Calculate Moment of Inertia About Y-Axis | Direct Integration Method

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Homework Help Overview

The problem involves calculating the moment of inertia about the y-axis using direct integration. The original poster references a specific figure and equations related to the curve but does not provide them in the thread.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to solve the problem using a double integral and expresses uncertainty about the differential area element, dA. Some participants discuss the form of the integral and whether it includes certain constants, such as pi.

Discussion Status

The discussion includes attempts to clarify the integral setup and the components involved in the calculation. Participants are exploring the structure of the integral and its implications for the solution, with no clear consensus reached on the correct formulation.

Contextual Notes

There is mention of an attached figure and equations that are not included in the thread, which may be relevant for understanding the problem context. The original poster also notes a discrepancy regarding the presence of pi in the solution.

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Homework Statement



Determine by direct integration the moment of inertia about the y-axis in the figure shown.

Homework Equations


See Iy on attached.
Equation for curve also on attached.


The Attempt at a Solution


My answer didn't include pi, and the answer apparently does. I'm trying to do this via a double integral as opposed to using one integral and doing something funky. My problem I THINK is in finding dA.
 

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You are right. There is no "[itex]\pi[/itex]" in the solution.

The moment of inertia of that figure, about the y-axis is
[tex]\int_{x=0}^a\int_{y= -b\sqrt{1-\frac{x^2}{a^2}}}^{b\sqrt{1-\frac{x^2}{a^2}}} y dydx[/tex]
That's easy to integrate and has no "[itex]\pi[/itex]".
 
Hmm - that's what I thought. In fact, I think that's the exact integral that I had. I'll give it another go. Thanks!
 
I lied - that's a y^2, not just a y in the integral. The answer is pi*a*(b^3)/8...Still no luck though.
 

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