"a torn place, a split or opening made by tearing," 1660s, from rend (v.). Rent (1530s), from the alternative form of the verb, or from past tense of the verb, was more usual as a noun, but it tended to be confused with the other noun rent.
"held in check, restrained," 1580s, past-participle adjective from control (v.). Of rent, from 1930.
1711, "rent made by ripping or tearing," from rip (v.). The U.S. colloquial meaning "a rapid rush" is by 1855. The parachutist's rip cord (1906) originally was a device in ballooning to open a panel and release the hot air (1868, also ripping-cord).
"loud, disorderly, confusing noise," 1560s, probably imitative. Klein and Century Dictionary compare Gaelic racaid "noise, disturbance," but OED says this "is no doubt from Eng."
Meaning "dishonest activity" (1785) is perhaps an extended sense, from the notion of "something going on" or "noise or disturbance made to distract a pick-pocket's victim." Or it might be from racquet, via the notion of "a game," or from or reinforced by rack-rent "extortionate rent." There also was a verb racket "carry on eager or energetic action" (1753), and the gangster sense might be via the notion of "exciting and unusual." Weakened sense of "way of life, one's line of business" is by 1891.
late 14c., rendre, a legal term, "act of yielding, giving, or restoring; a return, a payment," especially of rent; see render (v.). Probably at least in part from French noun use of the infinitive.