When we pull a tablecloth off a table with a glass on it On doing a Google search, it says the glass stays put if we pull the tablecloth fast enough, as in, the glass does not move at all. I have seen some videos and the objects put on the tablecloth seem to do just that, not move at all.
But is it really the case? The glass does not move at all? Not even a tiny bit? I understand the physics here (or maybe not). According to my understanding, if we yank the tablecloth, it accelerates very quickly and loses contact with the glass in a fraction of a second. But during that split second, as the tablecloth is sliding under the glass, there is a dynamic friction acting on the glass due to the relative motion of the tablecloth. That dynamic friction might be very small, but it is still a force acting on the glass. Should it not move the glass a tiny bit? The shift might be so small that eyes can't perceive it. But it should be there, no?
Or am I wrong and the glass does indeed not move at all?
Edit : There is no 'Hem' around the edges of the tablecloth. Friction is the only force acting here
 A: I think a slow motion video is better than a long explanation. The glasses are still but the plates move in this first video, but move in this second one.
To answer your questions. Yes the object on the table cloth moves relative to the table. There is a friction force between the object and the tablecloth that imparts an impulse onto the object. Why is the object moving a lot when slowly pulling the cloth and almost not moving at higher speed? At higher speed, the time of contact between the object and the cloth is smaller, therefore, the transferred impulse $  \triangle P= F_{friction} \triangle t $  is also smaller.
Why are the glasses not moving in the first video?
It can be due to either a very small displacement or friction force with air that would lower the displacement below the observable level.
A: 
the objects put on the tablecloth seem to do just that, not move at all.

Nope, that can't be the case, unless tablecloth has zero static friction coefficient. Otherwise, objects must move, due to some tablecloth momentum passed to the objects which were on it. The only difference can be in magnitude of tablecloth momentum transferred to each object, which may depend on exact move trajectory, object distance from a force application (pulling point) and/or object mass.
At first look it may seem to the untrained eye, that things likes glasses don't move in a video. However I have exported a couple of frames from one of such videos and made an animated GIF image for clearly  to see that even glasses moves a bit (a couple of millimeters or so).

