Find the angular speed of the minute hand of a clock.

Answer

To find the angular speed of the minute hand of a clock, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Motion of the Minute Hand:**
The minute hand of a clock completes one full revolution (360 degrees) in 1 hour.

2. **Determine the Time Period (T):**
Since the minute hand takes 1 hour to complete one full revolution, we convert this time into seconds.
\[ T = 1 \text{ hour} = 60 \text{ minutes} = 60 \times 60 \text{ seconds} = 3600 \text{ seconds} \]

3. **Use the Formula for Angular Speed (ω):**
The angular speed (ω) is given by the formula:
\[ \omega = \frac{2\pi}{T} \]
where \(2\pi\) radians corresponds to one full revolution.

4. **Substitute the Value of T:**
Now we can substitute the value of T into the formula:
\[ \omega = \frac{2\pi}{3600} \]

5. **Calculate the Angular Speed:**
Using the approximate value of \(\pi \approx 3.14\):
\[ \omega = \frac{2 \times 3.14}{3600} \approx \frac{6.28}{3600} \approx 0.001745 \text{ radians per second} \]

6. **Round the Result:**
Rounding this value gives us:
\[ \omega \approx 0.0017 \text{ radians per second} \]

### Final Answer:
The angular speed of the minute hand of a clock is approximately \(0.0017 \text{ radians per second}\).

---