Rotational Dynamics

In this class I will teach rotational dynamics of rigid body. The question is mentioned below:

"A plank of length 21 and mass M lies on a frictionless plane.
A ball of mass m and speed v0 strikes its end as shown. Find the final
velocity of the ball, vf, assuming that mechanical energy is conserved
and that vf is along the original line of motion.
b. Find vf assuming that the stick is pivoted at the lower end. "

A variation in problem is also disussed which students find difficult to solve. the variation is that when the rod is free to rotatate on a frictionless surface. Now the students face difficuly in choosing the point about which linear momenum has to be conserved.

The concepts are based on (i) conservation of linear momentum(ii) conservation of angular momentum

The problem disussed will be about a ball strirking a rod. I will sove this problem with different methods.