Problem 4.

How fast should the earth spin in order for a 150 lb human not to be able to walk on the ground?

Solution:

The condition that the human cannot walk on the ground is that there is no contact between human and the ground. It means that the normal force is 0.

Let us assume that the earth is rotating with angular velocity . Then the human on the ground will have centripetal acceleration with the magnitude

Where is the radius of the earth.

This acceleration is provided by the gravitation force and the normal force, so that

Then

Then condition that the normal force is 0 (or negative) is

Then

and