 Constant-power rotation against dry friction

For positive angular velocity, a motor delivering constant mechanical power $P$ produces torque $P/\omega$. With constant opposing kinetic friction torque ${\tau }_f$, angular momentum balance gives the displayed equation and a steady speed ${\omega }_{\ast }=P/{\tau }_f$. A small increase in speed reduces the driving torque below the friction torque, making this equilibrium stable within the model. The constant-power idealization is singular at exact rest and requires a separate starting regime in a real motor.