angular momentum and its conservation

tsopatsopa

1. The problem statement, all variables and given/known data
Check out the attached image. A is a fixed axis.
An impulsive force P =FΔT is given to the rod from a distance x. As a reaction to that, an impulsive force P_A =F_A ΔT is transmitted to A.

The rod has a length l and mass M.


2. Relevant equations
a. Velocity v of the center of mass G just after the collision. (express in function of P, P_A and M )
b. The value of the impulsive force P_A (express in function of l, x and P)


3. The attempt at a solution
a. I think the center of mass is supposed to translate just after the collision.
According to the law of the translating motion:
[itex]\sum external forces[/itex] = change in momentum.
So, I did P = P_A + Mv
And I can get v from that. (Am I right here?)
What I don't know is: The axis A is fixed ===> The center of mass IS NOT SUPPOSED TO TRANSLATE but ROTATE. If I am thinking of using the angular momentum stuff, I will get a new variable: l (length of the rod). However the question asked if to express v in function of P, P_A and M and l is not mentioned.

b. NO IDEA.
I was thinking of using the angular momentum and apply its conservation but if I call the angular momentum, I will get a new variable M (mass of the rod) which is not asked to use to express P_A

Looking forward for your help.
Tsopa,
Japan :D

Attached Thumbnails

 

tsopatsopa

SORRY, I accidentally put the question in the "relevant equations" paragraph (I thought it was "relevant questions" not "equations" lol)
The questions are:

a. Express the velocity v of the center of mass G just after the collision. (express in function of P, PA and M )
b. Find the value of the impulsive force PA (express in function of l, x and P)