  We report direct observation of gyromagnetic reversal, which is the sign
change of gyromagnetic ratio in a ferrimagnet Ho$_3$Fe$_5$O$_{12}$, by using
the Barnett effect measurement technique at low temperatures. The Barnett
effect is a phenomenon in which magnetization is induced by mechanical rotation
through the coupling between rotation and total angular momentum $J$ of
electrons. The magnetization of Ho$_3$Fe$_5$O$_{12}$ induced by mechanical
rotation disappears at 135~K and 240~K. The temperatures correspond to the
magnetization compensation temperature $T_{\rm M}$ and the angular momentum
compensation temperature $T_{\rm A}$, respectively. Between $T_{\rm M}$ and
$T_{\rm A}$, the magnetization flips over to be parallel against the angular
momentum due to the sign change of gyromagnetic ratio. This study provides an
unprecedented technique to explore the gyromagnetic properties.
