The kanji character for the Japanese word mawaru is one of the most memorable. Mawaru means "to go around, to go in a circle" and the kanji is the closest any kanji comes to a circle, being a box with a smaller box inside, conveying a sense of both endlessness and repetition.
Mawaru is used by itself, and as a suffix, in Japanese. At its most literal, it is used much the same as "to go around"—or "turn" is used in English. For example, in the negative, handoru ga mawaranai means "the handle won't turn," or, to take someone around with you is tsuretemawaru つれて回る, tsureru meaning to "take someone along" with the mawaru conveying the sense of "around." Other examples are tachimawaru 立ち回る (literally "stand around" but actually meaning "walk around"—the Japanese for "stand around" being tsuttatsu 突っ立つ) or arukimawaru 歩き回る (literally "walk around"). kagimawaru 嗅ぎまわる ("sniff around") and urotsukimawaru うろつき回る("snoop around") are other examples. Then there is the phrase furemawaru 触れ回る, fure being a "proclamation" and the mawaru giving the sense of extra exposure to all and sundry, for the meaning of "to make a show of," "to bandy about," "to broadcast," "let the world know," etc.
This hints at the "come full circle" sense of mawaru as in the English phrase "what goes around comes around," which in Japanese is tsuke ga mawaru 付けが回る (literally "the bill being due for payment" but with the just-mentioned meaning of inevitable payback for one's actions.) This sense of pendulum-like change is expressed in the phrase shiji ni mawaru 支持に回る, shiji meaning "support," and means to "come around" to a cause or person, i.e. for support to shift to a certain cause or person. It can be translated as "jumping on the bandwagon" or "declaring one's support."
mawatte kuru 回ってくる (literally "around come") means "to come up," as in one's waiting list number coming up. demawaru 出回る (literally "come out and around") means for a product to appear (and then "go around") the market, and as a noun, demawari 出回り, it means the state of supply of a commodity.
Going around various places, such as on a presidential tour, is kakuchi o mawaru 各地を回る ("to go around every area"), so it makes sense that yoi ga mawaru 酔いが回る ("the drunkenness is going around") does not mean that everyone is starting to get drunk, but means "to start feeling the effects of alcohol," i.e. the alcohol has gone around your blood system and is starting to work on your brain. Similarly. uwamawaru 上回る (literally "above around") and shitamawaru 下回る (literally "below around") mean, respectively, "to top" and "to fall below," the "around" bit here also hinting at scope: with shitamawaru, a scope whose boundaries are defined by a top value, or, with uwamawaru, a scope that is gone beyond.
You might think that ki ga mawaru 気が回る (literally "spirit going around") means something to do with your head spinning, but that's heya ga mawaru 部屋が回る ("the room spinning") in Japanese. ki ga mawaru shares the "scope" meaning of uwamawaru and shitamawaru in that it means to give everything its full scope in being attentive to detail, or to others and their concerns. Your spirit is properly "doing the rounds," going over everything it is supposed to, and checking up carefully on everything. However, in other contexts, ki ga mawaru can also have the meaning of one's mind groundlessly turning to negative thoughts, i.e. "turning, or flipping, over" to negativity.
enjin ga mawaranai エンジンが回らない, means the engine won't start (or turn over, as can also be said in English), but it is extended to mean the workings of anything. atama ga mawarani 頭が回らない (literally "head not turning"), means "muddleheaded" or "unable to think straight." shita ga mawaranai 舌が回らない ("tongue not turning") means being unable to get your tongue around a word or words (whether the fault of the word for being difficult or your state of mind). te ga mawarani 手が回らない (literally, "hand won't turn") means not being able to handle a job, work, a project etc. because it's beyond your ability. This meaning could, however, be related to the mawaru of shitamawaru 下回る in the sense of being limited in scope and not being able to operate above a certain level. Another body part connected with "not being able to turn" is the neck: kubi ga mawarani 首が回らない (literally "neck not turning") is neatly parallel to the English "up to your neck" in debt.
By the way, don't be misled by the frequently encountered uketamawaru which means to "hear, be told, receive (an order), take (a reservation)" etc. uketamawaru actually has nothing to do with mawaru but is a word formed from two kanji: uke 受け("receiving") and tamawaru 賜る ("to bestow") (although, confusingly, uketamawaru can also be, and usually is , written using the single kanji 承る).
Finally, a memorable idiom: ohachi ga mawaru お鉢が回る: hachi is "bowl" (prefixed with the honorific "o") and for the "bowl to come around" simply means it's your turn.
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