A particle is moving with uniform speed `0.5 m//s` along a circle of radius `1m` then the angular velocity of particle is (in `rad s^(-1)`)

Options

A. `2`
B. `1.5`
C. `1`
D. `0.5`

Explanation

To find the angular velocity of a particle moving in a circular path, we can use the relationship between linear velocity and angular velocity. The formula that relates these two quantities is:

\[ v = \omega r \]

Where:
- \( v \) is the linear velocity (in meters per second),
- \( \omega \) is the angular velocity (in radians per second),
- \( r \) is the radius of the circular path (in meters).

### Step-by-Step Solution:

1. **Identify the given values:**
- Linear velocity, \( v = 0.5 \, \text{m/s} \)
- Radius of the circle, \( r = 1 \, \text{m} \)

2. **Use the formula to find angular velocity:**
Rearranging the formula \( v = \omega r \) to solve for \( \omega \):
\[ \omega = \frac{v}{r} \]

3. **Substitute the known values into the equation:**
\[ \omega = \frac{0.5 \, \text{m/s}}{1 \, \text{m}} \]

4. **Calculate \( \omega \):**
\[ \omega = 0.5 \, \text{rad/s} \]

5. **State the final answer:**
The angular velocity of the particle is \( 0.5 \, \text{rad/s} \).

### Final Answer:
\[ \omega = 0.5 \, \text{rad/s} \]