A fundamental aircraft motion is a banking turn. This maneuver is used to change the aircraft heading. The turn is initiated by using the ailerons to roll or bank, the aircraft to one side. The deflection of the aileron surfaces by an angle θ generates a torque due to air pressure on these surfaces. This causes a rolling motion of the aircraft. An aircraft is free to rotate around three axes that are perpendicular to each other and intersect at its center of gravity (CG). To control position and direction a pilot must be able to control rotation about each of them.
The lateral axis passes through an aircraft from wingtip to wingtip. Rotation about this axis is called Pitch. Pitch changes the vertical direction that the aircraft's nose is pointing.
The longitudinal axis passes through the aircraft from nose to tail. Rotation about this axis is called Roll. Rolling motion changes the orientation of the aircraft's wings with respect to the downward force of gravity. The pilot changes bank angle by increasing the lift on one wing and decreasing it on the other. This differential lift causes bank rotation around the longitudinal axis. The ailerons are the primary control of bank. The rudder also has a secondary effect on bank.
The vertical axis passes through an aircraft from top to bottom. Rotation about this axis is called Yaw. Yaw changes the direction the aircraft's nose is pointing, left or right. The primary control of yaw is with the rudder. Ailerons also have a secondary effect on yaw. It is important to note that these axes move with the aircraft, and change relative to the earth as the aircraft moves. For example, for an aircraft whose left wing is pointing straight down, its "vertical" axis is parallel with the ground, while its "lateral" axis is perpendicular to the ground.
Rotational inertia: An aircraft has three rotational moments of inertia. (i) Rolling Inertia (ii) Pitch Inertia (iii) Yaw Inertia. The more mass an aircraft has on the wings, the more resistant it is to roll (more roll inertia). The more mass an aircraft has on the nose and tail, the more resistant it is to pitch (more pitch inertia). The more mass on the wings and/or nose/tail tends to make the aircraft more resistant to yaw (more yaw inertia).
Angular Momentum: When a large airplane rolls, it develops considerable angular momentum that must be overcome to stop the roll. A propeller aircraft, has a significant amount of angular momentum in roll because of the rotation of the propeller.
Angular Acceleration: If a rolling moment is applied to the aircraft (such as with an aileron deflection), then angular acceleration in roll will result. If a positive rolling moment is applied, a positive roll angular acceleration will result. For a given rolling moment, the larger the moment of inertia, the smaller the roll angular acceleration. The angular acceleration terms can be thought of as describing the motion that results from the application of torque to a rotating body with a moment of inertia.