Let's say we have some magical way to keep the earth in a disc form even though the gravity would try to pull it into a sphere.

Let's say it is like a pizza and has the same height everywhere.

This means the center of mass is in the middle.

You would not notice lots of difference until you get to the edges where the gravity would pull you to the center of the world.

Different model: earth has a lot more mass in the center and is still somehow flat on top and the mass is hidden under it.

Now you would always be drawn to the center of the world. Only a few hundred Kilometers outwards you would already be standing at an ankle.

Ok lets say in order to get the earth keep a disc under normal physics we replace the material it is made from with some kind of rubber like stuff.

A fast rotation pulls it out and keeps the disc flat. Well now the rotation cancels out the gravity and the elastic effect of the material. People would just fly of the world into space except in the center however you probably would rotate with sth. About one rotation every few minutes.