The postalveolar approximant (r in "red" in General American) is so weird linguistically.
Also it's always amused me how dog noises are onomonopoeitized in GA English as "bark" or "woof", when dogs lack lips to make a labial plosive, and their tongues can't really form proper postalveolar approximants or velar stops. I think it has to do with how we hear the third formant.
I guess I'd transcribe it like...
/ɚa◌˞'/
It's almost like "rorch" but more glottal less velar.
Try different languages. ra re ri ro ru is my favorite little run of most of them.