Find angular velocity using angular momentum

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A 20kg girl stands on a large turntable 4m from its center. The turntable has a moment of inertia (about its roation axis) of 200kgm^2. Assume that the girl is a point mass.

a) Assume that the girl and turntable are rotating at 1 rad/s. If the girl walks inwards to a radius of 3m and stops, what is the new angular velocity?

b) Find the change in kinetic energy.

I got these two parts, but I am stuck with c and d



c) Assume that the turnable is initially stationary and the girl is at r=4m.

The girl starts walking in a circle around the turntable at a speed of 2m/s relative to the ground. Find the angular velocity of the turntable relative to the ground.

d) The girl starts walking in a circle around the turntable at a speed of 2m/sy relative to the turntable. Find the angular velocity of the turntable relative to the ground.


c) I got from part a that w_i = 1 rad/s and w_f 1.37 rad/s. I know that that I = 200 + mr^2

However, I have no idea what to do when she walks 2m/s. As she gets closer to the center, the turntable will spin faster. But I don't know what to do for c and d.
 

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  • #2
OlderDan
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For c and d the girl is no longer rotating at the same rate as the table. Don't try to find a moment of inertia for the system. Treat the girl as one object and the table as a second object and think about their individual angular momenta. The total angular momentum of the girl/table system is conserved. This is directly analogous to a linear momentum problem of a person walking on a plank that is on a frictionless surface. Starting from rest, if one thing goes one way, the other thing goes the other way.
 
  • #3
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For part c, you know the inital momentum is zero, that will be conserved. Set the angular momentum of the girl equal to the angular momentum of the turntable.

Edit: Wow, Dan you are all over the place.
 
  • #4
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Thank you.
 

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