Cool video: How a differential works
 

That's pretty cool. Even a dumb guy like me gets it...

You don't even wanna think about how an electronic limited-slip works... ;) j/k

(basic idea is simple, but when you start talking control algorithms, it gets REAL complicated - BTDT)

that's one of my favorite videos on YouTube - however, I don't understand the following:

1. how the assembly on the axle (the one the person rotates by hand) can alternately rotate about the axle when the person applies resistance, but also rotate the axle when there's no resistance.
2. what that assembly is mounted on one side for - what if there were one on both axles

924RACR "limited slip differential"

please oblige! but keep it simple?

BTW since we are off-topic, see if you can guess how the gears will rotate in this video:

Under the ruler faster than the ruler - YouTube

Sorry, but that's the point, it's very much not a simple discussion. Mechanical LSDs, OK, fairly simple and easy to understand what they do to the car. Once you start varying that through a wide range, the impact gets very complex as it now is a significant contributor to vehicle dynamics as well as traction...