  We investigate quantum sensing of rotation with a multi-atom Sagnac
interferometer and present multi-partite entangled states to enhance the
sensitivity of rotation frequency. For studying the sensitivity, we first
present a Hermitian generator with respect to the rotation frequency. The
generator, which contains the Sagnac phase, is a linear superposition of a z
component of the collective spin and a quadrature operator of collective bosons
depicting the trapping modes, which enables us to conveniently study the
quantum Fisher information (QFI) for any initial states. With the generator, we
derive the general QFI which can be of square dependence on the particle
number, leading to Heisenberg limit. And we further find that the QFI may be of
biquadratic dependence on the radius of the ring which confines atoms,
indicating that larger QFI is achieved by enlarging the radius. In order to
obtain the square and biquadratic dependence, we propose to use partially and
globally entangled states as inputs to enhance the sensitivity of rotation.
