The Pump Motor Hums when the switch is turned on. Remove the pump and the impeller turns freely.
Any AC motor will hum when it is stalled. This could happen because of mechanical binding. You say the impeller turns freely. What about the motor shaft? If it turns freely, you could have a bad motor start/run capacitor. These components equalize the current-voltage lead/lag (power factor) of the motor so it will start easily and run efficiently. A shorted or open capacitor could cause the same problem.
the motor 'hums because it does not know the words to the song. lol
Impeller shaft may be bent.
THE MOTOR NEEDS TO REPLACED
