On the nature of torque ....

[WhiteBlue]

I have eventually had a look in a book and found the formula that explains it all.

W=M*phi

W is the spring energy of a torsion spring
M is the torque or moment
phi is the dimensionless angular displacement

This is the reason why torque has the same dimension as the stored energy. The angular displacement is a non dimensional variable.

The confusing thing is that the angular displacement in a system with fixed geometry grows proportionally with the torque. So you can say that the energy grows proportionally with the torque in a fixed geometry system. There is in this case a fixed factor between torque and spring energy.

If you look at different geometries the angular displacement becomes highly variable because the stiffness goes with the power of 4 of the radius. So stored energy from the same torque is much bigger in a shaft that is slim and weak than in a shaft that is thick and strong.

Sorry for taking very long to understand it.

Now if we go back to an engine crankshaft for all practical purposes its geometry is fixed and it has a fixed torsional spring rate. So in this case we can also say that the torque applied to a crank shaft of given geometry only varies from the spring energy by a fixed factor which is inherent to the geometric design.

http://www.f1technical.net/forum/viewto ... 43#p443943

Wuzak has explained the formula on page 1. At that point I got confused by the proportionality in a fixed geometric system and I did not check how the spring rate depends of the radius. A pity I can't give the vote up that he deserves.

Edit: changed moment for momentum, thanks to Wuzak

[wuzak]

I have eventually had a look in a book and found the formula that explains it all.

W=M*phi

W is the spring energy of a torsion spring
M is the torque or momentum
phi is the dimensionless angular displacement

You have to be careful with your terminology.

Moment is similar/the same as torque, but momentum is different.

While Moment have the units Nm, momentum is the product of mass and velocity, so it has units of kgm/s. There is also angular momentum, but I'd have to look up the units for that.

[WhiteBlue]

Ok, use moment please instead. A language problem. I wasn't fully aware of the proper translation.

The interesting point is that torque is not exactly equal to the deformation energy. But it is different only by a dimensionless factor, that comes from the geometry. Hence torque must be energy, which was one of the points of contention.

If you write the equation:

A = factor * B

If A is an energy it follows that B must be an energy as well. You cannot change the physical nature of something by multiplying it with a number.

So in the end we can say that torque is a part or a multiple of the deformation energy applied to a rotational elastic system and that the proportion between the torque and the deformation energy depends of geometrical factors.

[wuzak]

Ok, use moment please instead. A language problem. I wasn't fully aware of the proper translation.

The interesting point is that torque is not exactly equal to the deformation energy. But it is different only by a dimensionless factor, that comes from the geometry. Hence torque must be energy, which was one of the points of contention.

If you write the equation:

A = factor * B

If A is an energy it follows that B must be an energy as well. You cannot change the physical nature of something by multiplying it with a number.

So in the end we can say that torque is a part or a multiple of the deformation energy applied to a rotational elastic system and that the proportion between the torque and the deformation energy depends of geometrical factors.

The dimensionless factor is the angular deflection, which is rather important for calculating the spring energy.

Torque is a factor in determining that energy, as force is a factor in calculating work.

[WhiteBlue]

Yes, that is understood. But the mathematic principle still stands. You cannot multiply an energy with a constant and get any thing else but an energy. Hence torque cannot be anything but an energy. The multiplication with the angular distortion only determines the amount of energy that is absorbed by the system and nothing else.

[rjsa]

You are taking dimensional analysis too seriously. It's a tool, not the Delphi oracle.

1N.m means one newton at one meter. Half a newton at two meters and two newtons at half a meter. Never one joule.

[WhiteBlue]

You are taking dimensional analysis too seriously. ..

Thanks for that lovely opinion. I return the compliment and say that you don't take mathematics seriously enough. In this world it is impossible to multiply anything but energy with a dimensionless number and arrive at energy again.
if f is a dimensionless factor you can say:

Voltage1 = f * Voltage2
Energy1 = f * Energy2
Power1 = f * Power2

but you cannot say:

Apples1 = f * bananas1

Apples simply are not equal to any number of bananas. Or perhaps you are in a world where you can compare apples with bananas. Perhaps we live in a parallel universes where different mathematics are valid?
Or perhaps I'm simply right with saying that torque is energy and some people cannot accept it.

1Nm = 1J Isn't that very simple and true? As simple as saying torque is energy.

[Blanchimont]

[youtube]http://www.youtube.com/watch?v=heCsKujaxs4[/youtube]

[amc]

So, if torque is analogous to energy, how the hell do you apply the conservation of energy (read: torque) to a gearbox ?

In this world it is impossible to multiply anything but energy with a dimensionless number and arrive at energy again.

Have you considered that angular deflection may not be a dimensionless number?

