### Determining the Moment of Inertia about the x-axis for Specific AreasIn the given problem, you are asked to determine the moment of inertia about the x-axis for the areas shown in Figure P9–1. #### Figure P9–1 Explanation:The figure depicts a rectangular area standing upright with the following dimensions:- **Width:** 80 mm - **Height:** 200 mm The x-axis is positioned along the base of the rectangle.For a rectangular section, the moment of inertia \(I_x\) about its base (x-axis) can be calculated using the formula:\[ I_x = \frac{1}{3} b h^3 \]Where:- \(b\) is the base width (80 mm)- \(h\) is the height (200 mm)By substituting the given dimensions into this formula, one can determine the moment of inertia about the x-axis for this particular rectangle.This example serves to illustrate the process of determining moments of inertia for various geometric shapes, which is a fundamental concept in mechanics and structural engineering.

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Determine the moment of inertia about the x-axis of each of the areas shown in Figures P9-1 to 80 mm 200 mm FIGURE P9-1

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Question

### Determining the Moment of Inertia about the x-axis for Specific Areas

In the given problem, you are asked to determine the moment of inertia about the x-axis for the areas shown in Figure P9–1.

#### Figure P9–1 Explanation:
The figure depicts a rectangular area standing upright with the following dimensions:
- **Width:** 80 mm
- **Height:** 200 mm

The x-axis is positioned along the base of the rectangle.

For a rectangular section, the moment of inertia \(I_x\) about its base (x-axis) can be calculated using the formula:

\[ I_x = \frac{1}{3} b h^3 \]

Where:
- \(b\) is the base width (80 mm)
- \(h\) is the height (200 mm)

By substituting the given dimensions into this formula, one can determine the moment of inertia about the x-axis for this particular rectangle.

This example serves to illustrate the process of determining moments of inertia for various geometric shapes, which is a fundamental concept in mechanics and structural engineering.

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