Conservation of angular momentum in a collision Suppose I have a stick hinged to a pivot and it is released from its horizontal position and just after it becomes completely vertical, it strikes a ball completely stationary as in the given figure below.

The collision is completely elastic.
QUESTION: Will angular momentum be conserved during the collision?Why?
 A: Angular momentum of an isolated system is always conserved. But it does require you to define what you consider part of your system - the hinge will provide a reaction force on the stick at the moment of collision, and that means there is an "external force" (that is, external to the stick and ball) to be taken into account. Your "system in which angular momentum is conserved" has to be something that has no external forces on it.
In other words - the question as posed cannot be answered unless you define your system more precisely. But if you define it as including just the ball and stick, the answer will be "no" because at the time of impact there is an external force that doesn't pass through the center of mass.
A: One more difficult way to see why Floris is right: Imagine a different problem, one in which instead of a pivot you have a mass $M$. In this case there are no external forces and angular momentum is conserved in the collision with the ball. Just before the collision you have (in a reference frame centered at the initial position of the ball): $L_i=\frac{1}{3}l^2m\omega _i=L_f=(\frac{1}{3}l^2m +Ml^2)\omega_f$. 
both $\omega$'s will be positive, that is, M moves to the right after the collision.
If you make $M \rightarrow \infty$ you recover the pivot, and get $\omega_f=0$.
But, we know that if the ball is large, the stick will bounce backwards, meaning $\omega_f<0$, and thus L cannot be conserved.  
