Etymology
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rolling 

14c. as a present-participle adjective from roll (v.), "that turns over and over, moving by means of rolling." The meaning "moving on wheels or as if on wheels" is by 1560s. Of thunder, etc., "making continuous noise," 1650s. The sense of "waving, undulating," of prairie land, etc., is from 1819. The meaning "staggered, rotating," of strikes, blackouts, etc., is by 1961.

From mid-15c. as a verbal noun. Rolling-pin "cylindrical piece of wood, etc., with a handle at each end, with which dough, etc. are reduced to proper thickness," is recorded from late 15c. Rolling-paper for cigarettes, etc., is by 1969. Rolling stock "wheeled vehicles on a railroad" (locomotives, carriages, etc.) is by 1853.

The rollyng stone neuer gatherth mosse. [John Heywood, "A dialogue conteinying the nomber in effect of all the proverbes in the Englishe tongue," 1546]

Hence figurative use of rolling stone, of persons, "a rambler, a wanderer" (1610s).

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log-rolling (n.)

also logrolling, in the legislative vote-trading sense, "mutual aid given in carrying out several schemes or gaining individual ends," 1823, American English, from the notion of neighbors on the frontier joining forces for rolling logs into heaps after the trees have been felled to clear the land (as in phrase you roll my log and I'll roll yours); see log (n.1) + verbal noun from roll (v.). "Sometimes many neighbors were invited to assist, and a merrymaking followed. [Century Dictionary]. In lumbering, in reference to rolling logs into a stream where they bound together and floated down to the mills.

LOG-ROLLING. 1. In the lumber regions of Maine it is customary for men of different logging camps to appoint days for helping each other in rolling the logs to the river, after they are felled and trimmed — this rolling being about the hardest work incident to the business. Thus the men of three or four camps will unite, say on Monday, to roll for camp No. 1, — on Tuesday for camp No. 2, — on Wednesday for camp No. 3, — and so on, through the whole number of camps within convenient distance of each other. [Bartlett]

However the phrase is not attested in any literal sense, only the political sense, until 1848.

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roll (v.)

early 14c., rollen, "turn over and over, move by rotating" (intransitive); late 14c. in the transitive sense of "move (something) by turning it over and over;" from Old French roeller "roll, wheel round" (Modern French rouler), from Medieval Latin rotulare, from Latin rotula, diminutive of rota "wheel" (see rotary). Related: Rolled; rolling.

From c. 1400 as "wrap or cover by rolling or enclosing" in something, also "wrap round and round an axis;" early 15c. as "press or level with a roller." From 1510s as "to move or travel on wheels or by means of rolling." Of sounds (such as thunder) somehow suggestive of a rolling ball, 1590s; of a drum from 1680s.

Of spoken sounds, "to utter with vibrations of the tongue," by 1846. Of eyes, from late 14c. (rolle his eyne), originally suggestive of ferocity or madness. Of a movie camera, "to start filming," from 1938. Sense of "rob a stuporous drunk" is by 1873, from the action required to get to his pockets. To roll up "gather, congregate" is from 1861, originally Australian. To roll with the punches is a metaphor from boxing (1940). To roll them bones was old slang for "play at dice" (1929). Heads will roll is a Hitlerism:

If our movement is victorious there will be a revolutionary tribunal which will punish the crimes of November 1918. Then decapitated heads will roll in the sand. [1930]
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rofl (interj.)

by 1993, online chat abbreviation for rolling on the floor laughing.

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Rolodex (n.)
1958, said to be from rolling + index.
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malleability (n.)

"capability of being shaped or stretched by pressure," especially by beating or rolling, 1680s, from malleable + -ity.

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log-roll (v.)
also logroll, 1835, a back-formation from log-rolling.
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roll (n.2)

1743, "act of rolling," from roll (v.). By 1836 as "a rolling gait or motion." From 1680s as "a rapid, uniform beating" (on a drum). The slang meaning "act of sexual intercourse" is attested from 1942 (compare roll in the hay). By 1862 as "an act of rotation." The sense of "a throw" (at dice) is attested by 1926. The colloquial expression on a roll for "enjoying a run of success" is by 1976.

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barrel (v.)
mid-15c., "to put in barrels," from barrel (n.). Meaning "to move quickly" is 1930, American English slang, perhaps suggestive of a rolling barrel. Related: Barreled; barreling.
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rollback (n.)

also roll-back; 1937 as "action of rolling backward;" 1942, American English, as "a reduction" in prices, etc., a journalist's and advertiser's word, from the verbal phrase; see roll (v.) + back (adv.).

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