2 vs 4 vs 6 pole AC motor HP

[Froneck]

Often I'm reading on other sites that if a 2 pole 3600RPm (synchronous speed) motor were connected so that the ratio would lower the speed to the same as a 4 pole (2X) and so on with 6 pole (3x) the output HP will remain the same. However the larger the number of poles the larger the motor and like wise the cost! If that were so why would anyone want to buy a more expensive 4 or 6 pole motor if the same HP output were available by gearing or belting a 2 pole motor?
I remember when in High School my father bought a lathe for me but the motor had a bad start winding. It was a 1750rpm 1HP single phase motor. Once started the motor ran fine. Getting it started was the problem and done with a rope to pull start it! I went to Sears back when they had all their stuff made in USA and seen that a 3500rpm, 1HPmotor was half the price of a 1750rpm, 1HP motor so I purchased it and belted it down to the same speed. However it did not have the same power as the replaced 1750rpm motor and could be easily stalled with a heavy cut that would not stall the other motor.
Some time later when in Collage I mentioned it to my Electrical Engineering Professor and he showed me why! Been a Loooooong time ago. Can anyone provide me the calculation similar to his.

Frank

 

[anorlunda]

You may have been told wrong. A 60 Hz motor needs to run at a speed of 3600/N RPM, where N is the number of pole-pairs. 2 poles=1 pair, 3600 RPM. 4 poles=2 pair, 1800 RPM.