An solid cylinder of mass `20 kg` and radius `20 cm` rotates about its axis with a angular speed `100 rad s^-1`. The angular momentum of the cylinder about its axis is.

Options

A. 40 J s
B. 400 J s
C. 20 J s
D. 200 J s

Explanation

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

### Step 1: Identify the given values
- Mass of the cylinder (m) = 20 kg
- Radius of the cylinder (r) = 20 cm = 0.2 m (convert cm to m)
- Angular speed (ω) = 100 rad/s

### Step 2: Calculate the moment of inertia (I) of the solid cylinder
The formula for the moment of inertia of a solid cylinder rotating about its axis is given by:
\[ I = \frac{1}{2} m r^2 \]

Substituting the values:
\[ I = \frac{1}{2} \times 20 \, \text{kg} \times (0.2 \, \text{m})^2 \]
\[ I = \frac{1}{2} \times 20 \times 0.04 \]
\[ I = \frac{1}{2} \times 0.8 \]
\[ I = 0.4 \, \text{kg m}^2 \]

### Step 3: Calculate the angular momentum (L)
The angular momentum (L) is given by the formula:
\[ L = I \omega \]

Substituting the values of I and ω:
\[ L = 0.4 \, \text{kg m}^2 \times 100 \, \text{rad/s} \]
\[ L = 40 \, \text{kg m}^2/\text{s} \]

### Final Answer
The angular momentum of the cylinder about its axis is:
\[ L = 40 \, \text{kg m}^2/\text{s} \]

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