This post is for the "Forces and Motion" inquiries.
One of my favorite podcasts is National Public Radio's Science Friday. This video is on the show's webpage, where you can download it:
If you're interested, check out this web link about the TMS Bicycle - a stable bicycle, for more facts, and many more videos.
You can read a summary of the research at the Science magazine site, (published 15 April 2011), and the whole article can be downloaded as a .pdf file. You can also listen to (and download) a very interesting podcast about the article. The podcast section about bicycles begins about minute 17.40.
There are more good links to the research on Andy Ruina's (one of the researchers) web page.
This page, from Arend Schwab, has many more links, videos, and a history of his research into bike stability. He explains his ideas in this video:
(There's a full text transcript of the video's sound track on the YouTube page.)
You can follow Science Friday on Twitter