Rod on a Plane: Calculating Angular and Linear Motion After Impact"

[Nexus99]

This looks good

You have to take the angular momentum around the CM of the system. And also the total moment of inertia around the CM of the system. I can't understand what the term $I_{TOT}V_{CM_y}(R-x_{CM})$ is about?

The terms is an error, i tought that $R - x_{CM}$ was the radius of the circumference along which the system rotates.
I'm not understanding perfectly what you mean (probably because I'm a little dumb) but if i fix that term i got:
$-m_0 v_0 R = I_{TOT} V_{CM_y} (x_{CM}) + I_{TOT} \omega_{CM}$
is it right?

 

[Delta2]

To be honest i am not sure myself either at this point, i think the correct equation is $$-m_0v_0(R-x_{CM})=I_{TOT}\omega_{CM}$$, where $I_{TOT}$ the moment of inertia of the system around the CM.

 

[Nexus99]

To be honest i am not sure myself either at this point, i think the correct equation is $$-m_0v_0(R-x_{CM})=I_{TOT}\omega_{CM}$$, where $I_{TOT}$ the moment of inertia of the system around the CM.

Ummm ok.
Is the total moment of inertia that I found in post 22 correct?

 

[Delta2]

Yes it is correct.

 

[Nexus99]

Yes it is correct.

Ok thanks for your patience, but this problem was difficult as f*ck.
I hope this year the exam will be a little easier

 

[Delta2]

Yes i agree, quite hard problem, testing to the extreme the understanding of concepts and principles.
Is it college level or university level exams this is from?

 

[haruspex]

If we don't make this assumption, then a mini paradox will appear if we do the balance of the kinetic energy when the particle returns to A. Somehow the total kinetic energy will be increased (in point A , with regards to point B after the inelastic collision), and we won't be able to infer where this surplus "ghost" energy has come from.

Ah yes, it wouldn’t make it back to A if it were not elastic.

 

[Delta2]

Ah yes, it wouldn’t make it back to A if it were not elastic.

Thanks for resolving the paradox, if i tell you that i spend part of last night before sleep thinking where does the surplus of kinetic energy comes from you ll laugh with me won't you?

 

[Nexus99]

Yes i agree, quite hard problem, testing to the extreme the understanding of concepts and principles.
Is it college level or university level exams this is from?

University.