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Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume ho = 0.34h, bo = 0.16b. y

Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume ho = 0.34h, bo = 0.16b. y

Elements Of Electromagnetics
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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**Problem Statement:** Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume \( h_0 = 0.34h \), \( b_0 = 0.16b \). **Diagram Description:** The diagram shows a rectangular area with width \( b \) and height \( h \). The rectangle is oriented with its longer side horizontal. The origin point \( O \) is located at a distance \( h_0 \) from the top edge along the vertical y-axis and \( b_0 \) from the left edge along the horizontal x-axis. - \( h \): height of the rectangle - \( h_0 \): vertical distance from point O to the top edge, \( h_0 = 0.34h \) - \( b \): width of the rectangle - \( b_0 \): horizontal distance from point O to the left edge, \( b_0 = 0.16b \) **Answers:** 1. \( I_x = \quad \frac{bh^3}{12} \) 2. \( I_y = \quad \frac{hb^3}{12} \) 3. \( I_z = \quad \frac{bh^3}{12} + \frac{hb^3}{12} \) These formulas provide the moments of inertia about the x-axis, y-axis, and the polar moment of inertia about point O, respectively.
Transcribed Image Text:**Problem Statement:** Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume \( h_0 = 0.34h \), \( b_0 = 0.16b \). **Diagram Description:** The diagram shows a rectangular area with width \( b \) and height \( h \). The rectangle is oriented with its longer side horizontal. The origin point \( O \) is located at a distance \( h_0 \) from the top edge along the vertical y-axis and \( b_0 \) from the left edge along the horizontal x-axis. - \( h \): height of the rectangle - \( h_0 \): vertical distance from point O to the top edge, \( h_0 = 0.34h \) - \( b \): width of the rectangle - \( b_0 \): horizontal distance from point O to the left edge, \( b_0 = 0.16b \) **Answers:** 1. \( I_x = \quad \frac{bh^3}{12} \) 2. \( I_y = \quad \frac{hb^3}{12} \) 3. \( I_z = \quad \frac{bh^3}{12} + \frac{hb^3}{12} \) These formulas provide the moments of inertia about the x-axis, y-axis, and the polar moment of inertia about point O, respectively.
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