Final answer:
When Diego moves toward the center of the merry-go-round, the moment of inertia decreases and the angular speed increases.
Step-by-step explanation:
When Diego moves quickly toward the center of the merry-go-round, both the moment of inertia and the angular speed of the system will change.
The moment of inertia is a measure of how resistant an object is to changes in its rotational motion. It depends on the object's mass and how the mass is distributed relative to the axis of rotation. As Diego moves toward the center, the moment of inertia of the merry-go-round decreases because the mass is being concentrated closer to the axis. This means that it will be easier to change the merry-go-round's rotational motion.
The angular speed of the system is a measure of how fast the merry-go-round is rotating. As Diego moves toward the center, the angular speed of the system increases. This is because, in order to conserve angular momentum, the decrease in moment of inertia must be compensated by an increase in angular speed.