tear and rip are used interchangeably. tear is often used for fabric, and rip is often used for paper (ripping the pages out of something). actually, come to think of it, so is tear. you can say either.
but i cannot think of any cases where you should use one or the other - you can choose either.
there are other, more specific uses of these words that may require using one - this is by convention. for example, "to rip a CD" is sort of slang for making a digital copy of a CD.
but in the root sense, if you ask a native speaker to tell you the meaning of "rip" the first word they will say is "to tear", and if you ask them the meaning of "tear" the first thing they will say is "to rip" :)
(remember that there is another word also spelled "tear" but pronounced "teer" - a homonym).