In this diagram, assuming there is no friction between the pin joint and the rod, I understand that the rod will rotate about $O$. However, let's say that the rod is released from $ \theta = 0$ and that when $ \theta = 90$ the rod is vertical at that instant in time. If we drew the forces on the rod at this instant, there would be a weight force and a horizontal and vertical reaction force acting at $O$. What is confusing me is that surely the horizontal reaction force at this instant must be 0 since there is no other force to balance it and no acceleration occurs in the x direction (the angular acceleration at 90 degrees will be 0 and so it follows that the linear acceleration is also 0 from $ a = r \alpha$).
However, in order for the rod to keep rotating doesn't a moment need to be applied about $O$? And in the situation where $ \theta = 90$ the horizontal reaction force is the only force that can provide this moment, leading me to believe that this force is indeed non zero. Therefore, at $ \theta = 90$ will the horizontal reaction force be 0 N or non zero and if it is non zero how would you calculate it?