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5 in. 1 in. 3. For the plate shown to the right, determine the location of the centroid. 3 in. 3 in. -1 in. 2 in. Ans: =0, y = 0.018in. r= 6 in. 2 in. 6 in.

5 in. 1 in. 3. For the plate shown to the right, determine the location of the centroid. 3 in. 3 in. -1 in. 2 in. Ans: =0, y = 0.018in. r= 6 in. 2 in. 6 in.

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:** 3. For the plate shown to the right, determine the location of the centroid. **Answer:** \(\bar{x} = 0\), \(\bar{y} = 0.018 \text{ in.}\) --- **Diagram Explanation:** The diagram illustrates a composite plate consisting of a semicircle and a rectangle, with a smaller square cutout. - The semicircle has a radius of 6 inches and is positioned on the left side. - The rectangle is positioned to the right of the semicircle, measuring 5 inches in width and 6 inches in height. - A square with sides of 2 inches is cut out from the top right corner of the rectangle. - Dimensions are marked to show distances across the structure: - The distance from the leftmost edge to the edge of the semicircle is 3 inches. - Horizontal and vertical axes are marked as x and y, respectively. **Key Measurements:** - Semicircle radius \(r = 6\) inches. - Rectangular section: 5 inches wide, full height of 6 inches. - Cutout square: 2 inches by 2 inches. The centroid's coordinates are provided with respect to the origin set at the center of the semicircle's flat side.
Transcribed Image Text:**Problem Statement:** 3. For the plate shown to the right, determine the location of the centroid. **Answer:** \(\bar{x} = 0\), \(\bar{y} = 0.018 \text{ in.}\) --- **Diagram Explanation:** The diagram illustrates a composite plate consisting of a semicircle and a rectangle, with a smaller square cutout. - The semicircle has a radius of 6 inches and is positioned on the left side. - The rectangle is positioned to the right of the semicircle, measuring 5 inches in width and 6 inches in height. - A square with sides of 2 inches is cut out from the top right corner of the rectangle. - Dimensions are marked to show distances across the structure: - The distance from the leftmost edge to the edge of the semicircle is 3 inches. - Horizontal and vertical axes are marked as x and y, respectively. **Key Measurements:** - Semicircle radius \(r = 6\) inches. - Rectangular section: 5 inches wide, full height of 6 inches. - Cutout square: 2 inches by 2 inches. The centroid's coordinates are provided with respect to the origin set at the center of the semicircle's flat side.
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