hree children are riding on the edge of a merry-go-round that is 182 kg, has a 1.60 m radius, and is spinning at 17.3 rpm. The children have masses of 19.9, 27.5, and 40.8 kg. If the child who has a mass of 40.8 kg moves to the center of the merry-go- round, what is the new angular velocity in rpm?

To find the new angular velocity when a child moves from the edge to the center of a merry-go-round, we can use the principle of conservation of angular momentum. The angular momentum of the system before the child moves is equal to the angular momentum of the system after the child moves. By calculating the initial angular momentum and the new moment of inertia, we can solve for the new angular velocity using the equation L = Iw.

Explanation:

To solve this problem, we can use the principle of conservation of angular momentum. The angular momentum of the system before the child moves is equal to the angular momentum of the system after the child moves. Angular momentum (L) is given by L = (moment of inertia) x (angular velocity). The moment of inertia of the merry-go-round with all the children on the edge can be calculated using the formula I = MR^2, where M is the mass of the merry-go-round and R is the radius.

Before the child moves, the total angular momentum of the system is equal to the sum of the angular momentum of the merry-go-round and the children. After the child moves, the angular momentum of the merry-go-round remains the same, but the moment of inertia changes because the child moves to the center. We can find the new angular velocity by rearranging the formula L = Iw and solving for w, the angular velocity.

Using the given values, we can calculate the initial angular momentum of the system and the new moment of inertia when the child moves. Plugging these values into the equation L = Iw, we can solve for w, the new angular velocity.

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