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Homework Help: External forces and external moments

  1. Jul 2, 2016 #1
    1. The problem statement, all variables and given/known data
    While reading course lecture at ocw.mit i have stumpled upon such an equation

    $$\dot H_O = \sum_{i=1}^n (\dot r_i \times m_i v_i) + \sum_{i=1}^n (r_i \times m_i \dot v_i) = 0 + \sum_{i=1}^n (r_i \times (F_i + \sum_{j=1, j\ne i}f_{ij} )) = \sum_{i=1}^n (r_i \times Fi) + \sum_{i=1}^n M_i$$

    I don't understand from where term with ##M_i## came.

    2. Relevant equations
    $$\begin{equation}r_i \times f_{ij} + r_j \times f_{ji} = (r_i − r_j ) \times f_{ij} = 0 \end{equation}$$

    3. The attempt at a solution
    Because of equation (1) ##\sum_{i=1}^n r_i \times \sum_{j=1, j\ne i} f_{ij} = 0##, so the term ##\sum_{i=1}^n M_i## came from nowhere.

    And later they write: "Note that external forces in general produce unequal moments about O and G while applied external moments (torques) produce the same moment about O and G."

    So what are these external moments and where they came from, and why they don't change?

    EDIT: Oh, i see, probably it is all about force couples. They provide us with pure moment. Ok:) Though, would be nice to have somebody to confirm my guess.
    Last edited: Jul 2, 2016
  2. jcsd
  3. Jul 2, 2016 #2


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    I think your interpretation is correct. I agree that the way they just threw in the sum over external couples M is confusing.
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