balai

The base finally arrives. When balailo landed at rank 2,367, its page had to explain the word with half of it missing: -il- is the tool suffix, bala- is to sweep, and the verb had no page here yet. It does now, five hundred ranks later. This is the ordinary shape of a frequency-ordered course - people say broom more often than they say sweep - and it is worth noticing when it happens, because the derived word is very often the commoner one and you end up working backwards to the machinery.

So, closing the loop: balai is the verb, balailo is the sweeping-tool, and the suffix in between is the most reliable one in the language.

Watch the vowels, in both words. Bala-i is three syllables: ba-LA-i. The ai is not a diphthong. Esperanto has exactly two of those, aŭ and eŭ, and ai is not among them, so the a and the i are pronounced separately every time. That carries through the whole paradigm: balaas is four syllables, balaita four, and balailo four again, ba-la-i-lo. Learners who have just got aŭto right routinely compress this one by mistake.

Transitive, and it takes what gets swept. Balai la plankon, balai la straton, balai la neĝon de la ŝtupoj. The figurative sense is as free as in English: forbalai is to sweep away, and an Esperanto newspaper will forbalai a government or an objection with no more ceremony than an English one.

The rest of the cleaning cupboard. Balaaĵo is the sweepings, the polvo and rubbish you gather up. Balaisto is a road sweeper. Balailtenilo is the broom handle if you really need it by itself, though tenilo de la balailo is what anyone would say. And the witch flies on a plain balailo, because Esperanto saw no reason to invent a separate word for a broomstick.