How long would it take for the Earth to complete a full turn if a person at 49.6° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,384 km for the radius of Earth.
The radius of rotation at that latitude is
r= Re*cosLatitude
If mw^2/r= mg and w=2PIr where r is above formula.
The problem with this analysis, is that centrepetal force is not directed to the center of the Earth at that latitude, and mg is. So they never can be equal and opposite, and the person "floats" about the room. I assume your teacher forgot about that, or wants you to ignore it. centripetal force is directed to the center of rotation on the Earth's axis, not the center of the Earth.