Final answer:
The detailed answer would need additional specific information to calculate the angular velocity of link AB. Related concepts such as angular acceleration are covered, and angular acceleration can be calculated using the formula a = (Δω) / (Δt), where Δω represents the change in angular velocity and Δt represents the change in time.
Step-by-step explanation:
The question asks about the angular velocity of link AB at a given instant. To answer this, we'd need more specific information from the scenario that is mentioned in the question, such as the rotational speed, the position at the initial time, or some other relationship that allows us to calculate angular velocity. However, the additional information provided does cover a variety of related concepts, such as how to calculate angular acceleration when given initial and final angular velocities alongside the time interval, and it also demonstrates how to find the tangential speeds and angular acceleration of objects in rotational motion.
For instance, for the object whose angular velocity changes from 3 rad/s to 8 rad/s over 5 seconds, the angular acceleration (a) can be calculated using the formula a = (Δω) / (Δt). Plugging in the values gives an angular acceleration a = (8 rad/s - 3 rad/s) / 5 s = 1.0 rad/s², which is not featured in the given options.