Find the moment of inertia of a washer

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Homework Help Overview

The discussion revolves around finding the moment of inertia of a washer that has a hole of radius r/2. The problem is situated within the context of rotational dynamics and involves integral calculus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the moment of inertia using the integral of x^2 dm, but expresses uncertainty about their result. Participants raise questions regarding the dimensions of the washer and the appropriateness of the variables used, such as γ and L, suggesting a need for clarification on the definitions and setup.

Discussion Status

The discussion is ongoing, with participants seeking clarification on the problem's parameters and the original poster's approach. Some guidance has been offered regarding the need for a diagram and the expression for dm, indicating a productive exploration of the problem's assumptions and definitions.

Contextual Notes

There is a lack of information regarding the thickness of the washer, which has led to differing interpretations of the problem. Participants are questioning whether the washer should be treated as a three-dimensional object or a two-dimensional lamina.

Pablo
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Homework Statement



Find moment of inertia of a washer with a hole of radius r/2.

Homework Equations



Moment of inertia = integral of x^2 dm
γ = m / L

The Attempt at a Solution



I think I can find the moment of inertia of the washer using integral of x^2 dm. So, I know my γ = m / L = m / (R/2) = 2m / R

I = (2m / R) * [((R/2)^3 / 3) - 0] = (m * R^2) / 12

However, that is not correct. Where am I going wrong?
 
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Is there a diagram that shows the washer's dimensions? Is it a thick washer or a thin washer?

Also, you can find a LaTeX tutorial under INFO at the top of the page. Click on Help/How-To. That will help you post with math equations that are much easier to read and respond to. :smile:
 
Pablo said:
γ = m / L
What are γ and L? This looks like an expression for linear density, but a washer has area.
 
This looks like a three-dimensional problem. What is your expression for dm?
 
Dr Dr news said:
This looks like a three-dimensional problem. What is your expression for dm?
No, I think it is just a lamina. No thickness is given.
 

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