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Vectors or not?

  1. Dec 13, 2009 #1
    I have a general question on presenting physics work:

    When is it appropriate to use vector (bold) notation? I understand the difference between vectors and scalar quantities, and always used to think an equation with a vector on the LHS needed to have a vector on the RHS, but in writing up a recent question, had this equation:

    E[tex]_{kin}[/tex]=1/2mv[tex]^{2}[/tex]

    which I then use to produce an equation involving momentum, p, and then the final result which is a dimensionless quantity.

    Now I know energy is not a vector quantity. Does that mean it is wrong to put the velocity reference in bold?

    The same goes for the expression involving momentum:

    E[tex]_{kin2}[/tex]=(p[tex]^{2}[/tex])/2(m+M)

    is it wrong to have the p in bold?
    Thanks for any advice.
    Tom
     
  2. jcsd
  3. Dec 13, 2009 #2

    D H

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    Staff Emeritus
    Science Advisor

    [Equation corrected]
    In my opinion, yes. If you want to use a vector you would need to be a bit more verbose:

    [tex]E_{kin}=\frac1 2 \,\frac{\mathbf p\cdot \mathbf p}{m+M}[/tex]

    or

    [tex]E_{kin}=\frac1 2 \,\frac{||\mathbf p||^2}{m+M}[/tex]

    The only time you need to be verbose like that is when you are already using (in this case) a scalar p that denotes something other than the magnitude of the momentum vector. Otherwise, use of a unbolded symbol, particularly when squared, indicates the magnitude of the corresponding vector. It's pretty clear, and that is the standard usage in texts and journals. (Suppose you write a paper in which p denotes momentum but p denotes pressure. This paper will probably come back with some scathing review comments along the lines of "Don't do that! You confused me, and I know the subject.")
     
  4. Dec 13, 2009 #3

    Doc Al

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    Staff: Mentor

    In an expression for KE, I would not use bold (or any other notation) to represent velocity or momentum as vectors, since only the magnitudes of those quantities are needed.

    Realize that: [tex]v^2 \equiv \vec{v} \cdot \vec{v}[/tex]

    Edit: While I was daydreaming, D H beat me to it.
     
  5. Dec 13, 2009 #4
    Thanks all.
    Much appreciated.
     
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