  We demonstrate that the angular momentum compensation temperature $T_A$, at
which the net angular momentum in the sample disappears, can be controlled in
Ho$_3$Fe$_5$O$_{12}$ by partially substituting Dy for Ho. The $T_A$ can be
detected using the Barnett effect, by which mechanical rotation magnetizes an
object due to spin-rotation coupling. We found that $T_A$ increases with the Dy
content and clarified that the $T_A$ of Ho$_{1.5}$Dy$_{1.5}$Fe$_5$O$_{12}$
coincides with room temperature. The Barnett effect enables us to explore
materials applicable to magnetic devices utilizing the angular momentum
compensation only by rotating the powder sample at room temperature.
