- #1
rakshit gupta
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I am unable to find it.
What is [s]motion[/s] moment of inertia of an equilateral triangle?
- Context: Undergrad
- Thread starter rakshit gupta
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Discussion Overview
The discussion revolves around the moment of inertia of an equilateral triangle, with participants exploring different interpretations and methods for calculating it. The scope includes theoretical aspects and mathematical reasoning related to the definition and application of moment of inertia.
Discussion Character
- Exploratory, Technical explanation, Debate/contested, Mathematical reasoning
Main Points Raised
- One participant expresses difficulty in finding the moment of inertia.
- Another participant suggests using the definition of moment of inertia and recommends drawing the shape to facilitate the integral calculation.
- A different approach is proposed, where placing the x-axis along the base of the triangle and the y-axis through the apex may simplify the integration process.
- There is a question raised about the term "motion of inertia," with a clarification that it may refer to either the second moment of area or the mass moment of inertia for an equilateral triangle.
- Participants inquire about the specific type of moment of inertia the original poster is interested in calculating, distinguishing between a region's second moment of area and a thin lamina's mass moment of inertia.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the interpretation of "motion of inertia" and what specifically is being sought. Multiple views on how to approach the calculation remain present.
Contextual Notes
There are unresolved questions regarding the definitions and assumptions related to the moment of inertia, as well as the specific context in which it is being applied (e.g., thin lamina vs. area). The discussion reflects varying levels of clarity on these points.
- #2
BvU
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Hello Rakshit, welcome to PF 
!
Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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!Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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- #3
Meir Achuz
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It is easier to do the integrals if you place the x-axis along the base of the pyramid, and the y-axis going vertically through the top apex.
Then you can use the parallel axis theorem to get the moment of inertia about the center of the pyramid.
Then you can use the parallel axis theorem to get the moment of inertia about the center of the pyramid.
- #4
SteamKing
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I'm not surprised. What does "motion of inertia" even mean?rakshit gupta said:
You can determine the second moment of area for a region which is an equilateral triangle, or the mass moment of inertia for a plate or thin lamina which has the shape of an equilateral triangle.
So which are you interested in finding?
- #5
rakshit gupta
- 2
- 0
BvU said:Hello Rakshit, welcome to PF
Here is an example. But you are well advised to make your own drawing and work out the integral from the definition of moment of inertia $$I \equiv \int r^2 \, dm$$
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For a thin laminaSteamKing said:
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