To calculate the angular velocity at the midpoint of a bar, it is important to note that the angular velocity is uniform across all points of a rigid body. While the midpoint may not exhibit tangential velocity, it does rotate around the pivot point, meaning it has the same angular velocity as the rest of the bar. The discussion highlights that a point itself cannot have angular velocity, but rather a small object can exhibit such motion. Ultimately, the midpoint's movement is tied to the overall rotation of the bar, despite its lack of mass. The conversation reflects a mix of confusion and clarification regarding the nature of angular velocity in rigid bodies.