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Thread: Concept of Centre of Mass

  1. #1 Concept of Centre of Mass 
    Forum Freshman Jasper's Avatar
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    What is the basic concept of centre of mass? Is there any good way to memorize this concept or any better way to view this?
    Also, can anyone give me some suggestions to place I can learn these? (internet links or books would be helpful)


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    isn't there no gravity at true or 'ideal' centre of mass?


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    The basic concept is that Newton's laws of motion apply to the motion of an object whose mass is concentrated at a single point. Real objects have masses that are distributed over a volume. Luckily, we do not have to calculate the motion of an infinite number of points, because for many purposes, the massive object behaves as if all its mass were concentrated at a single point - the center of mass.

    You can learn about it in any basic physics text. Wikipedia is also a good place to start.

    http://en.wikipedia.org/wiki/Center_of_mass
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    i kind of see as oversimplification the fact that newton obtain the gravitational formula analizing cogs but to explain tides analized it as gravity acting with gradient

    seems contradictory to me
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    Quote Originally Posted by luxtpm
    i kind of see as oversimplification the fact that newton obtain the gravitational formula analizing cogs but to explain tides analized it as gravity acting with gradient

    seems contradictory to me
    It's not. The model that fits best depends on the problem. Sometimes a simple model suffices, sometimes you need to take a more complex model.
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    i disagree if you have a very long stick the closer part to the star will experiment greater force of gravity

    with which obviously the cog will be closer to the star while the center of mass will be in the midle of the stick

    so they are different concepts i wont believe conclusions based on a false premise

    and this is quite known see spaghetization as you fall into a black hole
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    Quote Originally Posted by luxtpm
    i disagree if you have a very long stick the closer part to the star will experiment greater force of gravity

    with which obviously the cog will be closer to the star while the center of mass will be in the midle of the stick

    so they are different concepts i wont believe conclusions based on a false premise

    and this is quite known see spaghetization as you fall into a black hole
    I challenge you to find a stick that's so long that you can measure the difference in solar gravity on Earth.

    In fact, I challenge you to come up with a somewhat realistic design of such a stick, that could be built with less than a billion dollar. You don't actually have to provide it
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  9. #8 Re: Concept of Centre of Mass 
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    Quote Originally Posted by Jasper
    What is the basic concept of centre of mass? Is there any good way to memorize this concept or any better way to view this?
    Also, can anyone give me some suggestions to place I can learn these? (internet links or books would be helpful)
    It is basically a weighted average.

    If you have masses each with position vector



    Physically you can show that for forces that are equal and opposite that if is the center of mass that obeys Newtons where

    This same reasoning can be extended, using calculus to the center of mass of a arbitrary distribution of mass (not necessarily discrete).

    You ought to be able to find a treatment in any calculus book or any book on mechanics.

    Understanding the concept is far better than memorizing it.
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    its in my mind so somehow it exists
    its two m long weights one kg and orbits a 1 kg star at 3 meters distance

    are you gonna tell me cause it doesnt exist its cog is in the same place than the center of mass?

    if i knew how to integrate i could easily prove this is wrong, i bet most here can
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    Quote Originally Posted by luxtpm
    its in my mind so somehow it exists
    its two m long weights one kg and orbits a 1 kg star at 3 meters distance

    are you gonna tell me cause it doesnt exist its cog is in the same place than the center of mass?

    if i knew how to integrate i could easily prove this is wrong, i bet most here can
    I'm not telling you the cog is in the same place as the centre of mass, I'm telling you that for nearly all purposes, it might as well be. If you're going to use the most complicated model you can think of for every simple calculation, you are not going anywhere .
    Besides, even your overly complicated model is going to make approximations and thus won't be 100% correct. In fact, if you use a computer to calculate it, you probably will be stacking mistakes starting at anyway, and these mistakes tend to get higher the more complex your model is.
    If you can't measure it in any way and it has no measurable effect on anything you're interested it, it's safe to ignore it. It's in fact usually better to ignore it.

