An imaginary line perpendicular to the plane of motion of a system about which angular momenta and torques are calculated.
Real-world systems often involve rotating objects or objects which must be prevented from rotating. In some cases, the rotation is constrained to occur about an obvious axis (e.g. a door will rotate about the line defined by its hinges, a fixed pulley will rotate about its axle, etc.). In some cases, however, there is no obvious fixed axis of rotation. For example, a rolling ball or wheel translates and rotates, and a collision involving a rotating object will often result in a change in the "physical" axis of rotation. In these cases, it is important to understand the rules for choosing an axis that will allow (and ideally, simplify) analysis of the situation.
The clearest situation is the case of a system executing pure rotation if a specific axis fixed in an inertial frame is chosen. A more common possibility is that a significant component of the system is constrained to rotate about a fixed axle. Some examples that suggest a clear choice of the axis of rotation are: