Final answer:
The question subjects are about rotational dynamics, including concepts of angular velocity, acceleration, and momentum in various scenarios such as weighted rods, rotating disks, spinning satellites, and rolling boulders.
Step-by-step explanation:
The question appears to revolve around the concept of rotational motion and dynamics, which involves angular velocity, angular acceleration, and angular momentum. A variety of scenarios are provided, each dealing with objects in rotation, such as a whirling rock on a string, rods with attached weights, a rolling boulder, spinning satellites, and rotating pulleys with weights. For instance, when considering a stick with weights attached to both ends and released from a horizontal position, the problem concerns calculating the angular velocity as it swings down to the vertical position. Another example involves a disk with a small mass attached to its edge rotating at a certain speed, and subsequently the mass sliding to the center, prompting calculations regarding the final rotation rate of the disk due to conservation of angular momentum.