Does American English have /ʌ/ sound or /ɔː/ sound?

[Outre]

I saw this in American Accent Training.



Take /ɔː/ ("aw" sound) for example. If "aw" sound is not common, why do almost all dictionaries use the sound?





And different dictionaries select different pronunciations for the same word. I want to know which one is correct. (If both are correct, which one is more common?)





Thanks in advance.

 

[GoesStation]

I think you're asking about the sounds in the cot-caught merger. Many Americans pronounce these words the same, and many (including me) pronounce them differently. I'm not sure which pronunciation is most common.