Let us go to the rotating frame, in which the disc is stationary. In this frame the rod is subjected to Coriolis and centrifugal force, Fcor and Fcf, where
Where r is the position on an elemental mass of the rod (Fig.) with respect to point o (disc's centre) and
As the rod is vibrating transversely, so v' is directed perpendicular to the length of the rod. Hence 2dm(v' x vector ω) for each elemental mass of the rod is directed along PA. Therefore the net torque of Coriolis about A becomes zero. The not torque of centrifugal force about point A: