  We study the Pauli--Schr\"odinger equation in a uniformly rotating frame of
reference to describe a coupling of spins and mechanical rotations. The
explicit form of the spin-orbit interaction (SOI) with the inertial effects due
to the mechanical rotation is presented. We derive equations of motion for a
wavepacket of electrons in two-dimensional planes subject to the SOI. The
solution is a superposition of two cyclotron motions with different frequencies
and a circular spin current is created by the mechanical rotation.
