For all of Tolkien’s life, the Primitive Elvish root for “up” was √AM. Its best known derivatives are probably Q. ambo, S. amon “hill”. Tolkien introduced this root all the way back in the Qenya Lexicon of the 1910s, where Tolkien gave it as ᴱ√AM(U) “up(ward)” (QL/30). In The Etymologies of the 1930s it was ᴹ√AM “up” (Ety/AM²), and in 1967 notes Tolkien gave it as “AM, go up, especially of climbing” (PE17/157). In a separate set of notes on comparison from early 1967, Tolkien said:
But there existed a “base” that was intrinsically “comparative”, √AMA. This signified addition, increase, plus (PE17/91).
Tolkien did not explicitly connect this to √AM “up”, but it seems likely the two were related. See the discussion of √AMA for further details.
For most of Tolkien’s life, the Primitive Elvish root for “mother” was √AM. This began with the Qenya Lexicon of the 1910s, where Tolkien gave the root as ᴱ√AMA (QL/30). In The Etymologies of the 1930s it was ᴹ√AM with derivatives ᴹQ. amil and (archaic) N. emil “mother” (Ety/AM¹). In Quenya prayers of the 1950s, the word for mother was Q. Amille. In the last few years of his life, however, Tolkien toyed with the notion of changing this root to √EM. In notes associated with Eldarinwe Leperi are Notessi written in the late 1960s, Tolkien first gave the root as am, but then wrote em next to it with a question mark, along with several new em-derivatives (VT48/19 note #16). The Q. affectionate word emme for “mommy” appeared in the main article, indicating Tolkien did, in fact, adopt this new root, at least for some period of time.
Neo-Eldarin: For purposes of Neo-Quenya writing, I personally prefer to ignore this late change to the root for “mother” and stick with the √AM-forms Tolkien used for most of his life. However, the √AM-forms were less stable in the Sindarin branch of the languages, so I’d use √EM-forms like S. emel and emig, and would assume √AM and √EM were variants of the root, as they were on VT48/19 (see above).