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Equation that predicts the increasing values of mass

  1. Jan 9, 2004 #1
    Is there an equation that predicts the increasing values of mass of a spinning top that is increasing its velocity steadily towards " c ".
     
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  3. Jan 9, 2004 #2

    Nereid

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    Do you mean 'rotates about its spin axis increasingly quickly'?

    It might help if we make a simplifying assumption about the shape and distribution of (rest) mass in the top - how about a uniform cylinder? Another assumption - the cylinder is made of a perfectly inelastic, incompressible material. OK?
     
  4. Jan 10, 2004 #3
    Yes on

    Do you mean 'rotates about its spin axis increasingly quickly'?

    Any shape that you want - I am interested in the math and do not have a real or imagined object to "weigh".

    " But we now understand that a spinning top weighs more than a top which is not spinning by a few parts in less than a billion. If the top spins fast enough so that the speed of the edges approaches 186,00 miles a second, the weight increase is appreciable-but not until then."
    -Richard Feynman

    Is there an equation that describes this?


    thanks:smile:
     
  5. Jan 10, 2004 #4

    Nereid

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    one approach ...

    Suppose a top is made up of a set of nested, concentric rings. For your purposes, I guess a thin slice through the top, perpendicular to the spin axis, would be sufficient.

    As the elementary ring spins faster (we're assuming it remains at the same distance from the spin axis), it will become more massive. If the outermost ring has a speed of ~0.866c, its mass increase would be 100%.
    [tex]m = m_{0}/\sqrt{1-\frac{v^2}{c^2}}[/tex]

    Integrate across all rings and you will have your formula (for one slice through the top; integrate across all slices for the whole top).
     
  6. Jan 11, 2004 #5
    Solution for cylinder

    I took a crack at a solution for the rotating cylinder. Let the cylinder have a uniform mass density and a total rest mass of M0. Then the rest mass , Mrest, of the rotating cylinder (i.e. mass as measured in the zero momentum frame) is

    [tex] M_{rest} = \frac {2M_{0}c^{2}}{R^{2} \omega ^{2}} [1 - \sqrt{1-(\omega R/c)^{2}][/tex]


    Here is the calculation
    http://www.geocities.com/physics_world/sr/rotating_cylinder.htm

    Notice that as

    [tex]\omega R << c[/tex]

    the mass becomes

    Mrest ~ M0
     
  7. Jan 12, 2004 #6
    NEREID

    Nereid,

    thanks for your help.

    here's another HUGE problem in proving my theory that I'm working on-

    What is the frequency (or wavelength) of magenta?

    I have found lots of info on not knowing. I cannot buy the reasoning that the info is not available because it is a composite color. If the current R_G_B theory is right (I don't think so), then ALL other colors (on any Physics chart) are composite, and are neatly defined.

    any help here?
     
  8. Jan 13, 2004 #7

    Nereid

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    Magenta is composite.

    You know about cones and how the human eye (and brain) perceives colour, right?

    You also know about wavelengths of light and the rainbow, right?

    So, if your eye can only send your brain three lots of information about colour (the intensity as seen in each of the types of cones), how come you can see six colours in a rainbow?

    BTW, some women (but no men) actually have two different types of 'red' cones in their eyes. Those lucky enough to be born like this have a considerably richer perception of colours than the other women (and all men). :smile:
     
    Last edited: Jan 13, 2004
  9. Jan 13, 2004 #8
    women like pink?

    Nereid


    OK, magenta is composite. I pre-stated that hoping to avoid some of the "middle" discussion, but let's have a go at this. I like to learn.

    1. Does composite mean "a value of a combination of 2 or more things"?,

    OR

    2. Does it mean "that which can not be defined"?

    AND

    3. Are orange, green-blue (dk. turqoise), or indigo "composite" colors? -- I certainly thought they were, yet we have clearly defined values for these.

    Maybe this is Quantum proof that man will never define/understand women.


    LPF
     
  10. Jan 13, 2004 #9

    Nereid

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    Does composite mean "a value of a combination of 2 or more things"?
    Yes. If you looked at a chart of the intensity vs wavelength of a 'magenta' source, you'd see that it has (at least) two distinct peaks.

    Are orange, green-blue (dk. turqoise), or indigo "composite" colors?
    Not in the same way that magenta is. These colours are more like red, yellow, green, blue, and purple in that they are predominantly a narrow band of wavelengths. Of course, the English names of colours are imprecise; one person's 'purple' may be another's 'violet' :smile: However, with orange, green-blue, and indigo (maybe; I'm not sure what people mean by this one), it's easy to test - simply look at a rainbow (e.g. white light split by a prism; avoid something printed in a book, or on a computer screen) and see if you can see these three colours in the rainbow. If you can, then they're not composites.

