How Do We Calculate G From This?

The ball has an angular momentum pointing in the direct ion of its polar axis. And as we know, a force r cross f is a cross product m, that is tork. Tork is the derivative of angular momentum. So tork changes angular momentum. The torc being applied by the force of gravity, is actually causing the angular momentum vector to precess around and make the ball rotate. Now, how do we calculate g from this? This is the interesting part.