To convince is to bring someone around to your point of view: Leon convinced Joyce that he was right.
To persuade is to talk someone into doing something: Leon persuaded Joyce to trim the hedge his way.
(Convince and persuade have been misused as synonyms for so long that many dictionaries now consider them real synonyms, but the precise writer appreciates and honours the difference.)
To be compelling is to be gripping and persuasive: She wrote a compelling story.
To be compulsive is to act in a driven manner, as though unable to stop oneself: At the start of each new novel, she wrote compulsively.
To be compulsory is to be required by rule or law: Attendance is compulsory.
Wait is an intransitive verb: Jonah had to wait for the bus for nearly an hour. Await is a transitive verb: “Mr. Bus,” Jonah muttered, “I await you!” A disinterested person is impartial: They invited a disinterested third party to make the decision. An uninterested person is not interested: They appealed to their boss, but he was uninterested.
Farther refers to literal distance: India is farther away from Vancouver than China.
Further means “additional”: Let’s not try to extend this metaphor any further.
Well . . . officially further and farther are synonymous. But the distinction shown above is becoming the convention in North American usage guides.