ḱop-
“hoof, to strike”hoof, strike, stamp
Root for hooves/striking, yielding English hoof, Old English hof, Latin caper (goat).
Discussion
The PIE root *ḱop- (hoof, to strike with the hoof — extended to chopping, cutting with a blow) produced vocabulary connecting the horse's striking hoof to the human act of chopping and cutting.
English hoof (OE hōf, from PGmc *hōfaz) descends from this root — the hoof as "the striking thing," the hard part of the animal that strikes the ground. German Huf (hoof) confirms the Germanic cognate.
The related English chop (to strike with a blade, to cut with a blow) may connect through the "striking" sense, though the derivation is debated.
Greek kóptein (κόπτειν, "to strike, to cut, to chop") preserves the root in the Hellenic branch and gave English: comma (kómma, "a piece cut off" — the punctuation mark cuts the sentence), syncope (syn-kopē, "a cutting together" — the shortening of a word by cutting out a middle syllable, also a medical term for fainting), and the combining form -copt in Coptic (from Greek Aigýptios — the Copts as the native Egyptian people).
The root connects to the PIE horse vocabulary (*h₁éḱwos) through the striking hoof — the horse's most audible feature as it gallops. The sound of hoofbeats is the sound of *ḱop-.
Notes
Pokorny 530. English hoof, Latin capra, caper.