Etymology
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motorcycle (n.)

"a large bicycle propelled by a small motor," 1895, a hybrid from motor + -cycle, from bicycle. Motocycle also was used late 19c.

The horse follows the crooks of a country road, but then the training of the "motorcycle" (horrid name) will inevitably straighten out the crooks in the country road, and afford long ranges of straight tracks. [Payson Burleigh, "The Age of Steel," Oct. 12, 1895]

Related: Motorcyclist.

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motocross 

also moto-cross, "cross-country motorcycle racing," by 1956, from motorcycle + cross-country.

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biker (n.)
"motorcycle rider" (especially with reference to club affiliation), 1968, American English, from bike (n.) in its slang sense of "motorcycle" (1939). An Australian equivalent was bikie.
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motor-bike (n.)

also motorbike, "motorcycle," 1903, from motor (n.) + bike (n.).

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Harley 
surname attested from mid-12c., literally "dweller at the hares' wood." Harley Street in London from the 1830s was associated with eminent physicians and used metonymically for "medical specialists collectively." As a type of motorcycle, by 1968, short for Harley-Davidson, the motorcycle manufacturer founded in Milwaukee, Wisconsin, U.S., 1905 by engine designer William S. Harley (1880-1943) and Arthur Davidson.
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Hells Angels (n.)
motorcycle club, the name first attested 1957. They were called Black Rebels in the 1954 film "The Wild One." Earlier Hell's Angels had been used as the title of a film about World War I air combat (1930).
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kick-start (v.)

1919 (implied in kick-starter), "method of starting an internal combustion engine (of a motorcycle) by pushing down a lever with the foot," from kick (n.) + start (n.). Figurative sense of "take a course of action that will quickly start a process" is by 1995.

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chopper (n.)
1550s, "one who chops," agent noun from chop (v.1). Meaning "meat cleaver" is by 1818. Meaning "helicopter" is from 1951, Korean War military slang (compare egg-beater); as a type of stripped-down motorcycle (originally preferred by Hells Angels) from 1965.
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peel (v.)

"to strip off" the skin, bark, or rind from, developed from Old English pilian "to peel, skin, decorticate, strip the skin or ring," and Old French pillier, both from Latin pilare "to strip of hair," from pilus "hair" (see pile (n.3)). Probably also influenced by Latin pellis "skin, hide." Related: Peeled; peeling. Intransitive sense of "to lose the skin or rind" is from 1630s.

The figurative expression keep (one's) eyes peeled "be observant, be on the alert" is by 1852, American English, perhaps a play on the potato "eye," which is peeled by stripping off the skin. Peel out "speed away from a place in a car, on a motorcycle, etc.," is hot-rodders' slang, attested by 1952, perhaps from the notion of leaving behind a "peel" of rubber from the tire as it skids. Aircraft pilot phrase peel off "veer away from formation" is from World War II; earlier American English had slang peel it "run away at full speed" (1860). 

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cycle (n.)

late 14c., cicle, "perpetual circulating period of time, on the completion of which certain phenomena return in the same order," especially and originally in reference to astronomical phenomena, from Old French cicle and directly from Late Latin cyclus, from Greek kyklos "circle, wheel, any circular body," also "circular motion, cycle of events," from PIE kw(e)-kwl-o-, a suffixed, reduplicated form of the root *kwel- (1) "to revolve, move round."

From 1660s as "any recurring round of operations or events" (as in life cycle). From 1821 as "single complete period in a cycle." Extended by 1842 to "any long period of years, an age." In literary use, "the aggregate of the legends or traditions around some real or mythical event or character" (1835).

By 1884 as "recurring series of oscillations or operations in an engine, etc." From 1870 as short for motorcycle; by 1881 as short for bicycle or tricycle.

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