MadSci Network: Physics |
A 100 pound person weighs 45 kg. If she were standing on the equator, then the centrifugal force of the earth's rotation on her is given by m * omega ^2 * r. m, as just stated, is 45 kg. omega is 2 * pi radians per day, = 2 * pi / 86400 radians per sec. r, the equatorial radius of the earth, is about 6400 km. Putting all of this together, the centrifugal force comes out at 1.53 newton, or about 160 gram weight, or 5.5 ounces in your horrible imperial units. Of course, if she were standing at the pole, she would experience no centrifugal force from the earth's rotation at all - perhaps a slight dizziness from spinning around her own axis at most! ;-) The centrifugal force from revolution about the sun is around one seventh the size of that from the earth's rotation. The force of gravity at the equator is just over 1% lower than that at the poles. The centrifugal force effect is part of this difference (1/3 of it), but more important (2/3 of the effect) is the fact that the polar radius of the earth is 21 km smaller than the equatorial radius. Incidentally, when we talk about how much someone 'weighs' we are usually referring to mass rather than weight as a force. We do not usually travel to equatorial latitudes instead of going on a diet! But in the terms in which you originally framed the question, then an equatorial person would increase her weight from 100 pounds weight to 100.35 pounds weight if the earth stopped rotating, but she could get it up to 101.05 pounds weight by travelling to the north pole, whether or not the earth stopped rotating.
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