Aerodynamics
Aerodynamics deal with the forces acting on objects moving through air and the movement of air itself. There are four forces acting on any aircraft, including helicopters. Weight is the force of gravity. Lift is the force of air over the helicopter's rotor blades, countering the force of gravity. Thrust is the force moving the aircraft through the air, created by the main rotor blades. Drag is the force of air resistance against the aircraft as it moves through the air.
Bernoulli's Principle
The physicist Daniel Bernoulli discovered this principle by the way water pressure is increased when a pipe is narrowed. Air is affected by this same principle through helicopter airfoils. Both the main and rear rotor blades are airfoils. The curve of the airfoils causes the air traveling above the blade to move more quickly than the air beneath the blade. This creates a pocket of low pressure above the helicopter, creating lift, which allows the helicopter to rise. The amount of lift an airfoil creates is dependent on five factors: surface area, shape, speed, air density and the angle of the airfoil, or the angle of attack.
Torque
Newton's Third Law of Motion states that for every action there is an equal but opposite reaction. When the main rotor of a helicopter spins, it creates a counter-spin in the body of the helicopter. This is called torque. Large helicopters use a horizontal rotor, spinning in the opposite direction of the first rotor. Other helicopters have a vertical tail rotor, which uses Bernoulli's Principle to counteract the effect of torque.
Directional Control
A helicopter that just moved up and down would not be very useful. Adjustments to the pitch of the airfoils give helicopters directional control. When the airfoils of the main rotor are pitched forward, their lift creates forward motion. A greater angle of attack in their pitch means more forward velocity. When the airfoils are pitched backwards, the helicopter moves in reverse. When the speed of the secondary rotor is increased or decreased, the helicopter turns left or right.
Air Compressibility
As the airfoil moves through the air, the air is split into two streams which pass above and below the blade. At low speeds, it requires little energy to split the air. At fast speeds, however, the air striking the edge of the airfoil becomes compressed and more difficult to split. This compressibility limits the speeds possible for a helicopter. The effect is similar to that observed with water. When you slowly let yourself submerge, there is little resistance. Do a belly-flop, however, and you feel the effect of the water's compressibility.