# Torque.. what the @#\$ is Torque?

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Ok, I'm trying to think of more and more complicated ways to explain it:cool:

Imagine it in terms of an elastic shock wave in a solid.

If you apply a force to the side of an object, the part immediately being pushed will compress, allowing the solid boundary to move in the direction of the force. The part immediately behind that will then compress to allow the first element to return to its initial shape, but as the nearest part of the first element has moved and then the element returned to its initial shape, the furthest part of the element has also moved.

This shock wave will propogate from element to element, causing them all to eventually move a short distance in the direction of the force.

Similarly with torque, if you twist one annular ring of a disc, there will be a shear stress rather than a normal stress, but a similar "wave" will propogate to all other elements within the disk away from the annulus.

Thats what torque is.

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My son recently bought a car. I suggested replacing the standard lug wrench with one of those cross-shaped lug wrenches. Why? They offer more torque and purer torque than does the standard issue lug wrench.

As many have said, torque is defined as $\vec \tau = \vec r \times \vec F$. Suppose you have a pair of equal but opposite forces $\vec F_1=\vec F$ and $\vec F_2 = -\vec F$ applied to two different points on some solid body. The net force on the body is zero, so the body won't undergo linear acceleration. The two torques that result from the two forces are not equal but opposite. The net torque will be non-zero. This is called a pure torque, or a mechanical couple.

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But that's not a proper application of Newton's third law.

Sorry - Newton's first law then. Pedant.

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Sorry - Newton's first law then. Pedant.

It's just that the third law is so often misunderstood in precisely that way. I didn't want to reinforce the misunderstanding.

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Mooey the best way I can explain it is like this, Imagine a kids toy car, you put the batteries in and switch it on and it runs along the floor, you can easily stop the wheels moving with your fingers cant you, it has Low torque.

now think of an electric Screwdriver, you Might just about be able to stop that with your entire hand but certainly not with your fingers, it has a Greater Torque.

now think of an industrial drilling machine say for an Oil Well, you wouldnt be able to stop that with your entire body! that has a Massive Torque.

and yet all these can turn at exactly the same rate.

maybe That will help a little

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The problem with torque is that it's not a "real" thing, at least not in the same way that force is a "real" thing. There is no "torque force." There is just regular old Newtonian force. But very often those forces sum up in such a way that something ends up spinning, and because it generally sums the same way and that way can be represented with simple equations, we give it a name, "torque."

Since it's so common, it's also somewhat intuitive, in that we can "have a feel for it" in everyday experience. Torque is simply the force with which something turns. If you look more deeply than that, you won't find anything, because there is nothing deeper than that, because it's really just Newtonian forces adding up in a particular way. "Where is the torque?" Nowhere, really.

The same can be said for angular momentum. There is no "spinning momentum." There is just straight-line momentum. However, when different parts of one, connected object have momentum in different directions, the combination of that momentum and the forces holding the object together result in the object spinning, and behaving as if the spin, itself, had momentum.

Or another example: "centrifugal force." No such thing, and yet we've all felt it!

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The same can be said for angular momentum. There is no "spinning momentum." There is just straight-line momentum. However, when different parts of one, connected object have momentum in different directions, the combination of that momentum and the forces holding the object together result in the object spinning, and behaving as if the spin, itself, had momentum.

What about a particle's intrinsic spin (angular momentum)? Wouldn't that be "spinning momentum"?

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The problem with torque is that it's not a "real" thing, at least not in the same way that force is a "real" thing.

Torques are no less real than are forces. Forces in classical physics are anything that changes an object's linear momentum. Torques are anything that changes an object's angular momentum. Quantum mechanics nearly does away with forces and torques, using a Lagrangian or Hamiltonian formulation instead. (The Lagrangian does yield generalized forces, which encompass both linear forces and torques).

The same can be said for angular momentum. There is no "spinning momentum." There is just straight-line momentum.

Bunk. The disk in your computer disk drive has zero linear momentum but a lot of angular momentum. The shift symmetry and rotational symmetry of space lead to conservation of linear momentum and conservation of angular momentum, respectively. Linear and angular momentum are two distinct concepts.

