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Math Help - Vectors in mechanics

  1. #1
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    Vectors in mechanics

    Ok so I have a very basic clarification question about vector mechanics.

    It is obvious that with displacement vectors the rules of vectors and trig apply to combining them. I cannot, however, see why we should assume that force vectors, velocity vectors etc should combine in the same way. Of course I know that they do but is this something that can be proved on paper or is it just shown experimentally?

    I hope I have explained myself properly and I will try to rephrase my question and provide an example if I am not being clear.

    Thanks for your help!
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  2. #2
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    Re: Vectors in mechanics

    The "rules of vectors and trig" apply to vectors. It does not matter whether they are "displacement", velocity, acceleration, or force vectors.
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  3. #3
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    Re: Vectors in mechanics

    A vector is any quantity that has both magnitude AND direction, so the rules for vectors (which include using trigonometry to 'combine it all together') work for any of these quantities.
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    Re: Vectors in mechanics

    Quote Originally Posted by Prove It View Post
    A vector is any quantity that has both magnitude AND direction, so the rules for vectors (which include using trigonometry to 'combine it all together') work for any of these quantities.
    The "rules of vectors and trig" apply to vectors. It does not matter whether they are "displacement", velocity, acceleration, or force vectors.

    Yeah I see that and appreciate that it is the case, but my question is how do we know that velocity, acceleration and force should combine in the same way?
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  5. #5
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    Re: Vectors in mechanics

    Because they are vectors...
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    Re: Vectors in mechanics

    Ok lol

    What I mean then is how do we know that they are vectors? Sure they have magnitude and direction, but why should they combine according to geometrical methods?

    (By the way I'm not doubting that they do! I'm just trying to understand more fully.)

    thanks
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    Re: Vectors in mechanics

    Quote Originally Posted by kinhew93 View Post
    Ok lol

    What I mean then is how do we know that they are vectors? Sure they have magnitude and direction, but why should they combine according to geometrical methods?

    (By the way I'm not doubting that they do! I'm just trying to understand more fully.)

    thanks
    Because vectors have a geometric representation (i.e. the arrows in space, ergo showing the length/magnitude and direction). This means they have to follow the properties of geometry.

    I think you are over-thinking things. It is a question of DEFINITION. A vector is defined to be a quantity that has magnitude and direction. Therefore, IF a quantity has magnitude and direction, it is a vector. Geometric objects have to follow rules of geometry. Since a vector HAS a geometric representation, it must follow the rules of geometry.
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    Re: Vectors in mechanics

    Kin

    your question will be answered by yourself if you read a good book on vector analysis.
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    Re: Vectors in mechanics

    Quote Originally Posted by MINOANMAN View Post
    Kin

    your question will be answered by yourself if you read a good book on vector analysis.

    Ok cool can you recommend any?
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