College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a2e60b5-531b-408d-ad87-91178dbcae31%2F7e3bd9bc-ad25-4cdb-b018-9a78f67832bd%2Fs3pfl5_processed.gif&w=3840&q=75)
Transcribed Image Text:### 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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