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 the solid cylinder, we can follow these steps:

### Step 1: Identify the formula for angular momentum
The angular momentum \( L \) of a rotating object can be calculated using the formula:
\[ L = I \cdot \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

### Step 2: Calculate the moment of inertia \( I \)
For a solid cylinder rotating about its own axis, the moment of inertia is given by the formula:
\[ I = \frac{1}{2} m r^2 \]
where:
- \( m \) is the mass of the cylinder (2 kg),
- \( r \) is the radius of the cylinder (0.2 m).

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

### Step 3: Substitute values to find angular momentum
Now that we have \( I \), we can substitute it along with the angular velocity \( \omega \) (3 rad/s) into the angular momentum formula:
\[ L = I \cdot \omega = 0.04 \, \text{kg m}^2 \cdot 3 \, \text{rad/s} \]
Calculating this gives:
\[ L = 0.12 \, \text{kg m}^2/\text{s} \]

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

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