Final answer:
The question addresses calculating the new angular velocity of a merry-go-round when a child jumps on. It utilizes the conservation of angular momentum principle and does not require the mass of the merry-go-round solely to determine the new angular speed. The mass of the merry-go-round cannot be calculated from the given information about the change in angular speed.
Step-by-step explanation:
The question is asking to solve for the angular velocity of a merry-go-round after various interactions. The initial scenario mentions a merry-go-round that starts at rest, and then acquires an angular speed of 0.9250 rev/s in 3.50 s. However, the mass of the merry-go-round is not relevant information to find the angular velocity just based on the provided scenario and cannot be determined from the information given. The other scenario gives details about calculating the new angular velocity of a 120 kg merry-go-round when a 22.0-kg child acquires a position on the edge while it's already rotating.
For case 39, the use of the conservation of angular momentum is appropriate. The system starts with an initial angular momentum that must equal the final angular momentum after the child acquires a position on the merry-go-round. Since no external torques are acting on the system, we can set the initial angular momentum (moment of inertia of the merry-go-round times its angular velocity) equal to the final angular momentum (combined moment of inertia of the merry-go-round and child times the new angular velocity). This approach will yield the new angular velocity after the child gets on.