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Plutarck said:
Exactly right!
Why can't I understand Torque?
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Exactly right!
Walter Wayne
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A slighty more formal definition from www.dictionary.com
torque - the measure of a force's tendency to produce torsion and rotation about an axis
A note: Whenever a torque is applied, there are two forces involved. When you twist a door knob, you apply opposite forces on top and bottom. When you turn a lever you apply a force on one side, and an opposing force is applied at the fulcrum.
Walt
torque - the measure of a force's tendency to produce torsion and rotation about an axis
A note: Whenever a torque is applied, there are two forces involved. When you twist a door knob, you apply opposite forces on top and bottom. When you turn a lever you apply a force on one side, and an opposing force is applied at the fulcrum.
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Walter Wayne said:
No, I don't think so. A torque can be applied as a single vector to a point on a rotating disc. I remember having to work out problems about it. Think of a train engine wheel being pushed around by its whatchamacallit.
Also, when you turn a doorknob, you apply force in the same direction on the top and bottom, not the opposite direction (relative to the doorknob, which is what counts). If this weren't so, you'd be fighting yourself and the doorknob wouldn't move. In this scanario, every place your hand touches the doorknob, a torque is being applied, adding up to the total torque applied to the doorknob.
It seems my previous post requires a few more statements.
Horsepower is merely a unit of power. It is not 'a function of torque and rotational speed'. It is a constant numerical quantity.
The SI unit of power is the Watt. 1 Horsepower ~ 750 Watts. By definition: one Watt is one Joule of work performed in one second. One Joule is the amount of energy associated with the application of a force of one Newton over a distance of one meter. One Newton is the force required to impart an acceleration of one meter/second^2 to an object with a mass of one kilogram.
As I stated earlier power is a measure of how quickly a system can do work. Detonating a piece of dynamite may release as much energy as digesting a jam doughnut, in which case the capacity of both systems to do work is the same. Their respective powers are, however, very different.
Both work and power are scalar quantities.
Since angular momentum is the cross product of the position vector and the linear momentum, it is perpendicular to the plane containing r and p. Think of an artillery shell or rifle bullet, these may be spun about an axis of symmetry that is parallel to the gun barrel, thus imparting an angular momentum that points in the same direction. The shell will tend to 'resist' change in its direction due to conservation of angular momentum, and is hence more accurate. This also explains why bicycles are stable when moving, but are not when stationary.
Torque is not a 'kind of force'. There is only one definition of force, viz. the time rate of change of linear momentum. In the case of constant mass this is written as F = ma, where a is the acceleration. The unit of torque is the Newton.meter. You may think of torque as the angular analogue of force.
Both torque and force are vectors. However, since torque is the time rate of change of angular momentum it is perpendicular to plane containing r and F. The magnitude of the torque reduces to rF only when F is perpendicular to r.
Momentum is not 'what keeps a moving object moving'. An object has momentum by virtue of its mass and its velocity. Nothing is needed to keep an object moving in the absence of external forces.
Plutarck,
Remember what I said earlier about the definition of force in terms of linear momentum. Perhaps this helps you to get a handle on the concept of momentum.
Horsepower is merely a unit of power. It is not 'a function of torque and rotational speed'. It is a constant numerical quantity.
The SI unit of power is the Watt. 1 Horsepower ~ 750 Watts. By definition: one Watt is one Joule of work performed in one second. One Joule is the amount of energy associated with the application of a force of one Newton over a distance of one meter. One Newton is the force required to impart an acceleration of one meter/second^2 to an object with a mass of one kilogram.
As I stated earlier power is a measure of how quickly a system can do work. Detonating a piece of dynamite may release as much energy as digesting a jam doughnut, in which case the capacity of both systems to do work is the same. Their respective powers are, however, very different.
Both work and power are scalar quantities.
