[In the time I have been writing this there have been a number of new posts, seems like the hour for the DIYers
]
The critical thing here is to notice what the engine does.
The engine applies a force *between* the rotor blades and
the helicopter body. The engine tries to turn the blades in
one direction and tries to turn the body in the opposite
direction. Without something to resist the body turning,
it will do so. Generally this is not what is wanted:-)
Note that this is no different from any other rotating
machine. Your washing machine tries to turn the drum in
one direction and the earth in the other direction. Because
the earth is so large you do not notice the effect on it
*however* the effect is still there. The difference with the
helicopter is that it is not attached to the earth and the
effect on the body of the engine's efforts are significant.
The best 'normal life' example I can think of is
an electric drill. Like a helicopter it is a box
with an engine and an output shaft to which a rotational
force is applied. It works by creating a force *between*
the body and the output shaft.
In this analogy the place of the rotor blades is taken by
the drill bit.
The key thing is once again to notice that there are two
force outputs. Equal and opposite. One tries to turn the
drill bit in one direction and the other tries to turn
the body in the opposite direction.
What the drill motor does is to apply a torque
*between* the drill chuck and the drill body.
There is *no* favouritism. The torque applied
to the drill bit is *exactly* opposed by the
opposite torque applied to the drill body.
If you were to imagine restraining the drill bit
in a vise and turning on the motor the body of the
drill would rotate in the opposite direction
to the normal direction of rotation of the
bit. In normal use the operator must resist
the movement of the drill body to allow
the torque to be transmitted to the drill bit.
If you are studying this seriously you might be able to
get a drill and try it out for yourself. Don't blame me
if you lose any limbs, eyes or other parts of your body.
Power tools are dangerous. Get someone familiar with
them to make sure that you don't hurt yourself.