Couple

Consider a thin, uniform rod $AB$, whose center of mass sits at its midpoint $C$. Now apply two forces at the two ends $A$ and $B$ of the rod, both perpendicular to the rod, equal in magnitude, but pointing in opposite directions, with the two forces separated by a perpendicular distance of $2r$ (each a distance $r$ from the midpoint $C$).

Net force is zero. Since the two forces are equal in magnitude and exactly opposite in direction, they cancel each other completely, so the net force on the rod is zero, and the rod is in translational equilibrium.

But net torque is not zero. Taking moments about the center point $C$: the force applied at end $A$ produces a torque about $C$ in a certain rotational sense (say anticlockwise); crucially, the force applied at end $B$, even though it points in the opposite direction to the force at $A$, produces a torque about $C$ in the same rotational sense (also anticlockwise) — because the two forces, being on opposite sides of $C$, both tend to turn the rod the same way. So the two individual torques add together rather than cancelling, giving a nonzero net torque, and the rod is not in rotational equilibrium: it undergoes pure turning motion even while remaining in translational equilibrium.

This specific configuration — equal, opposite forces, offset by a perpendicular distance, producing zero net force but a nonzero net torque — is called a couple. Couples appear constantly in everyday activities: turning a steering wheel with both hands, twisting a screwdriver, or opening a bottle cap all apply a couple. …