A fan of moment of inertia 0.6 kg `xx` `"metre"^2` is to run upto a working speed of 0.5 revolution per second. Indicate the correct value of the angular momentum of the fan

Options

A. `0.6 pi kg xx("metre"^2)/("sec")`
B. `6 pi kg xx("metre"^2)/("sec")`
C. `3 pi kg xx("metre"^2)/("sec")`
D. `pi/6 kg xx("metre"^2)/("sec")`

Answer

To find the angular momentum of the fan, we can follow these steps:

### Step 1: Understand the formula for angular momentum
The angular momentum (L) of a rotating object is given by the formula:
\[ L = I \cdot \omega \]
where:
- \( L \) is the angular momentum,
- \( I \) is the moment of inertia,
- \( \omega \) is the angular velocity in radians per second.

### Step 2: Identify the given values
From the problem, we have:
- Moment of inertia \( I = 0.6 \, \text{kg m}^2 \)
- Speed of the fan \( = 0.5 \, \text{revolutions per second} \)

### Step 3: Convert revolutions per second to radians per second
To convert the speed from revolutions per second to radians per second, we use the fact that:
1 revolution = \( 2\pi \) radians.

Thus, we can calculate \( \omega \) as follows:
\[ \omega = 0.5 \, \text{revolutions/second} \times 2\pi \, \text{radians/revolution} = 0.5 \times 2\pi = \pi \, \text{radians/second} \]

### Step 4: Substitute the values into the angular momentum formula
Now that we have both \( I \) and \( \omega \), we can substitute these values into the angular momentum formula:
\[ L = I \cdot \omega = 0.6 \, \text{kg m}^2 \cdot \pi \, \text{radians/second} \]
\[ L = 0.6\pi \, \text{kg m}^2/\text{s} \]

### Step 5: Final answer
The angular momentum of the fan is:
\[ L = 0.6\pi \, \text{kg m}^2/\text{s} \]