A child on a merry-go-round moves from the edge to the center. What happens to the angular velocity of the merry-go-round?

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Q: A child on a merry-go-round moves from the edge to the center. What happens to the angular velocity of the merry-go-round?

Solution: Angular velocity increases due to conservation of angular momentum as moment of inertia decreases.

Steps: 8

Step 1: Understand what angular velocity means. Angular velocity is how fast something is spinning around a point.
Step 2: Know what a merry-go-round is. It spins around a center point, and a child can be at the edge or the center.
Step 3: Recognize that when the child moves from the edge to the center, they are changing their position relative to the center of the merry-go-round.
Step 4: Learn about angular momentum. Angular momentum is a property that helps us understand how things spin. It stays the same unless acted on by an outside force.
Step 5: Understand moment of inertia. Moment of inertia is how hard it is to change the spinning motion of an object. When the child is at the edge, the moment of inertia is larger than when they are at the center.
Step 6: Realize that when the child moves to the center, the moment of inertia decreases because they are closer to the center of the merry-go-round.
Step 7: Apply the conservation of angular momentum. Since angular momentum must stay the same, if the moment of inertia decreases, the angular velocity must increase to keep the angular momentum constant.
Step 8: Conclude that as the child moves from the edge to the center, the angular velocity of the merry-go-round increases.