Find the moment of inertia of a washer

AI Thread Summary
The discussion focuses on calculating the moment of inertia of a washer with a hole of radius r/2. The initial approach involves using the integral of x^2 dm, but the calculations yield an incorrect result. Participants question the assumptions about the washer's dimensions, specifically whether it is thick or thin, and clarify the definitions of linear density (γ) and length (L). There is confusion regarding the expression for dm, emphasizing the need for a proper understanding of the washer's geometry. The conversation highlights the importance of accurately defining the problem before proceeding with calculations.
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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