The angular speed of second hand in a watch is

Options

A. `(pi)/(60) rad//s`
B. `(pi)/(30) rad//s`
C. `(pi)/(120) rad//s `
D. `(pi)/(2) rad//s`

Explanation

To find the angular speed of the second hand in a watch, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Angular Speed**:
Angular speed (ω) is defined as the angle covered per unit time. It can be calculated using the formula:
\[ \omega = \frac{2\pi}{T} \]
where \( T \) is the time period for one complete revolution.

2. **Identify the Time Period for the Second Hand**:
The second hand of a watch completes one full revolution (which corresponds to an angle of \( 2\pi \) radians) in 1 minute. We need to convert this time period into seconds:
\[ T = 1 \text{ minute} = 60 \text{ seconds} \]

3. **Substitute the Time Period into the Angular Speed Formula**:
Now, we can substitute \( T \) into the angular speed formula:
\[ \omega = \frac{2\pi}{60} \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ \omega = \frac{2\pi}{60} = \frac{\pi}{30} \text{ radians per second} \]

5. **Final Answer**:
Thus, the angular speed of the second hand in a watch is:
\[ \omega = \frac{\pi}{30} \text{ radians per second} \]