Rod swinging and hitting a ball

[haruspex]

@haruspex
I'm thinking now, would it be possible to set your axis on the table that the ball sits on and treat the rod and ball as a single system?
This would eliminate frictional torque, I think.
Do you see anything wrong with that?

But then you would have torque from the unknown reaction at the rod's hinge.
You can take anywhere as your reference points for angular momentum, but if that means dragging in the reaction force from the hinge or the friction from the table then you will need to bring in a linear momentum equation as well in order to eliminate the unknown. The great benefit of using the rod's axis for its equation and the point of contact of the ball with the table for its equation is that we never get those impulses in the equations.

 

[erfz]

But then you would have torque from the unknown reaction at the rod's hinge.
You can take anywhere as your reference points for angular momentum, but if that means dragging in the reaction force from the hinge or the friction from the table then you will need to bring in a linear momentum equation as well in order to eliminate the unknown. The great benefit of using the rod's axis for its equation and the point of contact of the ball with the table for its equation is that we never get those impulses in the equations.

Ah, shoot. I forgot about that completely. Thank you very much!