The difference between the gravitational force and the centripetal force acting on our body is equal to our weight.
If the rotation of the Earth were speeded up, then the Earth's gravitational force would be used to provide the required extra centripetal force. Hence, the weighing machine would indicate less weight.
At a certain critical speed of rotation of the Earth, the gravitational force is just equal to the centripetal force. Then the reading on the weighing machine is zero.
Astronauts experience weightlessness when their spacecrafts orbit the Earth. It is very inconvenient in many ways.
Therefore, gravity is artificially provided in a spacecraft by building it in the form of a large wheel with a hollow rim. It is set into rotation so that centripetal force acts on the occupants.
