This [ʊ] sound is the vowel sound for words like hook, pull, and good. When I began to learn English a bit more seriously two decades ago, I used a book that taught me to pronounce it shorter and more relaxed than the long sound of [u], the vowel sound in words like pool, food, and cool. It also told me to round my lips too.
My pronunciation is fine (I hope, at least people around me seem to understand me perfectly), however I found a strange tendency in recent years, especially from Americans. (I can watch them on TV and video clips.) Many of them seem to not round their lips when pronouncing this [ʊ] sound.
The first time I noticed this was the time I heard an ESL teacher pronounced it with the [ɯ] sound (she is not a native English speaker, by the way). There is no [ɯ] sound in English, but there is one in Thai language. The [ɯ] sound, though being a close-back vowel, is always unrounded. So it sounds very strange to me at first, since [ʊ] is a near-back-near-close vowel, and I thought it is supposed to be rounded.
Wonder why she pronounced it that way, I started to watch native speakers on TV closely, and found that only some of them pronounce [ʊ] unrounded in normal speech. Most of them seem to round their lips a little (how much the little is little is another matter). But when they exaggerate the word, most of them don't round their lips, e.g., I saw one judge on a vocal-focused reality show exclaimed Good! for maybe three seconds long, and in that entire three seconds there was no lips rounding at all!
I consulted Wikipedia, and found that the matter of this rounding is unclear:
"Its vowel roundedness is generally rounded, which means that the lips are rounded to a greater or lesser degree, but is sometimes rather ambiguous. Because no language is known to contrast rounding with this place of articulation, the IPA has not created separate symbols to show this."
So which pronunciation is standard for the [ʊ] sound? Rounded or unrounded?