Look at car, care, and collar. Same two letters, AR, three completely different sounds. This is not chaos; it follows position and stress. Once you see the three jobs of AR, you can predict the right sound almost every time.
The Rule
AR has three settings.
1. Stressed AR before a consonant or at the end of a word = /ɑːr/, a wide open "ah + r": car, star, far, hard, park, sharp, large, market, garden.
2. AR before a silent E or another vowel = /ɛər/, the "air" sound: care, dare, share, scare, rare, aware, compare, parent.
3. Unstressed AR = /ɚ/, a quiet schwa + r identical to unstressed -ER and -OR: collar, dollar, sugar, grammar, similar, popular, standard, forward.
So the same spelling changes with its neighbors: a following consonant opens it up, a following vowel raises it to "air," and no stress shrinks it to a murmur.
Practice Words
The W Exception
One reliable exception: when AR follows a W, it usually becomes /ɔːr/, the "or" sound. That is why war, warm, ward, warn, dwarf, quart, and quarter rhyme with for, not car. Also note the verb are, which keeps /ɑːr/ despite the final E, and scarce, which uses the "air" sound /ɛər/.
Quick Tip
Test any AR word with two checks. Is it stressed? If not, it is the quiet /ɚ/ (dollar). If it is stressed, look right: a vowel next door gives "air" (care); a consonant or word end gives "ah + r" (car).