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Mass times acceleration doesn't belong to a free-body diagram, why?

  1. Dec 16, 2013 #1
    [itex]\sum[/itex][itex]\vec{F}[/itex] is intended to be the net force (this is the sum of all forces acting on an object). However I have read that such sum equals to the product of the mass of the object and the acceleration that undergoes, but it resulted confusing to me that I read that [itex]\textit{m}[/itex][itex]\vec{a}[/itex] doesn't belong in free body diagrams. What does this mean?
  2. jcsd
  3. Dec 17, 2013 #2
    No idea what it means, but its certainly used in free body diagrams, so either you misread the text or just disregard it.
  4. Dec 17, 2013 #3


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    Staff: Mentor

    No, Marco is correct that they aren't included. See example 3:

    A free body diagram is a tool and its use is a matter of convention. The convention (definition) is that externally applied forces are shown. This enables defining the term "net force" as a force causing acceleration. We recently had a thread where confusion over/misuse of these definitions led to a long and pointless argument...
  5. Dec 17, 2013 #4


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    It's because ma is equal to the sum of all forces on the diagram. It's not a separate force. In principle, you could label the net force, but it usually only leads to confusion.

    People talk about "inertia" as if it's a force, but this is just misunderstanding of reaction forces.
  6. Dec 17, 2013 #5


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    Dearly Missed

    You MAY, on the basis of d'Alembert's principle, add -ma to your repertoire of "forces", and then always get a closed drawing. But, it isn't really illuminative to do so. Not the least because the determination of the length and direction of the -ma-"force" can solely be determined by "whichever gap is left in my drawing", rather than by some independent means.
  7. Dec 17, 2013 #6


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    yeah, if you put ##m\vec{a}## into the free-body diagram, then this vector must be equal to the sum of all the actual forces. I think this is all that is meant when the textbook says ##m\vec{a}## does not belong in the free-body diagram.
  8. Dec 17, 2013 #7


    Staff: Mentor

    As was mentioned above, it is just a convention. It appears that your text book follows that convention, so you should too. If you don't follow the convention then you are likely to get confused and you will be unable to get un-confused since the book won't be able to help you if you don't use its conventions.

    Just be aware that there are alternative conventions (d'Alembert's approach), but you should not attempt those until you are fully comfortable with the standard convention.
  9. Dec 17, 2013 #8


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    For complicated dynamics problems (e.g. where there are several masses joined by links so they can move in different directions) it is often useful to draw two separate diagrams, one showing the forces, and the other showing the mass x acceleration vectors, and then writing the equations that make them equal.

    I agree with the other answers - there is more than one "right way" to draw these diagrams, but to avoid getting confused, or losing marks in tests, start by drawing them the same way as your teacher and textbook does it.
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