"tear apart," c. 1400, probably of North Sea Germanic origin (compare Flemish rippen "strip off roughly," Frisian rippe "to tear, rip") or else from a Scandinavian source (compare Swedish reppa, Danish rippe "to tear, rip"). In either case, from Proto-Germanic *rupjan-, from PIE root *reup-, *reub- "to snatch." Meaning "to slash open" is from 1570s. Related: Ripped; ripping.
In garments we rip along the line at which they were sewed ; we tear the texture of the cloth; we say, "It is not torn; it is only ripped." More broadly, rip, especially with up, stands for a cutting open or apart with a quick, deep strike: as, to rip up a body or a sack of meal. Rend implies great force or violence. [Century Dictionary]
Meaning "to move with slashing force" (1798) is the sense in let her rip, American English colloquial phrase attested from 1853. The noun is attested from 1711. The parachutist's rip cord (1911) originally was a device in ballooning to open a panel and release air.
"rough water," 1775, perhaps a special use of rip (v.). Originally of seas; application to rivers is from 1828.
"thing of little value," 1815, earlier "inferior or worn-out horse" (1778), perhaps altered from slang rep (1747) "man of loose character; vicious, reckless and worthless person," which itself is perhaps short for reprobate (n.).