Answered: Determine the moment of inertia about…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Problem 1.1MA

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Question

Determine the moment of inertia about the centroidal x and y axes for the composite area show.

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Step 1

To find:

The moment of inertia about the centroidal $x$ and $y$ axes for the composite area shown:

Formula used:

The $x$ coordinate of centroid $x$ is,

$x = \frac{A_{1} x_{1} + A_{2} x_{2}}{A_{1} + A_{2}}$

The $y$ coordinate of centroid $y$ is,

$y = \frac{A_{1} y_{1} + A_{2} y_{2}}{A_{1} + A_{2}}$

The moment of inertia with respect to centroidal $x$ axes $I_{x x}$ is.

$I_{x x} = I_{x x 1} + I_{x x 2}$

The moment of inertia with respect to centroidal $x$ axes by area 1 is,

$I_{x x 1} = I_{G 1} + A_{1} {(y_{1} - y)}^{2}$

The moment of inertia with respect to centroidal $x$ axes by area 2 is,

$I_{x x 2} = I_{G 2} + A_{2} {(y_{2} - y)}^{2}$

The moment of inertia with respect to centroidal $y$ axes $I_{y y}$ is.

$I_{y y} = I_{y y 1} + I_{y y 2}$

The moment of inertia with respect to centroidal $y$ axes by area 1 is,

$I_{y y 1} = I_{G 1} + A_{1} {(x_{1} - x)}^{2}$

The moment of inertia with respect to centroidal $y$ axes by area 2 is,

$I_{y y 2} = I_{G 2} + A_{2} {(x_{2} - x)}^{2}$

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