College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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![**Educational Content: Rotational Inertia Calculation**
To determine the rotational inertia (also known as the moment of inertia) of a system of masses about a particular axis, in this case, the y-axis, we utilize the formula for a point mass:
\[ I = \sum m_i x_i^2 \]
Here, \(I\) is the rotational inertia, \(m_i\) is the mass, and \(x_i\) is the perpendicular distance of the mass from the y-axis (the x-coordinate in this case).
**Given Data:**
1. For mass m1:
- Mass (\(m_1\)): 1.5 units
- Coordinates (\(x_1, y_1\)): (-0.2, 0.4)
2. For mass m2:
- Mass (\(m_2\)): 2.5 units
- Coordinates (\(x_2, y_2\)): (-4.8, 2.4)
3. For mass m3:
- Mass (\(m_3\)): 2.5 units
- Coordinates (\(x_3, y_3\)): (0.8, -3.4)
### Steps to Calculate Rotational Inertia
1. **Square the x-coordinate for each mass:**
- For \(m_1\):
\[
x_1^2 = (-0.2)^2 = 0.04
\]
- For \(m_2\):
\[
x_2^2 = (-4.8)^2 = 23.04
\]
- For \(m_3\):
\[
x_3^2 = (0.8)^2 = 0.64
\]
2. **Multiply each result by the corresponding mass:**
- For \(m_1\):
\[
m_1 \times x_1^2 = 1.5 \times 0.04 = 0.06
\]
- For \(m_2\):
\[
m_2 \times x_2^2 = 2.5 \times 23.04 = 57.6
\]
- For \(m_3\):
\[
m_3 \times x_](https://content.bartleby.com/qna-images/question/d2932a05-99f3-41c1-989e-7dbca32c3377/adfca9d3-716f-4f7d-b4b8-25d120785c10/2sxul_processed.png)
Transcribed Image Text:**Educational Content: Rotational Inertia Calculation**
To determine the rotational inertia (also known as the moment of inertia) of a system of masses about a particular axis, in this case, the y-axis, we utilize the formula for a point mass:
\[ I = \sum m_i x_i^2 \]
Here, \(I\) is the rotational inertia, \(m_i\) is the mass, and \(x_i\) is the perpendicular distance of the mass from the y-axis (the x-coordinate in this case).
**Given Data:**
1. For mass m1:
- Mass (\(m_1\)): 1.5 units
- Coordinates (\(x_1, y_1\)): (-0.2, 0.4)
2. For mass m2:
- Mass (\(m_2\)): 2.5 units
- Coordinates (\(x_2, y_2\)): (-4.8, 2.4)
3. For mass m3:
- Mass (\(m_3\)): 2.5 units
- Coordinates (\(x_3, y_3\)): (0.8, -3.4)
### Steps to Calculate Rotational Inertia
1. **Square the x-coordinate for each mass:**
- For \(m_1\):
\[
x_1^2 = (-0.2)^2 = 0.04
\]
- For \(m_2\):
\[
x_2^2 = (-4.8)^2 = 23.04
\]
- For \(m_3\):
\[
x_3^2 = (0.8)^2 = 0.64
\]
2. **Multiply each result by the corresponding mass:**
- For \(m_1\):
\[
m_1 \times x_1^2 = 1.5 \times 0.04 = 0.06
\]
- For \(m_2\):
\[
m_2 \times x_2^2 = 2.5 \times 23.04 = 57.6
\]
- For \(m_3\):
\[
m_3 \times x_
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