What If the Earth Suddenly Turned Flat?

According to our understanding of physics, a planet such as Earth couldn't be a flat disk, as the force of its own gravity would cause it to collapse into a ball. But, for a fun hypothetical's sake, let's assume a disk-Earth is possible. In this case, gravity would prevent you from simply walking to the edge. Its pull toward the center would become stronger as you walked away from it, eventually causing you to feel as though you are climbing a steeper and steeper hill. Reaching the edge itself would be near impossible, because at that point, "down" and "behind you" would be the same direction.