A cone rolls without slipping on a table. The half-angle at the vertex is ?, and the

Question:

A cone rolls without slipping on a table. The half-angle at the vertex is ?, and the axis of the cone has length h (see Fig.). Let the speed of the center of the base (label this as point P) be v. What is the angular velocity of the cone with respect to the lab frame (at the instant shown)? There are many ways to do this problem, so you are encouraged to take a look at the three given solutions, even if you solve it.