A pair of equal and opposite forces acting along distinct lines has zero resultant force but a nonzero torque. If acts at and at , the total torque about any origin is . 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.
In mechanics, a couple refers to a system of forces that consists of two equal forces acting in opposite directions on an object, but not along the same line. This arrangement creates a rotational effect or torque on the object without producing any net force that would translate it linearly. The forces in a couple are often described in terms of their magnitude and the distance between the lines of action of the forces, known as the "moment arm.
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