Question

In: Physics

A 4.0 ? diameter merry-go-round (mass 270 ??) is spinning at 15 ???. A child of...

A 4.0 ? diameter merry-go-round (mass 270 ??) is spinning at 15 ???. A child of 35.0 ?? runs tangent to the merry-go-round at 3.0 ?/?, in the same direction that it is turning, and jumps onto the outer edge. Calculate the merry-go-round’s angular velocity, immediately after the child jumps on.

Expert Solution

This is a problem in conservation of angular momentum. The sum of the initial angular momenta of the merry-go-roud and boy will be equal to their combined angular momenta.

Initial angular momenta

Merry-go-round

Since its a disk, it moment of inertia is

It angular velocity is

Therefore, its angular momentum is

The boy

Considering the boy as a point mass, his angular momentum is

The total initial angular momentum is

Final angular momentum

The moment of inertia of the combined bodies, considering the boy to be a point mass is

Let the final angular velocity be

Therefore, the final angular momentum is

Equating the two, we get

genius_generous answered 2 years ago

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