Find the polar moment of inertia for the entire area shown. The dimensions are a = 15.0 mm and b= 20.0 mm. The entire area's moment of inertia about the x axis is given byIx = S₁ y² dAand the moment of inertia about the y axis is given byIy = S₁ x² dAAThe polar moment of inertia is a stiffness parameter based onshape and is given byJo = S₁r²dA y음x||a있고x

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Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Find the polar moment of inertia for the entire area shown. The dimensions are a = 15.0 mm and b= 20.0 mm.

The entire area's moment of inertia about the x axis is given by
Ix = S₁ y² dA
and the moment of inertia about the y axis is given by
Iy = S₁ x² dA
A
The polar moment of inertia is a stiffness parameter based on
shape and is given by
Jo = S₁r²dA

Expert Solution

Step 1

Introduction

With the help of the moment of inertia about the x-axis and the moment of inertia about the y-axis, we will calculate the polar moment of inertia of the provided area in this problem. The moment of inertia about the z-axis, which is the sum of the moments about the x-axis and y-axis, is known as the polar moment of inertia.

Given data:

$\begin{array}{rcl} thel horizontal length (a) & = & 15 mm \\ the vertical length (b) & = & 20 mm \end{array}$

Find out:

The polar moment of inertia of the entire area (J).

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