The way helicopters are able to operate

[Ry122]

If a helicopter was to increase its omega of blades while in the air, and not completely do it while fixed to the ground before taking off, why would this cause the body and rotor to rotate in opposite directions while the helicopter is airbourne? This is assuming no air resistance. And no bearing friction. omega = radial velocity

 

[rcgldr]

It's Newton's 3rd law applied to torque. The helicopter exerts a torque on the main rotor, and the main rotor exerts and equal and opposing torque onto the helicopter. Usually a tail rotor is used to counter the torque exerted by the main rotor onto the helicopter, which results in a net side force, so for a true hover, the helicopter has to lean a bit into the direction of thrust from the tail rotor.