determine the magnitude of the yo-yo's angular velocity
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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Question
![**Understanding Yo-Yo Dynamics**
A 200 g yo-yo is being pulled along the ground where it rolls without slipping. The string is wrapped around the central hub of the yo-yo and is subjected to a force \( F = 2t^2 + 3 \) N, where \( t \) is in seconds. If the yo-yo can be treated as two outer disks with a radius of \( r_2 = 4.5 \) cm and an inner disk (central hub) with a radius of \( r_1 = 3.5 \) cm, each with the same mass, determine the magnitude of the yo-yo’s angular velocity after \( t = 0.4 \) s if it initially starts at rest. Assume the string has negligible mass.
### Diagram Explanation
The image displays a yo-yo with the following features:
- **Labels for Radii**: \( r_1 \) and \( r_2 \) are shown, indicating the inner disk (central hub) radius and the outer disk radius, respectively.
- **Point \( G \)**: Marks the center of mass of the yo-yo.
- **Force \( F \)**: An arrow shows the direction of the applied force \( F \).
Below the diagram, the problem statement and task instructions are described. There is a textbox for submitting the calculated angular velocity \(\omega\) in radians per second (\(\frac{rad}{s}\)).
### Problem Analysis
To calculate the angular velocity \(\omega\), we need to consider the equations of motion for both linear and rotational dynamics, utilizing the given force function \( F(t) \) and the constraints of the yo-yo's physical properties.
Use the provided textbox to submit your answer:
\[
\omega = \ \frac{rad}{s}
\]
**Submit Question**
*Powered by UBC Engineering (CC BY License).*
Ensure all calculations adhere to the principles of mechanical engineering and physics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42a8b670-f4b9-41aa-8a38-e9f581824926%2F1384c78a-e7e8-4f83-8e70-a2308738dec8%2Fo6v5pc_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Yo-Yo Dynamics**
A 200 g yo-yo is being pulled along the ground where it rolls without slipping. The string is wrapped around the central hub of the yo-yo and is subjected to a force \( F = 2t^2 + 3 \) N, where \( t \) is in seconds. If the yo-yo can be treated as two outer disks with a radius of \( r_2 = 4.5 \) cm and an inner disk (central hub) with a radius of \( r_1 = 3.5 \) cm, each with the same mass, determine the magnitude of the yo-yo’s angular velocity after \( t = 0.4 \) s if it initially starts at rest. Assume the string has negligible mass.
### Diagram Explanation
The image displays a yo-yo with the following features:
- **Labels for Radii**: \( r_1 \) and \( r_2 \) are shown, indicating the inner disk (central hub) radius and the outer disk radius, respectively.
- **Point \( G \)**: Marks the center of mass of the yo-yo.
- **Force \( F \)**: An arrow shows the direction of the applied force \( F \).
Below the diagram, the problem statement and task instructions are described. There is a textbox for submitting the calculated angular velocity \(\omega\) in radians per second (\(\frac{rad}{s}\)).
### Problem Analysis
To calculate the angular velocity \(\omega\), we need to consider the equations of motion for both linear and rotational dynamics, utilizing the given force function \( F(t) \) and the constraints of the yo-yo's physical properties.
Use the provided textbox to submit your answer:
\[
\omega = \ \frac{rad}{s}
\]
**Submit Question**
*Powered by UBC Engineering (CC BY License).*
Ensure all calculations adhere to the principles of mechanical engineering and physics.
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