    You illustrate my point nicely by admitting you can't integrate, since you probably can calculate the trajectory of a ball quite accurately.
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    if you want to calculate moons orbit you have to know centripetal force balances with gravity force and while centrifugal force is applied in the center of mass force of gravity applies in the cog

    the moon has approximatley a diameter of 4000 km and is at 400000 km distance

    do you see the huge mistake newtonian phisics prediction makes taking the cog in the same place than the center of mass?

    edit:

    and plz someone show me a link where this is explained or ill believe newtonian physics are a fraud and what im pointing out is not even taken into account by science
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    Quote Originally Posted by luxtpm
    if you want to calculate moons orbit you have to know centripetal force balances with gravity force and while centrifugal force is applied in the center of mass force of gravity applies in the cog

    the moon has approximatley a diameter of 4000 km and is at 400000 km distance

    do you see the huge mistake newtonian phisics prediction makes taking the cog in the same place than the center of mass?
    No, I don't see the huge mistake. First of all, this entire discussion is about Newtonian physics, whether you consider all masses to be point masses or not. Second of all, even without doing any maths, 4000 km is only 1% of 400000 km, so any error you might be making would be even less than that: the gravitational force of the furthest part is 0.5% smaller, and that of the closest part 0.5% larger. The effects negate each other up to 0.005%. For everyday purposes, that's more than accurate enough, especially if you know that the gravitational constant isn't even known with that accuracy, so your error is going to be bigger anyway, whatever model or method you use.
    Newtonian physics serves really well to predict the motion of the moon, even if you consider both moon and Earth as point masses.

    Quote Originally Posted by luxtpm
    and plz someone show me a link where this is explained or ill believe newtonian physics are a fraud and what im pointing out is not even taken into account by science
    Here you go
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    The difference between the gravitational force of a 1kg object on the surface of the moon and the Earth varies by between the near side and the far side. The numbers are 0.002465 N and 0.002514 N respectively.

    so the cog will be quite off the center of mass maybe someone here can calculate it

    and no they wont both balance in the midle since the dont grow linearly but sqaured
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    Quote Originally Posted by luxtpm
    The difference between the gravitational force of a 1kg object on the surface of the moon and the Earth varies by between the near side and the far side. The numbers are 0.002465 N and 0.002514 N respectively.

    so the cog will be quite off the center of mass maybe someone here can calculate it

    and no they wont both balance in the midle since the dont grow linearly but sqaured
    The gravitational field is completely irrelevant to the center of mass. Gravity has no influence on the center of mass whatever. See the formula for calculating the center of mass in my earlier post.

    Your approach is simply wrong.
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    of course gravity doesnt affect center of mass what it affects is cog
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    The centre of mass is the point in a body at which gravity has the maximum influence. This is a very general statement to get an idea of this.

    If you stand upright your centre of mass is in your upper torso, If you lean forward your centre of mass changes, to outside your body until you fall over. If you wear a heavy hiking pack your centre of mass is now in the pack, so you have to lean forward to compensate, or you'll fall backwards.

    Objects become more unstable as the centre of mass is raised, and more stable, as it is lowered.
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    will the litle prince fall into his litle planet?

    i think not
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  19. #18  
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    Quote Originally Posted by luxtpm
    The difference between the gravitational force of a 1kg object on the surface of the moon and the Earth varies by between the near side and the far side. The numbers are 0.002465 N and 0.002514 N respectively.

    so the cog will be quite off the center of mass maybe someone here can calculate it

    and no they wont both balance in the midle since the dont grow linearly but sqaured
    Now you're mixing up completely different things: you look at the centre of mass of a 1 kg object, and the cog of the moon and the Earth together (the 1 kg mass is pretty irrelevant here). Recalculate with all mass of the Earth in the middle of the Earth and all mass of the moon in the middle of the moon, and you'll get a very accurate result.

    You deny the usefulness and necessity of models, but by not using a consistent model yourself, you prove yourself wrong.
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