In rotational motion of a rigid body, all particles move with

Options

A. same linear and angular velocity.
B. same linear velocity and different angular velocities.
C. different limear velocities and same angular velocity.
D. different linear and angular velocities.

Answer

To solve the question regarding the motion of particles in a rigid body during rotational motion, we can break down the concepts step by step.

### Step-by-Step Solution:

1. **Understanding Rigid Body and Rotational Motion**:
- A rigid body is an object with a fixed shape that does not deform under the influence of forces. In rotational motion, all points in the rigid body rotate about a fixed axis.

2. **Linear Velocity of Points**:
- In rotational motion, different points on the rigid body can have different linear velocities. For example, consider two points A and B on the rigid body. If point A is closer to the axis of rotation than point B, point A will have a lower linear velocity compared to point B.

3. **Angular Velocity**:
- Angular velocity (ω) is defined as the rate of change of angular displacement and is the same for all points in a rigid body undergoing rotational motion. This means that every point in the rigid body rotates through the same angle in the same amount of time.

4. **Relationship Between Linear and Angular Velocity**:
- The linear velocity (v) of a point in a rigid body can be expressed in terms of angular velocity (ω) and the radius (r) from the axis of rotation:
\[ v = r \cdot \omega \]
- This equation shows that the linear velocity depends on both the distance from the axis of rotation and the angular velocity. Hence, points at different distances from the axis will have different linear velocities.

5. **Conclusion**:
- In summary, during the rotational motion of a rigid body, all particles do not move with the same linear velocity; however, they all share the same angular velocity. Thus, the correct answer to the question is that in the rotational motion of a rigid body, all particles move with the same angular velocity but different linear velocities.