Torque may be thought of as the cross product of force and distance, suggesting the unit newton metre, or it may be thought of as energy per angle, suggesting the unit joule per radian.

While most sources will say that the radian can be ignored, for the purposes of differentiating torque and energy through dimensional analysis, it should be included. You would not argue that angular velocity has units Hertz, and certainly not Becquerels. (Maybe you would )

On the Nature of Torque... it is a vector. Therefore it cannot be added to a scalar (e.g. energy) regardless of the units.

[wuzak]

You are taking dimensional analysis too seriously. ..

Thanks for that lovely opinion. I return the compliment and say that you don't take mathematics seriously enough. In this world it is impossible to multiply anything but energy with a dimensionless number and arrive at energy again.
if f is a dimensionless factor you can say:

Voltage1 = f * Voltage2
Energy1 = f * Energy2
Power1 = f * Power2

but you cannot say:

Apples1 = f * bananas1

Apples simply are not equal to any number of bananas. Or perhaps you are in a world where you can compare apples with bananas. Perhaps we live in a parallel universes where different mathematics are valid?
Or perhaps I'm simply right with saying that torque is energy and some people cannot accept it.

1Nm = 1J Isn't that very simple and true? As simple as saying torque is energy.

I thought we had talked ou around to believing the truth - that torque is not any form of energy - not potential energy, not kinetic energy, not nuclear energy.

Torque is the "moment of force" acting on a lever. That is how it is defined.

And yes, you can multiply torque with a dimensionless value to get work/energy - if that value is angular deflection, motion. Also, note that while angular deflection is dimensionless, it is not unitless - it has units of radians.

Since you uare fond of mathematics, you will know that the radian is the angle subtended by an arc whose length is the same as its radius.

The problem for you is that while energy Joules is equal to Nm it is a force and distance moving in the same direction, not perpendicular to one another.

Torque is the rotational analog to Force. There are other analogs, and they all have different units (and dimensions) to their linear counterparts.

Code: Select all

Linear                Rotational
Mass (kg)             Mass Moment of Inertia (kg.m^2)
Force (N)             Torque (Nm)
Distance (m)          Angle (radians)
Velocity (m/s)        Angular Velocity (radians/s)
Acceleration (m/s^2)  Angular acceleration (radians/s^2)
Momentum (kg.m/s)     Angular Momentum (N.m.s or kg·m^2/s or J.s)

FWIW, dimensional analysis is helpful for scaling properties - such as calculating the wind speed required for a scale model to replicate the effects at full scale, or for using different fluids (like water instead of air).

It does not tell you if one is the same as the other.

[WhiteBlue]

Wuzak, the problem is you think of units in a popular way and not in a scientific way. If an entity with a unit is dimensionless it is just a number, a ratio, a factor or a percentage even. It can even be a physical quantity, but it is a dimensionless quantity. It is irrelevant if you can see it in the mechanical system or not. But it is nothing that can change the dimensional balance of an equation that expresses a law of nature between physical quantities.

It is the same effect that you can see between the cross section of a 3D object and it's shadow. The physical quantity of both is area and the base unit m to the power of two. Because you see the shadow under a visible angle the area of the shadow may be bigger or smaller than the cross section of the object. But the angle does not change the fact that both entities - the cross section and the shadows - have the same physical quantity and the same dimension. The same is true for torque and torsional spring energy. The angular distortion affects the size of the energy that gets stored as a result of the torque, but it does not change the nature of the physical quantity and its dimension. Torque and torsional spring energy have the same dimension, they share the same physical quantity and hence they are a form of energy.

We do agree that the energy law of the torsion spring applies and is correct. But you keep mixing up the properties of reciprocating displacement and angular displacement. Because the reciprocating displacement has a dimension the product of force and stroke is energy. Both stroke and force themselves are different in their physical quantity from energy. Only their product belongs to the physical quantity "energy".

Because the angular displacement is visible it does not mean it has a physical dimension. It cannot contribute a dimension, it can only contribute a scaling effect on the energy that is already provided by the torque. Compare the example above about the shadow.

Dimensional analysis is helpful for scaling properties... It does not tell you if one is the same as the other.

I believe it actually does that, although you may not recognize it. Perhaps you can give me an example - other than torque - where you perform a dimensional analysis and you can show that both entities have the same SI base units and dimensions but do not share the same physical quantity.

To put it even simpler. Entities that show the same dimensional structure also share the same physical quantity. That is my firm believe. But I'm prepared to learn if I'm wrong.

[bhall]

So, if torque is analogous to energy, how the hell do you apply the conservation of energy (read: torque) to a gearbox ?

In this world it is impossible to multiply anything but energy with a dimensionless number and arrive at energy again.

Have you considered that angular deflection may not be a dimensionless number?

