Conservation of Angular Momentum problem

[nahanksh]

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?

 

[rock.freak667]

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. I_total would be the sum of the I_disk+I_mass

 

[nahanksh]

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 !