A flywheel is accelerated using two cords attached to the top and bottom of the outer radii. Its acceleration when the forces are first applied is ?=−50 ????̂ α=−50 radk^. Where ?̂ k^ points upwards out of the diagram. The moment of inertia is equal to ?=??2/2=100 ??(0.1 ?)2/2=0.5 ??−?2I=mr2/2=100 kg(0.1 m)2/2=0.5 kg−m2. Use the Newton-Euler equations. What are the applied forces, ?F?
A flywheel is accelerated using two cords attached to the top and bottom of the outer radii. Its acceleration when the forces are first applied is ?=−50 ????̂ α=−50 radk^. Where ?̂ k^ points upwards out of the diagram. The moment of inertia is equal to ?=??2/2=100 ??(0.1 ?)2/2=0.5 ??−?2I=mr2/2=100 kg(0.1 m)2/2=0.5 kg−m2. Use the Newton-Euler equations. What are the applied forces, ?F?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A flywheel is accelerated using two cords attached to the top and bottom of the outer radii. Its acceleration when the forces are first applied is ?=−50 ????̂ α=−50 radk^. Where ?̂ k^ points upwards out of the diagram. The moment of inertia is equal to ?=??2/2=100 ??(0.1 ?)2/2=0.5 ??−?2I=mr2/2=100 kg(0.1 m)2/2=0.5 kg−m2. Use the Newton-Euler equations. What are the applied forces, ?F?
![### Understanding the Flywheel Acceleration Problem
**Diagram Explanation:**
This diagram illustrates a flywheel being accelerated using two cords. These cords are attached to the top and bottom of the flywheel's outer radii. The forces applied via these cords result in the flywheel’s rotational acceleration, denoted as \( \alpha \).
- **Coordinate System:**
- The x-axis is horizontal.
- The y-axis is vertical.
- A positive counterclockwise rotation is represented by the angular acceleration \( \alpha \).
- The forces \( F \) are applied tangentially in the x-direction.
**Problem Description:**
1. The flywheel undergoes an angular acceleration \( \alpha \) of \(-50 \, \text{rad/s}^2\), with \( \mathbf{\hat{k}} \) pointing upwards and out of the diagram.
2. The moment of inertia \( I \) for the flywheel is calculated as follows:
\[
I = \frac{mr^2}{2} = 100 \, \text{kg}(0.1 \, \text{m})^2/2 = 0.5 \, \text{kg} \cdot \text{m}^2
\]
3. The task is to use the Newton-Euler equations to determine the applied forces \( F \).
**Objective:**
To understand and calculate the forces needed to produce the specified angular acceleration using the given properties of the flywheel.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6b656b52-bb2e-489d-9bef-8a32efc9339f%2F82c13da8-2a05-442e-baea-5a2a32db8f7c%2Fg54va0h_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding the Flywheel Acceleration Problem
**Diagram Explanation:**
This diagram illustrates a flywheel being accelerated using two cords. These cords are attached to the top and bottom of the flywheel's outer radii. The forces applied via these cords result in the flywheel’s rotational acceleration, denoted as \( \alpha \).
- **Coordinate System:**
- The x-axis is horizontal.
- The y-axis is vertical.
- A positive counterclockwise rotation is represented by the angular acceleration \( \alpha \).
- The forces \( F \) are applied tangentially in the x-direction.
**Problem Description:**
1. The flywheel undergoes an angular acceleration \( \alpha \) of \(-50 \, \text{rad/s}^2\), with \( \mathbf{\hat{k}} \) pointing upwards and out of the diagram.
2. The moment of inertia \( I \) for the flywheel is calculated as follows:
\[
I = \frac{mr^2}{2} = 100 \, \text{kg}(0.1 \, \text{m})^2/2 = 0.5 \, \text{kg} \cdot \text{m}^2
\]
3. The task is to use the Newton-Euler equations to determine the applied forces \( F \).
**Objective:**
To understand and calculate the forces needed to produce the specified angular acceleration using the given properties of the flywheel.
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