newtonian mechanics - torque in zero gravity

Possibly that's a duplicate.

Say we have two drums $A$ and $B$ in a zero gravity with moments of inertia $J_a$ and $J_b$ respectively, placed on a same axis, running through their centers of mass. Drum $A$ contains a motor, which applies torque $T$ to drum $B$. How $\dot \omega_a$ and $\dot \omega_b$ are related to $T$? I understand that

$J_a \omega_a + J_b \omega_b=0$ (conservation of angular momentum)

and

$J_a \dot \omega_a + J_b \dot \omega_b = 0$ (Newton's second and third laws).

but what about $J_a \dot \omega_a - J_b \dot \omega_b$ ? Does it equal to $T$ or $2T$ or what? How $T$ is distributed over these two drums?