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Torque is the rotational equivilent of force, like angular velocity is the rotational equivilent of velocity. That's the easiest way to think about it, anyhoo.

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where do you feel energy? where do you feel momentum?

the only things your really "feel" are mass and if you like charge, everything else is pretty much abstraction

torque is to angular momentum as force is to linear momentum both things are related however thats essentialy all there is to it. Once you rationalize why levers work (I did this by thinking about conservation of energy) all you have to do is work out the math on the things

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Torques are no less real than are forces. Forces in classical physics are anything that changes an object's linear momentum. Torques are anything that changes an object's angular momentum.

I'm not denying it's a useful shorthand, but the one is most definitely derived solely from the other. Don't they demonstrate that in physics classes anymore?

Bunk. The disk in your computer disk drive has zero linear momentum but a lot of angular momentum.

My computer disk as a whole has no linear momentum, but it's parts all have linear momentum perpendicular to its radius. Since there are forces holding it together, the result is a spinning, with "angular momentum."

What about a particle's intrinsic spin (angular momentum)? Wouldn't that be "spinning momentum"?

True enough. But that's quite a bit different than what mooeypoo is asking about, no? Any torque we actually experience is going to stay in the realm of classical physics.

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the only things your really "feel" are mass and if you like charge, everything else is pretty much abstraction

I'm pretty sure I can "feel" an acceleration, and "if you like charge" is a pretty strange characterisation of the whole gamut of forces.

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I'm not denying it's a useful shorthand, but the one is most definitely derived solely from the other. Don't they demonstrate that in physics classes anymore?

Umm, no. At least not beyond freshmen level physics. Please demonstrate how conservation of angular momentum is derived solely from conservation of linear momentum. Please show how to analyze general central force motion or the precession of a torque-free symmetric top without invoking angular momentum.

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Mooey, another way to think about it is Gearing ratios, Do you Drive?

you see, in 1st gear it will allow you move the entire weight of the car without stalling the engine, it has a Huge amount of Torque (although you cant travel very fast at that speed).

now think about 5th gear you may move at 100Kmph in 5th no problem at all, but you Cannot pull-off from Stationary in that gear!

it doesn`t have enough Torque to move the inertial mass of the car before the engine dies (or you end up with a box of metal Kitty litter where your gears used to be).

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Umm, no. At least not beyond freshmen level physics. Please demonstrate how conservation of angular momentum is derived solely from conservation of linear momentum. Please show how to analyze general central force motion or the precession of a torque-free symmetric top without invoking angular momentum.

Obviously you think I'm a crank and/or I've somehow insulted you, but I'm not going to get in an Internet Pissing Contest about something so trivial. Look it up yourself, or ask your teacher.

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I thought she said she understood the maths relating torque to force amongst other things. Explanations such as "you can stop a toy car wheel but not an oil drill so the drill has more torque" (there have been many so I'm not just getting at you yt2095) just exemplify the mathematical principles. If you need more force at a greater distance from the exis of rotation, you have a bigger torque is just another way of saying T=Fr (or whatever vector equivalent you want to use).

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sysiphus thats not strictly true, for instance electrons and other fundamental particle have intrinsic angular momentum that has nothing to do with inear momentum this is known as "spin"

also DH is a working physicist he tends to konw what he's talking about.

its true that most angular momentum's are consequences of an objects linear momentum, but that is not true in general. in fact the better way to look at it is in terms of the various smmetries of problems.

for instance in classical mechanics if you are analyzing the total system, then you will find that two of the symmetries are going to be translational, and rotational.

the translational symmetry implies conservation of linear momentum, and the rotational symmetry implies conservation of angular mometum

the 3rd main symmetry is time translational, and this implies conservation of energy.

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in fact the better way to look at it is in terms of the various symmetries of problems.

Exactly. Time displacement, translational displacement, and rotational displacement are three distinct concepts that lead to three distinct conservation laws. The age-old question, "What do you get when you put a spinning flywheel in a casket and turn a corner", is best answered by invoking conservation of angular momentum.

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