The support can both turn and slide freely along the lamp post. However, when you take your hand off the shelf, after adjusting it into the desired position, the support beneath the shelf blocks itself on the lamp post under its own weight.
I made the support off some recycled wooden boards. First, cut the shape of the shelf that you want. Then measure the diameter of the the floor lamp post. Using a hole saw, cut a hole for the post. The hole should not be too big for the post or the support mechanism will not work. It should be snug yet allows for movement.
The form of the support is a pure improvisation. I cut a triangle piece and glued it against the back of the shelf. The long edge of the triangle must be placed against the rod so that it can lock itself against its own weight.