Chaos IPA and application

[La Tiche de Inglé]

There is an IPA system which is supposed to have a symbol for each sound. When studying British and American English, I see that the same symbol is assigned to different sounds, depending on the accent.

I am watching videos by Rachel's English on Youtube (American accent). I find that [ɔ:], differs from the sound taught in the British accent. She is not alone in doing this, there is confusion everywhere.

According to this chart: https://www.phonemicchart.com/
There are 4 sounds that I would like to analyse:
 /ɔ/ (AmE -oo- "door")
 /ɔ:/ (BrE -oo- "door") - This sound is more closed and longer
 /ɑ/ (AmE -a- "far")
 /ɑ:/ (BrE -a- "far") - more closed than the above and longer, like an American "AW".

For example, if I had to transcribe the word "awesome" phonetically, I'd write:
 BrE we say --  /ˈɔːs(ə)m/
 AmE -- /ˈɑ:s(ə)m/

However,
1) many dictionaries (especially American ones) use another type of transcription (merriam-webster for example). It seems to my that Americans either decide not to use IPA or they dont know how... not sure. I’m lost.
2) This is what Cambridge says about the AmE and BrE pronunciation of awesome https://dictionary.cambridge.org/dictionary/english-spanish/awesome
The 2 dots ( : ) make the sound longer (although, in the examples of the 4 sounds above, I also detect more closure in vowel sounds when placing the dots).
I believe this isn't the case, though. It's a whole different sound when pronouncing AWESOME in BrE and in AmE.
If we check here https://www.ipachart.com/ and click on /ɔ/, we can clearly hear that this phoneme does not represent any sound in the American version of "awesome".
3) Rachel distinguishes between /ɔ/ (as in the American AW) and /ɑ/ (as in "Father" AmE).
The vowel sounds in AWESOME and in FATHER may have a slight, but almost unrecognizable difference, depending on each individual PERSON and their way of speaking. But, what I don't understand is how sounds were assigned to symbols that already exist and have totally different pronunciation.

[Daniel]

IPA system which is supposed to have a symbol for each sound

That's not quite correct, or at least needs to be explained more precisely.

The IPA is not a system of sounds, but a system of phoneme categories. Accents may still differ below the level of phonemic contrasts. IPA also has some additional ways to specify sub-phonemic differences (usually with diacritics). The basic symbols are used for broad transcriptions (indicating phonemes), while the more precise usage (of additional symbols and diacritics) can be used for narrow transcriptions, trying to represent specific pronunciations (e.g. by different speakers of the same language).

The other factor is that for some or most languages, including English, there is a more or less standard way of using IPA to represent it. And for consistency, it might be used with the same symbols even with different accents. In some ways, it's similar to an orthography, more than a recording.

One important point to understand about IPA is that it really is not about representing actual sounds, but about indicating different phonemes, so that you are able to understand that contrasts in the language. Since de Sausurre (and others) we have known that languages are primarily systems of constrasts, rather than systems of absolute values: sounds don't exist on their own, but only by being different from other sounds. In that way, in principle, we could use any symbols we want for phonemes, although of course something approximately similar to the sound itself is useful.

Another perspective on this question is that this is also why it's difficult to reform English orthography: we would lose the common spelling across dialects. So we have to find a balance that works best. You will find that this differs in different sources. Since you're talking about English learning materials, this is probably designed to help you understand all dialects, rather than just knowing the specific sounds of one.

[panini]

It is difficult to figure out the "theory" of the IPA, because it is a social construct developed over the centuries (well, it has been a work in progress for over a century), and it does not have any absolutely immutable principles (though changing the principle is similar to changing the US Constitution). One premise that seems to be the most true is that it is a system for notating segments (sounds). In the chart, half of the sub-charts are symbols for segments (consonants and vowels), and half are "diacritics" that describe general phonetic properties that can apply to a segment, for example [a] versus [ã].

On the one hand, IPA explicitly eschews diacritics (hence a separate symbol is required for [ʃ] as opposed to putting hacek on [ s ] to give [š]). Yet it also embraces diacriticky symbols, such as apostrophe for ejectives. The principle is that diacritics are acceptable when they represent general phonetic parameters of segment production. The dot-diacritic for retroflex and hacek for alveopalatal aren't general, they describe just one opposition (between alveolar and retroflex, or alveopalatal which they call postalveolar). It is still a puzzle why they use separate symbols θ ð for dental fricatives but diacritic modifications on t̪ d̪ for dental stops.

There is a tendency but not a strict principle that when a certain sound is phonemically contrastive in some language, there should be a separate symbol for it. If a phonetic property, on the other hand, is "general" to some level (intuitively, "it would be ridiculous to invent 20 new symbols in order to avoid using a diacritic"), one just uses the diacritic.

Theoretically, one could dispense with many of the IPA vowel letters, by using a diacritic. For example, we could get rid of [ɪ] and just write [i̞] (i with tack-down), and [ɛ] could be likewise notated as [e] with tack-down (which means "lowered"). Since that vowel difference is phonemic in many languages, there is a pressure to not use a diacritic. The phonetic fact that you noted between British vs. American English is not a phonemic contrast within a language. Therefore, to describe that difference, one can't call on different primary symbols, you have to appeal to diacritics. These same diacritics (raised, lowered, retracted tongue root, less round, more round) are used for more precise phonetic descriptions which don't rise to phonemic status within a single language / dialect, especially for describing contextual variants ("the vowel is slightly raised before velar consonants").

IPA is designed to make it possible to be more precise than "what is phonemic", but IMO it should be seen as a system for phonemic writing that has been augmented with other descriptive resources so that you can be a little bit more precise about phonetic properties.

IPA letters are quite vague at the level of phonemic contrast, which is why there are a dozen IPA-consistent transcriptions of English vowels as in "say", "go". Ideally, you use the symbol that is "closest" to the particular sound of the language. That means: you have to refer to the standard. https://www.internationalphoneticassociation.org/IPAcharts/inter_chart_2018/IPA_2018.html is the standard. It would be an interesting exercise to collect recordings of words by speakers of different dialects and then attempt to characterize the phonetic differences. I think British English has a lower, backer, rounder vowel that in the American pronunciation. You can use diacritics to describe that, or you can write the British vowel as [ɒ].

[Daniel]

Good points. Only comment:

it is a social construct developed over the centuries (well, it has been a work in progress for over a century)... It is still a puzzle why they use separate symbols θ ð for dental fricatives but diacritic modifications on t̪ d̪ for dental stops.

For any kind of inconsistency, the reason is almost always history and tradition. Simply put, the dental fricatives are found in historically important/familiar languages (from the perspective of traditional linguistics in Europe) like English and Greek (and in fact already had symbols ready to go), so they got their own symbols. At some point, available symbols started running out, and for less typical contrasts, newly "discovered" in lesser known languages (to linguists, not to their own speakers, of course), they sometimes used diacritics. The IPA does have a Eurocentric bias, although that's not always consistent either. And today I think the IPA does a reasonable job of adding new symbols for other newly discovered sounds, but actually correcting inconsistencies would mean violating the tradition, e.g. of using diacritics for dental stops.