Gears and torque...
 

I know that proper gearing can reduce torque on the knees and body. Will it also reduce torque on the bike - gears, chain, bearings, etc?

Well, your knees and body don't see a torque, they see force. Torque applied to your knees is really bad!

Bearing see very little torque, providing the drag due to lubrication or binding is neglegible.

Chains see no torque, only force.

For the purposes of a chain-driven bicycle, torque is the tangential force times the radius at which it is applied. For example, a force of 10 lbf applied tangentially to a sprocket at a distance 2" will give you a torque of 20 in-lbf.

(For the time being, please don't argue with me about in-lbf, vs. lbf-in as a unit of torque. That's another discussion :D)

If you want to apply a specific torque to the rear wheel, the tangential force would be less the further it is from the center of rotation. Hence, for the same torque, the larger sprocket on the rear cluster will require a lower tangential force than your smallest sprocket would. For example:

2" * 10 lbf = 20 in-lbf = 4" * 5 lbf

Does this answer your question?

I think the short answer to your question is yes. Proper gearing will reduce the force you have to apply to the pedals. Unless you're really strong, don't push those tall gears. Your knees will thank you.

Ooops! Yes...and proper gearing then also reduces the force on components as well?

Without getting into a bunch of exceptions, in general, yes.

Hmm, actually lower gears reduce force on your knees and increases torque at the rear wheels for any given fixed force at the pedals. However, power would remain constant.

If you want to reduce wear & tear on the components, apply less force on the pedals and go slower.

To go at a given speed on a given grade requires the same torque at the rear wheel, regardless of what gear you're in. That is, it takes the same power. Gears multiply or divide torque and force and speed but not power. Power out of a gearing system equals power in minus losses.

Torque is force times radius, so a bigger rear sprocket will require less force in the chain, for instance, for the same resulting torque.

Power is torque times rotational speed, so lower gears require less torque at the input and less force throughout the system, at the expense of requiring higher rotational speed at the input (the pedals).

On a fixed gear or singlespeed, it's popular to use larger chainrings with larger cogs or freewheels (like a 52t paired with an 18t cog). The more teeth that the force is spread out on, the less wear they will see. However, you should still replace your chain often.

This article is pretty good for gears and torque and stuff, though I'm guessing you've allready seen it:

http://users.frii.com/katana/biketext.html

Chain and sprocket wear is probably proportional to chain tension, and chain tension in turn is the force you put into it while pedalling. Then again, the faster speed at which the chain moves internally and against the sprockets could also mean higher losses and greater wear. I'm not a drive train engineer...

Power is force*speed, so you can double the speed and halve the force and still put out the same power. That shift in the speed/force ratio is what you use gearing for.