Angular velocity

Options

A. radially outward
B. radially inward
C. along the tangent to the circular path
D. along the axis of rotation

Answer

### Step-by-Step Solution:

1. **Understanding Angular Velocity**:
- Angular velocity (denoted by \( \omega \)) is defined as the rate of change of angular displacement. It describes how quickly an object rotates around a specific axis.

2. **Formula for Angular Velocity**:
- The formula for angular velocity is given by:
\[ \omega = \frac{\theta}{t} \]
where \( \theta \) is the angular displacement in radians, and \( t \) is the time taken for that displacement.

3. **Direction of Angular Velocity**:
- Angular velocity is a vector quantity, meaning it has both magnitude and direction. The direction of angular velocity can be determined using the right-hand thumb rule.

4. **Applying the Right-Hand Thumb Rule**:
- To use the right-hand thumb rule, curl the fingers of your right hand in the direction of the rotation (for example, anticlockwise). Your thumb will then point in the direction of the angular velocity vector.

5. **Identifying the Axis of Rotation**:
- For a body rotating in a circle, the axis of rotation is perpendicular to the plane of the circle. If the rotation is anticlockwise, the angular velocity vector points upwards along the positive z-axis.

6. **Evaluating the Given Options**:
- The options provided are:
- A) Radially outward
- B) Radially inward
- C) Along the tangent of the circle path
- D) Along the axis of rotation
- We analyze each option:
- **Radially outward**: This direction is in the plane of the circle; hence, it is incorrect.
- **Radially inward**: This direction is also in the plane of the circle; hence, it is incorrect.
- **Along the tangent of the circle path**: This direction is tangential to the circle and lies in the plane; hence, it is incorrect.
- **Along the axis of rotation**: This direction is perpendicular to the plane of the circle and points along the axis of rotation; hence, it is correct.

7. **Conclusion**:
- The correct answer is option D) Along the axis of rotation.