Since angular momentum is the cross product of the position vector and the linear momentum, it is perpendicular to the plane containing r and p. Think of an artillery shell or rifle bullet, these may be spun about an axis of symmetry that is parallel to the gun barrel, thus imparting an angular momentum that points in the same direction. The shell will tend to 'resist' change in its direction due to conservation of angular momentum, and is hence more accurate. This also explains why bicycles are stable when moving, but are not when stationary.
Torque is not a 'kind of force'. There is only one definition of force, viz. the time rate of change of linear momentum. In the case of constant mass this is written as F = ma, where a is the acceleration. The unit of torque is the Newton.meter. You may think of torque as the angular analogue of force.
Both torque and force are vectors. However, since torque is the time rate of change of angular momentum it is perpendicular to plane containing r and F. The magnitude of the torque reduces to rF only when F is perpendicular to r.
Momentum is not 'what keeps a moving object moving'. An object has momentum by virtue of its mass and its velocity. Nothing is needed to keep an object moving in the absence of external forces.
Plutarck,
Remember what I said earlier about the definition of force in terms of linear momentum. Perhaps this helps you to get a handle on the concept of momentum.
A couple of comments...
we have by substitution:
You may think of torque as a kind of force.
That is to say, without the pedantry.
Do you really think that makes it clearer for a person that is new to the concept?LucyR said:
Which was quickly followed by:
And, where "a kind of" = "the angular analogue"
we have by substitution:
You may think of torque as a kind of force.
That is to say, without the pedantry.
Sorry, but inertia is what is needed to keep an object moving. No inertia, no coasting. It is the definition of inertia.
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LucyR said:
From dictionary.com:
Momentum: Impetus of a physical object in motion.
So the best word is really inertia:
Inertia: the tendency of a body at rest to remain at rest or of a body in straight line motion to stay in motion in a straight line unless acted on by an outside force.
"What keeps a moving object moving" is a perfectly valid way of stating this.
Tez
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not sure this'll help the specific question at hand, but a great demonstration none-the-less.
Take a broom - one with a wooden handle. Find the point where you can balance it on your finger, and mark that point with a pen.
Cut the broom at the marked point.
Feel the weight of both pieces. Are they the same?
Once you understand that you understand the difference between force and torque...
Take a broom - one with a wooden handle. Find the point where you can balance it on your finger, and mark that point with a pen.
Cut the broom at the marked point.
Feel the weight of both pieces. Are they the same?
Once you understand that you understand the difference between force and torque...
Tez
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because the broom is asymmetric, the two pieces wont weight the same.
The balance point is when the torque around that point is 0, not when the weight of the two pieces is the same.
Say the (point particle!) head of the broom weighs 5 Kg, the broom is 2m long, and the wood has a (uniform) mass per unit length of 1 kg/metre. (Dont let anyone attack you with such a broom).
Let "x" be the distance from the head of the broom to the balance point.
Then the balance occurs when
5*x+M*x*(x/2)=(L-x)/2*M*(L-x)
putting M=1,L=2 gives some value of x which I cant be bothered working out (I've ignored "g" - acceleration due to gravity becoz it cancels from both sides).
Whatever that value of x is, use it to calculate the mass of the two pieces - they will not be the same (see if you can guess which will be greater before the calculation!)...
The balance point is when the torque around that point is 0, not when the weight of the two pieces is the same.
Say the (point particle!) head of the broom weighs 5 Kg, the broom is 2m long, and the wood has a (uniform) mass per unit length of 1 kg/metre. (Dont let anyone attack you with such a broom).
Let "x" be the distance from the head of the broom to the balance point.
Then the balance occurs when
5*x+M*x*(x/2)=(L-x)/2*M*(L-x)
putting M=1,L=2 gives some value of x which I cant be bothered working out (I've ignored "g" - acceleration due to gravity becoz it cancels from both sides).
Whatever that value of x is, use it to calculate the mass of the two pieces - they will not be the same (see if you can guess which will be greater before the calculation!)...
Gary,
I was not meaning to be unduly pedantic, and I was not attempting to belittle you, or the other posters.
The point is that there are perfectly good extant and distinct definitions of both force and torque, so why not use them?
