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OK so, someone is arguing that if the earth was a globe water would be flung out in space because of the spin...yeah, I know....and no matter how many times I tell her that the centrifugal force is so minimal that the earth would have to come to a stop for such a thing to happen, she just keeps bringing up "water in a cup always stays level..." those types of simplistic arguments and I don't know what to do anymore...

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    $\begingroup$ Earth's gravity overrides the outwards force of its spin. Interestingly enough, the planet does actually bulge slightly at its equator as a result of its rotation. Gravity keeps it intact. $\endgroup$
    – 4NT4R3S
    Apr 2 at 18:31
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    $\begingroup$ What is your question. Please clarify. What you should do is say "Okay, I'm not going to to talk about this anymore, wanna watch a movie?" (and I'd recommend Interstellar) It's pretty obvious that you can't win an irrational argument by being rational - so don't try. Go and do something more interesting instead. $\endgroup$
    – James K
    Apr 2 at 19:46
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    $\begingroup$ Mathematician / artist Jos Leys made some great videos debunking flat earth. josleys.com/show_gallery.php?galid=384 But "I realise, from the comments on my films on YouTube by flat Earth believers, that what I'm showing here does not make the slightest difference to them. Not one [of] them has come back with some remotely reasonable argument. So I give up. It was fun making the above videos: debunking flat Earth is so easy! The sad thing is that it is not going to change anything." $\endgroup$
    – PM 2Ring
    Apr 2 at 22:22
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    $\begingroup$ "I don't know what to do anymore" <- suggest tackling more tractable problems, like whether P=NP. $\endgroup$
    – geometrian
    Apr 3 at 5:39
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    $\begingroup$ Everyone knows such people, and the easiest solution is just not to discuss about science with them, because it's just a waste of time, for both of you. For advice on a social aspect (if needed), please consider asking on Interpersonal SE. $\endgroup$
    – Trang Oul
    Apr 3 at 6:23

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The centripetal acceleration from rotation is not that hard to calculate. It's pretty standard in engineering, usually for working out the forces on things that are spinning very fast, like propellers. Earth rotates quite slowly but has a very large radius, and if you work through it all, you wind up with the centripetal acceleration at the equator being approximately 0.03 m/s^2, or around 0.003 g. (At the poles it is, of course, zero, since you're just spinning in place and going nowhere.) Objects at the equator weigh about 0.3% less than they do at the poles, and this is easily shown experimentally (though it requires a good bit of travel).

I'm not sure what that has to do with water being level in a cup. The water in a cup would stay level no matter how high the centripetal acceleration were, as long as it's less than 1 g -- if there's any 'down' force on it, then the water will eventually reach level.

I'm not sure you have any chance of arguing somebody out of flat earth theory. It isn't a position that's rooted in a real desire to find truth.

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    $\begingroup$ +1 for the last sentence. Many, if not most, flat earthers belief is rooted in religion. Specifically, they believe that the entire bible is literally true. Trying to prove the world is not flat is essentially an attempt to get them to abandon their religious beliefs. $\endgroup$
    – JimmyJames
    Apr 3 at 18:24
  • $\begingroup$ It's also in many ways rooted in a desire to be a special person who's in on the big secret, like most conspiracy theories. There's a lot of psychological stuff going on in conspiracy theorism that this isn't the right place to unpack, but I think the one crucial thing to understand is that flat-earth is couched in terms of learning and discovery, but it's not actually an unbiased search for truth, so "here, let me show you what we know" is not a helpful argument. Fighting the specific claims of a conspiracy theory is just pruning leaves off a tree -- even if you "win", new leaves will grow. $\endgroup$ Apr 5 at 12:25
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As this could be a flat-earth argument you will probably not "win" however much you argue.

I find that at times a different approach works. I talk about models. In physical sciences we create models of the world. It could be as example a model that the sun revolves around the earth (for about a thousand years between, say 400AD to 1400AD this was the accepted model). In many ways this is a good model, it actually makes predictions that can be tested. In physics I tend to avoid talking about which model is "true" or "absolute" as every model created so far is incomplete. As example, we know that General Relativity (otherwise a very good model) is incomplete as it cannot be used toghether with quantuum theory (otherwise a very good model).

In physics we should avoid the fallacy to mistake the model for the reality. The model will always describe only parts of the reality. One way to talk about models is to look at how useful they are. This could be in areas like describing observations, or in making predictions that we can test. Generally, in physics sciences we do not like models that cannot be tested (the word to use is falsifiable). We also tend to like models best that have a mathematical underpinning: examples could be Newtons Gravity model.

So, if the person you are talking to stays with the flat-earth model you can basically accept that as a workable model. It is indeed a very good model in some respects, the water in the glass is flat. But in other respects it seems to be a less good model to me as some aspects of observations seems to be difficult to explain within the model. A good question could be to ask what kind of predictions the model makes - where will we see the planet mars on the sky next week or how much smaller is the gravity on the equator as compared to on the poles. Other models do make predictions about this kind of things, predictions that can be tested, and as such other models may be more "useful". To me this avoids the discussion of what is real and true, as we agree that all models are incomplete and not the real world.

Anyway, my two cents.

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A practical intuitive demonstration might help. Attach a tennis ball or rock to a string, and spin it around your head. The force you feel pulling on the string is the centripetal acceleration, or equivalently, the centrifugal "flinging out" force in the rotating frame.

Now spin the ball more slowly - you'll find that the slower you spin, the less force it takes to keep the ball moving in a circle. Imagine spinning the ball so slowly that it took 24 hours to make one rotation, like the earth does - it would take very little force indeed.

Now, start to let the string out and spin the ball at a greater radius - you'll find that the larger the arc, the less force it takes to keep the ball moving in a circle. Imagine spinning the ball in an arc the size of the earth, with a radius of over 6,000km - it would again take very little force.

Combining these two, it takes very, very little force to spin a tennis ball on a 6,000km-long string once every 24 hours. In fact, it takes just 0.3% of the force of gravity - the earth is far too large and spins far too slow to overcome gravity and fling things from the surface.

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