Formulas for AC Synchronous motors

Question

I have this questions:

1. At what frequency must a 4-pole motor be supplied so that its synchronous speed is 1200 rev/min?

2. The nameplate of a standard 50 Hz induction motor quotes full load speed as 2950 rev/min. Find the pole number and the rated slip.

3. A 4-pole, 60 Hz induction motor runs with a slip of 4%. Find:
   (a) the speed;
   (b) the rotor frequency;
4. A 440 V, 60 Hz induction motor is to be used on a 50 Hz supply. What voltage should be used?
5. Why can an induction motor never run at its synchronous speed?
6. Choose suitable pole numbers of cage induction motors for the following applications:
   a. a grindstone to run at about 3500 rev/min when the supply is 60 Hz;
   b. a pump drive to run at approximately 700 rev/min from a 50 Hz supply;

I now the number of poles and slip formulas. Is there any other formula that could help me for this task?

Answer 1

S = f x 120 / N

Where:

• S = Synchronous speed in RPM
• f = frequency in Hz
• N = number of motor poles
• 120 = a mathematical constant

% Slip = (S - Full load RPM / S) x 100

Use those two formulae to solve all of the above.

By the way, your thread title says "synchronous motors", which would not be inclusive of "slip".