    You can also use this same test to show that magenta must be a composite colour - can you see it in a rainbow? If not, it can't be a pure colour!
     
  11. Jan 13, 2004 #10

    selfAdjoint

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    Nereid, what are the "colors" of the three bands? I mean, rather than giving their spectral frequency or wavelength, could you estimate where they fall in terms of our color sense. And is there any online source you know about which discusses the details of the extra red band you spoke of, in particular how the enhanced color sense actually falls out in practivce. Psychometric studies? Seems like this distinction could give us at least a narrow window into the structure of the color sense.
     
  12. Jan 13, 2004 #11

    Nereid

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    some women may have five!

    Some sources for colours and bands, in general (probably gives you more than what you asked for) :
    http://www.photo.net/photo/edscott/vis00010.htm
    http://ergo.human.cornell.edu/studentdownloads/DEA350pdfs/vision.pdf
    http://www.yorku.ca/eye/specsens.htm

    Here's one article on the sex differences (looks like some women may have 5 different types of cones - blue, two green, and two red):
    http://teachpsych.lemoyne.edu/teachpsych/faces/script/Ch09_HTM/color_vision.htm

    How does this happen? The genes for cones are on the X chromosome, and women have two. What if the expression of a red cone in one cone is different from the expression of that in a neighbouring red cone?

    SelfAdjoint: this thread doesn't really have much to do with TOE, maybe it could be moved? Or should a new thread be started?
     
  13. Jan 13, 2004 #12
    Nereid,

    Let me come at this from the backside-

    Are there any colors other than magenta that we do not have freq./wavelength for?

    It's my exerience that the answer is no, I have been able to identify every other color imaginable. They can all be found on THE chart ( or extrapolated). So, if magenta is a tertiary composite, then what are the peaks that you mentioned that produce it?

    Note: I found MORE info on this topic in general in 3 NON-PHYSICS areas than from Physics specifc sources.

    1. TV & computer monitor manufacturers. (reproducing color w/light)
    2. Color copiers/printer manufactures. (color w/ inks)
    3. Eyesight/medical

    The latter provides some interesing data (apparantly contradictory to your last post) The "red" cones actually percieve yellow @ peaks. Deep violet (395nm approx.) can not be produced by any combination of other colors. All eyes have evolved along the same route, I find it highly unlikely that females have a different # of such a basic, universal item. I think they're talking about having more feedback (nerve receptors) than males which allows them to "read" body language for danger, and sense what an unhappy baby needs through minute facial expressions. Also interesting- smaller diameter eyes see into UV range (cats,mice), and larger eyes can see into IR [whales,elephants (which also both communicate in ELF range of sound for long distances)].
    No color is peceived in periphery vision, only movement (speed)


    SelfAdjoint-
    By the way, a true TOE is going to be as wide as it is tall. Physics is not the only branch of science that will benefit.


    And lastly, magenta is seen in the rainbow, and green is only seen because of the "slit" shape the light comes through (dark-light-dark).


    LPF
     
  14. Jan 13, 2004 #13

    selfAdjoint

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    Re: some women may have five!

    I'll start a thread in the biology subforum. The links you provided on the cone-gene linkage were very interesting, and I believe I now have a feeling for the bands and their content. I am also interested in the other end, that one of your links referred to, how the conscious sense of color is constructed in the brain. Does it happen in the visual cortex or somewhere else? What is recent and ongoing research focussing on? You know there are constantly reappearing arguments on the philosophy boards about qualia, and what they do or do not mean for a "reductive", or scientific account of consciousness. I feel that some acquainance with modern neurophysiology of color can help me hold up the scientific side in such discussions.
     
  15. Jan 14, 2004 #14

    Nereid

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    Questions posted in Biology subforum

    LPF -> You'll see that both SelfAdjoint and I have started new threads in the Biology subforum of PF. I'd encourage you to start a thread there with content similar to that of your last post here (women, what ranges of EM that other animals perceive, etc) - could be of significant interest.

    SelfAdjoint -> I believe that colour perception - eye and brain - is an intensive area of research by brain scientists. As the system is perhaps more complex than touch, taste, and feel - and arguably the most important of the human senses - it may be a good one for philosophers to get their teeth into.
     
  16. Jan 14, 2004 #15
    Nereid,


    Back to magenta. If this requires you to do work, I am not asking. A lead will suffice- somewhere to look, something to read. I don't care if it takes 8 composites to make it, what is its value?

