What resistance should my mountain bike be set on for a good workout?

[OakLeaf]

The point of gears on a bicycle is the same as the point of gears on a car. You pedal most efficiently in a small range of RPMs. A good place to start is 90 rpm - which might feel fast to a beginner - but if you work on your pedal stroke to where you can pedal consistently at 90 and smoothly at much higher RPMs, then you can play around to find your personal "power band."

You shift gears - as the motorcycle safety course teaches - "to match engine speed to road speed," i.e., so that you're pedaling at about the same cadence (RPM) regardless of whether you're going slow up a steep hill or fast downhill.

The bigger the cog, the easier the gear is.

On the rear cluster, the "cassette," controlled by the right shifter. The smaller the front cog, the "chainring," the lower the gear. It's just the same kind of simple machine you learned in fourth grade (and probably forgot like the rest of us did ). Take as an example a 42-tooth chainring with a 21-tooth rear cog. For every revolution of your pedals, your rear (drive) wheel will revolve twice (42/21). If you downshift in the back so that you're now driving a 28-tooth rear cog with that same 42-tooth chainring, now your rear wheel will revolve one and a half times (42/28).