Final answer:
The problem involves the conservation of angular momentum to determine the new angular velocity when two children on a merry-go-round move closer to the center. Initial and final angular momenta are equated, and the change in moment of inertia is calculated to solve for the new rotational speed in rpm.
Step-by-step explanation:
The student's question relates to the concept of conservation of angular momentum in physics. When Sanjay and Ting, each with a mass of 25 kg, move inward on a merry-go-round, they change the distribution of mass and thus the moment of inertia of the system. Initially, the merry-go-round is rotating at 23 revolutions per minute (rpm).
Since angular momentum (L) is conserved,
we can set the initial angular momentum equal to the final angular momentum (Li = Lf).
The moment of inertia (I) of a point mass at a distance (r) from the axis of rotation is I = mr2,
and the angular momentum L = Iω,
where ω is the angular velocity. The initial moment of inertia for each child is (25 kg)(1.5 m)2 since the diameter is 3.0 m.
When both children move to 35 cm (0.35 m) from the center, the new moment of inertia for each child is (25 kg)(0.35 m)2.
The total change in moment of inertia must account for both children and the merry-go-round itself, which does not change.
To find the new angular velocity, set the initial angular momentum (which includes the combined moment of inertia of the merry-go-round and both children at the edge) equal to the final angular momentum (which includes the new combined moment of inertia with the children 35 cm from the center).
Solve for the new angular velocity. The result will be in radians per second, which can be converted back to rpm for the final answer.