1690s in the scientific use in mechanics, "product of the mass and velocity of a body; quantity of motion of a moving body," from Latin momentum "movement, moving power" (see moment). Figurative use, "force gained by movement, an impulse, impelling force," dates from 1782.
"the movement of small particles by some agency," from Greek phorēsis "a being carried," from pherein "to carry" (from PIE root *bher- (1) "to carry").
coined 1958 by San Francisco newspaper columnist Herb Caen during the heyday of -nik suffixes in the wake of Sputnik. From Beat generation (1952), associated with beat (n.) in its meaning "rhythm (especially in jazz)" as well as beat (adj.) "worn out, exhausted," and Century Dictionary (1902) has slang beat (n.) "a worthless, dishonest, shiftless fellow." Originator Jack Kerouac in 1958 connected it with beatitude.
The origins of the word beat are obscure, but the meaning is only too clear to most Americans. More than the feeling of weariness, it implies the feeling of having been used, of being raw. It involves a sort of nakedness of the mind. [New York Times Magazine, Oct. 2, 1952]
"Beat" is old carny slang. According to Beat Movement legend (and it is a movement with a deep inventory of legend), Ginsberg and Kerouac picked it up from a character named Herbert Huncke, a gay street hustler and drug addict from Chicago who began hanging around Times Square in 1939 (and who introduced William Burroughs to heroin, an important cultural moment). The term has nothing to do with music; it names the condition of being beaten down, poor, exhausted, at the bottom of the world. [Louis Menand, New Yorker, Oct. 1, 2007]