Nonuniform Circular Motion

This might be an easy problem, but I am missing something and am not sure where to start so here is the problem:

A student ties a 500g rock to a 1.0-m-long string and swings it around her head in a horizontal circle. At what angular velocity, does the string tilt down at a 10 degree angle?

If anyone can help me get going on this problem I would greatly appreciate it.
 Have you thought about the problem? Please show us what you have done. Begin with a free-body diagram and the formula $$F_{centripetal}=\frac{mv^{2}}{r}$$