balailo

Decode it. Balai, which arrives at rank 2,876 in the last chapter, is the verb to sweep. -Il- is the tool suffix, one of the most reliable in the language: the tool for doing X is X-ilo. So balailo is the sweeping-tool, the broom. You have met the pattern already in kombilo (a comb, from kombi, to comb), tranĉilo (a knife, from tranĉi, to cut), ŝlosilo (a key, from ŝlosi, to lock) and manĝilaro (cutlery, the collection of eating-tools). Once -il- is in your hands, a large slice of the household vocabulary stops being vocabulary.

Watch the double vowel. The root ends in -ai and the suffix begins with -il, so the word is bal-a-i-l-o, four syllables, with the a and the i pronounced separately: ba-la-i-lo. It is not a diphthong, and it is not ŭ. Learners who have just internalised aŭ as one sound routinely compress this one by mistake.

The rest of the cleaning cupboard. Balai la plankon is to sweep the floor; balaaĵo is the sweepings, the dust and rubbish you gather up; balaisto is a road sweeper; and forbalai is to sweep away, used as freely in the figurative sense as English does with a government or an objection.

And the flying kind. Esperanto keeps the same word for the witch's broomstick, so sorĉistino sur balailo needs no special term. Balailtenilo exists if you really need the handle by itself, though tenilo de la balailo is what anyone would actually say.