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Author Topic: If the earth stopped rotating would it's mass decrease?  (Read 10563 times)

Offline thescienceofacne

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It is commonly understood that mass and velocity are directly related.  Basically, the faster an object travels the more mass it has.  Is the same true for rotational motion?  If you take an object and spin it very fast, does it now have more mass than it would if it were at rest?  Is the original assumption about the relationship between mass and velocity even correct?


 

Offline Bored chemist

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If the earth stopped rotating would it's mass decrease?
« Reply #1 on: 27/02/2011 10:48:00 »
"It is commonly understood that mass and velocity are directly related."
By whom?
 

Offline abacus9900

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If the earth stopped rotating would it's mass decrease?
« Reply #2 on: 27/02/2011 12:03:16 »
It's my understanding that mass and energy are interchangeable, hence we have E=mc^2. Also, we know that the closer to the speed of light an object with mass gets the closer its mass approaches infinity so it would seem mass increases with velocity.

Special Relativity tell us that an object's mass increases with speed but the effect is negligible with something like the rotational speed of the earth.
« Last Edit: 27/02/2011 12:20:51 by abacus9900 »
 

Offline yor_on

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If the earth stopped rotating would it's mass decrease?
« Reply #3 on: 27/02/2011 13:45:56 »
Ah :)

Speed is a description of 'distance' split with 'times arrow'
10 meters split with 5 seconds gives you 2 meter per second.

Mass on the other hand exist in one form. 'Invariant mass' that's the only invariant measurable part of any piece of lasting matter. Then we have momentum and relative mass. They are descriptions of what we expect to happen depending on 'speed' and 'invariant mass' in a possible interaction with something else. We can count on those two and isolate them as belonging to any object 'moving' relative something else, and so we don't need the relation or 'interaction' per se to find those existing. But they do not express themselves as something measurable in the objects themselves, that is, you will not find their 'atoms' 'jiggling' more, getting all stressed up, just because that something 'moves' faster relative something else.

It's important to differ between what we can measure and what we define conceptually. The measurements tells us what exist, our conceptualization tells us why and how that might relate to the rest of SpaceTime.

So no, your 'invariant mass' do not increase with speed, as the 'jiggling' will show you. Your momentum and relative mass does though, conceptually, and as seen/proven in any later interaction.
==

Momentum can also be used to define lights interactions depending on energy, but that's a very different idea. What we do find with matter is that with 'speed' comes a Lorentz contraction and a 'time dilation'. and also that a objects 'energy', expressed through an interaction, will differ depending on the objects 'invariant mass and speed'

And then there is weight that is a relation between your 'invariant mass' and the 'invariant mass' or 'stress energy tensor' of the place where you are, like suspended on Earths surface.
« Last Edit: 27/02/2011 14:16:30 by yor_on »
 

Offline abacus9900

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If the earth stopped rotating would it's mass decrease?
« Reply #4 on: 27/02/2011 15:11:48 »
Not quite clear on what you mean.

What happens to the mass when something starts moving from rest mass? How is the mass changing?


 

Offline yor_on

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If the earth stopped rotating would it's mass decrease?
« Reply #5 on: 27/02/2011 17:35:11 »
Invariant proper rest mass is what will be the same in all frames of reference, on the moon, a Black Hole or on Earth. Relative mass and momentum is the associated 'mass' relative motion.

Motion is a relative thing, you able to get a different answer to your possible 'speed' just by choosing a different frame of reference, whereby you also will find yourself having a different 'relative mass' or momentum, it's firstly being a conceptual factor. When it comes to lights 'momentum' light have one specified 'speed', invariant from/in all frames observed, expressing its relation relative what measures it in blue or red shift aka 'energy/momentum'.

So the only, ah, invariant mass you have is your, eh, 'invariant mass', also called 'proper mass' or 'rest mass'. :) The rest are relations, undergoing transformations relative each frame you define your possible motion/speed from.

So 'mass' and speed, is defined from where you define your 'inertial frame of reference' and that will then create whatever 'relative mass or momentum' you will have theoretically. The other method is to await a interaction as colliding and therefrom define what possible array of 'relative mass' or momentum you had, depending on how you define the objects motion you collided with, as being still, or you being still, or anything in between motion-wise.

So what happens with your 'mass' when you start traveling?

Nothing, as far as I know, if it did you could expect more 'energy' stored in the hull the faster you move, which should mean more jiggling of the hulls atoms, as well as of yours, etc. And that should very fast make it very hard to survive as you would sit in a radiating hull, yourself radiating too. But that won't happen.
==

Cleaned it a little..

