A dimensional problem in relativistic mechanics

  1. Shyan

    Shyan 1,663
    Gold Member

    [tex]{F}=\frac {{\gamma}^3 {m} {v}^2}{{c}^2} + \gamma {m} {a} [/tex]

    You all know this equation.Relativistic newton's second law.
    The problem is as follows:
    As you know [tex]\gamma[/tex] is dimensionless.So the first term of the right side has dimension of mass.but it should have the dimension of force!
    what's wrong here?
  2. jcsd
  3. Hi Shyan. :smile:

    F = dp/dt.

    However, the equation that you write, I don't know it.
    See http://en.wikipedia.org/wiki/Special_relativity (scroll down to the section on force).
    It looks like you forgot a dv/dt term.

  4. Bill_K

    Bill_K 4,160
    Science Advisor

    You left out a factor. The first term is actually

    γ3 m/c2 (v.a) v
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