Moment of inertia of a regular triangle

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Homework Help Overview

The discussion revolves around calculating the moment of inertia of a triangle about the OY axis. The original poster is exploring methods to approach this problem, particularly through the use of the Huygens-Steiner theorem and the concept of dividing the triangle into strips or rods.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster considers different ways to split the triangle for calculation, questioning the validity of their approaches. Some participants suggest that using strips parallel to the axis may be more natural, while others express confusion about discrepancies in their calculations.

Discussion Status

Participants are actively engaging with the problem, providing feedback on the original poster's splits and calculations. There is a recognition of mistakes in the approaches discussed, and some participants are exploring multiple interpretations of the problem setup.

Contextual Notes

There are indications of confusion regarding the geometry of the splits and the areas being calculated. The original poster is also checking the feasibility of different methods, which may suggest constraints in their understanding of the problem.

Who_w
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Homework Statement
Calculate the moment of inertia of a triangle relatively OY
Relevant Equations
Given the height of the triangle
Please, I need help! I need to calculate the moment of inertia of a triangle relatively OY. I have an idea to split my triangle into rods and use Huygens-Steiner theorem, but after discussed this exercise with my friend, I have a question: which of these splits are right (picture 1 and 2)? Or maybe my idea is wrong?
 

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Each can work, but it would be more natural to use the one where the strip is parallel to the axis.
 
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I found a mistake in the first split, thanks a lot! I would be very grateful if you tell me where the error is (attached the file). With another split, I got a different answer. I solved it 3 times in this way, but did not find an error.
 

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Last edited:
Who_w said:
I found a mistake in the first split, thanks a lot! I would be very grateful if you tell me where the error is (attached the file). With another split, I got a different answer. I solved it 3 times in this way, but did not find an error.
(l-x)dx? Both of those distances are parallel to the x axis. It is not the area of a rectangle in the figure.
Also, you seem to be taking a strip parallel to the x axis, which is not what I recommended. Are you just checking it can be done both ways?
 
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haruspex said:
(l-x)dx? Both of those distances are parallel to the x axis. It is not the area of a rectangle in the figure.
Also, you seem to be taking a strip parallel to the x axis, which is not what I recommended. Are you just checking it can be done both ways?
Oh! I understood my mistake! Thank you a lot :)
Yes, I'm tried to check both ways. The first way worked (strip parallel to the y axis), but it was really interesting for me why I couldn't to solve it the second way.
Thanks again!
 
Who_w said:
Oh! I understood my mistake! Thank you a lot :)
Yes, I'm tried to check both ways. The first way worked (strip parallel to the y axis), but it was really interesting for me why I couldn't to solve it the second way.
Thanks again!
I commend your inquisitiveness.
 

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