A child of mass 46.2 kg sits on the edge of a merry-go-round with radius 1.9 m and moment of inertia 130.09 kg m2 . The merrygo-round rotates with an angular velocity of 2.4 rad/s. The child then walks towards the center of the merry-go-round and stops at a distance 0.779 m from the center. Now what is the angular velocity of the merry-go-round

The angular velocity is

Explanation:

From the question we are told that

   The mass of the child is  

    The radius of the merry go round is  

     The moment of inertia of the merry go round is

      The angular velocity of the merry-go round is  

       The position of the child from the center of the merry-go-round is  

According to the law of angular momentum conservation

    The initial angular momentum  =  final  angular momentum

So  

=>    

Now   is the initial moment of inertia of the system which is mathematically represented as

Where   is the initial moment of inertia of the boy which is mathematically evaluated as

substituting values

Thus

Thus  

Now  

Where   is the final  moment of inertia of the boy which is mathematically evaluated as

substituting values

Thus

Thus

Hence

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