Why Is Momentum Defined as 'Quantity of Motion'?

[simpatico]

I know definition is hard job, expecially

I) verbal definition,
which must find the essence (nature, substance,...) of an entity (being: [ object, thing..], [concept, idea, category...]),
and needs interdisciplinary help from ontology, linguistics (morpho-syntax, semantics), logic and epistemology...
but I do hope a phisicist could explain why Quantity of Motion ?
just two questions:

1) why motion? it doesn't seem a technical (precise,defined...) term, I never found it elsewhere. Is it different from movement, speed ,velocity v ?
I know v is a vector, speed is not. But motion?

2) Why add quantity? is "quantity of motion" a different category from motion
is "quantity of energy", (books,pears...) different from energy (...)


II) numeric definition : p = m * v (mass-by-velocity)
seems simpler (just arithmetics) and more precise, effective, decisive, conclusive...

But please read the following with care, it is not a joke but a very profound issue

1) we have ...
... 10 (sweets) and 5 (children), let's multiply :
... 10 * 5 = 50 (fifty what? I say: children, and I am not joking)

someone says: NO WAY! it's sweets.He is using commonsense and (probably) he's right, but can he disprove me with scientific foolproof arguments?

2) Now we have 10 (crates) and 5 (boxes) , we get 50 what?

3)are we allowed to create a new category just by multiplication?...

so we'd have sweet-by-child, crate-by-box, jam-by-jar ... ad lib ?

 

[mikeph]

You would multiply the units as well as the numerical values. So 10 sweets times 5 children equals 50 sweets.children. The units (what you call category) don't make any sense which reflects the nonsensical multiplication. But if you stick to this process, you will at least be self-consistent. Look at some physical constants... Stefan-Boltzmann constant, 5.67...*10^-8 J m^-2 s^-1 K^-4. To me that number doesn't make any sense. It's an energy per unit area per second per temperature^4. But if you discard the units, you are losing valuable physical information that could possible be very useful later on.

I've never heard it "quantity of motion", I guess you can call it whatever you want as long as your understanding of its meaning matches everyone else's. I don't like that definition for reasons that you posted. "Motion" is neither scalar nor vector, and "quantity" does not give you any idea that we are measuring mass.

 

[Dale]

1) we have ...
... 10 (sweets) and 5 (children), let's multiply :
... 10 * 5 = 50 (fifty what? I say: children, and I am not joking)

someone says: NO WAY! it's sweets.He is using commonsense and (probably) he's right, but can he disprove me with scientific foolproof arguments?

No, he is wrong. It is 50 children sweets. Is he not aware of how to multiply units?

3)are we allowed to create a new category just by multiplication?...

so we'd have sweet-by-child, crate-by-box, jam-by-jar ... ad lib ?

Of course you are allowed. You may even find something useful for your new units (e.g. predicting the number of screaming children), but you are allowed regardless.

 

[simpatico]

1) The units (what you call category) don't make any sense ...

2)I've never heard it "quantity of motion",
3) I guess you can call it whatever you want ...(this doesn't sound scientific to me)

1) unit is different from category, you might call it "a basic category" (space, time...)
or other(joule,...)
I purposedly avoided this word because
a) in physics it has a precise technical meaning, a 'connotation' I want to avoid in a verbal definition
b) It brings along the shadow of dimension
c) I do not wish that students who do not grasp the issue bring in elements, (such as inertia,unit,dimension,energy...) foreign to the discussion

2)I'm sorry about that.
It was started by Newton and Wallis, who,as it seems independently used the Latin 'quantitas motum'.It was then translated in most languages as
( 'cantitad de movimiento, quantità di moto, quantitè de mouvement, bewegungsmenge,quantity of motion..English prefers the short term,...)

3)I'm sorry about that too, because I asked for a better definition not for a worse!
Thank you anyway, your post is very useful for future posts

 

[jambaugh]

Here's the thing about formal definitions. Since you have to use terms to define terms then definitions are either cyclic (as in common language) or you start with certain undefined terms (as in formal mathematics) or a mixture of both (science).

Ultimately in physics observable quantities are defined by how they are observed. Other derivative quantities are defined in terms of observable quantities.

