At the core is plain wanting (לִרְצוֹת). From it the root fans out in two directions. As a noun it becomes will, desire, intent (רָצוֹן); as an adjective it becomes what is wanted, desirable, welcome (רָצוּי). The pi'el and hif'il twist the want into action: making someone content (placating, satisfying) and, oddly, lecturing. This is a final-ה (lamed-he) root, so the third letter softens to a vowel in many forms; the want is still there under the surface. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
The pi'el לְרַצּוֹת means "to make someone content" (placate, satisfy), and from "satisfying the sentence" it also came to mean serving prison time. The hif'il לְהַרְצוֹת drifted semantically to "lecture". The passive partners pu'al and huf'al exist in the system but are not lexicalized here, which is normal: not every root fills all seven binyanim.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.