Conservation of Angular Momentum problem

AI Thread Summary
The discussion revolves around a conservation of angular momentum problem involving a turntable and a small object. The turntable, with a mass of 1 kg and a radius of 0.17 m, initially rotates at 78 rpm. When a small object is dropped onto it, the final angular velocity of the combined system is 72.7 rpm. Participants clarify that the final angular velocity provided accounts for both the turntable and the object, leading to the conclusion that the initial and final angular momentum must be equated to find the mass of the small object. The problem emphasizes the importance of understanding angular momentum conservation in systems with no external torques.
nahanksh
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Homework Statement


A turntable has a mass of 1 kg and a radius of 0.17 m and is initially rotating freely at 78 rpm (ωi,t = 8.168 rad/s). There are no external torques acting on the system. The moment of inertia of the turntable can be approximated by that of a disk (Idisk = MR^2/2).
http://online.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/oldexams/exam3/sp09/fig23.gif
A small object, initially at rest, is dropped vertically onto the turntable and sticks to the turntable at a distance d of 0.10 m from its center as shown in the figure. When the small object is rotating with the turntable, the angular velocity of the turntable ωf,t is 72.7 rpm (7.613 rad/s). What is the mass of the small object that was dropped onto the turntable?


Homework Equations





The Attempt at a Solution



Here i have got everything but the angular velocity of the object when combined with the disk...
I only know the smaller radius, the higher angular velocity, but i am not sure how to get the exact value with numerical calculation...

Please Could someone help me out here to get the angular velocity of the object?
 
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nahanksh said:

The Attempt at a Solution



Here i have got everything but the angular velocity of the object when combined with the disk...
I only know the smaller radius, the higher angular velocity, but i am not sure how to get the exact value with numerical calculation...

Please Could someone help me out here to get the angular velocity of the object?


But you have the final angular velocity as 72.7rpm.

Just find the initial angular momentum and equate that to the final angular momentum. Itotal would be the sum of the Idisk+Imass
 
Oh!
I thought the final velocity given was only for the disk without considering the object...
But it turns out it's the velocity of combined system ( obj + disk...)

I've got it.
Thanks a lot !
 

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