I need to build something that turns at a low speed and would be on a vertical shaft.
It sounds like you need a 175 rpm motor, or there abouts. It is not practical to slow that motor that much, by supplying it with 6 hertz ac, or by cooling the motor. You need a gear motor or a pulley system; perhaps a worm gear. PWM = pulse width modulation is for DC motors. Neil
There are ways to force the speed of an A/C motor, but only works with certain motor types. With A/C motors it's all about the windings, number of them, sequence, and power frequency. If you built a control circuit to generate a 30 cycle supply for example the motor would run half as fast as being powered by 60 cycles. You may be best to use a reducer, gearing that changes the input by a specific ratio to the output.
