Understanding Torque: The Basics and How It Relates to Rotational Force

[RadiantL]

So I'm just a little confused about what torque is exactly, what does the number you get from torque tell you? What is it? My friend says it is how much force is applied to cause something to rotate but wouldn't that just be F?

Anyway so my question are

What is torque?
What does the number tell you?

 

[navynuclear]

Torque is the force required to rotate an object around an axis. Ft/lbs is the energy transferred on applying a force of one pound-force (lbf) through a displacement of one foot. Picture it how tight a nut is on a stud.

 

[HeLiXe]

There was a really good example to explain torque in my physics textbook (Halliday Resnick)...when you push a door open by the knob you are using a torque to rotate the door about it's axis or hinge in this case. Force times lever arm...the positive direction of torque is counter-clockwise and the negative direction clockwise.

Here's a good picture of it

or this one is probably better at showing the difference between the actual force and torque

The "T"'s are the torques and "F" the force.

 

[JHamm]

Torque is the change in angular momentum with respect to time.

 

[I like Serena]

@HeLiXe: Nice pictures!

 

[A.T.]

https://www.youtube.com/watch?v=Sm4pV3xyJRE

 

[cmb]

Torque is the change in angular momentum with respect to time.

Not so.

Attach a handle to a brick wall and apply torque to it with your hand ... Say! Nothing's moving!

Think of it more like a rotational version of a force. A 'linear' force causes the linear velocity of a thing to change (unless there is a 'linear reaction force' exactly opposing the applied force). Torque is the same in rotational terms - it is a force displaced from an axis of rotation that causes the angular velocity of a thing to change (unless there is a 'torque reaction' exactly opposing the applied torque).

Whether an applied force is a 'linear force' or a 'torque' depends on whether the object to which the force is applied is caused to rotate about a pivot (which might not be fixed, but could be its CoG or other 'instantaneous centre of rotation'), or not. In the real world, most forces on free bodies have the effect of causing both linear and rotational displacements, so the same applied force may be responsible for both a linear and an angular acceleration.

This is a conceptual description. In a shaft 'carrying a torque', it may be difficult to see the 'forces' involved. But ultimately it comes down to the same mechanism of transmission of forces between molecules, it is essentially the effect that is different between a 'force' and a 'torque' (namely, it is a force displaced from a pivot).

 

[D H]

Torque is the change in angular momentum with respect to time.

Not so.

Yes so. $\tau=dL/dt$ is the rotational equivalent of $F=dp/dt$.

Attach a handle to a brick wall and apply torque to it with your hand ... Say! Nothing's moving!

The same goes for F=ma. Push on the brick and ... Say! Nothing's moving!

Just as F=ma is with regard to net force, JHamm's statement is with regard to net torque.

 

[cmb]

Yes so. $\tau=dL/dt$ is the rotational equivalent of $F=dp/dt$.

Say you are trying to unscrew a rusted-in bolt and it does not move. Are you not applying torque because it does not move?

You are dealing with singularities in that equation, unless you are talking about things that are moving.

 

[I like Serena]

Say you are trying to unscrew a rusted-in bolt and it does not move. Are you not applying torque because it does not move?

You are dealing with singularities in that equation, unless you are talking about things that are moving.

Aren't you forgetting that action=-reaction?

In other words, the resultant torque is zero, and the bolt does not move.

 

[cmb]

Aren't you forgetting that action=-reaction?

In other words, the resultant torque is zero, and the bolt does not move.

Not at all. There are two torques, one + and one -. Are you not reading my post above?

Having two opposed torques are not at all the same scenario as having none at all. 'Net torque' was not the subject the OP raised.

I wrote;

Torque is the same in rotational terms - it is a force displaced from an axis of rotation that causes the angular velocity of a thing to change (unless there is a 'torque reaction' exactly opposing the applied torque).

 

[bp_psy]

Having two opposed torques are not at all the same scenario as having none at all. 'Net torque' was not the subject the OP raised.