• time is what we measure with clocks,
• distance is what we measure with measuring rods,
• speed is distance/time or time rate of change of distance,
• velocity is displacement/time (keeping track of direction as well.)

momentum is usually a primary observable (what we measure in momentum observation experiments e.g with a http://en.wikipedia.org/wiki/Ballistic_pendulum" ) and we use the relationship between momentum and velocity to define (inertial) mass.

Of course the conventions of definitional primacy vary depending on the sub-discipline.

 

[simpatico]

1) then definitions are either cyclic (as in common language)
2) you start with certain undefined terms (as in formal mathematics) or a mixture of both (science).

3) derivative quantities are defined in terms of observable quantities.

Hi, Sir, I'm honoured you're here... ( )
...your arguments are so sound!, it's the first time I hear a scientist (mad or not) acknowledge his limits. Now..
..
1)(Common language), Linguists are lucky because most words mean objects, so they can use ostensive definitions, pictorial dictionaries, also use basic intuitive terms and so often are able to avoid circular (or cyclic) definitions.
2)Chemists are the luckiest,as , in a way,
they are Ontologists because they deal with essences
they can create new categories by addition... what is water ? (H+H+O)
...wonderful! .
3) pardon my ignorance , I don't understand what is a derivative quantity.
I guess an observable quantity may be
g, (the effect, the phenomenon)
but from that you derive (deduce), I suppose,
(the cause) e.g. force, but not quantities.
or do you mean the formula ?
Please give example
...
Now, coming to physics, the question is:
Can we ( I mean you, specialists, I am just alien,an autistic savant)
accept that physics (science by definition) give
circular definitions :
"energy is capacity to do work" and "work is...transferred energy" ?
(isn't it dangerous for the development of any sound theory?..If you acknowledged what really momentum is you wouldn't entangle in the photon-momentum senseless debate), or
intuitive definitions: Force is an influence, a push or a pull...

once,discussing with a friend, I questioned the force of gravity and its formula but could not conclude the debate, because he wouldn't produce a definition (and so a justification of its formula).
...
Lastly, what do you think, we get 50 what ?
(please do not mention units: that's simple arithmetic, not definition.)

 

[Dale]

Can we ( I mean you, specialists, I am just alien,an autistic savant)
accept that physics (science by definition) give circular definitions

You missed the most important part of his post.

Ultimately in physics observable quantities are defined by how they are observed.

That is what keeps physics definitions from being circular.

 

[simpatico]

1) unit is different from category, ...
...
c) I do not wish that students who do not grasp the issue bring in elements, (such as ...unit,dimension....) foreign to the discussion

the reason for this is very simple : unit is an ambiguous word, in physics:
it has pole-asunder meanings
abstract idea : space
concrete thing: meter, rod
multiple (concrete): kilometer
...
it is also used as an inappropriate synonym for dimension
which is a meaningless word ,a non-existing category, when you use, as you should, ONE system of units.
It is a tool which is necessary only when you keep more than one, to convert from one to the other avoiding BABEL
It is dangerous in a formal (theoretical) discussion

 

[Dale]

In physics, when you plug numbers into equations those numbers have units. If you are not talking about units then your topic seems to be not relevant to physics. In particular, you seem concerned about whether or not it is valid to multiply a mass by a velocity to get a new quantity: it is.

Are you actually interested in discussing physics here or not?

 

[mikeph]

Units are anything but ambiguous. 'space' is not a unit, nor is 'rod'. Without units, numbers have no connection to observations. If I weigh some apples and someone forbids me to use units, I'll end up saying "three ____ weigh seven ___ on this scale". The sentence is missing all its nouns. They're a crucial part of any coherent thought about reality.

 

[BruceW]

I)
I went on wikipedia, and apparently "quantity of motion" was a term that Rene Descartes used to describe the product of size and speed. (Not the same meaning as momentum). And then when the concept of momentum was beginning to be invented, the term "quantity of motion" was initially used in several places. (I guess because the phrase seemed similar to what they were trying to describe).
So I guess the meaning of the phrase "quantity of motion" has changed since Descartes first invented it.

1) The term "motion" could mean several things. Einstein used it to mean the velocity, I think.
II) 3) Yeah, we can make whatever units we want, for example I could use foxes times rabbits as a unit useful for measuring the biodiversity.