輪 = noun = wheel, as verb = rotate or turn. Using "turn" can be misleading because it has no circular definition of returning to the same spot. 輪流 = rotating and flowing, like a water wheel; forever changing but returning to the same state (the time may be short or long). So It can also mean to wait for your turn. However, the actual meaning has religious significance, especially used for reincarnation. Also, it is the duality nature of Taoism, what lives must and die and where there is death, there is life reborn; what must separate must reunite and what is whole must divide. (Life starts off whole like an egg and then division occurs and the chicken comes out whole; Chinese history that flourishes and then decays; and from decay, comes the rise; etc). So 輪到你 is the better term to mean "waiting for your turn" and carries no religious significance. An English analogy would be, "You are saved" vs "Your salvation". 轉世輪流, the simpliest translation would be reincarnation. 風水輪流, the geomancy changes and will alternate from good to bad and bad to good since landscape features are ever changing. So the best translation would be "The wheel of fortune is ever changing". 分合輪流, the ever spliting and reuniting (said of the Chinese history about the empire. This is unique since regimes/societies/dynasties change but not the culture and its people) 衰興輪流, the alternating rise and fall, like the death and rebirth of a phoenix (in western mythology) 輪流坐莊 waiting for your turn to power... In mahjong, the "banker" (the one who starts the new round of the game and enjoys certain privileges such as having an extra tile at the beginning of the game) is always rotated to the next person unless the current banker wins the current round. Here 輪流 is used because it gives the sense of rotation back to the original status. You can use 輪到你坐莊. However, this is longer and no too poetic a language :)

Wow HSK 5! In this case, I believe you need someone majoring in Chinese. And I am not. But I'd like to 抛砖引玉 here. Since one replied this good question. Perhaps my answer can seduce some scholars into posting against me with an academic explanation. I sense that 轮到你了,轮流去做, and 轮着去做 sounds better in rhyme. It has a better...er, pace? It must have academic terms and theories (音韵学？). I have only this guess. It's not a problem with 轮 or 轮流. It's about 1-character verbs and 2-character verbs. Sometimes people choose among some one-character Chinese verb and their two-character synonyms only because of length. Sometimes we add 了、 着，ect only to make the sentences sound 'smooth'. I might have read about it online somewhere but I can't recall it now. Perhaps you'd know after passing HSK 5 with full mark:)

1. 轮流 他们轮流玩滑梯。 They take turns on the slide. 2. 轮，轮到 Now, before we proceed on, a short story... A long long time ago in a far away place, there was a village, a poor village. The children had nothing but only a wheel to play with. They would take turns to play on the wheel. And every 10 minutes, they would pass the wheel on to the next child, and when doing so, say: 轮到你了。 literal translation: The wheel has reached you. meaning: It's your turn. You're up. In today's context, of course, that story didn't make much sense. To describe the action "轮" in English, it would mean something like "rotate", "turn", "shift". and likewise, 轮到 would mean "rotate to", "turn to", "shift to". So back to the example, 轮到你了。 literal translation: It's shifted to you. meaning: It's your turn. You're up. Distinction between 1.轮流 and 2.轮 1. 轮流 describes many people taking turns, one at a time, until everybody had a turn, and then cycles back. 2. 轮 describes the shifting of responsibility at doing certain task from one person to the next, and the next... It doesn't set the rules on how it moves between the individuals.

轮 wheel -> in circular -> take turns Basically, your question is the difference between 轮(到) and 轮流/轮着. 轮流/轮着 + 去做 describe individuals do things "in circular" -> It focuses on the approach that individuals shares their duty. 轮/轮到 + 你了 describe individuals do things in circular and this is your turn to finish your job. 到 marks a stop in temporal and spatial sequence. 这条路接到国会山庄 = 这条路接国会山庄

Where is no "why" in vocabulary -- this is how Chinese works.