cleave vs tear

cleave is not a noun while tear is a noun.

Word	Noun	Adjective	Verb	Adverb
cleave	No	No	Yes	No
tear	Yes	No	Yes	No

As verbs, tear is a hypernym of cleave; that is, tear is a word with a broader meaning than cleave:

cleave (noun)	tear (noun)
	a drop of the clear salty saline solution secreted by the lacrimal glands
	the act of tearing
	an occasion for excessive eating or drinking
	an opening made forcibly as by pulling apart

cleave (verb)	tear (verb)
separate or cut with a tool, such as a sharp instrument	separate or cause to separate abruptly
make by cutting into	to separate or be separated by force
come or be in close contact with; stick or hold together and resist separation	strip of feathers
	move quickly and violently
	fill with tears or shed tears