Now what exactly does momentum mean

[bomba923]

Now this may sound silly, but what does it exactly represent? (i'm taking physics..getting an 'A'...no problem, but momentum came up)

Now what exactly does momentum mean??
We think of force as a push or pull...
We acceleration as change in motion (speeding up/down, turning..etc-etc...)
We think speed as amt. distance/time...

But momentum??What is it---i need a definition OTHER than mass*velocity...
I need a definition other than a change in impulse (force*change in time)

What does momentum PHYSICALLY (push/pull, speed up/down) represent?

The closest thing in my head is "inertia with respect to velocity"--

But yeah...what does momentum PHYSICALLY represent? The product of mass and velocity...what does it MEAN? ("physically-speaking")?

 

[PBRMEASAP]

Well here's a start. If you accept "push or pull" as a definition for force, then momentum is something that is conserved in the absence of a force. It's not the most physical picture in the world, but maybe its a little better than p=mv. Note that momentum itself does not measure the resistance to change in motion--that is the mass. Mass = Inertia.

The concept of momentum conservation is actually pretty deep. It is a direct consequence of the idea that space has translational symmetry. All that means is that, far away from any massive objects that might attract me, space looks the same to me in one place as it does if I were to move in a straight line to some other place. Similarly, conservation of angular momentum is a result of the rotational symmetry of space. That means that space looks the same to me (again, far away from anything) if I look in one direction as it does if I turn 45 degrees and look that way. That space has both translational and rotational symmetry is not something to be taken lightly. It probably says something about the distribution of matter in space. Maybe if the universe were more lopsided, we wouldn't have these handy physical laws.

 

[Galileo]

Newton himself called the quantity mass times velocity: 'Quantity of Motion'.

 

[PBRMEASAP]

Newton himself called the quantity mass times velocity: 'Quantity of Motion'.

That's right! Actually, that was the first thing that came to my mind when I saw the question being asked. But after thinking about it some, I realized that 'quantity of motion' does not convey much to me in the way of physical intuition either. I'm now of the opinion that the physical significance we normally attach to momentum would have to be modified if the universe were less "homogeneous". On the other hand, I think the concept of velocity would remain unchanged, since velocity really is defined as the rate of change of position. I think the original poster brings up a great point that p=mv is really more of a formula for calculating momentum than it is a physical definition.

A somewhat different way of looking at things is this: when using Newton's laws to work out mechanics problems, the quantity mass-times-velocity often crops up in equations, so it is convenient to assign a name to it. Again, not a very physical explanation, but I imagine other "physical" variables have come about this way.

 

[arildno]

As an aside, we antiquarian Norwegians STILL use the phrase "quantity of motion" (bevegelsesmengde)

 

[pmb_phy]

Loosely speaking - The momentum of a body represents either the ability to keep a body in its state of motion or the ability to impart a change in the motion of other bodies, but collision.

Pete

 

[DaveC426913]

BTW, it is a fundamentally unanswered question in physics as to what exactly is the property of inertia or momentum. We still don't know what causes a mass to have that property.

 

[gerben]

You can think of momentum as 'Quantity of Motion' like this:

If a moving object has a higher velocity there is a larger 'Quantity of Motion', because it moves more.
If a moving object has more mass there is a larger 'Quantity of Motion', because there is more mass moving.

You must multiply mass and velocity, because you want the 'Quantity of Motion' to double when you double the mass (or the velocity).

 

[bomba923]

A somewhat different way of looking at things is this: when using Newton's laws to work out mechanics problems, the quantity mass-times-velocity often crops up in equations, so it is convenient to assign a name to it. Again, not a very physical explanation, but I imagine other "physical" variables have come about this way.

Now that's what i guess i thought--but now i see: just because it has a "name", doesn't mean the physical definition can be directly (easily, more or less) derived

 

[bomba923]

You can think of momentum as 'Quantity of Motion' like this:

If a moving object has a higher velocity there is a larger 'Quantity of Motion', because it moves more.
If a moving object has more mass there is a larger 'Quantity of Motion', because there is more mass moving.

You must multiply mass and velocity, because you want the 'Quantity of Motion' to double when you double the mass (or the velocity).

Well of course...but that wasn't really the physical definiton i was seeking

 

[bomba923]

BTW, it is a fundamentally unanswered question in physics as to what exactly is the property of inertia or momentum. We still don't know what causes a mass to have that property.

do we not accept by definition that mass is a measure of inertia within an object?

 

[quantumdude]

I need a definition other than a change in impulse (force*change in time)

What's wrong with that one? It makes good intuitive sense to me. If you push on something with a force of 10 N for 1 sec, you make it move. If you push on it with a force of 10 N for 10 sec, you make it move faster because you push on it longer. This happens to have the same effect as pushing on it with a force of 1 N for 10 sec.

*shrug* Like I said, it makes sense to me.

 

[Physicsguru]

Now this may sound silly, but what does it exactly represent? (i'm taking physics..getting an 'A'...no problem, but momentum came up)

Now what exactly does momentum mean??
We think of force as a push or pull...
We acceleration as change in motion (speeding up/down, turning..etc-etc...)
We think speed as amt. distance/time...

