The angular velocity of second's hand of a watch will be.

Options

A. `pi/60rads^-1`
B. `pi/30rads^-1`
C. `60pirads^(-1)`
D. `30pirads^(-1)`

Answer

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

### Step 1: Understand the concept of angular velocity
Angular velocity (ω) is defined as the rate of change of angular displacement with respect to time. It can be calculated using the formula:
\[ \omega = \frac{\text{Angular Displacement}}{\text{Time Taken}} \]

### Step 2: Determine the angular displacement for the second's hand
The second's hand of a watch completes one full revolution in 60 seconds. The angular displacement for one complete revolution is:
\[ \text{Angular Displacement} = 2\pi \text{ radians} \]

### Step 3: Determine the time taken for one revolution
The time taken for the second's hand to complete one full revolution is:
\[ \text{Time Taken} = 60 \text{ seconds} \]

### Step 4: Substitute the values into the angular velocity formula
Now we can substitute the values of angular displacement and time taken into the formula for angular velocity:
\[ \omega = \frac{2\pi \text{ radians}}{60 \text{ seconds}} \]

### Step 5: Simplify the expression
Now, simplify the expression:
\[ \omega = \frac{2\pi}{60} = \frac{\pi}{30} \text{ radians per second} \]

### Conclusion
Thus, the angular velocity of the second's hand of a watch is:
\[ \omega = \frac{\pi}{30} \text{ radians per second} \]

### Final Answer
The correct option is \(\frac{\pi}{30}\) radian per second.

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