Conservation of Angular Momentum Problem Help

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The problem involves a putty mass landing on a rotating turntable, requiring the application of conservation of angular momentum to find the final angular speed after the putty flies off. The initial angular momentum is given by the product of the turntable's moment of inertia and its initial angular speed. After the putty lands, the new angular speed can be calculated using the combined moment of inertia of the turntable and the putty. The discussion raises questions about the relationship between the angular velocities of the turntable and the putty after separation, specifically whether they are the same or different. Clarification is sought on the correct interpretation of angular momentum conservation in this context.
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Homework Statement


Ok... "A small bob of putty of mass m falls from the ceiling and lands on the outer rim of a turntable of radius R and moment of inertia I_0 that is rotating freely with angular speed of w_i, about its vertical fixed symmetry axis..."

"After several turns the blob flies off the edge of the turntable. What is the angular speed of the turntable after the blob flies off."




Homework Equations





The Attempt at a Solution


Ok.. so angular momentum is conserved... so when the blob hits the turn table

..
I_0*w_i=(I_0+m*R^2)w_f

Solve for w_f...

but when the blob flies off, do they does the final angular velocities of the turntable and putty different or similar? Does the putty fly off with a velocity of w_f or something else... does this look logical?

Angular Momentum Initial= Angular Momentum Final...
But what next?
 
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Additional Question

Additional Question...
Go to...

http://www.nd.edu/~agoussio/10310_spring2006/2006_exam3.pdf

MC5

... Wouldn't the answer be that w_0=w_f... because when you put two things in the opposite direction, that means they'll be moving at the same velocity... is this right? Or it is that they'll move slower and w_0>w_f...

.5*m*w_0*(3R^2)=.5*m*w_f*(R^2)?

Wrong or Right? Thanks.
 
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