stick out your lips forʊ sound?

I learned that /ʊ/ sound as in 'good', 'book', 'hook', 'put', etc is a more relaxed sound than /u/ as in 'pool', 'cool', 'sue', etc.
And I learned in a video lesson Pronunciation of English Vowel Sounds 3 - Back Vowels - Part 1 (with captions) - YouTube, you stick out your lips just a little bit for /ʊ/ , but actually I heard from an American that they just make their lips unmoving, making the sound from the throat and I've observed it from many native spakers a lot of times.
Which is true? Do you stick out your lips even a little bit or never? Or does it depend on individuals or mood? The reason I'm asking this is depending on the movement of lips, the sound can vary a little bit and I'd like to make the perfect sound.