A large turntable has moment of inertia I. Person A, mass mA stands at a distanc

Question

A large turntable has moment of inertia I. Person A, mass mA stands at a distance halfway to the outer edge of the turntable of radius R, whereas Person B, mass mB, stands right at the outer edge of the turntable, as shown below. The turntable and people spin with angular speed ?0. The people can be regarded as point masses for this problem. What is the angular speed ?1 of the turntable after person A walks to the center of the table?

With Person A at the center of the turntable, Person B jumps off in a direction parallel to his instantaneous velocity, with vB relative to the ground. What is angular speed ?2 of the turntable now? To keep your expression simple, you may consider ?1 to be a known value.

Explanation / Answer

we use the conservaion of angular momentum

initially the total angular momentum is ,

( I +ma*0.5R2 +mBR2)0

when the person walks to the middle, new momentum,

( I +mBR2)1

using conservation of momentum ,

( I +mBR2)1 = ( I +ma*0.5R2 +mBR2)0

=>1= ( I +ma*0.5R2 +mBR2)/ (( I +mBR2)1 )

when the person jumps off , new angular momentum ,

( I )2

using conservation of momentum ,

( I )2 = ( I +mBR2)1

=>2=( I +mBR2)1 /(I)

=(( I +mBR2)( I +ma*0.5R2 +mBR2))/ (I*( I +mBR2)1 )

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