Third-law interaction pair (source code)

= Third-law interaction pair
{title2=$\mathbf F_{A\mathrm{\ on\ }B}+\mathbf F_{B\mathrm{\ on\ }A}=\mathbf0$}

= Action-reaction pair
{synonym}

A <third-law interaction pair> consists of the two <forces> belonging to the same mutual interaction, with their agent and recipient exchanged. The names <action-reaction pair> do not imply a delay: in the instantaneous model, the two <forces> occur together. Test a proposed pair by naming both bodies and the interaction, rather than merely noticing equal magnitudes and opposite directions.

For a book resting on a table, the table's upward <normal force> and <Earth>'s downward <gravitational weight> both act on the book. They can balance in the book's <free-body diagram>, but they are not a <third-law interaction pair>. The partner of the table's <normal force> on the book is the book's downward contact <force> on the table. The partner of <Earth>'s gravitational <force> on the book is the book's gravitational <force> on <Earth>. Their equality does not require equal <accelerations>: <Earth>'s much greater <mass> makes its response correspondingly smaller for a given net <force>.

Similarly, <friction> on a sliding block from a surface is paired with <friction> on that surface from the block. For the collection containing only the block, that <friction> is an <external force>; including the contacting surface makes both members <internal forces>. Changing the collection changes the bookkeeping of <momentum>, not the physical interaction.

\Image[/newtons-third-law-body-and-system-forces.png]
{title=Equal opposite interaction forces act on different bodies and cancel only in the combined momentum balance}
{description=Original one-dimensional model with right positive, $m_A=1\,\mathrm{kg}$ and $m_B=2\,\mathrm{kg}$. The upper arrows are the mutual <forces>; the lower panels retain the <force> on $A$ alone and add both bodies' <momentum> equations. Only horizontal <forces> are shown; balanced vertical support is omitted.}