The first thing you learn about helicopters: Helicopters are inherently unstable.
This is not a joke. Aircraft can have “positive stability”, “neutral stability”, or “negative stability”. If an aircraft is positively stable and you change the pitch/roll/yaw, it will seek to return to equalibrium in ever smaller oscillations. A neutrally stable aircraft will tend to stay where you point it and continue in the new direction. An aircraft with negative stability, like a helicopter, will make greater and greater deviations unless they are corrected by the pilot. Helicopters have negative stability.
As for the rotor/prop question, remember that the rotors on a helicopter have to support the entire weight of the aircraft. The propeller on an airplane only has to provide thrust.
Propellers can be fixed-pitch or constant-speed. They have a high angle of attack near the roots, and a lower AOA at the tips; and they tend to be thicker and have longer chords at the roots, and thinner with shorter chords at the tips. The reason for this is obvious: The roots are moving more slowly than the tips, and so the propeller must be designed so as to generate approximately the same amount of thrust (“horizontal lift”) across its diameter.
A constant speed propeller is a variable pitch propeller. The pitch can be changed in flight so that the engine/propeller system can be adjusted for peak efficiency. The blades increase or decrease their AOA the same amount, and at the same time. The first variable-pitch propellers (as opposed to constant-speed propellers) were adjustable on the ground.
There are three kinds of helicopter rotors: Fully articulated, semi-rigid, and rigid. A fully articulated rotor system has “feathering hinges” (pitch, like on the constant speed prop), “flapping hinges” (to allow the bladed so move up and down), and “lead-lag” hinges to allow the blades to move fore and aft. Why?
The pitch is adjusted by the cyclic stick and the collective stick. The collective changes the pitch of each blade the same amount at the same time, like a constant speed prop. The cyclic feathers the blades a different amount, depending upon where the blade is on its circular trip around the centre. By tilting the “stationary star” (the “plate” to which the controls are attached), the “rotor disc” (the disc described by the rotating blades) is tilted. Due to precession (a force applied to a rotating disc will manifest itself 90° later in the direction of rotation), the stationary star does not tilt in the same direction as the rotor disc. For example, on U.S. helicopters (the rotors of French and Russian helicopters spin the opposite direction) tilting the stationary star to starboard will cause the rotor blades to reach their highest point at the rear. This means that the rotor disc is tilted forward and the helicopter moves forward.
When the rotor disc is under load, it “cones”. The tips are higher than the roots. Most rotor systems are “underslung” to minimize this. When the tips rise, they are closer to the centre of rotation than they are when they are flat. If you’ve ever seen an ice skater raising his or her arms above his or her head while spinning, you will have seen that the skater spins faster. This is the “coriolis effect”. Conservation of motion requires the faster spin. Since the tips are spinning faster, they need to move forward. This is taken care of by the lead-lag hinges.
In horizontal flight, the advancing blade has a higher airspeed than the retreating blade. To keep the helicopter from rolling into the retreating blade, the pitch is changed upward and the advancing blade’s pitch is moved downward (via the stationary star). The retreating blade “flaps” downward on its flapping hinge, which results in a higher relative AOA, and the advancing blade “flaps” downward, resulting in a lower relative AOA. The flapping hinges keep the bending and rolling moments from being transfered to the airframe. Basically, the rotor blades “flap to equilibrium”. That is, the lift on each side of the helicopter is approximately the same.
If you think about it, the blades of a fully articulated rotor system in flight move round and round, forward and backward, up and down, and are twisting all at the same time.
A semi-rigid rotor system is a two-bladed system like on a Robinson, a JetRanger, or a Huey. A semi-rigid system lacks flapping hinges, and the blades flap as a unit on the “teeter hinge”.
A rigid rotor system uses the flexibility of the blades (often or usually composite) to do away with the lead-lag and flapping hinges. I don’t have the bucks to fly a rigid-rotor helicopter.