What word or phrase does your mother always say?
"upper limb," Old English earm "arm," from Proto-Germanic *armaz (cf. Old Saxon, Danish, Swedish, Middle Dutch, German arm, Old Norse armr, Old Frisian erm), from PIE root *ar- "fit, join" (cf. Sanskrit irmah "arm," Armenian armukn "elbow," Old Prussian irmo "arm," Greek arthron "a joint," Latin armus "shoulder"). Arm of the sea was in Old English. Arm-twister "powerful persuader" is from 1938. Arm-wrestling is from 1899.
They wenten arme in arme yfere Into the gardyn [Chaucer]
"weapon," c.1300, armes (plural) "weapons of a warrior," from Old French armes (plural), "arms, war, warfare," mid-13c., from Latin arma "weapons" (including armor), literally "tools, implements (of war)," from PIE root *ar- "fit, join" (see arm (n.1)). The notion seems to be "that which is fitted together." Meaning "heraldic insignia" (in coat of arms, etc.) is early 14c.; originally they were borne on shields of fully armed knights or barons.
arm 1 (ärm)
An upper limb of the human body, connecting the hand and wrist to the shoulder.
used to denote power (Ps. 10:15; Ezek. 30:21; Jer. 48:25). It is also used of the omnipotence of God (Ex. 15:16; Ps. 89:13; 98:1; 77:15; Isa. 53:1; John 12:38; Acts 13:17)