and the relationship between mass and density. Some guidance has been offered regarding the need to express "dm" in terms of density and distance from the axis, but no consensus has been reached on the approach to take.

Contextual Notes

There is mention of a third integral by the original poster, indicating potential constraints or additional complexities in the problem setup. The participants are also navigating the definitions and applications of the moment of inertia in this context.

revres75
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Homework Statement



This was an exam question that I got wrong, my teacher tried to explain it but it only left me more confused. I found some websites that also had explanations but they were also confusing.

"Derive the moment of inertia of a uniform disk which rotates along a central axis , radius R , disk thickness d, mass M , density p
I= R^2 dm"


Homework Equations


I= 1/2*M*R^2 ?


The Attempt at a Solution



mass M = Pi*R^2*d*p

My teacher mentioned something about a third integral.
 
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Presumeably you are to derive the moment of inertia by evaluating [itex]\int r^2 dm[/itex]. So what did you do?
 
If I derive [itex]\int r^2 dm[/itex] I get 2r but I not sure what to do with the dm
 
revres75 said:
If I derive [itex]\int r^2 dm[/itex] I get 2r but I not sure what to do with the dm
By "derive" I didn't mean "take the derivative". You need to evaluate that integral, which is the definition of moment of inertia. Start by expressing "dm" in terms of density and distance from the axis. (Hint: Think in terms of concentric rings.)
 

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