### Problem Statement:The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity \( v_A = 0.70 \, \text{m/s} \) to the right, compute the velocity of the center \( O \) (positive if to the right, negative if to the left) and the angular velocity \( \omega \) (positive if counterclockwise, negative if clockwise) of the reel.### Diagram Description:1. **Side View of the Reel:** - A drawing of a vertical reel with a height of 1.72 meters and a width of 0.60 meters is shown. - There is a horizontal line passing through point \( A \) to the right, labeled with a velocity \( v_A \).2. **Front View of the Reel:** - A circular representation of the reel is depicted with the same dimensions.### Answers:- The velocity of the center \( O \) of the reel is \( v_O = 1.075 \, \text{m/s} \).- The angular velocity \( \omega \) of the reel is \( \omega = 1.25 \, \text{rad/s} \).### Detailed Explanation:To fully understand the provided solutions, students should be aware that they need to use principles of rolling motion dynamics and kinematics, which involve relationships between linear and angular velocity under no-slip conditions. This problem typically requires using the equations such as:- \( v_O = R \omega \)- Incorporating the motion velocity \( v_A \) and the geometric constraints given.Students should be familiar with calculating parameters in rotational motion and applying the no-slip condition to solve for unknowns such as the center of mass velocity and angular velocity.

Given data as per the question vA=0.7 ms

The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity VA = 0.70 m/s to the right, compute the velocity of the center O (positive if to the right, negative if to the left) and the angular velocity w (positive if counterclockwise, negative if clockwise) of the reel. 1.72 m A Answers: Vo = W = 0.60 m 1.075 1.25 m/s rad/s

The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity VA = 0.70 m/s to the right, compute the velocity of the center O (positive if to the right, negative if to the left) and the angular velocity w (positive if counterclockwise, negative if clockwise) of the reel. 1.72 m A Answers: Vo = W = 0.60 m 1.075 1.25 m/s rad/s

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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### Problem Statement:
The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity \( v_A = 0.70 \, \text{m/s} \) to the right, compute the velocity of the center \( O \) (positive if to the right, negative if to the left) and the angular velocity \( \omega \) (positive if counterclockwise, negative if clockwise) of the reel.

### Diagram Description:
1. **Side View of the Reel:**
- A drawing of a vertical reel with a height of 1.72 meters and a width of 0.60 meters is shown.
- There is a horizontal line passing through point \( A \) to the right, labeled with a velocity \( v_A \).

2. **Front View of the Reel:**
- A circular representation of the reel is depicted with the same dimensions.

### Answers:
- The velocity of the center \( O \) of the reel is \( v_O = 1.075 \, \text{m/s} \).
- The angular velocity \( \omega \) of the reel is \( \omega = 1.25 \, \text{rad/s} \).

### Detailed Explanation:
To fully understand the provided solutions, students should be aware that they need to use principles of rolling motion dynamics and kinematics, which involve relationships between linear and angular velocity under no-slip conditions.

This problem typically requires using the equations such as:
- \( v_O = R \omega \)
- Incorporating the motion velocity \( v_A \) and the geometric constraints given.

Students should be familiar with calculating parameters in rotational motion and applying the no-slip condition to solve for unknowns such as the center of mass velocity and angular velocity.

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