Calculating omega (ω) in a separately excited DC motor
The applied field voltage for a separately excited motor is held constant while Va is changed. So you can use If = Vf/Rf to calculate flux. Then use the equation for torque in terms of flux and Ia to calculate Ia in terms of torque and flux. Substitute that for Ia in the equation for omega in terms of Torque and Va. Divide the torque terms in the numerator by the torque in the denominator and the equation for omega will be in the desired form.