    If we evloved with the same rules (as unification demands), and ALL scientific observation must go through our eyes, then there can be no difference (except symmetrical mirroring) between our "perception", and what energy or matter is doing. Eyesight did not evolve randomly, it has to be an antenae to receive signals that already existed from moment One.
    So far, all scientific? studies of light have observed what has already happened, and nobody has hypothesised on what IS happening. This does not require multi-dimensions, or multi-million dollar testing. They (portions of current theory) have been "red-shifted" into false assumptions. What happened to counter testing, testing under different conditions and environments, etc? (the anti-slit experiment).

    I am not being "tricky" here, if the answer to my question is known to science, please direct me to it.


    LPF
     
  17. Jan 19, 2004 #16
    magenta

    ..anyone......





    LPF
     
  18. Jan 20, 2004 #17

    selfAdjoint

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    The problem with magenta of course is that it's a combination of bands from opposite ends of the visible spectrum, red and violet. Given that the brain forms its color categories by differencing of the three bands it inputs (see the threads in biology) this means the two extreme bands would difference to a low value and the differences with the central band would be high. Thus I think magenta is entirely a construction of the brain. More information might come from functional MRI studies of people as they saw and visulaized different colors.

    I don't see that your metaphysics of seeing carries much weight. Also if you are going to get your information from people like TV tube manufacturers, you owe it to yourself to google up the work of Land (developer of the instant camera) who long ago was able to create a (washed out but genuine) full perceived spectrum using IIRC blue and red light. Fooled the brain you see.
     
  19. Jan 20, 2004 #18

    Nereid

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    CIE chromaticity diagram

    ... such as on this page:
    http://www.yorku.ca/eye/ciediag1.htm
    give a pretty good idea of what's going on.

    The 'pure colours' (narrow bands from the spectrum) lie on the curved line that is the border of the diagram. The straight line that forms the bottom connects the extremes of violet and red; nothing on this line is a pure color (except for the endpoints themselves).

    It's easy to read and then quickly forget, but
    *phospors can only represent colours within the triangle
    *the colours printed (or displayed on your screen) are NOT the colours you'd see at any particular point in the diagram!
     
  20. Jan 20, 2004 #19
    photon emission

    Nereid and selfAdjoint,

    Thank you both for taking the time to reply! (I felt abandoned for a day or 2)

    I sought out this forum, and the specific threads that I placed, with physics in mind. I mentioned the info gathered from tv, eyes, etc. because, after a long search, they had offered the most data. (Not all relevant)

    What I was (am) really searching for is does the photon ever make an emission at the wavelength formerly known as "magenta"? This, of course, must be precluded by what the wavelength is, hence my original question.

    Do either of you know of a good web site that shows the spectral charts of all the elements?
    I do not recall seeing magenta on any, the reds are always deep colored.

    Also, do you know of other ways to measure wavelength of man made lights? (NOT through hot gas etc.) I would shine a blue light at "the machine", and it would read 460nm.

    Or, last idea... computer generated (nor real) quanta of a combination of the colors required to make magenta spits out the magic answer for me... any such program exist?

    I need to be sure it either doesn't exist naturally, or even if so, can we assign a value to it. I'm doing simple math, so the number (or the non-existance of it) is critical. Not knowing leaves me at an impasse.

    LPF
     
  21. Jan 21, 2004 #20

    Nereid

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    LPF: What I was (am) really searching for is does the photon ever make an emission at the wavelength formerly known as "magenta"? This, of course, must be precluded by what the wavelength is, hence my original question.

    There is no single wavelength which, when perceived by the human eye, results in a colour perception called 'magenta'. To get magenta, you need at least some 'red' and some 'blue' photons.

    LPF: Do either of you know of a good web site that shows the spectral charts of all the elements?

    This site has a quite nice Java applet showing the spectrum of various ionised elements:
    http://www.colorado.edu/physics/2000/quantumzone/

    To see what 'colour' the emission spectrum of an element is, you'd need to combine the lines (at the right strengths). There's probably a way to do it with a computer monitor, but it'd be tricky (from the CIE diagram you can see that single wavelengths - which is what each emission line is - are outside the triangle). Alternatively, you could just look at the flame in an atomic flame spectroscope! Much the same effect can be seen by sprinkling a salt of your favourite element into a gas flame - you've seen this I'm sure; when it's sodium chloride, the flame goes orange-yellow (from those very strong D lines).

    LPF: Also, do you know of other ways to measure wavelength of man made lights? (NOT through hot gas etc.) I would shine a blue light at "the machine", and it would read 460nm.

    Spectroscope, or spectrometer. As 'blue light' is surely a mixture of wavelengths, your spectroscope will show you a graph, with intensity vs wavelength. The display could be as fancy as you'd be prepared to pay for!
     
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