Conservation of Angular Momentum in a Three Mass System

[neelakash]

Homework Statement

Two masses M each are connected by a rigid rod of negligible mass having length a.The CM of the system is stationary in a gravity free space and the system rotates about the CM. with angular velocity w.One of the rotating masses strikes a third stationary ball of mass M which sticks to it.What is the angular momentum of the three mass system before and after collision?

Homework Equations

The Attempt at a Solution

For the collision conservation of linear momentum will be applicable.
Mv=2Mv' or,v'=v/2=wa/4. From this w' can be calculated.

Prior collision,L=Iw where I is the MI of the two mass system.

After collision, L'=I'w'

Please check if I am correct.

 

[mukundpa]

the system will rotate about new center of mass. Check for the position of new center of mass!

 

[neelakash]

So,we are to be careful to calculate I for the second time.
Second time, CM will be a/3 rd distance away from the mass 2M.Accordingly,I will change.

But angular velocity would be same as w'.Right?

 

[neelakash]

There will be no linear momentum...
angular momentum will be conserved...
CM will change the position...
And if one wants to find w',one has to find I' carefully.