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A shunt-connected $DC$ motor operates at its rated terminal voltage. Its no-load speed is $200$ radian/second. At its rated torque of $500$ Nm, its speed is $180$ radian/second. The motor is used to directly drive a load whose load torque $T_{L}$ depends on its rotational speed $\omega _{r}$ (in radian/second), such that $T_{L}=2.78 \times \omega _{r}$. Neglecting rotational losses, the steady-state speed (in radian/second) of the motor, when it drives this load, is _________.
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