Chosse the correct altarnatives

Options

A. For a general rotational motion , angular momentum L and angular velocity `omega` need not be parallel .
B. For a rotional motion about a fixed axis , angular momentum L and angular velocity `oemga` are always parallel .
C. For a gereral translational motion , momentum P and velocity V are always parallel .
D. For a general transational motion , acceleration a and velocity V are always parallel.

Explanation

To solve the question, we need to analyze each option provided and determine which statements are correct regarding angular momentum, angular velocity, momentum, and velocity in both rotational and translational motion.

### Step-by-Step Solution:

1. **Understanding Angular Momentum and Angular Velocity**:
- Angular momentum (L) is defined as \( L = I \omega \), where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.
- In general rotational motion, the angular momentum vector \( L \) and angular velocity vector \( \omega \) need not be parallel. This is true when the rotation axis is not fixed.

**Conclusion**: Option A is correct.

2. **Fixed Axis Rotation**:
- For rotational motion about a fixed axis, both angular momentum \( L \) and angular velocity \( \omega \) are always parallel. This is because the direction of both vectors is aligned along the axis of rotation.

**Conclusion**: Option B is correct.

3. **Understanding Momentum and Velocity in Translation**:
- Momentum (P) is defined as \( P = mv \), where \( m \) is mass and \( v \) is velocity.
- In general translational motion, momentum and velocity are always parallel since they are both vectors pointing in the same direction.

**Conclusion**: Option C is correct.

4. **Acceleration and Velocity**:
- Acceleration (A) is the rate of change of velocity (V). While acceleration can be positive or negative depending on the direction of velocity and the nature of motion, it is not always positive. Thus, this statement is incorrect.

**Conclusion**: Option D is incorrect.

### Final Answer:
The correct alternatives are:
- Option A: Correct
- Option B: Correct
- Option C: Correct
- Option D: Incorrect