1956, from Swedish (c.1952), from (trampcykel med) mo(tor och) ped(aler) "pedal cycle with engine and pedals" (the earliest versions had auxiliary pedals). Cf. obsolete English mo-bike (1925), from motor bicycle.
1560s, "to move and act unconsciously;" 1580s, "to be listless and apathetic," the sound of the word perhaps somehow suggestive of low feelings (cf. Low German mopen "to sulk," Dutch moppen "to grumble, to grouse," Danish maabe, dialectal Swedish mopa "to mope"). Related: Moped; moping; mopey; mopish.