What is the angular velocity of the child and the merry-go-round?

AI Thread Summary
The discussion revolves around calculating the angular velocity of a child who jumps onto a stationary merry-go-round. The problem involves applying the conservation of momentum, treating the child as a point mass at the rim of the merry-go-round. The moment of inertia for the child is calculated as 180 kgm², leading to a total moment of inertia of 540 kgm² when combined with the merry-go-round's moment of inertia. The final angular velocity is determined to be 0.500 rad/s. The conversation highlights the importance of understanding the conservation of momentum in rotational motion problems.
jk2455
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the statement:

a child runs at 3m/s and jumps tangentially onto a stationary merry-go-round. the moment of inertia of the merry-go-round is 360kgm2 and the radius is 2.0m. what is the angular velocity of the child and the merry-go-round?

answer- 0.500rad s-1 or 0.500s-1[/SUP

i honestly have no idea what to do could someone please break the question down to a bit easier understanding.
 
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This is a conservation of momentum problem. Treat the child as a point mass on the rim of a circle to find the child's moment of inertia and then add it to the MGR to find total I.
 
so this is what i did but now I am stuck and don't know if I am on the right track

Ichild=45x22
= 180kgm2
Itotal=Imgr+Ichild
=540kgm2
Vf=m1v1+m2v2/(m1+m2)
=m1v1/(m1+m2)
=1 m/s
 

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