Phonetics
How to know when a vowel + 'r' in English is transcribed with 3^: or with the vowel + 'r' ???
example: workshop [w3^:Shlp]
perform [pe^fO:rm] sembra naturale?

In General American English, both of those are pronounced with an /ɚ/ (/wɚkʃɑ:p/ and /pɚfɔ:ɹm/). /ɚ/ sounds the same as an /ɹ/. The only difference is that it's longer and is used as a vowel. (so the words sound like "wrrkshop" and "prrform")

Vowel + r can be pronounced either like a <vowel sound + /ɹ/>, or simply just </ɚ/>. There's really no rule to this so you just have to memorize it.

Examples:
A lot of -ur-, -er-, -ir- = /ɚ/ (burn, fern, bird)
Some -ear- = /ɚ/ (heard)
Some -or- = /ɚ/ (work, worm)

Some -or- = /ɔ:ɹ/ (born, tore, core)
Some -ar- = /ɔ:ɹ/ (warm)
Some -ar- = /ɑ:ɹ/ (barn, farm, harm)
Some -ear- = /i:ɹ/ (hear, ear, shear)
Some -ear- = /ɛ:ɹ/ (bear, wear)
Some -air- = /ɛ:ɹ/ (hair, air)
and many more