A circular disc is rotating about its own axis at uniform rate completes `30` rotations in one minute.The angular velocity of disc in rad `s^(-1)` is

Options

A. `2pi`
B. `pi`
C. `pi/2`
D. `pi/4i`

Explanation

To find the angular velocity of the circular disc in radians per second, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: The disc completes 30 rotations in one minute. We need to convert this into angular velocity in radians per second.

2. **Convert Rotations to Revolutions per Second**:
- Since there are 60 seconds in a minute, we can find the number of rotations per second (n) by dividing the total rotations by the number of seconds in a minute.
\[ n = \frac{30 \text{ rotations}}{60 \text{ seconds}} = \frac{1}{2} \text{ rotations per second} \]

3. **Use the Formula for Angular Velocity**:
- The angular velocity (ω) in radians per second can be calculated using the formula:
\[ \omega = 2\pi n \]
- Substitute the value of n we found:
\[ \omega = 2\pi \left(\frac{1}{2}\right) \]

4. **Calculate Angular Velocity**:
- Simplifying the equation gives:
\[ \omega = \pi \text{ radians per second} \]

5. **Final Answer**:
- The angular velocity of the disc is:
\[ \omega = \pi \text{ rad/s} \]