That is incorrect.
Objects right now traveling with the rotation of the Earth do not fly into space ( but stopping the Earth would then fling them into space? ) At the equator, an object is traveling at 1000mph along with the rotation of the earth. With a non-rotating earth, that same object would be traveling still at 1000mph but over a non-rotaing Earth along the surface.
Why the distinction between free and attached objects. All objects make up the Earth - air, people, birds, continents, oceans, core, mantle. If the rotation of the Earth stopped suddenly, then all objects of the Earth would comply with the non-rotation and not just some and not others, simply because the Earth is considered a sum of all of its parts. No catastophic building collapse or giant earthquakes would occur with the only consideration in mind of the Earth going from the rotating to the non-rotating.
Unless of course, in this ficticious scenario, the unknown mysterious force can distinguish between the elementary particles ( electrons, protons, quarks, etc ) of say an iron atom deep within the Earth to that of an iron atom in the frame of your car, and have an affect on either one diferently.