There are a number of good comments about the centrifugal switch and the capacitor given above. Though I am of the opinion that you need to look elsewhere, for a couple of reasons.
In the first place, when I bought this house(1975) and before I rewired it, there was a 30Amp, 120Volt, 2 wire service. Grossly underpowered even for '75. The power was so low that a vacuum cleaner would run, but not my saws. I knew up front that the house had little power and had laid plans to rewire it properly once I was in it. It took a while to do, but now I have a 225Amp, 240Volt, 3 wire feed. Never a burp, even on the "sub-feeds", of which there are three.
Then there is the matter of my current table saw. I had a newer one(Craftsman 12") and horse traded around till I got an older one with an external motor and with an eight inch blade. A lot of my tooling was is small. And I do small work. But I do cut old oak flooring and have ripped 2X4s the long way, making 2 pieces 1X4.(nominal) The motor I rely on for this is only a 1/3 HP, 1750RPM, 120Volt Motor split phase fan motor. Conceded, I do small work and work slowly. but I'm an old fart and do so anyway. And I depend on a radial saw and a chop saw for much of my larger work. I don't rip 3/4 CDX plywood, that's for the Skil saw.
That said, you might consider if the blade and shaft are free. You speak of a cabinet saw rather than a direct drive. Spinning the blade with some force should cause it to make several revolutions before stopping. Do it without the belt using a scrap of wood against the blade. Less is indicative of tight or worn bearings. Also follow up on the power supply. Even a newer house with 120Volt, 15Amp circuits will give trouble with a motor starting while on an extension cord. Not only a too small wire but distance in feet from the main supply on the pole. Each factor in itself is not alone in power drop, but several combined might well be. And lastly, look at the nameplate, if there is one, for rated speed. Many old saws used four pole(1800-1750RPM) motors. A two pole (3600-3450RPM) motor may have trouble overspeeding the blade.
If you have an analog voltmeter, you can watch how far the needle swings when you start the motor. Digital meters will work if there is a bar graph. The numeric display is usually too slow updating. Voltage drop is a variable thing. If it drops more than 5%, you need to follow up on it. If it drops 10%, you got real problems, don't run the saw until it is fixed.
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