Hello, I'm trying to get a conceptual understanding of why switching gears makes pedaling easier or harder. I think I understand what's happening with the rear gears, but I'm not sure I understand what's going on with the front gears. I will outline my thinking: Let's suppose our bicycle has one cog at the front, and two sprockets at the back. Since no changes can be made at the front, let's focus on the back: when the chain is on the largest sprocket, the moment arm is at its longest and therefore maximum torque is applied, requiring less force to complete one full rotation of the wheel but requiring a lot of angular displacement of the sprocket for that rotation to complete. This translates to "easier" pedaling, but lower speed (more crank turns required to turn the wheel fully once). If we switch to the second, smaller sprocket at the back, the moment arm is shortened, reducing torque. This translates to "harder" pedaling, and higher speed (fewer crank turns required to turn the wheel fully once). Please correct me if I am wrong on any of this. Now, let's magically add one extra cog to the front, making for two in total. This new cog is twice as large as the one we've been using so far. Without making any changes to chain position on the rear (let's assume the chain is on the largest rear sprocket), we switch from the smaller front cog, to the "new" larger front cog. What I am unclear on is why does this make it harder to pedal? Changing the front gear does not seem to impact torque on the rear wheel. My thinking so far is the following: because we are now using a frontal cog that is twice as large, we are effectively required to move twice as much chain with one full rotation of the crank (due to the 2x larger cog circumference). This means that, for each single rotation of the crank, we are now doing double the work on the rear sprocket, and therefore on the wheel. So essentially: changes at the back make it easier/harder to pedal due to change in torque. Changes at the front make it easier/harder to pedal due to increasing/reducing the number of sprocket rotations we achieve with a single rotation of the crank. I am not certain on my final conclusion. And even if my final conclusion is correct, I'm not 100% certain my train of thought that brought me there is accurate. Am I correct in my assumptions above, as well as my conclusion? Thanks.