  The problem of the speed of the objects inside the Schwarzschild black hole
is considered. The general result is that the value of the relative speed of
the objects following their non-zero angular momentum trajectories, both of
geodesic and non-geodesic character, when approaching the ultimate singularity,
tends to the value of speed of light. There is only one exception when both
objects move in the same plane and have parallel angular momenta. This outcome
appears to have a deeper sense: it reflects the anisotropic character of the
dynamics of interior of this particular black hole. The result in question
means that near the singularity, collisions of two particles lead to an
indefinitely large energy in the center of mass frame. Aforementioned
properties have their counterpart in the phenomenon of an indefinitely large
blueshift near the singularity. Thus the angular momentum of a particle turns
out to be an important feature that affects the final behavior of particle near
the singularity. Motivated by this fact, we generalize the Lema\^{\i}tre frame
under the horizon in such a way that reference particles themselves have
nonzero angular momentum. Our results apply not only to the Schwarzschild
singularity but also to other space-like ones for which the scale factor
$g\rightarrow \infty $. We also analyze another type of singulairites for which
the circumference radius vanishes but $g$ remains finite.
