To solve the problem, we need to analyze the two statements related to circular motion and determine their validity.
### Step 1: Analyze Statement A
**Statement A:** In uniform circular motion, \(\vec{\omega}\), \(\vec{v}\), and \(\vec{a}\) are always mutually perpendicular.
1. **Understanding Uniform Circular Motion:**
- In uniform circular motion, a particle moves in a circular path with a constant speed.
- The velocity vector \(\vec{v}\) is always tangent to the circular path.
- The acceleration vector \(\vec{a}\) in uniform circular motion is the centripetal acceleration, which points towards the center of the circle.
2. **Relationship Between Vectors:**
- The velocity \(\vec{v}\) is tangent to the circle, and the centripetal acceleration \(\vec{a}\) is directed towards the center, making them perpendicular.
- The angular velocity vector \(\vec{\omega}\) is directed along the axis of rotation (perpendicular to the plane of motion). In a right-handed coordinate system, it points out of the plane of the circle.
- Therefore, \(\vec{\omega}\) is also perpendicular to both \(\vec{v}\) and \(\vec{a}\).
**Conclusion for Statement A:** True. In uniform circular motion, \(\vec{\omega}\), \(\vec{v}\), and \(\vec{a}\) are mutually perpendicular.
### Step 2: Analyze Statement B
**Statement B:** In non-uniform circular motion, \(\vec{\omega}\), \(\vec{v}\), and \(\vec{a}\) are always mutually perpendicular.
1. **Understanding Non-Uniform Circular Motion:**
- In non-uniform circular motion, a particle moves in a circular path with a variable speed.
- The velocity vector \(\vec{v}\) is still tangent to the circular path.
- There are two components of acceleration:
- Centripetal acceleration \(\vec{a}_c\) directed towards the center of the circle.
- Tangential acceleration \(\vec{a}_t\) which is directed along the tangent to the path (in the direction of increasing speed).
2. **Relationship Between Vectors:**
- The net acceleration \(\vec{a}\) is the vector sum of \(\vec{a}_c\) and \(\vec{a}_t\). This net acceleration will not be perpendicular to the velocity vector \(\vec{v}\) because it has a tangential component.
- While \(\vec{\omega}\) remains perpendicular to the plane of motion, the presence of the tangential acceleration means that \(\vec{a}\) is not perpendicular to \(\vec{v}\).
**Conclusion for Statement B:** False. In non-uniform circular motion, \(\vec{a}\) is not perpendicular to \(\vec{v}\), hence \(\vec{\omega}\), \(\vec{v}\), and \(\vec{a}\) are not mutually perpendicular.
### Final Conclusion
- **Statement A:** True
- **Statement B:** False
Thus, the correct answer is that Statement A is true, and Statement B is false.
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