I do not know if A_U_P understands the cross product or not, but it's nevertheless important for understanding the distinction between the two concepts.
I do not think that 'a kind of' and 'an analogue of' are synonymous. I'd say that a Labrador is 'a kind of' dog but not 'an analogue of' a dog. An analogue would presumably be something that fulfills a similar role in the same, or a different context, but is nevertheless intrinsically different. The way I think about it force and torque are analogues in the sense that they are both vectors, they can both give rise to motion, and can both be expressed as the time-derivative of momentum or a quantity that involves momentum. On the other hand, force produces linear motion, torque produces angular motion. I must say that I don't believe its unusual to describe the following quantities as analogues of one another:
linear displacement, velocity, acceleration, momentum /angular displacement, etc.
force/torque.
When I said that momentum is not what keeps an object moving, I was replying to Sundog who stated that it is. I said that an object has a momentum by virtue of its mass and its velocity. I said that nothing is needed to keep an object moving in the absence of external forces. I assume in this discussion we are limiting ourselves to Newtonian particles having non-zero rest masses. Mass is a quantitative measure of inertia, i.e. no mass - no inertia - no object. Inertia is intrinsic. Let me know if you're not happy with this.
In any case, I appreciate being able to have these discussions, and do not want to end up merely pissing people off.
Sundog,
Dictionary definitions are not always appropriate. The common meaning of terms such as force, momentum, work, and power, are often only distantly related to their scientific definitions (and this is after all the science forum). Once again, momentum is defined as the product of an object's mass and its velocity, no more no less. An object is accelerated by a force, it possesses a momentum as a result of that force. Its changing momentum is indicative of the continued application of a net force, etc., etc., etc.
In the absence of external forces, the object either remains at rest or continues moving in the same direction. This is indeed the principle of inertia. However, since we regard mass as a measure of inertia, I think it sounds rather superfluous to state that an object needs inertia to continue in a str line etc. No inertia implies no mass, which in turn implies no object. Is this reasonable?
I was not meaning to be unduly pedantic, and I was not attempting to belittle you, or the other posters.
The point is that there are perfectly good extant and distinct definitions of both force and torque, so why not use them?
I do not know if A_U_P understands the cross product or not, but it's nevertheless important for understanding the distinction between the two concepts.
I do not think that 'a kind of' and 'an analogue of' are synonymous. I'd say that a Labrador is 'a kind of' dog but not 'an analogue of' a dog. An analogue would presumably be something that fulfills a similar role in the same, or a different context, but is nevertheless intrinsically different. The way I think about it force and torque are analogues in the sense that they are both vectors, they can both give rise to motion, and can both be expressed as the time-derivative of momentum or a quantity that involves momentum. On the other hand, force produces linear motion, torque produces angular motion. I must say that I don't believe its unusual to describe the following quantities as analogues of one another:
linear displacement, velocity, acceleration, momentum /angular displacement, etc.
force/torque.
When I said that momentum is not what keeps an object moving, I was replying to Sundog who stated that it is. I said that an object has a momentum by virtue of its mass and its velocity. I said that nothing is needed to keep an object moving in the absence of external forces. I assume in this discussion we are limiting ourselves to Newtonian particles having non-zero rest masses. Mass is a quantitative measure of inertia, i.e. no mass - no inertia - no object. Inertia is intrinsic. Let me know if you're not happy with this.
In any case, I appreciate being able to have these discussions, and do not want to end up merely pissing people off.
Sundog,
Dictionary definitions are not always appropriate. The common meaning of terms such as force, momentum, work, and power, are often only distantly related to their scientific definitions (and this is after all the science forum). Once again, momentum is defined as the product of an object's mass and its velocity, no more no less. An object is accelerated by a force, it possesses a momentum as a result of that force. Its changing momentum is indicative of the continued application of a net force, etc., etc., etc.
