If the Earth were to stop spinning, would we weigh more?

[Tice]

A friend and I are having a debate on this and I just need to know yes or no, and why?

 

[LukeD]

This depends on your definition of "weight", but if you're asking if your scale would read more, then the answer is yes.

Since the Earth is rotating, we are always moving sideways slightly. As the Earth continues to rotate, the ground falls beneath our paths slightly. This is similar to the effect you feel on one of those playground rides where you sit on a wheel and someone pushes it until you fly off. There's no force pushing you outward, but you feel a "pseudoforce" known as the "centrifugal force" because of your inertia.

 

[mgb_phys]

Yes
The spinning Earth is trying to throw you outwards (ie off), just like a carnival ride.
At the equator this force is about 0.25% of your weight

 

[mikeph]

Sorry to confuse things but my definition of weight is force due to gravity. This is always the same on the surface, the only difference is that you now feel the full normal force from the ground, rather than a discounted normal force as you did when some was used keeping you in circular motion. So the scale measurement rises but your weight technically (as m*g) is unchanged.

 

[imiyakawa]

So the scale measurement rises but your weight technically (as m*g) is unchanged.

Although your weight at future time t* will be different depending on whether the Earth stops spinning or keeps spinning due to the fact the moon will be in a different relative position and will thus be having a different gravitational pull on you.

 

[LURCH]

Unless you live at one of the poles, in which case your weight would remain constant, but you'll just be dang cold. People at the equator would gain the most weight, and everyone evrywhere would weigh about the same as if they were at the poles.

Not accounting, of course, for the fact that if the Earth suddenly stopped revolving, I would quickly lose about 5 lbs; just before I slammed itno the side of a mountain.

 

[D H]

So the scale measurement rises but your weight technically (as m*g) is unchanged.

That's not true, either. The Earth is not a sphere. It is an oblate spheroid. If the Earth were to stop spinning it would settle from this oblate spheroidal shape to a sphere. This would cause both the scale and freshman physics definitions of weight to increase (assuming you are standing at the equator).

 

[mikeph]

Ok plenty of 2nd order effects here. But I think there was still value in my (somewhat pedantic) point.

 

[D H]

We haven't started to get pedantic yet. LukeD made an abortive start in post #2 by saying "This depends on your definition of 'weight'." He made a short-cut past the pedantry by qualifying that with "but if you're asking if your scale would read more".

Scale weight is one of multiple meanings of the word "weight".

 

[Count Iblis]

What would the time scale for the changing of shape of the Earth be?

Also, the tides caused by the Moon would start to spin up the Earth, which would now lead to the Moon spiralling inward (because friction would cause the tidal bulge to be behind the Moon).

 

[Creator]

If the Earth were to stop spinning, would we weigh more?
A friend and I are having a debate on this and I just need to know yes or no, and why?

Yes,...and...in such a case don't forget these important and often neglected tragedies...

1.The average atmospheric pressure would increase...so the boiling point of water would increase (slightly)...making the idiom "A watched pot never boils" slightly closer to the truth.

2. The market price of steel and aluminum would suddenly plummet as world markets are flooded with millions of tons of scrap metal from the hundreds of millions of useless Satellite TV receivers as a result of the formerly (and now inoperable) geostationary satellites. (Glad I don't have satellite TV or cable).

3. and worst of all, the Gravity Probe-B experiment would be useless,,,,er, well, MORE useless than it already is. ;)).

Creator.

 

[sophiecentaur]

If the Earth stopped spinning then it would lose its oblate spheroid shape, eventually, as it would settle down to the minimum energy spherical shape. We'd all weigh pretty much the same then, unless we lived near some particularly large underground mass.

 

[LukeD]

I'm sorry, for some reason, I was thinking that he didn't literally mean "if the Earth would stop spinning", but instead meant "if we were on a planet with the same mass distribution that was not spinning". I don't know of any reasonable situation where the Earth would actually stop spinning suddenly, but it could certainly slow down!

Maybe a giant asteroid! Or a mad scientist. Do we have any mad scientists on this forum who are working on this?

 

[mikeph]

Two general time scales involved. The first would be a matter of hours: water would rush to the poles where the oblate spheroid Earth is "lower", creating two big oceans. Over a much longer (geological) time scale the Earth would deform due to the extra force of the crust near the equator- the "scale weight" of the equatorial bulge would increase and squeeze the Earth into a sphere.

 

[72Zorad]

I don't see any discussion here regarding the increased mass of a rotating body. Doesn't E=MC squared mean that any object in motion gains mass due to the kinetic energy. And if mass increases so does gravitational pull between the objects (earth and myself). Also, if the Earth stopped spinning I wouldn't have any centrifugal force from the spinning, right? Are both of these forces so small the difference would be negligible?

Thanks,

 

[mrspeedybob]

I don't see any discussion here regarding the increased mass of a rotating body. Doesn't E=MC squared mean that any object in motion gains mass due to the kinetic energy. And if mass increases so does gravitational pull between the objects (earth and myself). Also, if the Earth stopped spinning I wouldn't have any centrifugal force from the spinning, right? Are both of these forces so small the difference would be negligible?

Thanks,

Relativistic mass, aka, resistance to acceleration, increases with speed. Gravitational mass does not. I just learned this yesterday. Here is a thread that cites one paradox that could occur if gravitational mass increased.
https://www.physicsforums.com/showthread.php?p=2941898#post2941898