Actually it is the exact same scenario.You can't tell the difference between two equal opposite torques or no torque at all without invoking some kind of external knowledge of the system.This is the same for force you can't actually say that there is any force on a system if its acceleration is 0.You can say that it is in some field or is pulled or pushed but those causes are external and in the end irrelevant since they do not change anything about the system.

 

[cmb]

Actually it is the exact same scenario.You can't tell the difference between two equal opposite torques or no torque at all without invoking some kind of external knowledge of the system.

So how does a torque sensor work, when it is measuring a static torque load? If the scenarios are the same, then how can a 'sensor' detect any difference between 'no torque' and 'static torque'?

This is semantics, you can argue this until there is a smoking little hole of logic in the ground, but I do not see how it is helping the OP comprehend the nature of torque.

 

[cepheid]

Say you are trying to unscrew a rusted-in bolt and it does not move. Are you not applying torque because it does not move?

You are dealing with singularities in that equation, unless you are talking about things that are moving.

cmb -- keywords below emphasized for your viewing pleasure

Yes so. $\tau=dL/dt$ is the rotational equivalent of $F=dp/dt$.


The same goes for F=ma. Push on the brick and ... Say! Nothing's moving!

Just as F=ma is with regard to net force, JHamm's statement is with regard to net torque.

 

[cmb]

cephid,

DH's response was an objection to me saying that

Torque is the change in angular momentum with respect to time.

was incomplete.

If it HAD said 'NET TORQUE' then I'd not have posted anything at all. I was raising the point that you are actually accusing me of missing. I mean, talk about not bothering to read my post!

I do not see what the issue is. You are highlighting comments that DH made AFTER I made my point.

This is all a deviation to the OP's question. 'Torque', per se, is NOT uniquely manifest by a change of angular momentum. (I have made no contest that this is different for 'net torque' which the OP did NOT ask about.)

Sorry this has somehow confused you. I have nothing to add further.

 

[cepheid]

So how does a torque sensor work, when it is measuring a static torque load? If the scenarios are the same, then how can a 'sensor' detect any difference between 'no torque' and 'static torque'?

This is semantics, you can argue this until there is a smoking little hole of logic in the ground, but I do not see how it is helping the OP comprehend the nature of torque.

I don't know the technical details of how such a sensor is implemented, but one could equally well ask:

Q. How does a weigh scale work? Clearly when you stand on it, the net force is 0, since you're not accelerating. Yet, somehow, the device is able to measure the force with which gravity is pulling on you. Amazing! How does it do that?

A. The weigh scale knows how much opposing force is required to keep you from accelerating. (In this case it's the restoring force from the spring). So, by measuring ONE of the two forces in (what we know to be) the balanced pair, this "force sensor" is able to infer the value of the other one. It's not exactly magic.

 

[cepheid]

cephid,

DH's response was an objection to me saying that
was incomplete.

If it HAD said 'NET TORQUE' then I'd not have posted anything at all. I was raising the point that you are actually accusing me of missing. I mean, talk about not bothering to read my post!

I do not see what the issue is. You are highlighting commented that DH made AFTER I made my point.

This is all a deviation to the OP's question. 'Torque', per se, is NOT uniquely manifest by a change of angular momentum. (I have made no contest that this is different for 'net torque' which the OP did NOT ask about.)

Sorry this has somehow confused you. I have nothing to add further.

You still seemed to object to his point after he made it, because you argued that 0 net torque due to two balanced torques is not the same as 0 torque due to no applied torques, which is nonsense --- as indicated by that rotational version of Newton's 2nd law the two situations will be identical in terms of their dynamical effects. If there is no net torque, there is no change in angular momentum. It doesn't not matter how we have achieved this state of no net torque.

 

[cmb]

If there is no net torque, there is no change in angular momentum. It doesn't not matter how we have achieved this state of no net torque.

