Using Parallel-axis theorem, Moment of inertia of the rod about pivot point:
Imagine the rod is tilted at an angle w.r.t the horizontal. If you draw an F.B.D, there are three forces on the rod: (downward and acting on CM), (reaction force - to the rod and acting on the pivot point outward), and ( to the rod and pointing to the left, but also upward at an angle ).
● Considering the torque due to gravity about pivot point and hence finding angular acceleration as a function of ,
● Considering torque due to reaction force about CM,
● Using conservation of energy principle and hence finding angular velocity as a function of ,
● Considering the centripetal force that provides,