  We construct a cosmological model based on a free particle model which is
constrained on an embedded toroidal brane, with a general rotation around a
specific axis in the bulk space. Some related issues such as the rotation axis
of the brane, the presence of gravitomagnetic background and its relation to
the general angular velocity of the brane, and its quantum mechanics and
related issues such as minimal length and minimal momentum of the quantum model
in the $\mathbb{T}^3$ brane are studied. Also, some cosmological features such
as the constraint which is imposed upon the toroidal universe by the isotropy
and homogeneity conditions, the corresponding Hubble law, and accelerating
expansion for the spinning toroidal model without considering a cosmological
constant are also studied.
