Lag1989 problem number 1.50

A round cone with a half-angle of α = 30 ° and a base radius of R = 5 cm rolls evenly without sliding along the horizontal plane. The top of the cone is pivotally fixed at point O, which is flush with point C, the center of the base of the cone. The speed V of point C is 0.1 m / s. Find: a) the modules of the angular velocity and angular acceleration vectors of the cone; b) the angle that makes up the vector of angular velocity with the vertical.