Ever wondered how a differential gear on a car works? Well, if you're like me, your first question is just what the heck is a differential? Wikipedia says (emphasis added):
A vehicle's wheels rotate at different speeds, mainly when turning corners. The differential is designed to drive a pair of wheels with equal force, whilst allowing them to rotate at different speeds. In vehicles without a differential, such as karts, both driving wheels are forced to rotate at the same speed, usually on a common axle driven by a simple chain-drive mechanism. When cornering, the inner wheel needs to travel a shorter distance than the outer wheel, so with no differential, the result is the inner wheel spinning and/or the outer wheel dragging, and this results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drivetrain.
This video explains the whole thing (note: the first two minutes or so are a demonstration of synchronized motorcycle riding, which you may or may not find exciting). It's kitschy, but also educational -- through a step-by-step engineering demonstration, this vintage video makes it clear how all this technical car stuff works. Chevrolet Motor Division (General Motors Sales Corporation) Presents: AROUND THE CORNER...
See also: Richard Feynman Explains Trains, in which he explains a similar issue faced by trains turning corners on train tracks.