  When two particles collide at the horizon of a black hole and one of them
satisfies some critical conditions, the relative velocity between them can be
arbitrarily large, thus the energy of the center-of-mass will reach infinity.
Such a process is called BSW mechanism which can accelerate a particle to
arbitrarily high energy. There are also some studies showing that a Kerr naked
singularity can be more qualified as a particle accelerator for arbitrarily
high energy. Previous researchers mainly concentrate on geodesic motion of
particles. In this paper, we will take spinning particles which won't move
along a timelike geodesic and carry more parameters into our consideration. By
employing the Mathisson-Papapetrou-Dixon equation, we will prove that for a
spinning particle in hyper-extremal Reissner-Nordstrom or Kerr spacetime where
exists a naked singularity at $r=0$, its Effective Potential
$V_{eff}=-\dot{r}^2$ must be able to reach zero within the interval $0 < r <
M$, thus an ingoing particle will be able to turn back and then collide with
another ingoing particle at $r=M$. If the spacetime is ${\bf slightly}$
hyper-extremal, the energy of center of mass $E_{cm}$ will be arbitrarily high.
