= Couple
{disambiguate=mechanics}
{title2=$\mathbf G=(\mathbf x_1-\mathbf x_2)\times\mathbf F$}
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= Force couple
{synonym}
= Couple
{synonym}
A pair of equal and opposite <forces> acting along distinct lines has zero resultant <force> but a nonzero <torque>. If $\mathbf F$ acts at $\mathbf x_1$ and $-\mathbf F$ at $\mathbf x_2$, the total <torque> about any origin is $(\mathbf x_1-\mathbf x_2)\times\mathbf F$. Shifting that origin changes the moment by the <cross product> of the shift with the resultant <force>, which is zero. A prescribed <couple> therefore specifies a pure turning moment independently of its reference point. In <Stokes flow> it can drive a <rotating sphere in Stokes flow> without a directly imposed translational <force>.
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