If linear speed of a particle moving in a circular path is constant then,angular speed is proportional to (r is radius of circle)

Options

A. 1/r
B. `1/r^2`
C. `1/r^3`
D. `r^0`

Answer

To solve the problem, we need to understand the relationship between linear speed (v), angular speed (ω), and the radius (r) of the circular path.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The relationship between linear speed (v), angular speed (ω), and radius (r) in circular motion is given by the formula:
\[ v = r \cdot \omega \]

2. **Given Condition**:
It is stated that the linear speed (v) of the particle is constant. This means that v does not change as the particle moves along the circular path.

3. **Rearranging the Formula**:
Since v is constant, we can rearrange the equation to express angular speed (ω) in terms of linear speed (v) and radius (r):
\[ \omega = \frac{v}{r} \]

4. **Analyzing the Proportionality**:
From the rearranged equation, we can see that angular speed (ω) is inversely proportional to the radius (r) when linear speed (v) is constant. This means:
\[ \omega \propto \frac{1}{r} \]

5. **Conclusion**:
Therefore, if the linear speed of a particle moving in a circular path is constant, the angular speed is proportional to \( \frac{1}{r} \).

### Final Answer:
The angular speed (ω) is proportional to \( \frac{1}{r} \).