A wagon wheel heading down south from the land of the pines consists of a thin ring having a mass of me and six spokes made from slender rods with each having a mass of m... Tw Variable Value mc 7 kg mr 1.3 kg Tw 0.85 m a.) What is the moment of inertia through the center of the wheel in kg - m²? b.) What is the moment of inertia about point A in kg - m²?? A
A wagon wheel heading down south from the land of the pines consists of a thin ring having a mass of me and six spokes made from slender rods with each having a mass of m... Tw Variable Value mc 7 kg mr 1.3 kg Tw 0.85 m a.) What is the moment of inertia through the center of the wheel in kg - m²? b.) What is the moment of inertia about point A in kg - m²?? A
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![### Educational Resource: Moment of Inertia of a Wagon Wheel
**Introduction:**
A wagon wheel heading down south from the land of the pines consists of a thin ring having a mass of \( m_c \) and six spokes made from slender rods with each having a mass of \( m_r \).
**Diagram Explanation:**
In the diagram, a wagon wheel is depicted, showing a thin circular ring with six internal spokes. The wheel's parts and key points are labeled:
- **C** at the center of the wheel.
- **A** at the point where the wheel touches the ground.
- The variables shown in the diagram include:
- \( r_w \): the radius of the wheel.
- \( m_c \): the mass of the circular ring.
- \( m_r \): the mass of each spoke.
**Table of Variables and Their Values:**
\[
\begin{array}{|c|c|}
\hline
\text{Variable} & \text{Value} \\
\hline
m_c & 7 \, \text{kg} \\
\hline
m_r & 1.3 \, \text{kg} \\
\hline
r_w & 0.85 \, \text{m} \\
\hline
\end{array}
\]
**Questions:**
a.) What is the moment of inertia through the center of the wheel in \( \text{kg} \cdot \text{m}^2 \)?
b.) What is the moment of inertia about point \( A \) in \( \text{kg} \cdot \text{m}^2 \)?
**Detailed Information:**
1. **Moment of Inertia through the Center (C):**
For calculating the moment of inertia of the wheel through its center \( C \), consider the contributions from both the thin ring and the spokes:
- The moment of inertia of the ring ( \( I_{\text{ring}} \) ):
\[
I_{\text{ring}} = m_c \cdot r_w^2
\]
- The moment of inertia of each spoke (assumed as a slender rod rotating about one end):
\[
I_{\text{spoke}} = \frac{1}{3} m_r \cdot r_w^2
\]
Since there are six spokes,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2e6b1be0-596d-4af1-a341-a1c152f1c814%2Faf4dfb0e-5ec5-4c4c-a521-f2eb57360f99%2F3phmwhp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Resource: Moment of Inertia of a Wagon Wheel
**Introduction:**
A wagon wheel heading down south from the land of the pines consists of a thin ring having a mass of \( m_c \) and six spokes made from slender rods with each having a mass of \( m_r \).
**Diagram Explanation:**
In the diagram, a wagon wheel is depicted, showing a thin circular ring with six internal spokes. The wheel's parts and key points are labeled:
- **C** at the center of the wheel.
- **A** at the point where the wheel touches the ground.
- The variables shown in the diagram include:
- \( r_w \): the radius of the wheel.
- \( m_c \): the mass of the circular ring.
- \( m_r \): the mass of each spoke.
**Table of Variables and Their Values:**
\[
\begin{array}{|c|c|}
\hline
\text{Variable} & \text{Value} \\
\hline
m_c & 7 \, \text{kg} \\
\hline
m_r & 1.3 \, \text{kg} \\
\hline
r_w & 0.85 \, \text{m} \\
\hline
\end{array}
\]
**Questions:**
a.) What is the moment of inertia through the center of the wheel in \( \text{kg} \cdot \text{m}^2 \)?
b.) What is the moment of inertia about point \( A \) in \( \text{kg} \cdot \text{m}^2 \)?
**Detailed Information:**
1. **Moment of Inertia through the Center (C):**
For calculating the moment of inertia of the wheel through its center \( C \), consider the contributions from both the thin ring and the spokes:
- The moment of inertia of the ring ( \( I_{\text{ring}} \) ):
\[
I_{\text{ring}} = m_c \cdot r_w^2
\]
- The moment of inertia of each spoke (assumed as a slender rod rotating about one end):
\[
I_{\text{spoke}} = \frac{1}{3} m_r \cdot r_w^2
\]
Since there are six spokes,
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