What is the difference between impel and compel?
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To me, impel has a sense of motion/pushing, while compel is more of an obligation. Think of impulse vs. compulsion.
There's also a difference in origin: with impel, the primary force comes from within the object (albeit in response to an outside impetus), while compel comes from outside and acts on the object. I can compel you to do something, but I can only cause you to feel impelled. Or something like that.
To impel is to push someone or something forward, while to compel is to force someone to do something. The difference is subtle, but usually compel carries a connotation of coercion or obligation. Impel has its roots in the Latin word for "to push forward", while compel comes from that for "to drive together".