Angular velocity of hour hand of a watch is

Options

A. `(pi)/(43200)rads^(-1)`
B. `(pi)/(30)rads^(-1)`
C. `(pi)/(21600)rads^(-1)`
D. `(pi)/(1800)rads^(-1)`

Explanation

To find the angular velocity of the hour hand of a watch, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Angular Velocity**:
Angular velocity (ω) is defined as the angle rotated (in radians) divided by the time taken (in seconds). The formula is:
\[ \omega = \frac{\theta}{t} \]
where \( \theta \) is the angle in radians and \( t \) is the time in seconds.

2. **Determine the Angle Rotated**:
The hour hand of a watch completes one full rotation in 12 hours. One full rotation corresponds to an angle of \( 2\pi \) radians.

3. **Convert Time to Seconds**:
Since we need the angular velocity in radians per second, we need to convert 12 hours into seconds:
\[ 12 \text{ hours} = 12 \times 60 \text{ minutes} \times 60 \text{ seconds} = 43200 \text{ seconds} \]

4. **Calculate Angular Velocity**:
Now we can substitute the values into the angular velocity formula:
\[ \omega = \frac{2\pi \text{ radians}}{43200 \text{ seconds}} \]

5. **Simplify the Expression**:
To simplify \( \frac{2\pi}{43200} \):
\[ \omega = \frac{2\pi}{43200} = \frac{\pi}{21600} \text{ radians per second} \]

6. **Final Result**:
Therefore, the angular velocity of the hour hand of a watch is:
\[ \omega = \frac{\pi}{21600} \text{ radians per second} \]