The heating time constant is the time that an induction motor takes to reach it's operational temperature.
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on idle, probably 0. KWh = KW x time (hours) . eg. 20KW for 5 hours = 100KWh (edit. ignore this answer i do not know what exactingly a idle motor is)
"Induction" motors imply AC power Most AC motors do not have brushes or commutator If your motor does have brushes, a lot of sparking where the brushes meet the comutator is a good indication that it needs to be cleaned and/or "cutdown". If your motor does not have brushes, then you have more serious trouble. Need more details
The speed of an electric motor is directly proportional to the frequency of supply. The rpm written on the name plate is the maximum operating speed for the motor design. Typically, for a squirrel cage induction motors, the speed is constant by design and this type of motor cannot operate for a long time at speeds below the rated value. It is true that loading affects motor speed to some extend but the electric motor will accelerate to the rated speed. If the loading is within the design parameters of the motor, the electric motor speed will not drop. What typically happens is that if the loading increases, the speed goes down, and the current increases. Because voltage is constant, this result in a high I2R loss in the windings and the motor circuit protection trips on thermal and electrical overload. The formula for electric motor speed is SRPM=(120f)/P. The above is for AC motors. If you are referring to a DC motor, what you have stated is correct. The motor will slow down as load is added. That is why you are not supposed to run many DC motors under no load conditions - they will overspeed.
If you ever had a hamster as a kid, visualize the wheel that it used to exercise on. When the iron portion of the motor's rotor is removed this is the overall shape of the conductors embedded in the rotor. It is in this winding that the current is induced into. This in turn creates a magnetic field in the rotor that locks onto the revolving magnetic field in the stator. As for the terminology, a hamster cage induction motor does not convey the image of a motor that can do any heavy work. Its all about the spin, a squirrel is larger and stronger than a hamster and I guess that is about the largest caged animal that can use a wheel for exercising.Additional CommentAt the time when 'squirrel cage' motors were developed, people kept squirrels (rather than hamsters or gerbils) as pets.
A backward induction is a process of reasoning backwards in time, from the end of a problem, in order to determine a sequence of actions to be taken.