Google Translate translates "physicae artis" as "Physics". Is that correct? What would be the reasoning of it? Why isn't it "nature of the art" or "physics of the art"?
This is related to the previous question about "ars gratia physicae".
Physics is primarily ars physica in Latin. Literally, this means "the physical art", so physica is an adjective here. The word order is quite flexible, so physica ars works as well.
The word ars is very broad, and "art" might not do it full justice. In this use I might translate it as "field", so that ars physica is "the field of physics".
There are a lot of fields that come with an ars in Latin. Often the ars is left out and the adjective alone can refer to the field. Since ars is feminine, the adjective is in feminine form: physica, chemica, musica…
I am less familiar with Greek, but I've understood that τέχνη behaves very similarly to ars. In the specific case of physics, also the words ἀκρόασις and ἐπιστήμη are relevant. But if you want more details on Greek, do ask a separate question; this remark is only a pointer.
Physicae artis is physica ars in its genitive form. If physica ars is translated as "physics", then physicae artis is "of physics". The genitive has many uses in Latin, and the literal translation with "of" is not always good. For example, the word gratia requires a genitive, as was mentioned in my answer to your previous question.
When a pair consisting of a noun and an adjective is declined to different forms, both words are declined. In "physics of the art" only the arty part is in genitive. If we translate "physics" as physica, then "physics of the art" is physica artis. Observe the difference: the first word is physica, not physicae.
If you translate "physics" with the full ars physica, then "physics of the art" would be ars physica artis.
What Google Translate gave you is otherwise correct, but it did not mention that you got a genitive. In general, Google Translate is very untrustworthy with Latin, so take anything it offers with a truckload of salt.