High school circular motion?

Question

What should the period of earth be if it is rotating so fast that it feels apparent weightlessness?

Answer 1

Although your question is fairly unclear, I think you mean:  How fast should one rotation be if the earth is rotating so fast it's inhabitants feel weightless.(if that is not what you mean correct me)

We, the inhabitants of the earth will always feel the same weight as no matter how fast the earth is rotating, we are rotating at the same speed.  However when it is rotating extremely fast, we might notice stuff due to the centrifugal force in the middle of the earth, such as lava spewing out of the ground.