To expand on Jerry's comment a bit, there is a review article that describes the underlying physics here (caution PDF). The article is based on R. M. Wald's paper Gedanken experiments to destroy a black hole, Ann. Physics 82 548-556, though the paper is behind a paywall so that's not much use unless your college has access. The article actually describes a Kerr-Newman black hole, where the infalling particle can be charged and the attempt to create a naked singularity is to both increase the angular momentum and the charge.
As I'm sure you'd have guessed, the calculation is involved, but basically Wald concludes that you can't add enough charge because the field of the Kerr-Newman black hole ends up repelling your charged particle. You can't add enough angular momentum because the extra angular momentum stops the particle falling through the horizon.
This post imported from StackExchange Physics at 2014-05-04 11:16 (UCT), posted by SE-user John Rennie