  The dynamics of critical slope self-organized critical models is studied,
using a previous mapping into a linear interface depinning model dragged at one
end. The model is solved obtaining the complete set of scaling exponents. Some
results are supported by previous RG developed for constant force linear
interface depinning models but others, like the linear dependency of the
susceptibility with system size, are intrinsic of this model which belongs to a
different universality class. The comparison of our results with numerical
simulations of ricepile and vortexpile models reported in the literature
reveals that, as in the constant force case, there are two universality classes
corresponding to random and periodic pinning.
