A soild cylinder of mass 2 kg and radius 0.2 m is rotating about its owm axis without friction with an angular velocity of 3 rad `s^(-1)` . Angular momentum of the cylinder is

Options

A. 0.2 J s
B. 1.12 J s
C. 0.12 J s
D. 12 J s

Answer

To find the angular momentum of a solid cylinder rotating about its own axis, we can follow these steps:

### Step 1: Understand the formula for angular momentum
The angular momentum \( L \) of an 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.

### Step 2: Determine the moment of inertia for the solid cylinder
The moment of inertia \( I \) for a solid cylinder rotating about its own axis is given by the formula:
\[ I = \frac{1}{2} m r^2 \]
where:
- \( m \) is the mass of the cylinder,
- \( r \) is the radius of the cylinder.

### Step 3: Substitute the given values into the moment of inertia formula
Given:
- Mass \( m = 2 \, \text{kg} \)
- Radius \( r = 0.2 \, \text{m} \)

Substituting these values into the moment of inertia formula:
\[ I = \frac{1}{2} \times 2 \, \text{kg} \times (0.2 \, \text{m})^2 \]
Calculating \( (0.2 \, \text{m})^2 \):
\[ (0.2)^2 = 0.04 \, \text{m}^2 \]
Now substituting back:
\[ I = \frac{1}{2} \times 2 \times 0.04 = 0.04 \, \text{kg} \cdot \text{m}^2 \]

### Step 4: Calculate the angular momentum using the angular velocity
Given:
- Angular velocity \( \omega = 3 \, \text{rad/s} \)

Now substitute \( I \) and \( \omega \) into the angular momentum formula:
\[ L = I \cdot \omega = 0.04 \, \text{kg} \cdot \text{m}^2 \cdot 3 \, \text{rad/s} \]
Calculating \( L \):
\[ L = 0.12 \, \text{kg} \cdot \text{m}^2/\text{s} \]

### Conclusion
The angular momentum of the cylinder is:
\[ L = 0.12 \, \text{kg} \cdot \text{m}^2/\text{s} \]