I've been wondering the same, Jordan.
Today was my Physics midterm, and while i should be basking in knowing that its done, we have a robotics meeting tonight
Anyway, I'll try to help with what I can:
Torque (tao) = R x F (cross product)
that is T = R*F*sin(theta)
R being the radius in meters from the folcrum to where the force is applied. F being the force applied in Newtons and theta is the angle between the Force and the plane of the radius.
This seems to work and be happy for all the problems in my physics book dealing with rotation/translation and such, but I don't know how to apply it to gearing
any thoughts on this?
Also, to determine gearing speeds (in metric SI of course),
V = omega R
V is tangential velocity (meters/s), omega is the rotational speed (in radians/s), and R is radius (meters). When you're going from gear to gear, either omega or V will stay the same. V stays the same when connected directly tooth to tooth, or by a chain. Omega stays the same when two gears are attached and rotate around the same axis.
I may have screwed some things up in there, so if you find something wrong, please correct me - and does anyone know an equation to relate the initial rotational speed to the final speed to get the increased torque? there's gotta be one