If a body of moment of inertia `2kgm^2` revolves about its own axis making 2 rotations per second, then its angular momentum (in J s) is

Options

A. `2pi`
B. `4pi`
C. `6 pi`
D. `8 pi`

Answer

To solve the problem of finding the angular momentum of a body with a given moment of inertia and rotational speed, we can follow these steps:

### Step 1: Understand the given values
- Moment of inertia (I) = 2 kg·m²
- Rotations per second = 2

### Step 2: Convert rotations per second to angular velocity (ω)
Angular velocity (ω) in radians per second can be calculated using the formula:
\[ \omega = 2\pi \times \text{(rotations per second)} \]
Substituting the given value:
\[ \omega = 2\pi \times 2 = 4\pi \, \text{rad/s} \]

### Step 3: Use the formula for angular momentum (L)
Angular momentum (L) is given by the formula:
\[ L = I \cdot \omega \]
Substituting the values we have:
\[ L = 2 \, \text{kg·m²} \cdot 4\pi \, \text{rad/s} \]

### Step 4: Calculate the angular momentum
Now, we calculate:
\[ L = 8\pi \, \text{kg·m²/s} \]

### Step 5: Convert to Joules second (J·s)
Since 1 J·s = 1 kg·m²/s, we can express the angular momentum in Joules second:
\[ L = 8\pi \, \text{J·s} \]

### Final Answer
Thus, the angular momentum of the body is:
\[ L \approx 25.13 \, \text{J·s} \quad (\text{using } \pi \approx 3.14) \]