Difference between the verbs 轮 and 轮流 (meaning to take turns)

Question

In HSK 5, lesson 1, the word '轮' is part of the word list, with the translation: 'v. to take turns'. In lesson 3, the word '轮流' is part of the word list, again with the translation: 'v. to take turns'.

My teacher has told me that there are three differences between these two words:

1. 轮 is informal (口语) and 轮流 is formal (书面语)
2. You can't say 轮流到你了, but you can say 轮到你了（it's your turn)
3. You can't say 轮去做.., but you can say 轮流去做.. and 轮着去做.. (taking turns doing something)

This still doesn't really explain why you can't say such a thing and what the difference actually is, is there somebody who knows?

Answer 1

When 轮(rotate/ to take turn) is acting as a verb, most of the time it would include the result complement 到 - e.g "轮到你了" [it rotates to you (it is your turn)]

or followed by a word particle 着 (indicate continuous state) as in 轮着做 (taking turns to work)

or incorporated into a compound words along with a noun, like 轮米(getting in line for or queuing for rice handouts), 轮班 (in rotation; in shift)

轮 is also a noun for 'wheel' and 'turn'

轮流 (to take turns/ to alternate/to rotate) is also a verb, but it is only use as an auxiliary verb. For example, "轮流拜访他" - (take turns visiting him); 轮流看火 (take turns watching the fire). In other words, whenever you see 轮流, another verb must follow it directly. Meaning it can never be placed directly before the object

Answer 2

To distinct simply, you can take 轮(turn) as a verb and 轮流(in turn) as an adverb or adjunct.

轮流去做 or 轮着去做: do it in turn.

轮到你了: turn to you or it's your turn to do something.