Bsrhrki

As you many know, according to Newton's 3rd law for every action there is an equal and opposite reaction, as the main rotor of a helicopter turns in one direction, the fuselage tends to rotate in opposite direction but when there is no engine power during autorotation, there is no torque reaction, why???

Because the engine is not applying power to the rotors. No engine power means there will be no torque pushing the airframe in the opposite direction.

In auto, the main rotor essentially becomes a pinwheel, kept moving by the air rushing past it...

Auto doesn't really power the rotors, it keeps them moving so that the spinning rotor creates air resistance and slows the descent of the helicopter, and maintains enough inertia in the blades to flare and stop the descent.

Of course, that inertia is only sufficient for one attempt at flaring and stopping descent.

Because the torque to spin it is being generated within the rotor itself, being a forward thrust component of the lift being generated by the spinning blades, like any gliding aircraft. An autorotating rotor is like two gliders with velcro wingtips going toward each other in opposite directions, who when they pass each other hook wingtips and start to spin around each other, still gliding and moving forward, but forced into a circle who's axis is their inboard wing tips.

What ever rotational force is transmitted to the airframe (a tiny amount) is actually in the same direction as the rotor's rotation; not a torque reaction, just friction drag from the main shaft bearings and sprag clutch.

In autorotation, the engine and gearbox are not applying any turning force, or torque to the rotor system, so therefore there is no torque reaction in the opposite direction.