When a mass is rotating in a plane about a fixed point, its angular momentum is directed along: a) the radius b) the tangent the orbit c) the line at angle of 45 degree to the plane of rotation d) the axis of rotation

Options

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

Explanation

To solve the question regarding 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. **Understanding Angular Momentum**:
Angular momentum (\( \vec{L} \)) of a particle is defined as the cross product of the position vector (\( \vec{R} \)) and the linear momentum (\( \vec{p} = m\vec{V} \)). Mathematically, it is given by:
\[ \vec{L} = \vec{R} \times \vec{p} = \vec{R} \times (m\vec{V}) \]

2. **Identifying the Vectors**:
- The position vector \( \vec{R} \) points from the fixed point (the center of rotation) to the mass.
- The velocity vector \( \vec{V} \) is tangent to the circular path of the mass.

3. **Direction of the Cross Product**:
The direction of the angular momentum vector \( \vec{L} \) is determined by the right-hand rule applied to the cross product \( \vec{R} \times \vec{V} \).
- Point your fingers in the direction of \( \vec{R} \) (from the center to the mass) and curl them towards \( \vec{V} \) (the direction of motion).
- Your thumb will then point in the direction of \( \vec{L} \).

4. **Conclusion on Direction**:
Since \( \vec{R} \) and \( \vec{V} \) are both in the plane of rotation, the angular momentum \( \vec{L} \) will be directed perpendicular to this plane. Therefore, the angular momentum is directed along the axis of rotation.

5. **Final Answer**:
Based on the analysis, the correct option is:
**d) the axis of rotation**.