So answer my question; if there is no difference between the two scenarios, then how can a torque sensor measure a difference between static and zero torque? There clearly MUST be a difference for the sensor to be able to measure something!

The OP wants an 'exact' definition. JHamm's answer for him implies that torque can only exist where there is a change in angular momentum. That is confusing.

If you are saying 'ah, but it is true for 'net torque'' then I say 'so what'? Supplying an answer ONLY about net torque is not providing an 'exact' answer for TORQUE. The OP did not ask for an exact answer to 'define NET TORQUE', so why have the last several posts deviated to defining NET TORQUE?

 

[cepheid]

So answer my question; if there is no difference between the two scenarios, then how can a torque sensor measure a difference between static and zero torque? There clearly MUST be a difference for the sensor to be able to measure something!

I said there was no difference from the point of view of the object to which the (balanced or zero) torque is being applied. I even went further and stated specifically that there was no difference in terms of the dynamical effect on the object. For the answer to your question "how can it measure something!", please read post #16 (which you apparently didn't).

If you are saying 'ah, but it is true for 'net torque'' then I say 'so what'? Supplying an answer ONLY about net torque is not providing an 'exact' answer for TORQUE. The OP did not ask for an exact answer to 'define NET TORQUE', so why have the last several posts deviated to defining NET TORQUE?

It was my understanding that the exact definition of torque in terms of a cross product of a force with a position vector going from the point of rotation to the point of application of the force (i.e. τ = r X F), had already been supplied before the definition in terms of angular momentum was brought up. Now the question of whether τ = dL/dt is a complete definition is an interesting one. If you know the definition of L, then I would argue that it is, because you can then derive the first definition that I gave (which is the one you seem intent on passing off as "correct and "complete."):

τ = dL/dt

= d/dt (r x p)

= r x dp/dt

= r x F

...so, what say you?

 

[cmb]

I would ask, with dt appearing in your equation, how long does it take for a thing not to move? What dt do you put into that equation to describe the scenario of torques in equilibrium?

If, as I concluded above, it is not useful to describe torques in equilibrium, then how does it address the question?

 

[cepheid]

I would ask, with dt appearing in your equation, how long does it take for a thing not to move? What dt do you put into that equation to describe the scenario of torques in equilibrium?

What the hell are you talking about? "dt" by itself is not meaningful. d/dt is a differential operator representing differentiation with respect to time.

If, as I concluded above, it is not useful to describe torques in equilibrium, then how does it address the question?

The equation is, more properly, Ʃτ = dL/dt. Everyone has already acknowledged this. What more do you WANT?

EDIT: but the point is, that, if you want to, rather than starting with r x F, you can use the following as a starting point:

IF I have a single, unbalanced torque acting on an object, THEN it will be equal to the rate of change of angular momentum of that object.

From this, I can self-consistently arrive at r x F as I showed a couple of posts ago.

So I don't see why everything in italics cannot constitute a complete definition of "torque."

 

[bp_psy]

So answer my question; if there is no difference between the two scenarios, then how can a torque sensor measure a difference between static and zero torque? There clearly MUST be a difference for the sensor to be able to measure something!

Torque sensors use strain gauges. In order for them to function there must actually be some change in the shape of the material and of of the gauge.The actual measurement of torque then requires some information about the actual material.At this point we are not talking about the same idealized system as before but about something more complicated and we have to consider many other factors.If the strain gauge was deformed then at some point in time dL/dt was certainly not 0.

 

[cmb]

τ = dL/dt

= d/dt (r x p)

= r x dp/dt

= r x F

...so, what say you?

Sure. Clear enough to me what you are saying. If that works for the OP, then job done.

(I dispute nothing since #7, excepting that discussing 'change of angular momentum' does not appear to help define the case of static torques. A 'new' term, 'net torque' then had to be introduced to back it up. I view, equally, a problem with describing static forces in equilibrium with 'dp/dt'.)

 

[HeLiXe]

@HeLiXe: Nice pictures!

Thx ILS