  We study the amplification of rotation velocity with the Sagnac
interferometer based on the concept of weak-value amplification. By using a
different scheme to perform the Sagnac interferometer with the probe in
momentum space, we have demonstrated the new weak measure protocol to detect
the small rotation velocity by amplifying the phase shift of the Sagnac effect.
At the given the maximum incident intensity of the initial spectrum, the
detection limit of the intensity of the spectrometer and the accuracy of
angular velocity measurement, we can theoretical give the appropriate
potselection and the minimum of optical path area before experiment. In
addition, we put forward a new optical design to increase the optical path area
and decrease the size of the interferometer to overcome the limit of instrument
size. Finally, our modified Sagnac's interferometer based on weak measurement
is innovative and efficient probing the small rotation velocity signal.
