Length of clocks second hands 0.1 m what is the order of its angular velocity in radian per/sec.

Options

A. `10^(-1)`
B. `10^(-2)`
C. `10^(-3)`
D. `10^(-4)`

Answer

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

### Step 1: Understand the motion of the second hand
The second hand of a clock completes one full rotation (360 degrees) in one minute.

### Step 2: Convert the rotation into radians
One complete rotation is equal to \(2\pi\) radians. Therefore, the angular displacement for one complete rotation is:
\[ \theta = 2\pi \text{ radians} \]

### Step 3: Determine the time taken for one complete rotation
The time taken for one complete rotation is 1 minute, which can be converted into seconds:
\[ T = 1 \text{ minute} = 60 \text{ seconds} \]

### Step 4: Calculate the angular velocity
Angular velocity (\(\omega\)) is defined as the angular displacement divided by the time taken. Therefore, we can calculate \(\omega\) as follows:
\[ \omega = \frac{\theta}{T} = \frac{2\pi \text{ radians}}{60 \text{ seconds}} = \frac{\pi}{30} \text{ radians per second} \]

### Step 5: Determine the order of the angular velocity
To express \(\omega\) in terms of its order of magnitude, we can approximate \(\pi\) as approximately 3.14. Thus:
\[ \omega \approx \frac{3.14}{30} \approx 0.10467 \text{ radians per second} \]
This value is on the order of \(10^{-1}\) radians per second.

### Conclusion
The order of the angular velocity of the second hand is:
\[ \text{Order of } \omega \approx 10^{-1} \text{ radians per second} \]