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What would happen if the earth would stop spinning? How much heavier would we be? I mean absolutely stop spinning. How much does the centrifugal force affect us?

If you give technical answers (please do), please explain them in laymen's terms, thanks.

Edit: I am asking what would be different if the earth were not spinning. Nevermind the part about it stopping.

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Another what if question about Earth's rotation: physics.stackexchange.com/q/29235/2451 –  Qmechanic Sep 21 '12 at 17:32
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I think the question is badly stated because if the earth suddenly stopped spinning we would fly off on the tangent, since we still would have rotational velocity and are not attached to the ground. Think of a bus suddenly stopping and the standing passengers. Maybe there should be a "very gradually ended up with no spin", so that friction would absorb the change in our tangential velocity . –  anna v Sep 21 '12 at 17:39
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This seems like an excellent question for what-if.xkcd.com –  ewok Sep 21 '12 at 17:40
    
Another somewhat related question: physics.stackexchange.com/q/29182 –  Nathaniel Sep 23 '12 at 15:04
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3 Answers 3

up vote 3 down vote accepted

The acceleration of an object spinning with angular velocity $\omega$ at a distance $r$ is given by:

$$ a = r\omega^2 $$

The angular velocity of the earth is 2$\pi$ radians per day or $7.3 \times 10^{-5}$ per second, and the Earth's radius is $6.378 \times 10^6$ metres, so the acceleration is 0.034 ms$^{-2}$ or 0.0034g. So as a person standing on the surface you wouldn't notice.

However the acceleration does affect the shape of the Earth. Rock is viscous and will flow in response to a force but it does so very slowly. As a result of the Earth's rotation it's radius is about 31km greater at the equator than at the poles. When the rotation stopped it would gradually settle back to a sphere, though it would take a million years or so.

The Milankovic cycles are at leastly partly due to the fact the Earth is not a perfect sphere, and these would stop or at least be changed when the Earth settled back to a sphere. Assuming you believe the Milankovic cycles cause ice ages, one effct of rotationg stopping would be no more ice ages. Having said that, stopping rotation would play havoc with the weather as you'd get no Coriolis force so no jet stream. Mind you, there'd be no hurricanes either.

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In another question's answer you give " so the speed is 40,075/24 or about 1,670 km/hour or 464 m/sec." A sudden stop would affect us immediately. –  anna v Sep 21 '12 at 17:44
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Well yes, stopping instantly from 500m/s would be traumatic :-) However i don't think the OP was asking about this. The question seems to be specifically about the affect of rotation of the surface gravity. –  John Rennie Sep 21 '12 at 17:55
    
Water would flow a good deal quicker than rock. Empty oceans in the tropics, and bye bye Holland? –  Art Brown Sep 22 '12 at 17:37
    
I take it back. It looks like Holland is just south of the neutral latitude. Points north of 55 degrees (the zero of P2) get flooded, Amsterdam is at 52 N. –  Art Brown Sep 22 '12 at 17:59
    
Hmmm, good point. The sea level would presumably change by about half the 31m difference in the radii, and 15.5m is a big change! –  John Rennie Sep 22 '12 at 19:30
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The centripetal force we feel on the surface would immediately disappear, causing us to feel lighter. The centripetal force is equal to $E=mv^2/r$ and the acceleration is given by $a=v^2/r$. This results in a reduction of the acceleration towards the earth’s centre, also known as gravity. Therefore we would feel lighter

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At the equator, the centrifugal acceleration is $$R\Omega^2 = 6,378,000\times (2\pi / 86,400)^2 = 0.034 \,{\rm m/s}^2 $$ which is 0.3% of the gravitational acceleration. So at the equator, you would immediately feel heavier by 0.3% or so. However, the difference would be smaller at other places of the globe. That would force the water to flow away from the equator. The quasi-ellipsoidal Earth would try to rebalance and become spherical again. Something of order ten kilometers of matter near the equator would flow towards the poles.

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protected by Qmechanic Mar 2 at 12:14

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