As a person moves away from the equator to the poles, his weight increases. Why?
2 answers
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
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
5 answers