When a mass is rotating in a plane about a fixed point, its angular momentum is directed along.

Options

A. the radius
B. the tangent to orbit
C. line at an angle of `45^(@)` to the plane of rotation
D. the axis of rotation

Answer

To determine the direction of angular momentum when a mass is rotating in a plane about a fixed point, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the System**:
- Consider a mass (or a disc) rotating in a horizontal plane about a fixed point (the center of the disc).

2. **Identify Relevant Vectors**:
- The radius vector \( \mathbf{r} \) extends from the fixed point (axis of rotation) to the mass.
- The velocity vector \( \mathbf{v} \) is tangential to the path of the mass and lies in the plane of rotation.

3. **Use the Angular Momentum Formula**:
- The angular momentum \( \mathbf{L} \) of a particle is given by the cross product:
\[ \mathbf{L} = \mathbf{r} \times \mathbf{p} \]
- Here, \( \mathbf{p} \) (linear momentum) is \( m \mathbf{v} \), where \( m \) is the mass and \( \mathbf{v} \) is the velocity of the mass.

4. **Express Angular Momentum**:
- Substitute \( \mathbf{p} \) into the equation:
\[ \mathbf{L} = \mathbf{r} \times (m \mathbf{v}) = m (\mathbf{r} \times \mathbf{v}) \]

5. **Determine the Direction Using the Right-Hand Rule**:
- To find the direction of \( \mathbf{L} \), use the right-hand rule:
- Point your fingers in the direction of \( \mathbf{r} \) (from the axis of rotation to the mass).
- Curl your fingers in the direction of \( \mathbf{v} \) (the direction of motion of the mass).
- Your thumb will point in the direction of the angular momentum \( \mathbf{L} \).

6. **Conclusion**:
- The angular momentum \( \mathbf{L} \) is directed along the axis of rotation, perpendicular to the plane in which the mass is rotating.

### Final Answer:
The angular momentum is directed along the axis of rotation.

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