The middle of a uniform rod of mass m and length l is rigidly fixed to a vertical axis OO' so that the angle between the rod and the axis is equal to θ (see Fig. 1.71). The ends of the axis OO' are provided with bearings. The system rotates without friction with an angular velocity ω. Find:
(a) the magnitude and direction of the rod's angular momentum M relative to the point C, as well as its angular momentum relative to the rotation axis;
(b) How much the modulus of the vector M relative to the point C increases during a half-turn;
(c) The moment of external forces N acting on the axle OO' in the process of rotation.

Fig. 1.71.