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Bicycle are full of fascinating gears, levers, bearings, forces, counter-forces, momentum, inertia, fulcrums, pivots, friction, thrust and other nifty stuff.  But we can't do as good a job at explaining it as other people already have.  If you want to know more check out these sites:

Exploratorium Science of Cycling Bicycle science: Why and how bikes work.

Analytical Cycling Provides technical methods for evaluating and estimating cycling performance and parameters

Bicycle Science E-mail List

Bicycling Science by David Gordon Wilson, MIT Press, 2004. (full of high-powered analysis and lots of other good stuff.)

How Do Bikes Stay Up? by MinutePhysics (video) A fun demonstration of bicycle physics.

Material Science Engineering and the Bicycle

Seven Crazy Bikes You Have to See to Believe (video)

Bike Frame Buying, Building and Metallurgy

Physics of a Riderless Bicycle  (link to academic paper)

 
 

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The International Bicycle Fund is an independent, non-profit organization. Its primary purpose is to promote bicycle transportation. Most IBF projects and activities fall into one of  four categories: planning and engineering, safety education, economic development assistance and promoting international understanding. IBF's objective is to create a sustainable, people-friendly environment by creating opportunities of the highest practicable quality for bicycle transportation. IBF is funded by private donation. Contributions are always welcome and are U.S. tax-deductible to the extent allowed by law.

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