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B (orbital) momentum

  1. Jul 4, 2017 #1
    Hello everybody!
    I'm layman in physics, but recently I have very strong interest. Now I am struggling to obtain some knowledge all by myself. That's so complex, probably impossible for me... that's why i decided to sign up in the forum and I hope to get help from people who are versed and educated in physics.

    Here is the first question which I hope to get answer....
    I know about the notorious formulation: p = m x v
    p - momentum;
    m - mass;
    v - velocity.

    Two weeks ago, I read a text about "free moving (circulation) in gravitational orbit". In the text they talk about orbital momentum. The formulation of orbital momentum was presented as: p = miv/(2πl) = const
    p - orbital momentum;
    m - mass;
    iv - orbital velocity, also: velocity of circulation (it was represented as a kind of imaginary velocity; i - imaginary unit ???)
    2πl - orbital length (circumference).

    I searched in the physics textbooks, which I have at home... I searched in google... but i can't find information (and explanation) about this formulation.
    "p = m x v" is derived from "p = miv/(2πl)"? Or "p = miv/(2πl)" is derived from "p = m x v"?
    I will be very thankful for every comment about this mysterious formulation ( p = miv/(2πl) )....

    Have a nice day everybody! :approve::approve::approve:

    P.S. English is not my native language, but I hope I managed to ask my questions clearly enough..
  2. jcsd
  3. Jul 4, 2017 #2


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    Hello Fox, :welcome:

    Your i has nothing to do with imaginary numbers. Check out angular momentum and perhaps it becomes clearer.

    Your notation is understandable but leads to confusion: physicists use x for vector products and bold face for vectors (or an arrow above a vector quantity).
    So translational momentum vector ##\vec p## is defined as ##\vec p \equiv m\vec v ##
    And angular momentum ##\vec L \equiv \vec r \times \vec v## as you find in Wikipedia.

    Talking about orbital momentum is confusing. Could you refer us to the precise wording or post a piece of context ?
    looks weird dimensionally: mass/time ?
  4. Jul 4, 2017 #3
    The original text is written in bulgarian language, so it is difficult to translate it literally.
    I will try one more time to represent the question and i will make some corrections in my questions.

    Here it is in short:
    He (the author) talks about a free movement (circulation) in gravitational orbit and he describes the momentum like this: p = miv/(2πl) = const
    p - momentum;
    iv - orbital velocity (velocity of circulation);
    2πl - orbital length (perimeter of circumference).

    After that, he says:
    when we have 2πl= i (imaginary number), we get: p = mv

    I can't grasp his idea. The final formulation (p = mv) is OK, it is notorious.But his primary formulation ( p = miv/(2πl) = const )... I can't understand it...

    I hope I made my question more clear and I look for help.o_O
  5. Jul 6, 2017 #4


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    Can't say it helps me understand better. ##2\pi l = i ## simply can't be meaningful to me either.

    Is there a connection with the Kepler laws in the bul.. (sorry about the pun) story ?
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