= Variable-mass system
{title2=$m\dot{\mathbf v}=\mathbf F+(\mathbf u-\mathbf v)\dot m$}
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A body exchanging <mass> with material of inertial <velocity> $\mathbf u$ satisfies the displayed <momentum conservation> law for one stream, with signed $\dot m$ positive for entry and negative for exit. The <force> $\mathbf F$ excludes the incoming or outgoing momentum flux. A short time interval gives $d(m\mathbf v)/dt=\mathbf F+\mathbf u\dot m$, proving the formula. For stationary incoming matter, $d(m\mathbf v)/dt=\mathbf F$; for matter leaving at the body's own <velocity>, $m\dot{\mathbf v}=\mathbf F$. The <rocket equation> and accreting-drop motion are applications.
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