Final answer:
You cannot determine the mass of the merry-go-round from the given information regarding angular speed alone, without the moment of inertia. However, similar physics principles, such as the conservation of angular momentum, can determine changes in angular velocity when mass distribution changes, such as adding a child's mass to a merry-go-round.
Step-by-step explanation:
The question relates to the physics of rotational motion, specifically angular velocity and the conservation of angular momentum. Unfortunately, without knowing the moment of inertia of the merry-go-round, the exact mass cannot be calculated from the given angular acceleration and time period. The mass of a merry-go-round would typically have to be determined by other means, such as by measuring or using the specifications provided by the manufacturer.
In related scenarios that involve a known moment of inertia, you can use conservation of angular momentum to find the final angular velocity when the mass distribution changes, such as when a child hops onto a merry-go-round. For example, a merry-go-round with a mass of 120 kg and a radius of 1.80 m, with an initial angular velocity of 0.500 rev/s, would have a different angular velocity after a 22.0-kg child grabs it from rest.
This is due to the conservation of angular momentum, which states that the initial angular momentum (moment of inertia times angular velocity) must equal the final angular momentum, assuming no external torques are acting on the system.