Think of accelerating, when you do, do you expect your molecules and atoms to gain 'energy'? What do you think would happen if a acceleration really stored 'energy' inside those? That's also a very nice way of pointing out that gravity is no 'force', as if it was you really would store that energy, for real. We use relative mass and momentum to describe the possible result of interactions under motion. Mostly we define those from their origin of departure, like Earth.
« Last Edit: 27/02/2011 17:48:00 by yor_on »
 

Offline abacus9900

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If the earth stopped rotating would it's mass decrease?
« Reply #6 on: 27/02/2011 17:47:44 »
Thank you for replying.

So, in a nutshell, what you are saying is that if you measure the mass of an object you are in motion with that is its 'rest' mass; if you are measuring the mass of an object that is accelerating away from you then its mass would appear to increase relative to it remaining in your rate of motion, yes?

So, if the earth stopped rotating its mass would not change for observers that stopped rotating too, but would be slightly less massive in relation to a rotating earth from the point of view of a 'rotating' observer? Ah, wait a minute...the moving observer would see a non-moving object as moving too. Oh dear!!!
« Last Edit: 27/02/2011 18:12:49 by abacus9900 »
 

Offline yor_on

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If the earth stopped rotating would it's mass decrease?
« Reply #7 on: 27/02/2011 18:10:38 »
The invariant mass is the same in all frames.

When it comes to light we can see the difference in motion, from you or coming at you, expressed as a red respective blue shift. But when we speak about measuring the 'invariant mass' I'm not sure how you would do it? You can of course look at the way light bends too, and matter bend, 'space' to make an educated guess. But if we assume that any speed defined first need to be defined relative some arbitrarily defined frame/origin then any other speed you define will rest on that first choice of 'inertial frame'. And so the relative motion of that object won't tell you its invariant mass other than relative the frame you defined as 'not moving'.

You can also look at the orbital revolutions of any heavenly object relative what you want to measure, like some sun far away. Those orbits follow certain established ratios relative the invariant mass of whatever you want to measure. Any orbit you see is that object trying to 'fall down', at the same time as its own speed relative the object makes it constantly miss. "All objects accelerate to the Earth at exactly the same rate given the same distance from the Earths center. In other words, even the Moon is accelerating towards the Earth at a rate that is appropriate for its distance from the Earth's center...If you know how far an object is from the center of a planet or a sun and if you know the rate of acceleration that that object is accelerating towards that planet or that sun you can easily calculate the mass of that planet or sun because only an object of that planet's or sun's mass can accelerate an object towards it at that rate at that distance"
« Last Edit: 27/02/2011 18:13:36 by yor_on »
 

Offline abacus9900

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If the earth stopped rotating would it's mass decrease?
« Reply #8 on: 27/02/2011 18:17:15 »
Don't scientists talk more of 'energy' nowadays than mass?
 

Offline yor_on

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If the earth stopped rotating would it's mass decrease?
« Reply #9 on: 27/02/2011 18:23:23 »
"In 1905 Einstein wrote a paper entitled "Does the inertia of a body depend upon its energy content?", to which his answer was "yes". The first record of the relationship of mass and energy explicitly in the form E = mc2 was written by Einstein in a review of relativity in 1907. If this formula is taken to include kinetic energy then it is only valid for relativistic mass, but it can also be taken as valid in the rest frame for invariant mass. Einstein's conventions and interpretations were sometimes ambivalent and varied a little over the years, however examination of Einstein's papers and books on relativity show that he almost never used relativistic mass himself. Whenever the symbol m for mass appears in his equations it is always invariant mass. He did not introduce the notion that the mass of a body increases with velocity, just that it increases with energy content. The equation E = mc2 was only meant to be applied in the rest frame of the particle. Perhaps Einstein's only definite reference to mass increasing with kinetic energy is in his "autobiographical notes".

Ah, that was the answer to your Q about 'energy'. 'Energy' is a very strange subject :) as it's a description of 'relations' transforming, not having any isolated existence outside those as far as I know. When we speak of a photon as having a certain 'energy' we build that on our history of earlier interactions by light with a 'detector'.

"To find the real origin of the concept of relativistic mass you have to look back to the earlier papers of Lorentz. In 1904 Lorentz wrote a paper "Electromagnetic Phenomena in a System Moving With Any Velocity Less Than That of Light." There he introduced the "'longitudinal' and 'transverse' electromagnetic masses of the electron." With these he could write the equations of motion for an electron in an electromagnetic field in the Newtonian form F = ma where m increases with mass. Between 1905 and 1909 Planck, Lewis and Tolman developed the relativistic theory of force, momentum and energy. A single mass dependence could be used for any acceleration if F = d/dt(mv) is used instead of F = ma. This introduced the concept of relativistic mass which can be used in the equation E = mc2 even for moving objects. It seems to have been Lewis who introduced the appropriate velocity dependence of mass in 1908 but the term "relativistic mass" appeared later. [Gilbert Lewis was a chemist whose other claim to fame in physics was naming the photon in 1926."

