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Why does a helicopter need a second rotor for stability?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

A helicopter requires a second rotor—typically a small tail rotor—to counteract the torque reaction generated by the main lifting rotor.1

Because the main rotor is powered by the engine, it creates an equal and opposite force that tends to rotate the helicopter's fuselage in the direction opposite to the rotor's spin. Without an antitorque rotor to neutralize this effect, the aircraft would be unable to maintain a stable heading. The pilot manages this stability by using foot pedals to control the thrust of the tail rotor, effectively balancing the torque as needed.12

While the tail rotor is the most common solution, some designs utilize alternative configurations, such as "no tail rotor" systems that circulate air through the tail boom, or tandem and intermeshing rotor systems, to manage these rotational forces.34