What causes torque to exist?

Question

I know the formula for and the overall concept of torque, but why does it act the way it does? Why is a force farther away from the pivot more effective than one closer to it? I know what I'm saying is probably wrong, but shouldn't it be the other way? Since a point at a closer distance to the pivot has to travel less distance to cover a 360° round, shouldn't the torque be greater at a lesser distance? How does having a greater distance to cover make a force more effective? Thanks in advance.

Answer 1

Since a point at a closer distance to the pivot has to travel a smaller distance to rotate the same angle, a smaller force at a further distance from the pivot can exert a larger force precisely because it travels a further distance than the point closer to the pivot. Thus, because force times distance equals work, a smaller force can travel a long distance and do more work, which translates into a smaller distance times a bigger force nearer the pivot. That's why you can undo a nut with a spanner which you can't undo with your fingers, or why a screwdriver handle is thicker than the shaft - so that you can use a smaller force to turn something than would be necessary if you put it closer to the axis of rotation.