**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 Inertia1. **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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Answered: Find the rotation m1=1.5, x1=-0.2

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Physics

Find the rotation m1=1.5, x1=-0.2

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

**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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