In the absence of external forces, the object either remains at rest or continues moving in the same direction. This is indeed the principle of inertia. However, since we regard mass as a measure of inertia, I think it sounds rather superfluous to state that an object needs inertia to continue in a str line etc. No inertia implies no mass, which in turn implies no object. Is this reasonable?
a_unique_person
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Tez said:
thanks for the input all of you. This has generated more discussion than i expected.
Thanks for also putting this in the correct words I should have used, the difference between force and torque is what I am after.
I will simulate the experiment with something cheaper than a broom, I don't have any spare old ones lying around at the moment.
Lucy, I wasn't trying to be aggravating to you either. I merely wanted to point out that people that have a difficult time grasping what torque is, can't picture it, usually aren't helped with strictly scientifically and technically precise explanations. I didn't feel that adding confusing concepts like vectors (or even moments) was appropriate. Discussing cross products with someone that hasn't grasped the basics may make them feel that it's all too complicated and not worth the bother. Unless the person specifically asks about the vectors and such I tend to leave them out at first.
Describing torques as a "rotary force" is, imho, completely appropriate. Both cause acceleration, although one does so for linear motion and the other for rotary motion. Yes, I really believe that describing torque as a "type of force" is better than "an analogue of" because they do almost the same thing.
The distinction between force's linear effects and torque's rotational one was being emphasized, so I guess I don't see any harm in calling it "rotational force." We may agree to disagree here.
Likewise, your technically correct DEFINITION of horsepower was not as good (again, imho) at illustrating the point of how torque relates to a vehicle's engine output as the simple equation. By showing the relationship between the AMOUNT of horsepower it generates to its torque and speed it's easier to see how things work. Yes, of course, power is energy divided by time, but what that more general, esoteric concept means when thinking of an engine that generates 275 lb-ft. of torque at 3800 RPM and 320 Hp at 5600 RPM isn't particularly helpful.
I do like to start slowly and, given enough time, would likely start with more fundamental concepts. But when a post to a website forum asks for a simple understanding of the concepts of torque and power, I think it's easier and more appropriate to use analogies and reasonable simplifications that are easily grasped.
Regarding momentum and its relationship to "what keeps bodies in motion," you are correct. Momentum is entirely a mathematical construct (unlike torque, which is a physical phenomena we can create with a twist of the wrist). The correct term for what makes things tend to stay at one velocity is inertia. Similar to mass, yes, but when jumping back and forth between linear motion and rotational motion concepts in this case I guess the most technically correct term fits better. Most people have heard of inertia but many don't know what it really represents. Of course, it basically IS mass when considering linear motion but it's a bit more complicated when discussing rotational motion.
Describing torques as a "rotary force" is, imho, completely appropriate. Both cause acceleration, although one does so for linear motion and the other for rotary motion. Yes, I really believe that describing torque as a "type of force" is better than "an analogue of" because they do almost the same thing.
The distinction between force's linear effects and torque's rotational one was being emphasized, so I guess I don't see any harm in calling it "rotational force." We may agree to disagree here.
Likewise, your technically correct DEFINITION of horsepower was not as good (again, imho) at illustrating the point of how torque relates to a vehicle's engine output as the simple equation. By showing the relationship between the AMOUNT of horsepower it generates to its torque and speed it's easier to see how things work. Yes, of course, power is energy divided by time, but what that more general, esoteric concept means when thinking of an engine that generates 275 lb-ft. of torque at 3800 RPM and 320 Hp at 5600 RPM isn't particularly helpful.
I do like to start slowly and, given enough time, would likely start with more fundamental concepts. But when a post to a website forum asks for a simple understanding of the concepts of torque and power, I think it's easier and more appropriate to use analogies and reasonable simplifications that are easily grasped.
Regarding momentum and its relationship to "what keeps bodies in motion," you are correct. Momentum is entirely a mathematical construct (unlike torque, which is a physical phenomena we can create with a twist of the wrist). The correct term for what makes things tend to stay at one velocity is inertia. Similar to mass, yes, but when jumping back and forth between linear motion and rotational motion concepts in this case I guess the most technically correct term fits better. Most people have heard of inertia but many don't know what it really represents. Of course, it basically IS mass when considering linear motion but it's a bit more complicated when discussing rotational motion.
