I think everyone pretty much covered it. Just a minor physics clarification...
Originally Posted by 8bitevolution
I'm used to the way cars work - low gears produce more power output per revolution, and the higher gears are used to maintain speed without working the engine as much. I assumed this is how a bike's gearing would work.
Power-output is actually the same regardless of gear. It's the torque that changes with gearing. So if you're cruising down the freeway 65mph in 5th gear @2500rpm, you'll need about 20hp. You can also use 4th gear @3500rpm to also generate 20hp, but you'll notice that the throttle-opening is smaller. The 4th gear spins faster, you get more combustion pulses per second, so each pulse can be smaller to generate the same power-output.
The way that works on a bike is you can be cruising at 20mph in a gear that requires 75rpm. This requires a certain amount of force on teh pedals. You can also select a lower gear, so that 20mph requires 90rpms. The muscle-force needed on the pedals will only be 80% as much as before.
Originally Posted by 8bitevolution
Should my legs be burning after a 10 or 15 minute ride without too many hills due to a lack of exercise or am I just riding my bike all wrong? As I said, the seat height and pedal thing I know I was doing wrong so I can only assume I'm getting gearing all wrong, too. If this is due to a lack of exercise, how often should I be riding? Is there anything I need to do to help rebuild muscle after riding?
Burning legs are caused by lactic acid. This is due to anaerobic fermentation in your muscles due to high-effort. It's inefficient and requries a lot more oxygen to clear out and causes muscle soreness as well. The LT-lactate threshold is the exertion level where your muscles transitions between efficient aerobic operation into inefficient anaerobic mode. Stay below this exertion level by using lower gears and spinning your legs faster. Same power-output and speed, but you can push on the pedals lighter. This extends the distance you can ride before you have to stop due to muscle-fatigue.