As a person moves away from the equator to the poles, his weight increases. Why?
He moves closer to the center of the Earth, so weight increases, and, his veloicty around the Earth axis decreases (radius of rotation is smaller), so centripetal force decreases, which makes his apparent weight more than at the Equator. It should be noted, these differences are negligible, why don't you calculate them? Jenny Craig wouldn't get very excited.
Well, the total force down on mass m is m g
Part of that keeps the person going in a circle once a day around the axis through north and south poles
The other part of m g pushes down on the scale
w = angular velocity = v/R = 2pi radians/24 hours at the equator and everywhere else on earth.
At the equator where R is biggest, m v^2/R = m w^2 R is biggest so the minimum is on the scale.
As you approach the poles, w^2 R gets smaller because you get closer to the north/south pole axis of rotation, so more of m g is on the scale
As a person moves away from the equator towards the poles, their weight does not actually increase. Weight, which is the force exerted on an object due to gravity, remains constant regardless of location. However, there are a couple of factors that might create an illusion of increased weight as one moves away from the equator.
The first factor to consider is Earth's shape. Earth is not a perfect sphere; it is slightly flattened at the poles and bulges at the equator due to its rotation. This shape, known as an oblate spheroid, results in a slight increase in the distance from the center of the Earth to a person's location as they move towards the poles. Since weight is determined by the gravitational force between an object and the Earth's center, this increased distance can make a person feel slightly heavier.
The second factor is the effect of Earth's rotation. Because of the bulging at the equator, a person on the equator is farther from the Earth's axis of rotation compared to someone at the poles. As the Earth spins, it generates a centrifugal force that opposes gravity. This force is slightly stronger at the equator, countering some of the gravitational pull. Consequently, as one moves towards the poles, this centrifugal force diminishes, and the net effect is a slight decrease in its counteracting force. This decrease might give the illusion of increased weight.
In summary, a person's weight does not truly increase as they move away from the equator. However, Earth's shape and rotation can create an illusion that makes someone feel slightly heavier at the poles compared to the equator.