why did my record player slow down, speed up, then go back to normal?

First, is it idler drive, belt drive or direct drive? If idler, perhaps the idler wheel needs resurfacing, if belt the belt could be slipping. You can put the belt in a bag with talcum powder and shake it up and reuse the belt. If it still slips, get a new belt from the manufacturer.  If it’s direct drive, the speed controller circuitry could be defective.

Brief power outage or surge, bad capacitor, belt slippage, bad bearing, severe stylus drag, finger on the platter, platter rubbing on plinth, Schoenberg, bad karma for having been a troll.

@lewm 

Schoenberg

:D

If this is an older turntable with variable speed, one explanation might be that the speed controls or the speed selector switch are developing corrosion. If this is so, you can expect future events and more often.

Another explanation is a brief power outage.

On a deck with a synchronous motor (Elite Rock) a new phasing capacitor resulted in the pulley just quivering back and forth, until the deck was turned by hand when it kept going. After a while it would start on its own in the right direction but with momentary misses, which went after a few days. Was the new capacitor forming up after being unused for too long? No idea but the speed glitches never came back in ten years.

On a deck with a brushed DC motor and a feed forward power supply (Artemis SA-1) it was a symptom of the sintered motor bearing running out of oil. Getting some more in required removing the pulley but the adhesive had gone soft so it could be eased off and 100μl of oil (I used Nye Lubricants 181B but the designer recommended liquid bearing, however they wouldn’t supply that outside the US) run down the shaft to soak into the bearing, I did this 25μl at a time rather than all at once. When I replaced the bearing with a bit of loctite 648 retainer to hold it in place I made sure there was enough gap to get a micro syringe needle into to top up the oil in future.

There isn’t one answer to this one.