Confusion about the nature of torque.

[siddharth5129]

I just read another post on this website about torque and the reason for its definition as the product of the perpendicular distance of the point of application of the force from the axis of rotation and the force itself ( ignoring the vector properties of the above quantities). The explanation by one of the users gives an intuitive experimental verification process about tightening a screw using your fingers and using a wrench to do the same( which requires far less force) and states that it is a fundamental observation and is just the way things work. I don't know if this is entirely true. Can a justification for the above be drawn in terms of Newton's laws ( which i think are the set of fundamental observations in this case and are "just the way things work." ).

 

[zhermes]

Excellent question. Its admirable to seek out a true understanding of these simple concepts that so many people gloss over.

The way I try to think about torque, is in terms of conservations. You can think about the following example in terms of wrenches or in terms of levers, its the same idea. Consider a solid, rigid metal bar, fixed to rotate about its left end. Slightly to the right (lets say, point 'A') is some object that its doing work on as it is rotated (e.g. compressing a spring, or tightening a screw). At the opposite end (the right-end, let's call it point 'B'), you are able to turn the bar (exert a force on it).

As you push upon point B, and rotate the bar by some small amount, point A will be moved a lesser distance (or angle, or whatever). Thus for the work ($$W = F \times d$$) to be the same, the force is greater at A than at B, because the distance traversed is lesser at A than at B.

This is also the reason why only the perpendicular distance is relevant to the calculation, as it effects the change in traversed-distance for the two points. This is the same as for a 'parallax,' there must be a separation perpendicular to the direction of relative motion.

 

[siddharth5129]

hey thanks zhermes... that makes sense. But could this be explained in terms of Newtons laws. I was thinking something along the lines of rate of change of velocity of a point(which would be more for a point closer to the axis and less for a point further away , given the same displacement of the point) . But i seem unable to draw up a satisfactory explanation from there.

 

[HallsofIvy]

No, Newton's laws of motion have no application here- how fast you turn the screw has nothing to do with the force. It is entirely "conservation of energy" and "work= force times distance" as zhermes says.