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 Posted: Sat May 23, 2009 2:35 pm
Here's a good question for a physics nerd to answer:
How come people aren't lighter standing at the equator than when they're at one of the poles?
Shouldn't the rotation of the earth cause some force that pushes them out slightly? Why aren't things being pulled outward slightly?
There should be more acceleration around the equator than at the poles. And you're moving at a greater tangental speed at the equator.
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Posted: Sat May 23, 2009 4:29 pm
Jerba2 How come people aren't lighter standing at the equator than when they're at one of the poles? This is a bad question. It assumes things are not lighter at the equator, which is untrue. Centripetal force is greater at the equator than at the poles, and this in fact causes the Earth to become oblate. Rather than be a perfect sphere, the Earth is more of a squashed sphere, being wider at the equator than at the poles. This difference in radius actually causes things at the poles to be slightly heavier, as they are closer to Earth's center of gravity. This increase in weight (about .02 m/s^2), combined with the decreased weight due to the difference in centripetal force (about .03 m/s^2), is quite minor. The effect of gravity at the poles is about 9.83 m/s^2, while the effect of gravity at the equator is about 9.78 m/s^2. This is less than a one percent difference.
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Posted: Sat May 23, 2009 11:00 pm
here's a related question. if the earth were to speed up gradually, how fast would we have to go to notice a difference. also, is there a speed on which we'd be completely weightless?
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Posted: Sun May 24, 2009 8:08 pm
I can't give you numbers for when we'd start noticing, but probably pretty quickly. Although the Earth is actually slowing down slightly over time.
As for weightlessness, we can make rough estimates of that. We assume that the radius of the Earth would be the same, even though it wouldn't be, to get a bound:
9.8m/s^2 = radius of earth*(radians per second)^2 = 6.3781*10^6*(radians per second)^2
So we get 1.24*10^-3 radians per second, or a rotation in 2500 seconds. So we'd be completely weightless if Earth's day were about 42 minutes long.
Again, this assumes that the radius of the Earth remains constant throughout this, which it wouldn't; as the rate of the Earth's rotation increased, the radius would increase (well, the poles would probably actually squash inwards, but the equator would increase). So we wouldn't actually need the day to be as short as 42 minutes before we could reach weightlessness at the equator.
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Posted: Sun May 24, 2009 9:53 pm
Layra-chan I can't give you numbers for when we'd start noticing, but probably pretty quickly. Although the Earth is actually slowing down slightly over time. Part of the problem with this one is what you mean by "we." The average person in their day-to-day life probably would not notice a slight change. The world community as a whole would though. The biggest example of an immediately observable effect would be in the GPS systems of the world, as well as anything to do with satellites. Technology would cause us to notice far sooner than anything else (without clocks, who would notice a minor difference in the length of a day). Layra-chan mentioned the Earth's rotation is slowing down. This is true due to tidal acceleration. An interesting note is the Earth's rotation is actually not constant, but both speeds up and slows down. What Layra-chan mentioned is a long term trend, whereas these changes are instead oscillations. For example, every January to February the Earth's rotation slows slightly. Later in the year, it speeds up. This is tied to weather, with the conventional wisdom saying it affects weather. There are some who say the weather instead affects the rotation. Personally, I would assume it works both ways.
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Posted: Mon May 25, 2009 11:57 am
Look, half of the question was answered. Yes, we are lighter at the equator, but is centrifugal force a factor in it? We know that we're different weights when at different distances from the Earth's CG, but do centripetal and centrifugal force still make a difference?
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Posted: Mon May 25, 2009 9:45 pm
Aychesyu Look, half of the question was answered. Yes, we are lighter at the equator, but is centrifugal force a factor in it? We know that we're different weights when at different distances from the Earth's CG, but do centripetal and centrifugal force still make a difference? The first response in this topic, the one which I made, answers this question. Specifically, I say: zz1000zz the decreased weight due to the difference in centripetal force (about .03 m/s^2)
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