Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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### Example 2: Analyzing a Composite Area **Problem Statement:** Consider the shaded area shown in Figure 1. Suppose that \( a = 140 \, \text{mm} \), \( b = 200 \, \text{mm} \), and \( r = 80 \, \text{mm} \). **Diagram Explanation:** The figure depicts a composite shape consisting of a larger trapezoidal section with a circular cutout: - **Trapezoid Details:** - The trapezoid has a base width along the \( x \)-axis comprised of two segments, each labeled \( a \) and \( b \). These distances suggest that the entire base length is \( a + b = 340 \, \text{mm} \). - The height from the \( x \)-axis to the top parallel side is \( 2b = 400 \, \text{mm} \). - **Circular Cutout:** - A circle with radius \( r = 80 \, \text{mm} \) is subtracted from the trapezoidal area. The circle is centered at a position within the trapezoid. This diagram assists in understanding how composite geometric areas are calculated by combining simpler shapes and subtracting intersections or voids.
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Transcribed Image Text:### Example 2: Analyzing a Composite Area **Problem Statement:** Consider the shaded area shown in Figure 1. Suppose that \( a = 140 \, \text{mm} \), \( b = 200 \, \text{mm} \), and \( r = 80 \, \text{mm} \). **Diagram Explanation:** The figure depicts a composite shape consisting of a larger trapezoidal section with a circular cutout: - **Trapezoid Details:** - The trapezoid has a base width along the \( x \)-axis comprised of two segments, each labeled \( a \) and \( b \). These distances suggest that the entire base length is \( a + b = 340 \, \text{mm} \). - The height from the \( x \)-axis to the top parallel side is \( 2b = 400 \, \text{mm} \). - **Circular Cutout:** - A circle with radius \( r = 80 \, \text{mm} \) is subtracted from the trapezoidal area. The circle is centered at a position within the trapezoid. This diagram assists in understanding how composite geometric areas are calculated by combining simpler shapes and subtracting intersections or voids.
**Problem Statement:** Determine the moment of inertia of the shaded area about the \( y \) axis. **Instructions:** Express your answer to three significant figures and include the appropriate units. **Input Section:** - \( I_y = \) [Value] [Units] **Note:** There are also interactive elements such as buttons for grid view and formatting, but they are not the focus here.
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Transcribed Image Text:**Problem Statement:** Determine the moment of inertia of the shaded area about the \( y \) axis. **Instructions:** Express your answer to three significant figures and include the appropriate units. **Input Section:** - \( I_y = \) [Value] [Units] **Note:** There are also interactive elements such as buttons for grid view and formatting, but they are not the focus here.
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