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Angular momentum equation

  1. Aug 26, 2011 #1
    1. The problem statement, all variables and given/known data

    I found this in Goldstein, Poole, and Safko and have seen it in other books. What I don't understand is how the equation gets from the second expression to the third; specifically, why is the m divided by two in the last expression? I am at a loss on this but I know it is not a typo.

    2. Relevant equations
    [tex]\int \mathbf{F} \cdot d\mathbf{s} = m \int \frac{d\mathbf{v}}{dt} \cdot \mathbf{v} dt = \frac{m}{2} \int \frac{d}{dt}(v^2)dt [/tex]
  2. jcsd
  3. Aug 26, 2011 #2


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    Staff: Mentor

    [tex]\frac{d \; v^2}{dt} = 2 v \frac{d v}{dt} [/tex]
    so to make this simply [itex]\frac{dv}{dt} v[/itex] it needs to be divided by two.
  4. Aug 26, 2011 #3
    Thanks, I knew it was something simple that I just could not see.
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