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.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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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 image shows a telephone-cable reel. 
- There are two views: a front view and a side view.
- The reel has two radii:
  - The larger radius: \( r = 1.91 \, \text{m} \)
  - The smaller radius: \( R = 0.69 \, \text{m} \)
- Point A on the cable has a velocity vector \( v_A \) pointing to the right.
- The center of the reel is labeled as O.

**Answers:**

\[
v_O = \boxed{1.315} \, \text{m/s}
\]

\[
\omega = \boxed{1.376} \, \text{rad/s}
\]
Transcribed Image Text: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 image shows a telephone-cable reel. - There are two views: a front view and a side view. - The reel has two radii: - The larger radius: \( r = 1.91 \, \text{m} \) - The smaller radius: \( R = 0.69 \, \text{m} \) - Point A on the cable has a velocity vector \( v_A \) pointing to the right. - The center of the reel is labeled as O. **Answers:** \[ v_O = \boxed{1.315} \, \text{m/s} \] \[ \omega = \boxed{1.376} \, \text{rad/s} \]
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