A round cone A of mass m = 3.2 kg and half- angle a = l0° rolls uniformly and without slipping along a round conical surface B so that its apex O remains stationary (Fig. 1.38). The centre of gravity of the cone A is at the same level as the point O and at a distance l = 17 cm from it. The cone's axis moves with angular velocity ω Find:
(a) The static friction force acting on the cone A,. if ω = 1.0 rad/s;
(b) At what values of ω the cone A will roll without sliding, if the coefficient of friction between the surfaces is equal to k = 0.25.

2ct B Fig. 1.38.