This clip (and the others posted by 'ChristopherJSykes') are from the BBC show "Fun to Imagine". Been a few months, but I remember the 'Magnets (and 'Why?' questions...)' segment being particularly worthwhile if you're looking for good bang-for-buck timewise.

Incidentally, the guy releasing this also directed it.

Also in case you prefer text: http://varatek.com/scott/feynman_problems.html

Wow, neat. I'm not sure I should attribute all my amazement to Feynman, but it sure is lovely hearing that man explain things.

So now all I need to do is figure out what determines the angle of the taper on the wheels...

The difference between the circumferences would have to be such that the train could round the sharpest bend on the track.

That should approximate to a maximum angular change (in direction of travel) per metre:

angle per metre = tan( 2 PI (R-r) / inner track gauge ) x 2 PI r

where R is the largest contact circumference of the wheel and r the smallest.

?

What I don't get is how the train rounds a variety of curve radii. How do they control the part of the wheel that is riding the rail precisely enough to allow the train to turn at differing angles depending on the radius of the curve?

Hmm, sorry for the double post, not sure what happened there.

What I don't get is how the train rounds a variety of curve radii. How do they control the part of the wheel that is riding the rail precisely enough to allow the train to turn at differing angles depending on the radius of the curve?