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

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.

I wish i knew the table but if it was a direct drive maybe the drive servo had to reset itself.

If it is a table with no fixed speed controller, it could have been a surge or power change in the system temporarily.  in other words, if a large load came on-line in your area, the frequency would changes for a very short time so that additional generation can catch up with the load.

So, if you have a 60 hz system, it is fluctuating between say 59.5 hz and 60.7 hz.  (just an example).  So, most people use a stroboscope disc and a regular incandescent bulb and adjust the turntable speed for exactly the correct speed.  But, this only works if the system frequency does not change and it always changes.  Electrical system controllers and auto transformers adjust voltages to compensate for  system load changes.

So, you could have experienced a system surge in your area for a short moment.

If you have a speed controller, that is different.   A speed controller takes the 60 Hz frequency (USA) and voltage and converts it to DC, the converts it back to a fixed line voltage and a fixed unchanging 60 Hz, making your turntable speed always fixed regardless of changes in system frequency from the wall.

Unless one has a speed controller, internal or external, the turntable speed is subject to changes based on the electrical system changes based on loading.

Of course, this is assuming that nothing went wrong with your system.

I hope this helps.  

For fun, get an inexpensive (a few dollars) stroboscope disc and a incandescent bulb and check the turntable speed.  

enjoy

There are also apps on line that provide for your cell smart phone to do this same check.

It is interesting.

Apps such  as RPM, Rotor or true note.

enjoy,