And.

"Despite the general usage of an invariant mass in the scientific literature, the use of the word mass to mean relativistic mass is still found in many popular science books. For example, Stephen Hawking in "A Brief History of Time" writes "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." and Richard Feynman in "The Character of Physical Law" wrote "the energy associated with motion appears as an extra mass, so things get heavier when they move." Evidently, Hawking and Feynman and many others use this terminology because it is intuitive and is useful when you want to explain things without using too much mathematics. The standard convention followed by some physicists seems to be: use invariant mass when doing research and writing papers for other physicists but use relativistic mass when writing for non-physicists."

So I agree, it becomes easily confusing understanding what people mean by mass. But invariant mass is what signifies matter, nothing else. It's matters unique signature. The other definitions are used to define a 'mass' relative motion, as I see it.
« Last Edit: 27/02/2011 18:48:16 by yor_on »
 

Offline abacus9900

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If the earth stopped rotating would it's mass decrease?
« Reply #10 on: 27/02/2011 19:34:56 »
Yes, well, not to get too philosophical but when we peer into the heart of matter what do we see? My understanding is that what we see are fields of energy, so would it be true to say that matter isn't really 'matter' at all but fields of energy interacting with one another? If this is the case then it makes sense to me that when we observe, or measure if you like,  an object that is moving faster than us it has 'taken on' more energy than us and therefore has more mass (which is really energy). Is this terribly wrong?

When you say invariant mass is what defines matter I assume you mean relative to your frame of reference do you? If not I still haven't grasp the idea.
« Last Edit: 27/02/2011 19:39:08 by abacus9900 »
 

Offline yor_on

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If the earth stopped rotating would it's mass decrease?
« Reply #11 on: 27/02/2011 21:56:58 »
Invariant mass is defined as the amount of mass that will be invariant in all frames possible to think up, equivalent to a energy and momentum invariant in all frames of reference. It's an idea of what is left when we stop looking at its weight etc.

'Energy' is a intermediary between the idea of 'work' and 'work done'. In any interaction you will at least have two 'something something' interacting. The end result of that interaction will crave 'energy' and leave some constituents back transformed in a way that may be useful for further interactions but with some of what it used unfit for any further work, lost as 'energy'. Like a car uses gasoline and leave carbon dioxide, nitrogen, and water vapor with its engines 'work done'.

It's all transformations costing some 'energy', and as I understands it, also leaving us with less 'work' to be utilized from the rest products from those transformations, as each one take some 'energy' away. But 'energy' isn't tangible in itself, it's just a relation to the interaction. Reminding of relative mass, momentum etc.

We don't see fields of energy, as I know? We do see radiation/photons though, and they are the closest to the idea, being non-dimensional and massless. But that's 'light', not 'energy'. Look at it this way, when a photon interacted with your eye, its 'energy' transfered into your nerve-cells, got analyzed by your brain, and presented in a understandable pattern for your consciousness. That energy traveling was used up in those transformations creating the pattern, and is no longer 'existing' to be utilized any further, as far as I know. I mean, if it was we should self explode, constantly getting 'loaded' with more 'energy':) So 'energy' is a rather weird concept, especially considering 'conservation of energy' :)stating that it won't get 'lost'. That should mean that something we can't 'touch' somehow transforms into something else, as untouchable as the first idea..
« Last Edit: 27/02/2011 22:09:00 by yor_on »
 

Offline Bill S

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If the earth stopped rotating would it's mass decrease?
« Reply #12 on: 28/02/2011 02:51:11 »
thescienceofacne, did all that answer your question?  If not, you might like to try thinking in terms of inertia increasing with speed, which includes rotation. You can try this next time you are in a park with a child, or without a child if you don't mind getting odd looks.  ;D Get a roundabout going; the faster it is spinning the more energy you will need either to stop it, or to speed it up.  This is because its inertia increases with speed, which has the same effect as increasing its mass.
 

Offline Geezer

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If the earth stopped rotating would it's mass decrease?
« Reply #13 on: 28/02/2011 05:03:42 »
thescienceofacne, did all that answer your question?  If not, you might like to try thinking in terms of inertia increasing with speed, which includes rotation. You can try this next time you are in a park with a child, or without a child if you don't mind getting odd looks.  ;D Get a roundabout going; the faster it is spinning the more energy you will need either to stop it, or to speed it up.  This is because its inertia increases with speed, which has the same effect as increasing its mass.

