The spool has a weight of 40 lblb and a radius of gyration kOkOk_O = 0.4 ftft . A cord is wrapped around its inner hub and the end subjected to a horizontal force PPP = 8 lblb . Assume the spool rolls without slipping. (Figure 1) Determine the spool's angular velocity, measured clockwise, in 5 ss starting from rest.
The spool has a weight of 40 lblb and a radius of gyration kOkOk_O = 0.4 ftft . A cord is wrapped around its inner hub and the end subjected to a horizontal force PPP = 8 lblb . Assume the spool rolls without slipping. (Figure 1) Determine the spool's angular velocity, measured clockwise, in 5 ss starting from rest.
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
The spool has a weight of 40 lblb and a radius of gyration kOkOk_O = 0.4 ftft . A cord is wrapped around its inner hub and the end subjected to a horizontal force PPP = 8 lblb . Assume the spool rolls without slipping. (Figure 1)
Determine the spool's angular velocity, measured clockwise, in 5 ss starting from rest.
![### Problem Description
The spool has a weight of 40 lb and a radius of gyration \( k_0 = 0.4 \, \text{ft} \). A cord is wrapped around its inner hub and the end is subjected to a horizontal force \( P = 8 \, \text{lb} \). Assume the spool rolls without slipping.
#### Objective
Determine the spool’s angular velocity, measured clockwise, in 5 seconds starting from rest.
#### Instructions
Express your answer using three significant figures. Enter a positive value if the angular velocity is clockwise and a negative value if the angular velocity is counterclockwise.
---
### Input Box
\[
\omega = \quad \text{rad/s}
\]
#### Actions
- Click "Submit" to check your answer.
- Use the "Request Answer" option if needed.
- Click "Provide Feedback" for any comments or concerns about the problem.
---
### Diagram Explanation
#### Figure
The figure illustrates a spool with a cord wrapped around its inner hub.
- The spool has a radius of 0.9 ft while the cord is attached at a radius of 0.3 ft from the center \( O \).
- Point \( A \) and the horizontal force \( P = 8 \, \text{lb} \) act on the cord to induce motion.
- The spool's rotation and motion are indicated to be without slipping during the problem’s scenario.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98ba27a3-ab69-49b1-ad1c-2aa6f8226754%2F297e7bb4-09e7-400d-891e-578940af590e%2F1u08c4i_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description
The spool has a weight of 40 lb and a radius of gyration \( k_0 = 0.4 \, \text{ft} \). A cord is wrapped around its inner hub and the end is subjected to a horizontal force \( P = 8 \, \text{lb} \). Assume the spool rolls without slipping.
#### Objective
Determine the spool’s angular velocity, measured clockwise, in 5 seconds starting from rest.
#### Instructions
Express your answer using three significant figures. Enter a positive value if the angular velocity is clockwise and a negative value if the angular velocity is counterclockwise.
---
### Input Box
\[
\omega = \quad \text{rad/s}
\]
#### Actions
- Click "Submit" to check your answer.
- Use the "Request Answer" option if needed.
- Click "Provide Feedback" for any comments or concerns about the problem.
---
### Diagram Explanation
#### Figure
The figure illustrates a spool with a cord wrapped around its inner hub.
- The spool has a radius of 0.9 ft while the cord is attached at a radius of 0.3 ft from the center \( O \).
- Point \( A \) and the horizontal force \( P = 8 \, \text{lb} \) act on the cord to induce motion.
- The spool's rotation and motion are indicated to be without slipping during the problem’s scenario.
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