''Rotosphere'', where the component of 4-acceleration, radial relative
to the symmetry axis, of the stationary observer depends on his angul
ar velocity in a way going against our intuition, is demarcated in the
Kerr spacetime. Stationary observers with extremal value of this acce
leration (''extremally accelerated observers'') are introduced and the
ir privileged relation to circular geodesics in the equatorial plane i
s found. Possible translation of the results into ''force'' language i
s based on the definition of the ''centrifugal force'' with respect to
the zero-angular-momentum observers. It yields, in particular, a simp
le interpretation of the behaviour of acceleration of the stationary o
bserver in terms of gravitational, Coriolis and centrifugal forces.