But momentum??What is it---i need a definition OTHER than mass*velocity...
I need a definition other than a change in impulse (force*change in time)

What does momentum PHYSICALLY (push/pull, speed up/down) represent?

The closest thing in my head is "inertia with respect to velocity"--

But yeah...what does momentum PHYSICALLY represent? The product of mass and velocity...what does it MEAN? ("physically-speaking")?

Bomba, use logic.

Suppose you know what momentum means, and that momentum is defined as mass times velocity. Therefore, you know what 'mass' means, and you know what 'velocity'n means. Suppose that you don't know what momentum means. Therefore, either you don't know what 'mass' means, XOR you don't know what velocity means, or you don't know what either means.

Let it be stipulated that you know the meaning of the term 'velocity,' but that you don't know the meaning of the term 'momentum'; which category you seem to fall into. It therefore must be the case that you don't understand the term 'mass'.

In one of your posts, you state that you understand that 'mass' is a measure of the amount of inertia an object has. Inertia is a measure of a body's resistance to acceleration, or equivalently, resistance to change in velocity.

Therefore, either you don't understand what inertia is, or you do understand what momentum is, or you don't understand what velocity is.

As for the topic of inertia, there are multiple theories of inertia out there, and until we have a grand unified theory of inertia, the statement that "no man fully understands inertia" will continue to be true.

1. Galilean theory of inertia.
2. Newtonian theory of inertia.
3. Einsteinan theory of inertia.
4. Quantum theory of inertia.
5. Zero Point Field theory of inertia.
6. Collective Electrodynamical theory of inertia.

Regards,

Guru

 

[Physicsguru]

What's wrong with that one? It makes good intuitive sense to me. If you push on something with a force of 10 N for 1 sec, you make it move. If you push on it with a force of 10 N for 10 sec, you make it move faster because you push on it longer. This happens to have the same effect as pushing on it with a force of 1 N for 10 sec.

*shrug* Like I said, it makes sense to me.

Tom, what is the source of a body's inertial mass m, in the formula F = d(mv)/dt? And can you explain your answer in the maximum amount of detail that you are capable of? I think the problem this person is having, is centered around their lack of understanding of inertial mass.

Regards,

Guru

 

[quantumdude]

Tom, what is the source of a body's inertial mass m, in the formula F = d(mv)/dt? And can you explain your answer in the maximum amount of detail that you are capable of?

The source of the factor 'm' is the amount of stuff contained in the body. I really don't think any more detail than that is called for in this particular thread.

I think the problem this person is having, is centered around their lack of understanding of inertial mass.

How do you figure? He already stated that he has no trouble digesting the concept of force (which equals ma).

 

[vinter]

Momentum of a body simply measures how hard you will be hurt if that body hits you.

Taking into condiserations your muscular strength etc., the formula becomes

momentum = (pain you feel when the body hits you)/(how strong you are)

where '/' means 'divided by'

 

[Physicsguru]

The source of the factor 'm' is the amount of stuff contained in the body. I really don't think any more detail than that is called for in this particular thread.

Tom, mass is not a measure of the amount of 'stuff' in a body. Please think of friction.

How do you figure? He already stated that he has no trouble digesting the concept of force (which equals ma).

Does force = ma, or does force = d(mv)/dt = mdv/dt+vdm/dt=ma+vdm/dt ?

 

[quantumdude]

Russ,

Russ?

mass is not a measure of the amount of 'stuff' in a body.

I maintain that for the purpose of this thread, that notion of mass is sufficient.

Please think of friction.

What on Earth does friction have to do with it?

Does force = ma, or does force = d(mv)/dt = mdv/dt+vdm/dt=ma+vdm/dt ?

In Physics I (which I assume the original poster is taking), F=ma.

 

[Physicsguru]

Alright Tom, I get your point. Discussing ZPF field theory of inertia isn't appropriate for a beginner. But I do take issue with telling the original poster that mass is a measure of the amount of 'stuff' in a body. My personal stance is that inertia is the grand unifying concept of physics, not energy. Even a beginner would do well to try and deeply analyze the meaning of momentum. Logically, the central problem isn't too difficult:

Definition: Momentum = (inertial mass)(velocity)

I would say that for most people (beginners and otherwise), velocity is not the more difficult of the two concepts here... inertia is the more difficult one.

As for friction:

We have a wooden block, either on ice or sandpaper. On one surface you have to apply external force F1 to give the object a constant acceleration of a, and on the other surface you have to apply a different external force F2, in order to give the object the same acceleration a.

In the rest frame of the sandpaper, the inertia of the block is greater than in the rest frame of the ice. So did the inertia of the body change simply because it was placed on sandpaper instead of ice? Yes or no? Or more to the point, is mass an absolute, or relative quantity, and at what point does the concept of "inertial reference frame" become an issue for a beginner?

Regards,

Guru

 

[arildno]

force = d(mv)/dt = mdv/dt+vdm/dt=ma+vdm/dt ?

If you think this law is valid for a classical system of so-called "variable mass", you are simply mistaken.

