Subject: Fast-rotating planets and gravity effects on the surface

We know that the effects of the gravity on the surfaces of the planets are partly counterbalanced by the centrifugal force produced by their rotation. Does this mean that if a planet rotates at a critical speed, its gravity and its centrifugal force will become equal and opposite, cancelling each other? Would this occur over all the planet or only at the equator? What would hypothetic astronauts on the planet feel? And what if the planet's rotation speed was greater than the critical speed? Would a hypothetic astronaut on that planet feel a negative gravity force? Would he "fall up"? Or maybe the tidal forces would be so great to dismember the planet? If we suppose that the planet is strong enough to resist the tidal forces, what would happen to a spacecraft trying to land on the planet? I think that everything would seem normal for it, but when it touches the ground it would be violently thrown away by the planet: am I right?

Re: Fast-rotating planets and gravity effects on the surface