True, but the amount of matter remains constant, and if all that matter was converted into energy, the amount of energy released would also remain constant (I think  ;D)
 

Offline Bill S

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If the earth stopped rotating would it's mass decrease?
« Reply #14 on: 28/02/2011 19:35:08 »
Geezer, I'm not clear about your point, here.  Are you saying that the amount of matter remains constant, in spite of increased/decreased speed?
 

Offline Geezer

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If the earth stopped rotating would it's mass decrease?
« Reply #15 on: 28/02/2011 20:44:55 »
Geezer, I'm not clear about your point, here.  Are you saying that the amount of matter remains constant, in spite of increased/decreased speed?

Yes - I hope I am correct in saying that, but with this stuff, I'm never too sure!
 

Offline Soul Surfer

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If the earth stopped rotating would it's mass decrease?
« Reply #16 on: 01/03/2011 22:43:58 »
Yes and it is quite easily in principle to estimate how much mass the earth would loose.

Assume that the earth is a uniformly dense sphere of diameter 12,750Km and  mass 6x10^24 Kgm rotating one every 24 hours.
you can calculate the total rotational energy of the earth.  Equate this to mass via the famous E=mc^2 gives you the change in total mass which will be a significant amount but very small compared with the  total mass of the earth
 

Offline lightarrow

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If the earth stopped rotating would it's mass decrease?
« Reply #17 on: 02/03/2011 11:03:22 »
It is commonly understood that mass and velocity are directly related.  Basically, the faster an object travels the more mass it has.  Is the same true for rotational motion?  If you take an object and spin it very fast, does it now have more mass than it would if it were at rest?  Is the original assumption about the relationship between mass and velocity even correct?
It's true *only* for rotational motion (of a uniform symmetric object around its symmetry axis), because in this case the system momentum is zero, so you can write E = mc2.
 

Offline syhprum

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If the earth stopped rotating would it's mass decrease?
« Reply #18 on: 02/03/2011 15:47:31 »
Google allready has the answer mostly worked out, the mass equivalent of the Earths rotational energy 2.14*10^29J is 2.378 billion tons, an incredible amount
« Last Edit: 02/03/2011 20:00:34 by syhprum »
 

Offline Bill S

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If the earth stopped rotating would it's mass decrease?
« Reply #19 on: 03/03/2011 19:28:51 »
I suspect that I am easily confused.  ???

If the Earth stopped rotating it would decrease by 2.378 billion tons; but Geezer says its amount of matter remains constant, which seems to make sense.  ::)
 

Offline lightarrow

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If the earth stopped rotating would it's mass decrease?
« Reply #20 on: 03/03/2011 20:35:18 »
I suspect that I am easily confused.  ???

If the Earth stopped rotating it would decrease by 2.378 billion tons; but Geezer says its amount of matter remains constant, which seems to make sense.  ::)
mass is not matter.
 

Offline Bored chemist

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If the earth stopped rotating would it's mass decrease?
« Reply #21 on: 04/03/2011 06:54:50 »
"It is commonly understood that mass and velocity are directly related."
By whom?
Most of the mass of the Earth (the other 10^21 tonnes or so) is not related to velocity.
The original premise is flawed.
why are you still discussing this?
 

Offline Bill S

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If the earth stopped rotating would it's mass decrease?
« Reply #22 on: 05/03/2011 15:33:09 »
 
Quote from: lightarrow
mass is not matter.

Mass is matter + energy. Right?

Quote from: B C
why are you still discussing this?

Because some of us struggle with things that are obvious to the enlightened.  I think its called learning.  :-\
 

Offline lightarrow

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If the earth stopped rotating would it's mass decrease?
« Reply #23 on: 05/03/2011 21:25:19 »
Quote from: lightarrow
mass is not matter.

Mass is matter + energy. Right?
No. "Matter" is not a very precisely defined term, it essentially means "particles" as protons, neutrons, electrons. If you have, for example, a single hydrogen atom in its fundamental state, it's the same "matter" that the atom in an excited state (it's still one proton and one electron; all the properties of the proton and the electron are the same). But the mass is different, because the excited atom as a greater mass.
« Last Edit: 05/03/2011 21:27:19 by lightarrow »
 

Offline lightarrow

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If the earth stopped rotating would it's mass decrease?
« Reply #24 on: 05/03/2011 21:33:46 »
"It is commonly understood that mass and velocity are directly related."
By whom?
Most of the mass of the Earth (the other 10^21 tonnes or so) is not related to velocity.
The original premise is flawed.
why are you still discussing this?
"Most of the mass" but not "all". The OP didn't mention how much.
Certainly, in general, the statement "It is commonly understood that mass and velocity are directly related" is false. But in the specific case we are discussing, we can concede him mitigating circumstances  :)
 

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If the earth stopped rotating would it's mass decrease?
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