Answer :
Final answer:
The concept of moment of inertia and its relationship to angular velocity is key to answering this question. When a child on a merry-go-round move to the center, the moment of inertia decreases. As a result, to conserve angular momentum, the angular velocity must increase.
Explanation:
This question relates to the concept of moment of inertia and angular velocity. In the scenario, when the child with a mass of 29.5 kg moves to the center of the merry-go-round, the overall moment of inertia of the system decreases. To conserve angular momentum, the angular velocity must then increase.
Moment of inertia is a measure of the resistance of a body to angular acceleration. It depends on both the mass and distribution of mass in relation to the axis of rotation. A larger moment of inertia will lead to a smaller angular acceleration and vice versa.
To find the new angular velocity, we first calculate the total initial moment of inertia before the child moves, which includes the moments of inertia of the merry-go-round and the three children. Then, we would get the total moment of inertia after the child moves to the center. Using the principle of conservation of angular momentum, we can find the new angular velocity. This involves calculus and knowledge about moment of inertia and angular momentum.
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