A kid runs towards the edge of a merry-go-round that is not rotating and jumps o

Question

A kid runs towards the edge of a merry-go-round that is not rotating and jumps on. The merry-go-round then rotates with a constant angular velocity ?. Assume that the kid has a mass of 40 kg and is initially running at a speed of 4 m/s tangent to the edge of the merry-go-round. The merry-go-round is a uniform disk with a mass of 80 kg and a radius of 2 m. Assume that it rotates without friction.
What is the initial angular momentum Li of the system (kid plus merry-go-round)?


What is the final angular momentum Lf of the system?


What is the final moment of inertia If of the system after the kid jumps on the merry-go-round?


What is the final angular velocity ?f of the merry-go-round (with the kid riding)?


What is the speed of the kid riding on the edge of the merry-go-round?

Explanation / Answer

(considering only boy as a system)

iintial angular velocity=4/2=2s-1

intial moment of inertia=160

final angualr momentum =intial angular momentum=160*2=320

finaltotal moment of inertia=0.5m1r2+m2r2          m1  is mass of meery go round

                                                                   m2 is mass of boy

I=0.5*80*4+4*40=320

 

 

let w be the angular velocity of the system

 by  conservation of angualr momentum

i1w1=i2w2

320*w=320

w=1s-1

now speedof kid is  rw =2ms-1

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