  In this paper, we first investigate some aspects of frame dragging in strong
gravity. The computations are carried out for the Kerr black hole and for the
rotating Janis-Newman-Winicour solution, that is known to have a naked
singularity on a surface at a finite radius. For the Kerr metric, a few
interesting possibilities of gyroscope precession frequency, as measured by a
Copernican observer outside the ergoregion, are pointed out. It is shown that
for certain angular velocities of a stationary observer, this frequency might
vanish exactly, close to the ergoregion. Similar computations are repeated for
static observers in the naked singularity background, and strong enhancement of
the Lense-Thirring precession frequency compared to the black hole case is
established. Then, we study the nature of tidal forces in the rotating naked
singularity background, in Fermi normal coordinates. Here, physical quantities
characterizing tidal disruptions of celestial objects in equatorial circular
orbits are computed numerically. Our results here indicate that there might be
significant deviations from corresponding Kerr black hole calculations, up to
the level of approximation that we consider.
