14.8: Apparent Weight and the Earth's Rotation
Since all objects on the Earth's surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed towards the center of that circle. The points of the north and south poles are the only exception to this rule.
For an object on the Earth's equator, the net centripetal force that accounts for its rotation is the Earth's pull towards its center, or the weight minus the normal force that prevents it from piercing into the Earth's surface. This force, called the apparent weight, is thus the object's weight minus the centripetal force.
The centripetal force is proportional to the Earth's radius and the square of the Earth's angular speed. The angular speed is relatively small; hence, the centripetal force, which is also the difference between the true and apparent weights, is itself quite small. At the equator, an object's apparent weight is only 0.34% less than its true weight, a small correction.
We can further understand this minor correction by considering how quickly the Earth would have to rotate such that all objects on the equator would feel weightless owing to the Earth's rotation. Calculations imply that the orbital period of the Earth, which is 24 hours, would have to be only 84 minutes instead.
This text is adapted from Openstax, University Physics Volume 1, Section 13.2: Gravitation Near Earth's Surface.
