What is the direction of angular velocity? Why is angular velocity constant in uniform circular motion?

The direction of angular velocity is defined by the helix rule of the right hand. The four fingers of the right hand are the direction of rotation, and the direction of thumbs up is the direction of velocity
The real definition of angular velocity is in the form of cross product, w = R × V, W, R, V are all vector forms
In uniform circular motion, the vector form of R and V always changes, but their cross product direction is always perpendicular to their plane, so the w direction remains unchanged, and the size of W = RV also remains unchanged, so the angular velocity is constant

How to calculate angular velocity
It's about latitude in geography

The angular velocity is 0 at both north and south poles
All the rest are equal
for instance:
You draw a concentric circle and make two lines passing through the center of the circle
So the angular velocity of the earth's rotation is the same everywhere

A physics problem: the electric fan moves under the flash lamp. The flash lamp flashes 30 times per second, and the angle between the fan blades is 120 degrees. If the observer thinks there are six blades, what is the angular velocity of the electric fan?
What I want to ask is the minimum angular velocity, expressed in rad / s

The speed is 300 rpm
Angular velocity W = 2 π n = 600 π