There are two parts that go into equilibrium in a motor: There is electrical balance and there is mechanical balance.

Electrically the voltage connected to the motor equals the counter emf and the losses because of the resistance of the armature on a DC motor (or the voltage drop because of the AC impedance on an AC motor). Let's ignore for a bit any losses on the rotor, if there are. You can think of a motor as a 'transformer', it reflects in its 'primary' a voltage drop which is proportional to the mechanical torque it is delivering in its 'secondary'.

Mechanically the rotational force provided by the motor must overcome the mechanical load and the losses (friction, etc.). As in linear movement we have the mass, for rotational movement we have the moment which is the product of mass by rotational speed. As a mass tends to keep its linear movement status, a load tries to keep its rotational status. When the motor tries to rotate (faster or slower, namely, to change the rotational status), the mass of the load (and that of the motor itself) is 'against' this change and equilibrium is found when the torque provided by the motor meets the load of anything connected to it (fan, lift, pulleys, etc.) and any losses like friction. Usually the mechanical load grows proportional to speed. The faster you want a load to rotate, the more force the motor will have to give to achieve a faster rotational speed.

There are two parts that go into equilibrium in a motor: There is electrical balance and there is mechanical balance.

Electrically the voltage connected to the motor equals the counter emf and the losses because of the resistance of the armature on a DC motor (or the voltage drop because of the AC impedance on an AC motor). Let's ignore for a bit any losses on the rotor, if there are. You can think of a motor as a 'transformer', it reflects in its 'primary' a voltage drop which is proportional to the mechanical torque it is delivering in its 'secondary'.

Mechanically the rotational force provided by the motor must overcome the mechanical load and the losses (friction, etc.). As in linear movement we have the mass, for rotational movement we have the moment which is the product of mass by rotational speed. As a mass tends to keep its linear movement status, a load tries to keep its rotational status. When the motor tries to rotate (faster or slower, namely, to change the rotational speed), the mass of the load (and that of the motor itself) is 'against' this change and equilibrium is found when the torque provided by the motor meets the load of anything connected to it (fan, lift, pulleys, etc.) and any losses like friction. Usually the mechanical load grows proportional to speed. The faster you want a load to rotate, the more force the motor will have to give to achieve a faster rotational speed.