IN which case use of angular velocity is useful

Options

A. when the body is rotating
B. when the body moves in a straight line
C. when the body is changing its direction of motion
D. none of the these

Answer

To determine in which case the use of angular velocity is useful, we need to analyze the options provided in the question.

### Step-by-Step Solution:

1. **Understanding Angular Velocity**:
- Angular velocity (ω) is defined as the rate of change of angular displacement (θ) with respect to time (t). Mathematically, it is expressed as:
\[ \omega = \frac{d\theta}{dt} \]
- It is a vector quantity that indicates how quickly an object is rotating and in which direction.

2. **Analyzing the Options**:
- **Option A: When the body is in rotation**:
- In this case, the body is continuously changing its angular position. Therefore, angular velocity is very relevant as it describes how fast the object is rotating.

- **Option B: When a body moves in a straight line**:
- Here, there is no change in angular position since the movement is linear. Thus, angular velocity is not applicable in this scenario.

- **Option C: When a body is changing the direction of motion**:
- While the direction of motion may change, if the body is not rotating around a point, angular velocity is not the primary descriptor of the motion. It is more about linear velocity in this case.

- **Option D: None of these**:
- This option can be disregarded since we have already identified a scenario where angular velocity is applicable.

3. **Conclusion**:
- The most appropriate case for the use of angular velocity is **Option A: When the body is in rotation**. In this scenario, the angular displacement is changing over time, making angular velocity a useful and necessary concept.

### Final Answer:
The use of angular velocity is useful **when the body is in rotation**.