What Makes Torque Fundamental in Physics?

[iScience]

i am a junior physics student; i have already been exposed to the equation many times. Now i am more interested in getting more familiar with the nature of things; the nature of torque.. what IS it? i have an intuition of what force is, but torque, i have nothing. If i try to tighten a screw holding a wrench near the center of rotation, it requires more force and if i hold the wrench out farther (greater 'r'), then it requires less force. What is it about this system that allows the system to "know" so to speak, where i am holding the wrench?

 

[haael]

Torque is an angular analog to a linear force. Just as force is a derivative of a linear momentum, torque is a derivative of an angular momentum.

> What is it about this system that allows the system to "know" so to speak, where i am holding the wrench?

Angular momentum is a product of a rotational speed and a length of a leverage arm. That means, the angular momentum already "knows where you are holding the wrench". The shape of an object is already included in the definition of angular momentum (via the notion of a moment of inertia). This is the point where the analogy to linear momentum fails. Linear momentum depends only on a body mass, while angular momentum depends on mass and shape (density distribution).

 

[Philip Wood]

> What is it about this system that allows the system to "know" so to speak, where i am holding the wrench?

You've asked an excellent question. I asked a similar question many years ago, about the balancing on an off-centre fulcrum of a light bar loaded at each end. How did the bar know how far away the loads were, in order to know whether or not to balance? Something must be changed about the interior of the bar, in order to communicate the presence of loads, and their positions.

What satisfied me was to replace (on paper) the bar by a simple pin-jointed lattice of triangles (it is crucial that the bar have depth as well as length). By using force resolution at each pin, I then worked out the forces in all the members of the lattice, working from one end of the bar to the other, and found that if the weight W1 was distance d1 from the fulcrum, then the lattice forces at the other end, a distance d2 from the fulcrum, would balance a weight W2 given by W1d1/d2. All this without using the notion of moments! The balancing happened because of the forces inside the bar.

I'm not advocating abandoning the Principle of Moments - it's a great time-saver.

 

[namanjain]

Torque(ζ)
It's a physical qty. which provides rotation to body, actually angular acceleration.
Like in normal dynamics
F=ma,
F provides normal ∂,
ζ provides α BY eqn.

ζ=Iα i being moment of inertia analogous to mass

 

[Philip Wood]

Couldn't resist giving the analysis of torque (how a lever knows whereabouts a force is being exerted on it) that I mentioned in my earlier post. I realize that I've chosen a very special and artificial model of a lever, but I think it makes the point that various forces act within the lever, and that their sizes depend on where the load is placed. It also raises the question of how fundamental the principle of moments is - because we seem to have reached the right answer without using it.