Moments

I forget who said it, but there is a famous quote once said. "Give me a lever long enough and I can move the earth". In order to rotate, a torque is required. Torque is defined as force x distance. If you are trying to twist off a cap, you need to apply a certain torque to it. So that tourqe is an unchanging value. If you can produce it, you're all set. That said, if you look at the formula, its easy. Increase the distance and the force is less. Also, if you increase the force, the distance needs to be less for a given torque.

A. It was Archimedes, B. Not only turning or torque, it is also true for any force applied, The greater the arm is,(distance) lesser force is required to move an object.(remember vectors?). Wangito

Gearing, pulley systems, and levers all work on the same principal. You can think of a pulley, for example, as an infinite number of small levers radiating out from the center.

If you are looking for a more theoretical basis, in other words, if you are asking why does a lever work, then it has to do with the conservation of energy. The amount of work (distance * force) at the input has to equal the amount of work (distance * force) at the output.

You know, I've been wondering what moment meant for a while now. So it's related to the force necessary to cause a movement. I've seen it in moment of inertia, dipole moment, momentum, etc. Makes much more sense now.