Understanding electric torque of a motor
Motor torque is directly related to motor current, not with voltage. Ignoring motor resistance, friction etc, when you drive the motor with a current source that would give the same analogy as pulling a dumbell with force F.


  But we know that a motor's torque keeps changing with the load.  


This is only true when driving a motor with voltage source.

Using the electrical domain:
 - With a current source, we know that the voltage keeps changing with the load.
 - With a voltage source, we know that the current keeps changing with the load.