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**Problem Statement:** Calculate \( I_y \) about the centroid of the following shape. (It should look familiar). Recall that \( x_{\text{bar}} = 2.11 \text{ ft}. \) Remember you want to calculate \( I \) of each shape about its centroid, then use the parallel axis theorem to relate it to the global centroid. **Hint:** Break into 4 pieces: half circle, square, triangle, and open circle. Remember you want to subtract the empty circle! Use \( I_x' = 0.11r^4 \) for the half-circle. Then just figure out each distance from the centroid of the component to the global centroid and that is your \( D \) in the \( AD^2 \) term. Good luck! Enter your answer without units in the space below. Follow correct sig figs! --- **Diagram Description:** The diagram shows a composite shape consisting of several geometric elements. Here is a breakdown of the components: - **Half Circle:** A semicircle on the left with a radius of 1 ft. - **Square:** A square above the semicircle integrated into a rectangle. - **Triangle:** This shape forms part of the upper structure of the rectangle extending to the right. - **Open Circle:** A hole (or open area) with a diameter of 1 ft inside the half-circle. **Dimensions are marked as follows:** - The semicircle and circle have a radius of 1 ft. - The horizontal length spanning from the vertical y-axis to the end of the rectangle’s bottom is 6 ft (3 ft + 3 ft). - The vertical length from the x-axis to the top is not explicitly listed but corresponds with the combined height of the semicircle and the additional structures. **Axes:** - The horizontal axis is marked as \( x \). - The vertical axis is marked as \( y \). **Note:** Applying the parallel axis theorem and considering the correct subtraction of the hollow circle will help find the total moment of inertia about the centroid.

**Problem Statement:** Calculate \( I_y \) about the centroid of the following shape. (It should look familiar). Recall that \( x_{\text{bar}} = 2.11 \text{ ft}. \) Remember you want to calculate \( I \) of each shape about its centroid, then use the parallel axis theorem to relate it to the global centroid. **Hint:** Break into 4 pieces: half circle, square, triangle, and open circle. Remember you want to subtract the empty circle! Use \( I_x' = 0.11r^4 \) for the half-circle. Then just figure out each distance from the centroid of the component to the global centroid and that is your \( D \) in the \( AD^2 \) term. Good luck! Enter your answer without units in the space below. Follow correct sig figs! --- **Diagram Description:** The diagram shows a composite shape consisting of several geometric elements. Here is a breakdown of the components: - **Half Circle:** A semicircle on the left with a radius of 1 ft. - **Square:** A square above the semicircle integrated into a rectangle. - **Triangle:** This shape forms part of the upper structure of the rectangle extending to the right. - **Open Circle:** A hole (or open area) with a diameter of 1 ft inside the half-circle. **Dimensions are marked as follows:** - The semicircle and circle have a radius of 1 ft. - The horizontal length spanning from the vertical y-axis to the end of the rectangle’s bottom is 6 ft (3 ft + 3 ft). - The vertical length from the x-axis to the top is not explicitly listed but corresponds with the combined height of the semicircle and the additional structures. **Axes:** - The horizontal axis is marked as \( x \). - The vertical axis is marked as \( y \). **Note:** Applying the parallel axis theorem and considering the correct subtraction of the hollow circle will help find the total moment of inertia about the centroid.

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:** Calculate \( I_y \) about the centroid of the following shape. (It should look familiar). Recall that \( x_{\text{bar}} = 2.11 \text{ ft}. \) Remember you want to calculate \( I \) of each shape about its centroid, then use the parallel axis theorem to relate it to the global centroid. **Hint:** Break into 4 pieces: half circle, square, triangle, and open circle. Remember you want to subtract the empty circle! Use \( I_x' = 0.11r^4 \) for the half-circle. Then just figure out each distance from the centroid of the component to the global centroid and that is your \( D \) in the \( AD^2 \) term. Good luck! Enter your answer without units in the space below. Follow correct sig figs! --- **Diagram Description:** The diagram shows a composite shape consisting of several geometric elements. Here is a breakdown of the components: - **Half Circle:** A semicircle on the left with a radius of 1 ft. - **Square:** A square above the semicircle integrated into a rectangle. - **Triangle:** This shape forms part of the upper structure of the rectangle extending to the right. - **Open Circle:** A hole (or open area) with a diameter of 1 ft inside the half-circle. **Dimensions are marked as follows:** - The semicircle and circle have a radius of 1 ft. - The horizontal length spanning from the vertical y-axis to the end of the rectangle’s bottom is 6 ft (3 ft + 3 ft). - The vertical length from the x-axis to the top is not explicitly listed but corresponds with the combined height of the semicircle and the additional structures. **Axes:** - The horizontal axis is marked as \( x \). - The vertical axis is marked as \( y \). **Note:** Applying the parallel axis theorem and considering the correct subtraction of the hollow circle will help find the total moment of inertia about the centroid.
Transcribed Image Text:**Problem Statement:** Calculate \( I_y \) about the centroid of the following shape. (It should look familiar). Recall that \( x_{\text{bar}} = 2.11 \text{ ft}. \) Remember you want to calculate \( I \) of each shape about its centroid, then use the parallel axis theorem to relate it to the global centroid. **Hint:** Break into 4 pieces: half circle, square, triangle, and open circle. Remember you want to subtract the empty circle! Use \( I_x' = 0.11r^4 \) for the half-circle. Then just figure out each distance from the centroid of the component to the global centroid and that is your \( D \) in the \( AD^2 \) term. Good luck! Enter your answer without units in the space below. Follow correct sig figs! --- **Diagram Description:** The diagram shows a composite shape consisting of several geometric elements. Here is a breakdown of the components: - **Half Circle:** A semicircle on the left with a radius of 1 ft. - **Square:** A square above the semicircle integrated into a rectangle. - **Triangle:** This shape forms part of the upper structure of the rectangle extending to the right. - **Open Circle:** A hole (or open area) with a diameter of 1 ft inside the half-circle. **Dimensions are marked as follows:** - The semicircle and circle have a radius of 1 ft. - The horizontal length spanning from the vertical y-axis to the end of the rectangle’s bottom is 6 ft (3 ft + 3 ft). - The vertical length from the x-axis to the top is not explicitly listed but corresponds with the combined height of the semicircle and the additional structures. **Axes:** - The horizontal axis is marked as \( x \). - The vertical axis is marked as \( y \). **Note:** Applying the parallel axis theorem and considering the correct subtraction of the hollow circle will help find the total moment of inertia about the centroid.
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