A ody is in pure rotation. The linear speed v of a particle, the distance r of the particle from the axis and the angular velocity `omega` of the body are related as `omega=v/r`. Thus

Options

A. `omega prop1/r`
B. `omegapropr`
C. `omega=0`
D. `omega` is independent of r

Answer

To solve the problem, we need to analyze the relationship between linear speed (v), distance from the axis of rotation (r), and angular velocity (ω) of a body in pure rotation.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The relationship given is:
\[ \omega = \frac{v}{r} \]
where \( \omega \) is the angular velocity, \( v \) is the linear speed, and \( r \) is the distance from the axis of rotation.

2. **Rearranging the Equation**:
We can rearrange the equation to express linear speed in terms of angular velocity and radius:
\[ v = \omega \cdot r \]

3. **Analyzing Angular Velocity**:
In pure rotation, every point on the body has the same angular velocity \( \omega \). This means that regardless of the distance \( r \) from the axis of rotation, the angular velocity remains constant for all points on the body.

4. **Exploring the Implications**:
Since \( v \) depends on \( r \) (as \( v = \omega \cdot r \)), if \( r \) increases, \( v \) also increases proportionally, given that \( \omega \) is constant.

5. **Conclusion**:
From the relationship \( \omega = \frac{v}{r} \), we can conclude that:
- The angular velocity \( \omega \) is independent of \( r \).
- The linear speed \( v \) is directly proportional to the distance \( r \) from the axis of rotation.

### Final Answer:
Thus, the correct conclusion is that the angular velocity \( \omega \) is independent of the distance \( r \) from the axis of rotation.