Final answer:
Angular velocity is directed along the axis of rotation and for counterclockwise rotation, it points towards you, which is considered to be the conventional positive direction. Its magnitude is associated with the rate of change of the angle in circular motion, with radians per second as the unit of measure.
Step-by-step explanation:
Conventionally, angular velocity is directed along the axis of rotation, and its direction is determined by the right-hand rule. For counterclockwise rotation, which is considered to be the positive direction, the angular velocity vector points towards you along the axis of rotation. In contrast, for clockwise rotation, the angular velocity vector points away from you. Angular velocity, often denoted by ω, has units expressed in radians per second (rad/s). Additionally, the magnitude of angular velocity is the time rate of change of the angle ΔΘ during the circular motion of a particle, where greater rotation in a given time implies greater angular velocity.
The positive direction for angular velocity in the coordinate system is typically the positive z-direction, which follows from a counterclockwise rotation being positive. This is in line with the mathematical convention of positive angles representing counterclockwise rotation.