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What is the name of this principle?

If the speed of the centre of mass $\vec{v}_{CM}$ of a solid is constant ($cte$), then the sum of the exterior forces that exerts into this solid $\vec{F}_{ext}$ is zero, and the opposite is true, namely that:

$$\vec{v}_{CM}=cte\Leftrightarrow\sum\vec{F}_{ext}=\vec{0}$$

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As far as I know, it has no name but it is the simplest corollary of the first fundamental equation of dynamics of systems, reading $$\sum \vec{F}_{ext} = M_{tot} \frac{d\vec{V}_{CM}}{dt}\:.$$ The formula says that the centre of mass of the system evolves as a single material point with all the mass of the system concentrated in it and subjected to a force given by the sum of all the external forces acting on the system. Thus neglecting those whose pair action-reaction is contained in the system of points.

Therefore the equation also embodies the principle of action and reaction and not only the second principle of dynamics.

For this reason its corollary contains more information than the principle of inertia.

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  • $\begingroup$ Could you explain the equation more? Thanks btw!! $\endgroup$
    – possible
    Commented Jan 5, 2014 at 16:08
  • $\begingroup$ Do you mean: $\sum \vec{F}_{ext} = M_{tot} \frac{d\vec{V}_{CM}}{dt}\:.=M_{tot}a_{CM}=\vec {F}$ $\endgroup$
    – possible
    Commented Jan 5, 2014 at 16:14
  • $\begingroup$ One can argue that this is pretty close to Newton's first axiom, so it might have a name. $\endgroup$
    – Alexander
    Commented Jan 5, 2014 at 16:14
  • $\begingroup$ Its name in français is principe d'inertie. $\endgroup$
    – possible
    Commented Jan 5, 2014 at 16:19
  • $\begingroup$ In italian principle d'inertie corresponds to principio d'inerzia, but it is referred to a single material point, where, diefferently from here, there is no structure around CM. However it is matter of convention to some extent. $\endgroup$
    – Valter Moretti
    Commented Jan 5, 2014 at 16:25
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It is very similar to the first Newton's law: it says that for a body at rest or moving with a linear uniform motion there is no force acting on it or the vector sum of all forces acting on it is zero. This is in general true for an inertial frame.

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  • $\begingroup$ love you man!!! $\endgroup$
    – possible
    Commented Jan 5, 2014 at 16:26

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