A round cone with half-angle α = 30° and the radius of the base R = 5.0

Question:

A round cone with half-angle α = 30° and the radius of the base R = 5.0 cm rolls uniformly and without slipping over a horizontal plane as shown in Fig. 1.8. The cone apex is hinged at the point O which is on the same level with the point C, the cone base centre. The velocity of point C is v = 10.0 cm/s. Find the moduli of
(a) The vector of the angular velocity of the cone and the angle it forms with the vertical;
(b) The vector of the angular acceleration of the cone.