nap (n.1)
"downy surface of cloth," mid-15c., from Middle Dutch or Middle Low German noppe "nap, tuft of wool," probably introduced by Flemish cloth-workers. Cognate with Old English hnoppian "to pluck," ahneopan "pluck off," Old Swedish niupa "to pinch," Gothic dis-hniupan "to tear."
nap (v.1)
Old English hnappian "to doze, sleep lightly," of unknown origin, apparently related to Old High German hnaffezan, German dialectal nafzen, Norwegian napp. Related: Napped; napping.
nap (v.2)
"to furnish with a nap, raise the nap of," 1610s, from nap (n.1).
nap (n.2)
"short spell of sleep," c. 1300, from nap (v.). With take (v.) from c. 1400.