Confusion about moment of inertia

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Homework Help Overview

The discussion revolves around the concept of moment of inertia, specifically in relation to a T-section. Participants are exploring the requirements for calculating the moment of inertia with respect to different axes and the implications of the problem statement regarding the second moment of area.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning whether to calculate the moment of inertia with respect to both the x and y axes or just one, particularly in the context of a 2D shape. There is also discussion about whether to combine the moments of inertia to find the polar second moment of area.

Discussion Status

Some participants have provided guidance on considering the axis through the mass center and normal to the plane. There is an ongoing exploration of the definitions and implications of centroidal axes and the use of the perpendicular axis theorem, with no explicit consensus reached on the best approach.

Contextual Notes

Participants note the importance of the problem's wording and the need for clarity regarding the axes involved. There are mentions of issues with accessing diagrams, which may affect the discussion.

Hoshiiiiiiiiiiiii
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When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
 
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Hoshiiiiiiiiiiiii said:
When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
In the absence if any other information, it would be about an axis through the mass centre, but that still leaves open more than one possibility. If it is essentially a 2D shape I suggest an axis normal to that.
Please post the whole question, word for word, with any diagrams.
 
The question says "Calculate the second moment of area of the T-section given below" with this diagram
KSoA5Q2.jpg

I have found the moment of inertia with respect to both axes correctly, but I'm confused whether I should leave them like that or add them together to get the polar second moment of area.
 

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Hoshiiiiiiiiiiiii said:
The question says "Calculate the second moment of area of the T-section given below" with this diagram https://www.physicsforums.com/attachments/shear-stresses-on-beam-mechanics-of-solids-41-1-jpg.234480/?temp_hash=efb03e1eeffac051d9d9072edf2482c7

I have found the moment of inertia with respect to both axes correctly, but I'm confused whether I should leave them like that or add them together to get the polar second moment of area.
The image us not working for me. Nothing happens when I click the icon.
 
haruspex said:
The image us not working for me. Nothing happens when I click the icon.
I edited my reply. I think it's working now.
 
Hoshiiiiiiiiiiiii said:
I edited my reply. I think it's working now.
Yes, I see it now.
I stick with my earlier guess: take the axis as being through the mass centre and normal to the plane.
 
Thank you so much!
 
haruspex said:
take the axis as being through the mass centre and normal to the plane.

Does it simply mean calculating MOI at centriodal axis?
 
Benjamin_harsh said:
Does it simply mean calculating MOI at centriodal axis?
AS far as I am aware, a centroidal axis is any axis that passes through the centroid. See e.g. https://www.quora.com/What-is-the-difference-between-Neutral-axis-and-Centroidal-axis.
Also, please do not keep referring to an MoI "at" an axis. An axis is a line. Write MoI about an axis.

For a lamina, a centroidal axis could be within the plane of the lamina, at any angle, or not even within the plane.
A useful theorem is the perpendicular axis theorem. This says that you can find the MoIs about any two such axes at right angles in the plane and add them together to find the MoI about the axis through the centroid and normal to the plane.
 

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