A right circular cone of base radius R and half apex angle $\text{α}$  precesses about a vertical axis passing through it’s apex P such that it’s slant length is making angle $\text{θ}$  with vertical as shown in the figure. It is spinning about its own axis with angular velocity ${\omega }_{\text{s}}$. There is no slipping at the point of contact of cone and horizontal surface. At the instant shown A is a point on cone which is in contact with ground and B is diametrically opposite point on it’s base. C is centre of base circle. At this instant: