The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity VA = 0.84 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. Answers: Vo = W = 1.91 m 0.69 m 1.315 i 1.37705 Ja m/s VA rad/s

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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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 \( v_A = 0.84 \, \text{m/s} \) 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 Explanation:**

- The left diagram shows a side view of the reel on a horizontal surface.
  - The width of the reel is \( 1.91 \, \text{m} \).
  - The vertical distance from the horizontal surface to the center O of the reel is \( 0.69 \, \text{m} \).

- The right diagram shows a view of the reel from the front.
  - The point A on the cable is marked, and the velocity \( v_A \) is shown to be \( 0.84 \, \text{m/s} \) to the right.
  - It also indicates the center O of the reel.
  
**Answers:**

- Velocity of the center O, \( v_O \): \( 1.315 \, \text{m/s} \)
- Angular velocity of the reel, \( \omega \): \( 1.37705 \, \text{rad/s} \)
Transcribed Image Text:**Problem Statement:** The telephone-cable reel rolls without slipping on the horizontal surface. If point A on the cable has a velocity \( v_A = 0.84 \, \text{m/s} \) 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 Explanation:** - The left diagram shows a side view of the reel on a horizontal surface. - The width of the reel is \( 1.91 \, \text{m} \). - The vertical distance from the horizontal surface to the center O of the reel is \( 0.69 \, \text{m} \). - The right diagram shows a view of the reel from the front. - The point A on the cable is marked, and the velocity \( v_A \) is shown to be \( 0.84 \, \text{m/s} \) to the right. - It also indicates the center O of the reel. **Answers:** - Velocity of the center O, \( v_O \): \( 1.315 \, \text{m/s} \) - Angular velocity of the reel, \( \omega \): \( 1.37705 \, \text{rad/s} \)
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