The root for “head” was established very early in Tolkien’s Elvish languages, appearing in the Qenya Lexicon of the 1910s as ᴱ√KASA “head” (QL/45), though in this period its Qenya derivative was ᴱQ. kar (kas-) because [[eq|final [s] became [r]]] in Early Quenya (PE12/26). It had derivatives in the contemporaneous Gnomish Lexicon such as G. cas “head, skull” (GL/25), a word that reappeared in Early Noldorin word lists of the 1920s as ᴱN. cas “skull” (PE13/140).
The root ᴹ√KAS “head” reappeared in The Etymologies of the 1930s, still with the form ᴹQ. kár (kas-) “head” (Ety/KAS), but Tolkien eventually abandoned the Early Qenya phonology and the Quenya form became Q. kas after some vacillation (PE19/103). The root √KAS “head” continued to appear frequently in Tolkien’s later writing (PE17/114; PE21/70; VT42/12).
Tolkien introduced the root √KAR with the sense “do, make” very early, and it retained this form and meaning for his entire life. It appeared as ᴱ√KARA “do, make” in the Qenya Lexicon of the 1910s (QL/45), as ᴹ√KAR “make, build, construct” in The Etymologies of the 1930s (Ety/KAR), and in numerous other places in various notes, including a last known appearance in verbal notes from 1969 as √KAR “do” (PE22/155). Though its exact set of derivatives varied over time, the root itself was extremely stable in Tolkien’s mind.