This is considering an ideal scenraio where we have a 100% efficient motor at all RPMs.
If we start with $$\omega=\frac{P_{Mech}}{\tau}$$
Since the motor is provided with eletrical power, the mechanical power will be some multiple of this power. $$\omega=\frac{VI\eta}{\tau}$$ Now we let \$\eta=1\$ and notice that \$\frac{I}{\tau}=\frac{1}{k_{T}}\$ where \$k_{T} \$ is the torque constant. Therefore; $$\omega=\frac{V}{k_{T}}$$
So lets say we provide 5V and the no-load angular velocity is \$100 rad/sec\$. With this motor, according to the equation above the angular velocity should remain \$100 rad/sec\$ irrespective of the load we apply to the shaft of the motor. So the angular velocity of a 100% efficient motor is constant regardless of load applied?
Looking at the same equation but for a non-ideal motor; $$\omega=\frac{V\eta}{k_{T}}$$ At a constant voltage, when load torque is applied the efficiency decreases (Friction, internal power losses etc) which results in the decrease of angular velocity. But with no losses in electrical power this angular velocity should remain constant, right?