The angular speed of second hand in a watch is

Options

A. `pi/(1800)rads^(-1)`
B. `pi/(30)rads^(-1)`
C. `pi/(90)rads^(-1)`
D. `pi/(60)rads^(-1)`

Answer

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

### Step 1: Understand the movement of the second hand
The second hand of a watch completes one full revolution in 60 seconds. A full revolution corresponds to an angle of \(2\pi\) radians.

### Step 2: Calculate the angular speed
Angular speed (\(\omega\)) is defined as the angle rotated per unit time. The formula for angular speed is:

\[ \omega = \frac{\text{Angle rotated}}{\text{Time taken}} \]

### Step 3: Substitute the values
In this case, the angle rotated is \(2\pi\) radians and the time taken is 60 seconds. Therefore, we can substitute these values into the formula:

\[ \omega = \frac{2\pi \text{ radians}}{60 \text{ seconds}} \]

### Step 4: Simplify the expression
Now, we simplify the fraction:

\[ \omega = \frac{2\pi}{60} = \frac{\pi}{30} \text{ radians per second} \]

### Conclusion
Thus, the angular speed of the second hand in a watch is \(\frac{\pi}{30}\) radians per second.

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