"No gravity" spin on Earth?
I was recently asked this question in physics class:
If the day were shorter, you would weight less. How long would a fall day at the equator be (in hours) for you to be able to moon walk for the rest of your life?
After the ambiguity in the question was cleared up the question becomes: What would the length of a day be in order for an object, at the equator, to experience a net force of zero N towards the center of the Earth.
Any thoughts would we appreciated. I have come up with two different answers and would like to know which one is right.