Aplayground merry-go-round has a mass of 115 kg and a radius of 2.50 m and it is rotating with an angular velocity of 0.520 rev/s. the merry-go-round is a solid disk, and the moment of inertia is = 1/2 mr2. a 23.5 kg child is initially at rest, he then gets onto the merry-go-round by grabbing its outer edge. the child can be treated as a point mass located at the outer edge of the merry-go-round. his moment of inertia is mr2. after this rotational collision, the merry-go-round and the child have a commen final angular velocity (which is different from the merry-go-round's initital angular velocity). (e) what is the final angular velocity in rad/s after the child gets on?

Explanation:

For answer this we will use the law of the conservation of the angular momentum.

so:

where is the moment of inertia of the merry-go-round, is the initial angular velocity of the merry-go-round, is the moment of inertia of the merry-go-round and the child together and is the final angular velocity.

First, we will find the moment of inertia of the merry-go-round using:

I =

I =

I = 359.375 kg*m^2

Where is the mass and R is the radio of the merry-go-round

Second, we will change the initial angular velocity to rad/s as:

W = 0.520*2 rad/s

W = 3.2672 rad/s

Third, we will find the moment of inertia of both after the collision:

Finally we replace all the data:

Solving for :

4

explanation:

4

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explanation: