This invertible root and ones like it were the basis for “away” words for much of Tolkien’s life. The earliest iteration was ᴱ√AVA “go away, depart, leave” in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. au “away from” and ᴱQ. avanwa “going, passing, nearly gone” (QL/33). This early root remanifested as ᴹ√AB “go away, depart, leave” in The Etymologies of the 1930s, but the gloss of that root was revised to “refuse, deny” (Ety/AB). As a replacement, Tolkien introduced ᴹ√AWA “away, forth; out” with derivatives like ᴹQ. ava “outside”; Tolkien also considered deriving a privative prefix ᴹQ. ava- from this root (Ety/AWA).
The root √AWA was mentioned many times in Tolkien’s later writings, along with its inverted variant √WĀ, usually with the sense “away (from)” or a verbal sense “go (away), depart, pass away”. Its most detailed description appeared in the Quendi and Eldar essay of 1959-60, where Tolkien said:
> The element ✱AWA ... referred to movement away, viewed from the point of view of the thing, person, or place left. As a prefix it had probably already developed in CE the form ✱au-. The form ✱awa was originally an independent adverbial form, but appears to have been also used as a prefix (as an intensive form of ✱awa-, ✱au-). The form ✱wā- was probably originally used as a verbal stem, and possibly also in composition with verbal stems (WJ/361).
In this same document Tolkien said of Sindarin that:
> The only normal derivative [of √AWA] is the preposition o, the usual word for “from, of”. None of the forms of the element ✱awa are found as a prefix in S, probably because they became like or the same as the products of ✱wō, ✱wo (WJ/366).
Indeed, most of the attested derivatives of this root are in Quenya, but there are a couple in Sindarin, such as the aforementioned S. o, as well S. gwanwen “departed” (WJ/378) and the verb S. gwae- “go”, probably only in the limited sense “depart” (PE17/148).
In late notes from 1969 Tolkien gave the root √AWA the sense “before or ago (of time)” (PE22/167 note #117; PE22/168), but I suspect this was a transient idea.