Gears A$,$ B$,$ and C have masses $\backslash (1\backslash$mathrm$\{$~kg$\},4,\backslash$mathrm$\{$~kg$\}\backslash ),$ and $9$ kg $,$ and radii of gyration $\backslash (30\backslash$mathrm$\{$~mm$\},75\backslash$mathrm$\{$~mm$\}\backslash ),$ and $100$ mm $,$ respectively. The gears are initially at rest when a constant clockwise torque of magnitude $4$ N m is applied to gear C $.$ If the gears move without slipping, how many revolutions does gear A make before it reaches an angular velocity of $300$ rpm $?$