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.)

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### 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.**

\[ \text{kg} \cdot \text{m}^2 \]
Transcribed Image Text:### 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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