In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space.
The main use for planes of rotation is in describing more complex rotations in four-dimensional space and higher dimensions, where they can be used to break down the rotations into simpler parts. This can be done using geometric algebra, with the planes of rotations associated with simple bivectors in the algebra.
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.
The magnitude of the pseudovector, , represents the angular speed (or angular frequency), the angular rate at which the object rotates (spins or revolves). The pseudovector direction is normal to the instantaneous plane of rotation or angular displacement.
