# Formulas for AC Synchronous motors

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?

• Jorge, I know you are new here but there are buttons on the editor toolbar to format your post correctly. These include the numbered list button. Press [Enter] x 2 for a new paragraph and to start a numbered list. Read the preview before you submit the question. Edit required. – Transistor Mar 5 '18 at 22:36
• Also, looks like homework – Brian Drummond Mar 5 '18 at 22:38
• Good work on the edit. It's much more readable. Since this is obviously homework you should answer the bits you know and attempt the bits you don't. You'll get plenty of help but we won't do your homework for you. – Transistor Mar 5 '18 at 22:39
• it isn´t homework, they´re excercises to study for my mechatronics exam. I´m not asking for the solution, that won´t work for me to study. I have 2 formulas: slip and number of poles; I think I´m missing an important one. – Jorge Mar 5 '18 at 22:43
• one formula you need need is the relationswhip between the synchronous speed, the electrical frequency & the number of pole pairs... there are usually rad/s or rpm version of things given so be careful with units – AugustCrawl Mar 6 '18 at 1:24

## 1 Answer

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".

• I found F1(1/Zp)=Fm Zp=2p where p is the number of poles. Do you know where this formula comes from? – Jorge Mar 6 '18 at 4:32