Final answer:
To find the new angular velocity of a merry-go-round when a child moves to the center, the change in the system's moment of inertia is calculated and the conservation of angular momentum is applied.
Step-by-step explanation:
Calculating New Angular Velocity
When a child moves closer to the center of a merry-go-round, the system's moment of inertia changes, affecting the angular velocity due to the conservation of angular momentum.
The original moment of inertia (Iinitial) can be calculated by adding the moment of inertia of the merry-go-round (Im = 1/2 mmrm2) to the moments of inertia of the children (sum of mcrm2, where mc is the child's mass).
When one child moves to the center, their contribution to the moment of inertia becomes zero.
The initial angular momentum (Linitial) is equal to Iinitial multiplied by the initial angular velocity (ωinitial). Since angular momentum is conserved (Linitial = Lfinal),
when the child moves to the center, the new angular velocity (ωfinal) can be found by dividing Linitial by the new moment of inertia (Ifinal). Thus, ωfinal is higher than ωinitial if all other factors remain constant.