Angular velocity

Direction and rate of rotation

In kinematics, angular velocity (symbol ω or ⁠ ω → {\displaystyle {\vec {\omega }}} ⁠, the lowercase Greek letter omega), also known as the angular frequency vector, is a three-dimensional Euclidean vector that uniquely identifies the plane, direction and angular speed of rotation of a particle rotating in a circle at constant speed in three dimensions. The direction ω ^ = ω / ‖ ω ‖ {\displaystyle {\hat {\boldsymbol {\omega }}}={\boldsymbol {\omega }}/\|{\boldsymbol {\omega }}\|} is normal to the instantaneous plane of rotation. The sense of angular velocity is conventionally specified by the right-hand rule, implying counterclockwise rotations (as viewed from "above" the plane of rotation); negation (multiplication by −1) leaves the magnitude unchanged but flips the axis in the opposite direction.

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