What is the new period of rotation?

The period of rotation of the earth about its axis is 24 h. What should be its new rotational velocity for?

• The period of rotation of the earth about its axis is 24 h. What should be its new rotational velocity for an object at the equator to be weightless, meaning the normal force on it is zero?

• Answer:

  For weightlessness at equator, the earth should spin so fast that the centrifugal force acting on an object at the equator becomes equal to the weight. Weight = Mg Centrifugal force = Mω²R Equate both Mg = Mω²R g = ω²R ω = √(g/R) = √(9.8 / 6400 x 1000) = 0.0012 rad / sec Time period for this ω = 2π / ω = 2(3.14) / 0.0012 = 5075 seconds = 5075 / (3600) hrs = 1.409 hrs