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

Options

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

Answer

To solve the question about 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**:
- We have a mass rotating in a circular path around a fixed point. This defines a plane of rotation.

2. **Identify the Plane of Rotation**:
- Let's denote the plane of rotation as the XY plane. The center of rotation is at the origin, and the mass moves in a circular path around this point.

3. **Visualize the Motion**:
- As the mass rotates, it has a position vector \( \vec{r} \) extending from the center of rotation to the mass. The mass moves with a certain tangential velocity \( \vec{v} \) along the circular path.

4. **Apply the Right-Hand Rule**:
- To determine the direction of angular momentum \( \vec{L} \), we can use the right-hand rule.
- Point your fingers in the direction of the mass's motion (tangential direction), and curl them in the direction of rotation. Your thumb will point in the direction of the angular momentum.

5. **Determine the Direction**:
- Since the mass is rotating in the XY plane, using the right-hand rule, the thumb will point along the Z-axis, which is perpendicular to the XY plane.

6. **Conclusion**:
- Therefore, the angular momentum of the mass is directed along a line that is perpendicular to the plane of rotation.

### Final Answer:
The correct answer is: **A line perpendicular to the plane of rotation.**

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