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 1: Understand the motion of the minute hand
The minute hand of a clock completes one full revolution in one hour.

### Step 2: Convert the time taken into seconds
Since we need the angular speed in SI units (radians per second), we need to convert the time taken from minutes to seconds.
- 1 hour = 60 minutes
- 60 minutes = 60 × 60 seconds = 3600 seconds

### Step 3: Determine the angular displacement
One full revolution corresponds to an angular displacement of:
- 1 revolution = \(2\pi\) radians

### Step 4: Use the formula for angular speed
The angular speed (\(\omega\)) is given by the formula:
\[ \omega = \frac{\theta}{t} \]
where \(\theta\) is the angular displacement and \(t\) is the time taken.

### Step 5: Substitute the values into the formula
Substituting the values we have:
- \(\theta = 2\pi\) radians
- \(t = 3600\) seconds

So,
\[ \omega = \frac{2\pi \text{ radians}}{3600 \text{ seconds}} \]

### Step 6: Simplify the expression
Now we can simplify:
\[ \omega = \frac{2\pi}{3600} = \frac{\pi}{1800} \text{ radians per second} \]

### Final Answer
The angular speed of the minute hand of a clock is \(\frac{\pi}{1800}\) radians per second.

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