Conservation of angular momentum

[eprparadox]

Homework Statement

We have a rod of length l and mass M. It is lying on a frictionless surface and an impulse, I, is delivered to this rod a distance D above the center of mass. What is the angular velocity (omega, w) about the center of mass point.

Homework Equations

net external torque = time derivative of angular momentum
torque = r x F
angular momentum = I*w = r x p

The Attempt at a Solution

Essentially, I need to find the angular velocity (w) about the center of mass of this rod. I can do it if I choose as my reference point the center of mass of the rod. But I wanted to choose a point that was in line with the impulse which would eliminate the external torque on the system and thus allow me to use conservation of angular momentum to find the same value of w, just using this new reference point.

I get w(cm) = 12*I*D/(M*l^2) for the angular velocity about the center of mass. I want to find this same answer picking as my reference point a point, P, which is parallel to the impulse point so that r X F = 0 and so Li = Lf. I do know that Li must be zero since, of course, the rod isn't moving before the impulse. Afterwards, I also know that Lf = I(about that new point P) * w. I'm not sure if I am missing something in that final Lf term or not.

Any help would be greatly appreciated. Thank you very much.

 

[Doc Al]

When using reference point P, don't forget that the angular momentum will be the sum of the angular momentum about the center of mass plus the angular momentum of the center of mass.