抡 specifically means to swing something heavy in a circular arc, like an axe, a hammer, or a fist. You would not use it for waving a hand; that is 挥. A separate literary reading lún means 'to select', but it does not appear in modern words.
Left hand radical anchors 抡 in the manual-action family, here a sweeping, swinging motion of the arm. Hand-radical verbs of large physical movement include 挥 (wave), 揍 (thrash), 挑 (carry). It specifically means to swing something heavy in a wide arc.
Right 仑 supplies the sound, lún shifting to lūn. It is simplified from a fuller form and is the phonetic shared by 论 (discuss), 轮 (wheel), 伦 (ethics). Here it works purely as a phonetic, lending no meaning to the swing action.
