Very basic statics question/moment of inertia

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Discussion Overview

The discussion revolves around the calculation of the moment of inertia for a triangular shape located in the second quadrant, specifically addressing whether the formula \( \frac{hb^3}{12} \) is applicable in this context. The scope includes technical reasoning related to statics and moment of inertia calculations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the applicability of the formula \( \frac{hb^3}{12} \) for a triangular shape in the second quadrant, noting the need for clarity on which dimensions correspond to 'b' and 'h'.
  • Another participant asserts that the formula is correct and emphasizes that it is not limited to right triangles, stating that the triangle does not need to touch the x-axis or be in a specific quadrant, as long as one side is collinear with the y-axis.
  • A later reply acknowledges the initial formula's correctness but reiterates that it is applicable only to right triangles, suggesting that more general formulas for triangular shapes should be consulted.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of the moment of inertia formula, with some asserting its correctness for various triangle types while others limit its use to right triangles. The discussion remains unresolved regarding the general applicability of the formula.

Contextual Notes

There are limitations regarding the assumptions about the triangle's orientation and dimensions, as well as the specific conditions under which the formula is valid. The discussion highlights the need for clarity on these aspects.

encorelui2
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Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12
 
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encorelui2 said:
Statics: If computing the moment of inertia about the y-axis of a triangular shape in the 2nd quadrant(not touching the x-axis); would i still use hb^3 /12

Yes, you would, but be careful which sides you use for 'b' and 'h'. You haven't specified which is measured along the x-axis and which is measured along the y-axis. This formula only works for right triangles, incidentally.

http://en.wikipedia.org/wiki/List_of_area_moments_of_inertia
 
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encorelui2: So far, your formula looks correct. And, it is not limited to right triangles.

It does not matter whether it touches the x-axis or not. And it does not matter what quadrant it is in. It only needs to have one side coincident (collinear) with the y axis, assuming b is the horizontal width of your triangle.
 
nvn said:
encorelui2: So far, your formula looks correct. And, it is not limited to right triangles.

It does not matter whether it touches the x-axis or not. And it does not matter what quadrant it is in. It only needs to have one side coincident (collinear) with the y axis, assuming b is the horizontal width of your triangle.

I apologize for not posting more complete information, but the OP's formula for the moment of inertia of a triangle is indeed only applicable to right triangles. The following link gives formulas for the area properties for more general triangular shapes:

http://www.efunda.com/math/areas/triangle.cfm
 

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