OK, yes, of course. Thanks! That is an interesting illustration of torque, where the two pieces balance because of equal torques around the pivot but each has different weights.Tez said:
Sundog, after you do this experiment, note that the longer piece, being farther from the pivot, will need less weight to balance the shorter, heavier piece. This is because the balance requires that the TORQUES of each balance, and that happens when the torque of the left piece is the same as the torque of the right.
Torque(L) = Torque(R)
Weight(L) * Length (L) = Weight(R) * Weight(R)
If the left side has more weight than the right it will have a proportionately shorter length, so that both products are the same and the equation balances.
Thanks, Tez, good one!
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Sundog,
Dictionary definitions are not always appropriate. The common meaning of terms such as force, momentum, work, and power, are often only distantly related to their scientific definitions (and this is after all the science forum).
The equations are of course essential to understanding the concepts, but keep in mind the context: we are trying to make this clear to a layman. The dictionary definition given is, in fact, entirely compatible with the definition you gave, which is of course correct. I realized that I had used "momentum" where I meant "inertia." The dictionary definition is what mane me realize my error.
I think it sounds rather superfluous to state that an object needs inertia to continue in a str line etc.
Yes, to someone used to thinking about these things. (I don't think I said or implied that an object "needs" inertia to keep moving.) This is not a scientific debate, though; it's an attempt to convey intuitive understanding of these concepts to someone unfamiliar with them. I think in this context, my wording of the idea was perfectly appropriate, as was my description of torque as "force applied in a circle". Your very correct notation that it is actually the angular analogue doesn't help the layman much. I think.
But all of us together got the job done!
Dictionary definitions are not always appropriate. The common meaning of terms such as force, momentum, work, and power, are often only distantly related to their scientific definitions (and this is after all the science forum).
The equations are of course essential to understanding the concepts, but keep in mind the context: we are trying to make this clear to a layman. The dictionary definition given is, in fact, entirely compatible with the definition you gave, which is of course correct. I realized that I had used "momentum" where I meant "inertia." The dictionary definition is what mane me realize my error.
I think it sounds rather superfluous to state that an object needs inertia to continue in a str line etc.
Yes, to someone used to thinking about these things. (I don't think I said or implied that an object "needs" inertia to keep moving.) This is not a scientific debate, though; it's an attempt to convey intuitive understanding of these concepts to someone unfamiliar with them. I think in this context, my wording of the idea was perfectly appropriate, as was my description of torque as "force applied in a circle". Your very correct notation that it is actually the angular analogue doesn't help the layman much. I think.
But all of us together got the job done!
diddidit
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I wrapped my brain around it this way:
Torque is something you make with a rotational engine, like an electric motor.
That motor operates at some rotational speed, so speed is also something you make.
Power, being the product of torque and speed, is something you get.
SO: A crane requires a certain amount of torque from its motor, based on the mechanical advantage of the gears and rigging and the lifted load. That amount of torque is constant whether you are lifting that load at 5 feet per minute or 10 fpm. But, if the 10 fpm version uses an 1800 rpm motor, the 10 fpm one needs a 3600 rpm motor. The 3600 rpm motor will have the same torque as the 1800 but with twice the speed it will have twice the power.
(I was in the crane+hoist bidness until a few years ago).
did
Torque is something you make with a rotational engine, like an electric motor.
That motor operates at some rotational speed, so speed is also something you make.
Power, being the product of torque and speed, is something you get.
SO: A crane requires a certain amount of torque from its motor, based on the mechanical advantage of the gears and rigging and the lifted load. That amount of torque is constant whether you are lifting that load at 5 feet per minute or 10 fpm. But, if the 10 fpm version uses an 1800 rpm motor, the 10 fpm one needs a 3600 rpm motor. The 3600 rpm motor will have the same torque as the 1800 but with twice the speed it will have twice the power.
(I was in the crane+hoist bidness until a few years ago).
did