A circular disc of mass `4kg` and of radius `10cm` is rotating about its natural axis at the rate of `5 rad//sec`. Its angular momentum is

Options

A. `0.25 kgm^(2)s^(-1)`
B. `0.1 kgm^(2)s^(-1)`
C. `2.5 kgm^(2)s^(-1)`
D. `0.2 kgm^(2)s^(-1)`

Explanation

To find the angular momentum of a circular disc, we can follow these steps:

### Step 1: Identify the given values
- Mass of the disc (m) = 4 kg
- Radius of the disc (r) = 10 cm = 0.1 m (conversion from cm to m)
- Angular velocity (ω) = 5 rad/s

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

Substituting the values:
\[ I = \frac{1}{2} \times 4 \, \text{kg} \times (0.1 \, \text{m})^2 \]
\[ I = \frac{1}{2} \times 4 \times 0.01 \]
\[ I = \frac{1}{2} \times 0.04 \]
\[ I = 0.02 \, \text{kg m}^2 \]

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

Substituting the values:
\[ L = 0.02 \, \text{kg m}^2 \times 5 \, \text{rad/s} \]
\[ L = 0.1 \, \text{kg m}^2/\text{s} \]

### Final Answer
The angular momentum of the disc is:
\[ L = 0.1 \, \text{kg m}^2/\text{s} \]

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