Horizontal force of swinging beam In the diagram, a weighted beam is hinged to a vertical wall and is swinging downward.
As shown in the picture, when the beam is perpendicular to the wall, the horizontal force by the hinge is to the left acting as a centripetal force.
I am curious about the direction and magnitude of the horizontal force as the beam falls. I know that when the beam is just beginning to fall from a near vertically upwards position, the horizontal force has to point to the right because the center of mass's x component is accelerating to the right. However, I am not when the horizontal force flips to the left from this time to when the beam swings to a horizontal position as in the picture.

 A: You are right that the force is to the right at first. The center of mass starts at the wall. As the beam starts to fall, it starts to rotate. The center of mass starts to move down and away from the wall.
The total horizontal force is the horizontal component of the reaction force that keeps the end of the beam still. The reaction force pushes to the right. The center of mass acquires a velocity with a component to the right.
As the beam nears horizontal, the horizontal component of velocity of the center of mass decelerates toward $0$. The reaction of the hinge pulls back to the left.
Consider a similar beam toppling on a frictionless table. There is no horizontal component of force. The center of mass would drop straight down. The bottom end would slip left.
In this problem, the end cannot slip left. The reaction force of the hinge pushes it right.
Consider another beam that starts to topple on a table. This time it starts with friction, so the beam acquires a velocity to the right. And then friction disappears. The center of mass would keep the rightward component of velocity. The bottom end would slip right.
In this problem, the end cannot slip right. As the angular velocity increases, the magnitude of centripetal force increases. And so does the leftward component. The hinge pulls to the left after a certain point.
