'Shear' is PIE *sker- (to cut) — kin to 'share,' 'shirt,' 'skirt,' 'short,' and 'score.'
To cut the wool off a sheep; to cut something with shears; a strain produced by pressure in the structure of a substance.
From Old English 'sceran' (to cut, to shear, to clip), from Proto-Germanic *skeraną (to cut), from PIE *(s)ker- (to cut). This prolific PIE root produced one of the largest word-families in English: 'shear,' 'share' (originally a ploughshare — a cutting implement), 'sheer' (cut away, hence thin, pure), 'shirt' and 'skirt' (both from 'a cut piece' of fabric — the same word split by dialect, shirt from Old English and skirt from Old Norse), 'shore' (the land cut off by water), 'short' (cut off), 'score' (a cut, a notch for counting), 'scar,' 'scour,' and 'scrub.' The same