Yes, there are rules defining the usage of the words of the day, but they are quite simple.
Rule 1: The word must be used in the period specified.
i.e the word for period 3 must be used in period 3.
Rule 2: The word must be spoken directly to a teacher, in full view and hearing range of the class and the teacher.
i.e. You cannot mutter the word of the day so that no one can hear it.
Rule 3: The word must be used within a contextual sentence.
i.e. you cannot for example say: If the issue were to flies (Word of the day)... sorry arise...
Rule 4: You cannot structure a conversation with the expressed purpose of bringing up the word of the day, it must be spontaneous.
i.e. You cannot start a conversation about flatulence, so that you can use the word diarrhea (word of the day).
Rule 5: You may not let any teachers know about word of the day.
Seriously, just don't.