A clarification on some of Gr8Blu's information.
The torque of a motor depends mostly on the rotor current.
The Rotor current depends on the stator current which develops the magnetic flux.
But I will try to explain the other factors.
With given stator conditions, the rotor current depends on the impedance of the rotor circuit.
The rotor circuit impedance depends on the resistance of the rotor bars, the inductive reactance of the rotor circuit and on the effective or slip frequency.
Inductive reactance is frequency dependent. At locked rotor, the effective or slip frequency is line frequency. at full load the slip frequency is only a few cycles.
Then there is the position of the rotor bars in the iron core.
One design of motor uses hourglass shaped bars, The upper part of the hourglass s more effective at lower speeds, higher frequencies, the lower part of the hourglass is more effective at lower frequencies.
Even this is a very incomplete explanation of the electrical and magnetic interactions in a motor at arious speeds and loading.
But;
IT JUST DOESN'T MATTER.
These are design factors that you will probably never encounter aside from knowing the general characteristics of the common designs.
WHAT DOES MATTER?
The vast majority of integral HP induction motors are designed to one of several standard designs. Hence the design code on a motor.
From the standard curves associated with each standard design.
Check the motor design curve to evaluate whether a given motor is suitable for a given load.
Are temporary overloads anticipated and how does the motor perform when overloaded.
There is a technique called RMS loading which helps to determine whether a motor can handle a given pattern of temporary overloads.
High inertia machines with periodic peak loading.
Here are metal shears, alligator shears, punch press machines.
Large machines of these types typically use the inertia of a large flywheel to complete a work cycle.
A special design D motor is used to accelerate the motor backup to speed following each work cycle.
When a load slows a motor down much below the rated speed, these motors are designed to draw much less current than would other designs at the same low speed.
Another option for these types of loads is a wound rotor motor with permanent resistance in the rotor circuit.
These motors are often referred to as "High Slip" motors.
They are not particularly efficient, but they may spend much of the time idling at high speed and very low load.
The advantages outweigh the poor efficiency for special applications.
Knowing how motors in general and specific designs in particular react to various loads is what you really need to know and you find that in the published motor codes.
And be sure to check out the Cowern Papers for a lot more valuable and easy to read motor information.
https://www.baldor.com/Shared/manuals/pr2525.pdf