Bicycle Questions: Static Friction & Gear Ratios

[rcgldr]

But that's what it says at the link.

Now that I've read the article linked to before, it's worded awkwardly. Newton third law pair of forces do not act on the same object, so they don't "cancel". In this case, the third law pair of forces is the backwards force that acts upon the surface of the Earth (exerted by the wheel) and the forward force that acts upon the wheel (exerted by the surface of the earth). The article is either treating the Earth as if it had infinite mass, resulting in a force that is "canceled" because it's acting upon an object of infinite mass and has zero effect on the earth, or it's just ignoring the effect on the earth, so it's not a closed system where momentum of the system would be conserved.

The way you describe it now makes it look to me like the friction(force from ground to the wheel) changes the energy of the bike.

The origin of the friction force is the torque that the rider exerts onto the pedals. The momentum of Earth and bike are changed with equal magnitude but opposite direction. The energy of both Earth and bike are changed, but as mentioned before, since the Earth is massive compared to the bike, the velocity change of the Earth is tiny compared to the velocity change of the bike, so the bike gets most of the change in energy.

 

[A.T.]

Problem here is that there is not official definition of a force that redirects or transforms work or energy but oh well wth

There is an official definition of work. And forces that do no work are usually called "constraint forces".