The disk shown in the figure rolls without slipping. What is the velocity of the center point O? O2rw Orw² 00 Orw

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 disk shown in the figure rolls without slipping. What is the velocity of the center point \( O \)?

**Diagram Description:**

The diagram features a green circle representing a disk with center point \( O \), radius \( r \), and angular velocity \( \omega \). The disk is in contact with a horizontal surface at a point labeled \( C \). The arrow indicating \( \omega \) shows a counterclockwise rotation of the circle.

**Options:**

1. \( 2r\omega \)
2. \( r\omega^2 \)
3. \( 0 \)
4. \( r\omega \) 

---

**Solution:**

When a disk rolls without slipping, the linear velocity \( v \) of the center point \( O \) can be found using the relationship between the angular velocity \( \omega \) and the radius \( r \) of the disk:

\[ v = r\omega \]

Thus, the correct answer is:

\( \circ \) \( r\omega \)
Transcribed Image Text:**Problem Statement:** The disk shown in the figure rolls without slipping. What is the velocity of the center point \( O \)? **Diagram Description:** The diagram features a green circle representing a disk with center point \( O \), radius \( r \), and angular velocity \( \omega \). The disk is in contact with a horizontal surface at a point labeled \( C \). The arrow indicating \( \omega \) shows a counterclockwise rotation of the circle. **Options:** 1. \( 2r\omega \) 2. \( r\omega^2 \) 3. \( 0 \) 4. \( r\omega \) --- **Solution:** When a disk rolls without slipping, the linear velocity \( v \) of the center point \( O \) can be found using the relationship between the angular velocity \( \omega \) and the radius \( r \) of the disk: \[ v = r\omega \] Thus, the correct answer is: \( \circ \) \( r\omega \)
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