= Mass-loaded rotation
{title2=$I\dot\omega=\dot L_{\rm in}-\omega\dot I+\tau_{\rm ext}$}
When material sticks to a rotor, the incoming <angular momentum> flux $\dot L_{\rm in}$ and external <torque> $\tau_{\rm ext}$ obey $d(I\omega)/dt=\dot L_{\rm in}+\tau_{\rm ext}$. With zero incoming axial <angular momentum> and zero external axial <torque>, $I\omega$ is constant. For deposition at fixed radius $a$ at <mass flow rate> $\alpha$, $\dot I=\alpha a^2$ and the <rotational kinetic energy> satisfies $\dot K=-\alpha a^2\omega^2/2$. This loss is the irreversible cost of bringing the incoming material up to tangential <speed>; it does not violate <conservation of angular momentum>.
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