The angular momentum of a body with mass (m) moment of inertia `(I)` and angular velocity `(omega)" rad"//s` is equal to

Options

A. `Iomega`
B. `I omega^(2)`
C. `I/omega`
D. `1/omega^(2)`

Answer

To find the angular momentum of a body with mass \( m \), moment of inertia \( I \), and angular velocity \( \omega \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Angular Momentum**:
Angular momentum \( L \) of a rotating body is defined as the product of its moment of inertia \( I \) and its angular velocity \( \omega \). The formula is given by:
\[ L = I \cdot \omega \]

2. **Identify the Components**:
- **Mass \( m \)**: This is the mass of the body.
- **Moment of Inertia \( I \)**: This is a measure of how mass is distributed relative to the axis of rotation.
- **Angular Velocity \( \omega \)**: This is the rate of rotation of the body, measured in radians per second.

3. **Apply the Formula**:
Since we know the relationship between angular momentum, moment of inertia, and angular velocity, we can directly substitute the values into the formula:
\[ L = I \cdot \omega \]

4. **Conclusion**:
Therefore, the angular momentum of the body is given by:
\[ L = I \omega \]

### Final Answer:
The angular momentum \( L \) of a body with mass \( m \), moment of inertia \( I \), and angular velocity \( \omega \) is:
\[ L = I \omega \]