Torque may be thought of as the cross product of force and distance, suggesting the unit newton metre, or it may be thought of as energy per angle, suggesting the unit joule per radian.

While most sources will say that the radian can be ignored, for the purposes of differentiating torque and energy through dimensional analysis, it should be included. You would not argue that angular velocity has units Hertz, and certainly not Becquerels. (Maybe you would )

On the Nature of Torque... it is a vector. Therefore it cannot be added to a scalar (e.g. energy) regardless of the units.

So, I should probably stop looking for something like this, huh?

[langwadt]

Wuzak, the problem is you think of units in a popular way and not in a scientific way. If an entity with a unit is dimensionless it is just a number, a ratio, a factor or a percentage even. It can even be a physical quantity, but it is a dimensionless quantity. It is irrelevant if you can see it in the mechanical system or not. But it is nothing that can change the dimensional balance of an equation that expresses a law of nature between physical quantities.

It is the same effect that you can see between the cross section of a 3D object and it's shadow. The physical quantity of both is area and the base unit m to the power of two. Because you see the shadow under a visible angle the area of the shadow may be bigger or smaller than the cross section of the object. But the angle does not change the fact that both entities - the cross section and the shadows - have the same physical quantity and the same dimension. The same is true for torque and torsional spring energy. The angular distortion affects the size of the energy that gets stored as a result of the torque, but it does not change the nature of the physical quantity and its dimension. Torque and torsional spring energy have the same dimension, they share the same physical quantity and hence they are a form of energy.

We do agree that the energy law of the torsion spring applies and is correct. But you keep mixing up the properties of reciprocating displacement and angular displacement. Because the reciprocating displacement has a dimension the product of force and stroke is energy. Both stroke and force themselves are different in their physical quantity from energy. Only their product belongs to the physical quantity "energy".

Because the angular displacement is visible it does not mean it has a physical dimension. It cannot contribute a dimension, it can only contribute a scaling effect on the energy that is already provided by the torque. Compare the example above about the shadow.

Dimensional analysis is helpful for scaling properties... It does not tell you if one is the same as the other.

I believe it actually does that, although you may not recognize it. Perhaps you can give me an example - other than torque - where you perform a dimensional analysis and you can show that both entities have the same SI base units and dimensions but do not share the same physical quantity.

To put it even simpler. Entities that show the same dimensional structure also share the same physical quantity. That is my firm believe. But I'm prepared to learn if I'm wrong.

it should be obvious that distance moved and then length of lever, while both measured in meters, are not the same thing

the formal explanation is probably something long the lines of the lever and force being orthogonal so their dot product is
zero

force doesn't magically become energy when you pull on a string wrapped around a cylinder

[WhiteBlue]

So, if torque is analogous to energy, how the hell do you apply the conservation of energy (read: torque) to a gearbox ?
Have you considered that angular deflection may not be a dimensionless number?

Torque may be thought of as the cross product of force and distance, suggesting the unit newton metre, or it may be thought of as energy per angle, suggesting the unit joule per radian.

While most sources will say that the radian can be ignored, for the purposes of differentiating torque and energy through dimensional analysis, it should be included. You would not argue that angular velocity has units Hertz, and certainly not Becquerels. (Maybe you would )..

Nice argument, lets look at it in detail.

1. No problem with the conservation of energy. There are different energies in a gearbox and different formulae to evaluate them according to the balance and the model that you apply. You have the stored energy or the transmitted energy. Both are entirely different and described by different models and balances.

2. Angular deflection is a dimensionless physical quantity. I'm very happy to accept that torque is energy per angle or energy per a dimensionless quantity as defined by the International Bureau of Weights and Measures. It means that it is a distinguished form of energy, by merit of its vectorial quality. I'm even going so far to say that Energy per angle and Energy without angular specification cannot be mixed in the same energy balance, because one is a vector and the other is scalar. There are obviously differences between angular specific energy and non specific energy but there are also similarities. They still belong in the same group of physical quantities that use the same base units for measuring. I will settle on the distinction that torque is angular specific energy and in comparison carries a vectorial quality which makes it different for application purposes from non specific scalar energy.

3. If we compare angular velocity, electric frequency and nuclear decay event frequency the common thing is they all belong in the frequency class of physical quantities and they all are measured in per second. Again a distinction between scalar frequencies and vectorial frequencies should apply. You may not use them in one balance but they share the frequency quality and as such are part of the same class of physical quantities. Bequerel and Hertz are both scalar frequencies and therefore are on an abstract level the same. The angular velocity is a vector and more different from the other two in my view.

[rjsa]

Well, I guess one of the biggest mysteries in nature is now solved.

Gravity, since it's described in m/s^2, is just acceleration.

No need to go looking after strong and weak particle bonds and the curvature of the space time continuum.