Angular displacement is a vector quantity for __________ angles. (very small/even large)

Answer

To determine whether angular displacement is a vector quantity for very small angles or even large angles, we can analyze the properties of angular displacement.

### Step-by-Step Solution:

1. **Understanding Angular Displacement**:
Angular displacement is defined as the angle through which an object has rotated about a specific axis in a given direction. It is typically denoted by the symbol θ (theta).

2. **Vector Quantity Definition**:
A vector quantity has both magnitude and direction. For angular displacement, the direction is determined by the axis of rotation and the sense of rotation (clockwise or counterclockwise).

3. **Commutative Property**:
The commutative property states that the order of addition does not affect the result. For angular displacements, this property holds true, meaning that the addition of angular displacements is independent of the order in which they are added.

4. **Behavior for Small and Large Angles**:
- For very small angles, angular displacement can be approximated as a linear quantity, and its vector nature is still valid.
- For larger angles, the vector nature becomes more significant as the direction of rotation becomes more pronounced, and the effects of rotation can be more complex.

5. **Conclusion**:
Angular displacement is a vector quantity for both very small and even large angles. However, it is essential to consider the direction and the axis of rotation, especially for larger angles where the effects of rotation can be more complex.

### Final Answer:
Angular displacement is a vector quantity for both very small and even large angles.

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