**Problem Statement:**Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume \( h_0 = 0.34h \), \( b_0 = 0.16b \).**Diagram Description:**The diagram shows a rectangular area with width \( b \) and height \( h \). The rectangle is oriented with its longer side horizontal. The origin point \( O \) is located at a distance \( h_0 \) from the top edge along the vertical y-axis and \( b_0 \) from the left edge along the horizontal x-axis.- \( h \): height of the rectangle- \( h_0 \): vertical distance from point O to the top edge, \( h_0 = 0.34h \)- \( b \): width of the rectangle- \( b_0 \): horizontal distance from point O to the left edge, \( b_0 = 0.16b \)**Answers:**1. \( I_x = \quad \frac{bh^3}{12} \)2. \( I_y = \quad \frac{hb^3}{12} \)3. \( I_z = \quad \frac{bh^3}{12} + \frac{hb^3}{12} \)These formulas provide the moments of inertia about the x-axis, y-axis, and the polar moment of inertia about point O, respectively.

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Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume ho = 0.34h, bo = 0.16b. y

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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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

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**Problem Statement:**

Determine the moments of inertia of the rectangular area about the x- and y-axes and find the polar moment of inertia about point O. Assume \( h_0 = 0.34h \), \( b_0 = 0.16b \).

**Diagram Description:**

The diagram shows a rectangular area with width \( b \) and height \( h \). The rectangle is oriented with its longer side horizontal. The origin point \( O \) is located at a distance \( h_0 \) from the top edge along the vertical y-axis and \( b_0 \) from the left edge along the horizontal x-axis.

- \( h \): height of the rectangle
- \( h_0 \): vertical distance from point O to the top edge, \( h_0 = 0.34h \)
- \( b \): width of the rectangle
- \( b_0 \): horizontal distance from point O to the left edge, \( b_0 = 0.16b \)

**Answers:**

1. \( I_x = \quad \frac{bh^3}{12} \)
2. \( I_y = \quad \frac{hb^3}{12} \)
3. \( I_z = \quad \frac{bh^3}{12} + \frac{hb^3}{12} \)

These formulas provide the moments of inertia about the x-axis, y-axis, and the polar moment of inertia about point O, respectively.

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