A particle moves in a circle of radius 20 cm with linear speed of 10 m/s. Find the angular velocity

Options

A. `500 (rad)/s`
B. `150 (rad)/s`
C. `50(rad)/s`
D. `15 (rad)/s`

Explanation

To find the angular velocity of a particle moving in a circle, we can use the relationship between linear speed and angular velocity. The formula to relate them is:

\[ \omega = \frac{V}{R} \]

where:
- \(\omega\) is the angular velocity in radians per second,
- \(V\) is the linear speed in meters per second,
- \(R\) is the radius of the circular path in meters.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Linear speed \(V = 10 \, \text{m/s}\)
- Radius \(R = 20 \, \text{cm} = 0.2 \, \text{m}\) (conversion from cm to m)

2. **Use the Formula for Angular Velocity**:
- Substitute the values into the formula:
\[ \omega = \frac{V}{R} = \frac{10 \, \text{m/s}}{0.2 \, \text{m}} \]

3. **Calculate the Angular Velocity**:
- Perform the division:
\[ \omega = \frac{10}{0.2} = 50 \, \text{radians/s} \]

4. **Conclusion**:
- The angular velocity of the particle is \(50 \, \text{radians/s}\).