Angular Acceleration: Understanding [omega]^2/Time

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Tom83B
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I'm sorry if I put this question to the wrong question. But I have problems to understand why is the angular acceleration [omega]^2/time.

I know that I get it when I do the derivation, but it kinda seems that if the angular acceleration is eg. 4rad/s^2, that in the time 1s the angular velocity not 4rad/s but 2rad/s. I still can't see why...
 

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I don't understand [omega]^2/time.

Angular acceleration is the derivative of angular velocity wrt time...

knowing that the angular velocity is also the change in angle (theta) wrt time...
you can get that our angular acceleration is the second derivative of our position(in terms of theta) function.

so it is d^2*theta/(dt^2)
 
Sorry, my fault. I didn't realize something.

I was given description how it's like from "the view of y" and I thought it was the same generally:
y = y sin(wt + Fi)
v = v cos(wt + Fi)
a = −a sin(wt + Fi)

So, again I'm very sorry for even posting this question. Now I tried to derive the actual angular velocity and I see what I've done wrong.