When the rod is freely balanced, the lower end A is just below the O point of the rotating shaft, which means that the center of gravity is on the AO line, the gravity and supporting force are balanced, and the gravity moment is zero. When the rod rotates slowly from the vertical position, the gravity arm increases, its moment increases, the constant force decreases from the maximum value, and the F moment decreases. When the gravity moment is less than the F moment, the angular velocity of the rod rotation increases, and when the gravity moment is greater than the F moment, the angular velocity decreases again.

D, because the rod is irregular, the linear velocity directions of point A and point B on the rod are not always the same, so D is wrong;

So choose: C.