# External forces and external moments

1. Jul 2, 2016

### harmyder

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
$$$$r_i \times f_{ij} + r_j \times f_{ji} = (r_i − r_j ) \times f_{ij} = 0$$$$

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. Jul 2, 2016

### TSny

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