### Moment of Inertia Calculation**Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. (The mass values are given in the table.)**| \( m_1 \) (kg) | \( m_2 \) (kg) | \( m_3 \) (kg) | \( m_4 \) (kg) ||:--------------:|:--------------:|:--------------:|:--------------:|| 3.30 | 2.50 | 3.70 | 1.50 |**Figure Description:**The diagram shows a rectangle with masses at each corner. The dimensions of the rectangle are 6.00 meters along the y-axis and 4.00 meters along the x-axis. The masses are positioned as follows:- \( m_1 \) at the top left corner.- \( m_2 \) at the top right corner.- \( m_4 \) at the bottom left corner.- \( m_3 \) at the bottom right corner.The distances from the origin (O) to each mass are along the sides of the rectangle.**(a) Find the moment of inertia of the system about the x-axis.**\[ \text{kg} \cdot \text{m}^2 \]**(b) Find the moment of inertia of the system about the y-axis.**\[ \text{kg} \cdot \text{m}^2 \]**(c) Find the moment of inertia of the system about an axis through \( O \) and perpendicular to the page.**\[ \text{kg} \cdot \text{m}^2 \]

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Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. (The mass values are given in the table.)

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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Question

### Moment of Inertia Calculation

**Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. (The mass values are given in the table.)**

| \( m_1 \) (kg) | \( m_2 \) (kg) | \( m_3 \) (kg) | \( m_4 \) (kg) |
|:--------------:|:--------------:|:--------------:|:--------------:|
| 3.30 | 2.50 | 3.70 | 1.50 |

**Figure Description:**
The diagram shows a rectangle with masses at each corner. The dimensions of the rectangle are 6.00 meters along the y-axis and 4.00 meters along the x-axis. The masses are positioned as follows:

- \( m_1 \) at the top left corner.
- \( m_2 \) at the top right corner.
- \( m_4 \) at the bottom left corner.
- \( m_3 \) at the bottom right corner.

The distances from the origin (O) to each mass are along the sides of the rectangle.

**(a) Find the moment of inertia of the system about the x-axis.**

\[ \text{kg} \cdot \text{m}^2 \]

**(b) Find the moment of inertia of the system about the y-axis.**

\[ \text{kg} \cdot \text{m}^2 \]

**(c) Find the moment of inertia of the system about an axis through \( O \) and perpendicular to the page.**

\[ \text{kg} \cdot \text{m}^2 \]

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