This root and ones like it were used for “high” things for much of Tolkien’s life. It first appeared as unglossed ᴱ√TAHA in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. tā “high; high above, high up”, ᴱQ. tahōra or tayóra “lofty”, and ᴱQ. tāri “queen”; it had a variant form ᴱ√TAʕA where the ʕ might be a malformed Y (QL/87). The corresponding forms in the contemporaneous Gnomish Lexicon were G. dâ “high” and G. dara “lofty” (GL/29), indicating the true form of the root was ᴱ√DAHA, since initial voiced stops were unvoiced (d- > t-) in Early Qenya (PE12/17). Primitive forms like ᴱ✶dagá > ᴱN. dâ/ᴱQ. tá “high” in Early Noldorin Word-lists of the 1920s indicates the root continued to begin with D for the following decade (PE13/141, 161).
In The Etymologies of the 1930s Tolkien gave this root as ᴹ√TĀ/TAƷ “high, lofty; noble” with derivatives like ᴹQ. tára “lofty, high”, ᴹQ. tári “queen” and N. taen “height, summit of high mountain” (Ety/TĀ). In Definitive Linguistic Notes (DLN) from 1959 Tolkien gave the root as √TAG or Tā- “high”, and in notes from around 1967 Tolkien gave √TAƷ as the explanation of the initial element of Q. Taniquetil and contrasted it with √TĂR “stand” (PE17/186). In 1970 green-ink revisions to the Outline of Phonology (OP2), Tolkien wrote a marginal note giving √TAƷ > TĀ “high”, but this note was rejected with a statement “transfer to Gen. Structure. No [ʒ] existed in Eldarin” (PE19/72-73 note #22).
This last rejection seems to be part of Tolkien’s general vacillation on the nature and phonetic evolution of velar spirants in Primitive Elvish in 1968-70. For purposes of Neo-Eldarin, I would assume the root form was √TAH or √TAƷ > √TĀ as the basis for “high” words, much like √MAH or √MAƷ > ✶mā was the basis for “hand” words.
This root was the basis for Elvish words having to do with “running” and (in earlier notes) “rolling” for much of Tolkien’s life. It first appeared as ᴱ√NORO “run, go smoothly, ride, spin” in the Qenya Lexicon of the 1910s (QL/67), and it had derivatives in the contemporaneous Gnomish Lexicon such as G. nor- “run, roll” (GL/61) and dronn “race, course, track” < ✱n’rond- (GL/31). ᴹ√NORO “run as of wheels, roll along” reappeared in a page of roots in the Quenya Verbal System (QVS) from 1948, though this page was deleted (PE22/127 note #152). √NOR “run (or leap: of animals, men etc.)” also appeared in some etymological notes associated with The Lord of the Rings, probably from the late 1950s (PE17/168).
Neo-Eldarin: For purposes of Neo-Eldarin, I’d retain both senses “run” and “roll” for this root, but limit the latter to the rolling of wheels as an extrapolation from the movement of legs.