What is the angular velocity of (a) a second hand and (b) minute hand of a clock ?

Explanation

To find the angular velocity of the second hand and the minute hand of a clock, we can use the formula for angular velocity, which is given by:

\[ \omega = \frac{2\pi}{T} \]

where \( \omega \) is the angular velocity in radians per second, and \( T \) is the time period in seconds for one complete revolution.

### Step-by-Step Solution:

#### (a) Angular Velocity of the Second Hand:

1. **Identify the time period (T) for the second hand:**
- The second hand completes one full revolution in 60 seconds.

2. **Substitute the time period into the formula:**
\[ \omega_{\text{second hand}} = \frac{2\pi}{T} = \frac{2\pi}{60} \]

3. **Calculate the angular velocity:**
\[ \omega_{\text{second hand}} = \frac{2\pi}{60} \approx 0.105 \text{ radians per second} \]

#### (b) Angular Velocity of the Minute Hand:

1. **Identify the time period (T) for the minute hand:**
- The minute hand completes one full revolution in 3600 seconds (60 minutes).

2. **Substitute the time period into the formula:**
\[ \omega_{\text{minute hand}} = \frac{2\pi}{T} = \frac{2\pi}{3600} \]

3. **Calculate the angular velocity:**
\[ \omega_{\text{minute hand}} = \frac{2\pi}{3600} \approx 0.0017 \text{ radians per second} \]

### Final Answers:
- (a) Angular velocity of the second hand: \( \approx 0.105 \text{ rad/s} \)
- (b) Angular velocity of the minute hand: \( \approx 0.0017 \text{ rad/s} \)