Choose the correct option for rotational motion .

Options

A. The direction of angular velocity is perppendicular to the axis of rotation
B. The direction of angular velocity is ablong the axis of rotation
C. For rotational motion , the angular velocity of each particle is different
D. None of the above

Answer

To solve the question regarding the correct option for rotational motion, let's analyze the statements provided:

1. **Statement 1**: "The direction of angular velocity is perpendicular to the axis of rotation."
- This statement is **incorrect**. The direction of angular velocity is not perpendicular to the axis of rotation; rather, it is aligned with it.

2. **Statement 2**: "The direction of angular velocity is along the axis of rotation."
- This statement is **correct**. According to the right-hand rule, if you curl your fingers in the direction of rotation, your thumb points in the direction of the angular velocity vector, which is indeed along the axis of rotation.

3. **Statement 3**: "For the rotational motion, the angular velocity of each particle is different."
- This statement is also **incorrect**. In a rigid body rotating about a fixed axis, all particles of the body have the same angular velocity. For example, if a disk is rotating about its center, every point on the disk rotates with the same angular velocity (ω).

Based on the analysis above, the correct option for the question is **Statement 2**: "The direction of angular velocity is along the axis of rotation."

### Step-by-step Solution:
1. **Analyze Statement 1**: Determine if the direction of angular velocity is perpendicular to the axis of rotation. Conclusion: Incorrect.
2. **Analyze Statement 2**: Determine if the direction of angular velocity is along the axis of rotation. Conclusion: Correct.
3. **Analyze Statement 3**: Determine if the angular velocity of each particle in rotational motion is different. Conclusion: Incorrect.
4. **Final Conclusion**: The correct option is Statement 2.