 

[quantumdude]

But I do take issue with telling the original poster that mass is a measure of the amount of 'stuff' in a body.

*shrug*

There's a one-to-one correspondence between the two notions of mass. Objects with more inertia are bound to have more stuff in them, and vice versa.

We have a wooden block, either on ice or sandpaper. On one surface you have to apply external force F1 to give the object a constant acceleration of a, and on the other surface you have to apply a different external force F2, in order to give the object the same acceleration a.

Has the inertia of the body changed or what??

No, of course not. Newton's second law doesn't say that the applied force is equal to ma. It says that the vector sum of all the forces is equal to ma. If you have to push harder on the block on the sandpaper, it's only to overcome the frictional force so that that block will have the same net force acting on it as the block on the ice.

 

[Physicsguru]

Newton's second law doesn't say that the applied force is equal to ma. It says that the vector sum of all the forces is equal to ma.

Is the vector sum of all forces equal to ma, or is it equal to dP/dt?

 

[quantumdude]

Is the vector sum of all forces equal to ma, or is it equal to dP/dt?

It's equal to both of them, provided that the mass of the wooden blocks remain constant as they travel.

 

[Physicsguru]

It's equal to both of them, provided that the mass of the wooden blocks remain constant as they travel.

What is the most general answer, and exactly what things contribute to 'inertia' Tom?

Regards,

Guru

 

[arildno]

What is the most general answer, and exactly what things contribute to 'inertia' Tom?

Regards,

Guru

The most fundamental formulation classically, is that for A MATERIAL SYSTEM,
$$F=ma_{G}$$ while the law of mass conservation says that m is a constant.

Don't mix together geometric systems and material systems.

(After relativity, the fundamental laws governing a material system in the classical domain are most naturally F=dp/dt and mass conservation)

 

[quantumdude]

What is the most general answer,

You have my answer. Provided that the system does not lose mass, and that it is nonrelativistic, F=dp/dt reduces to F=ma. It's not that complicated.

and exactly what things contribute to 'inertia' Tom?

If you mean "How do bodies acquire mass?", then no one knows. It's still one of the open problems in theoretical physics. Until then, mass is an exogenous parameter to any theory of dynamics: Newtonian, relativistic, or quantum.

 

[Physicsguru]

If you mean "How do bodies acquire mass?", then no one knows. It's still one of the open problems in theoretical physics. Until then, mass is an exogenous parameter to any theory of dynamics: Newtonian, relativistic, or quantum.

More to the point, I am addressing the meaning of 'inertial mass.' Perhaps I should start by asking the following question, "Is inertial mass a reference frame dependent quantity?"


Guru

 

[quantumdude]

More to the point, I am addressing the meaning of 'inertial mass.' Perhaps I should start by asking the following question, "Is inertial mass a reference frame dependent quantity?"

It depends entirely on how you define mass. Some choose to define it as follows:

m=γm₀,

which is frame-dependent. This preserves the definition of momentum: p=mv.

Most particle physicists don't use that definition. They define it as the norm of the 4-momentum, which makes it a Lorentz invariant.

 

[ZapperZ]

More to the point, I am addressing the meaning of 'inertial mass.' Perhaps I should start by asking the following question, "Is inertial mass a reference frame dependent quantity?"


Guru

John Roche of Oxford has an excellent paper on the question "What is Mass?"[1] I strongly suggest you read it.

Zz.

[1] J. Roche, Eur. J. Phys. v.26 p.225 (2005).

 

[Mr. Therefore]

...what does momentum PHYSICALLY represent? The product of mass and velocity...what does it MEAN? ("physically-speaking")?

It is simple. Momentum was first discovered as a deduction made from a collision. Although, it wasn't fully comprehended as mass x velocity until we understood the conservation aspect. We could only see momentum as mass x velocity after we understood the conservation aspect. What was necessary to see the conservation aspect was deducing speed changes. With speed changes we could deduce mass. When we found speed change depending upon mass, we found their proportionateness. That was the conservation of momentum. Only from that point, we multiplied the velocity times the mass.

I think to teach momentum as mass times velocity is jumping ahead of the practical method by which it was discovered. For the best understanding, you must start with seeing speed changes in collisions, then deducing the mass from those speed changes and then looking for proportions in your results which will lead you to conservation of momentum.

 

[Andrew Mason]

Now what exactly does momentum mean??
We think of force as a push or pull...
We acceleration as change in motion (speeding up/down, turning..etc-etc...)
We think speed as amt. distance/time...

But momentum??What is it---i need a definition OTHER than mass*velocity...
I need a definition other than a change in impulse (force*change in time)

What does momentum PHYSICALLY (push/pull, speed up/down) represent?

The closest thing in my head is "inertia with respect to velocity"--

But yeah...what does momentum PHYSICALLY represent? The product of mass and velocity...what does it MEAN? ("physically-speaking")?

I'll take a stab at it, FWIW.

Momentum may be thought of as a measure of the amount of external pushing or pulling a system has experienced in its past. Since $p = \int Fdt$ a system accumulates all the impulses and stores them. We know it stores these impulses because in the absence of forces (ie. F=0), dp/dt = F = 0, so p does not change.

AM