Mountain Biking has an endless list of things that are physics, from the static friction of rolling tire to kinetic friction of a tire skidding to the force applied by your feet on the pedals or the force applied by your fingers on the brake levers. I bike a lot in summer and even sometimes in the winter, but the best story I have of biking pertaining to physics took place on a rainy summer day. My friend and I were biking and we got to a board walk and both had the same idea, that wet board walk is going to be really slippery lets go screw around on it. Well I dart over to the board walk and rather cautiously proceeded on it, then I had the great idea to kick out the back tire on the slippery surface little did I know the Kinetic co-efficient was much lower than the static co-efficient on this surface, and when I kick out the back tire it came around so fast I was on the ground with my friend laughing at me before I knew what had happened. My friend also clearly having no idea whatsoever of the physics in play, calls me another word for an idiot and rides onto the board walk and kicks out the back and ends up laying on his back on the ground just as fast as I did and never has being insulted been more satisfying.
Biking also has tons to do with air resistance and gravity for example the fastest speed I can hit normally on some of the biggest hills around my neighborhood is about 32mph this is the speed where the force of gravity can no longer overcome the drag that is created by myself and my bike and when this happens equilibrium is reached and I continue at a near-constant speed until the hill subsides.