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[user111_23]

I don't want to know what it's like, I want to know what it IS.

On an unrelated note, I read this excerpt from a Hyperphysics article on voltage;

"Like mechanical potential energy, the zero of potential (of voltage) can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful."

What does that mean? It's really bothering me.

 

[negitron]

It's exactly mass times velocity.

 

[maverick_starstrider]

It is what it is. It's mass*velocity, it's the abstract quantity that is changed by force, which is conserved in a closed system.

 

[Vanadium 50]

I don't want to know what it's like, I want to know what it IS.

I think you'll have to expect to be disappointed. Suppose someone answers you. You can then point at the answer and say, "Yes, but what IS it?" Eventually you can reach a point where all that can be said is how "it" behaves.

 

[gmax137]

I don't want to know what it's like, I want to know what it IS.

well I don't know what it is, but I know what it feels like to change it.

On an unrelated note, I read this excerpt from a Hyperphysics article on voltage;

"Like mechanical potential energy, the zero of potential (of voltage) can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful."

What does that mean? It's really bothering me.

If I say the potential energy of a bowling ball held 10 ft above the floor is 10 lb * 10 ft = 100 ft lb, we can use that to determine how fast the ball is going when it hits the floor (after I drop it). Now, if I tell you the floor is actually the 20th floor of the building, we can see that the "zero" is arbitrary. Voltage is the same, in the sense that the "zero" is arbitrary. Does that help any?

 

[Pinu7]

Momentum is defined as p=mv where m is mass v is velocity and p is momentum.

Newton's second law, F=ma, can be written as dp/dt this is because ma=m*dv/dt=d(mv)/dt=dp/dt

That has a qualitative implication; the more momentum an object has, the harder it is to change it's motion.

In Quantum Physics, de Brogle hypothesized that a particle was also a wave with the momentum defined as p=h/w where w is the wavelength and h is plank's constant which equals about 6.63*10^-34 J s.

 

[cfung]

I think you'll have to expect to be disappointed. Suppose someone answers you. You can then point at the answer and say, "Yes, but what IS it?" Eventually you can reach a point where all that can be said is how "it" behaves.

This happens most often to discussions that involve non-provable subjects. Not all physics concepts are so, at least I believe.

Einstein once said, "Imagination is more important than knowledge."
I take this to say, "To have a feeling of what momentum is is more important than to state p = mv."

A more sensible way to describe what momentum of a mass body, which is quite common to hear, is "a mass's persistence to continue its motion." Which is similar to the concept of inertia.

Imagine in empty space you have 2 objects. A drinking straw and a massive solid sphere of a bowling ball, both are drifting in space at the speed of a thrown baseball relative to you. Now if you try to stop either object by pushing them with the same force, you will have a much more difficult time in slowing the one with more mass (momentum directly depends on mass). Ask your self, compared to the straw, how does it feel the one that's heavier.

What ever abstract feeling you get from that should be the answer to "what momentum IS"

 

[Naty1]

Well, considering we really don't know what either velocity nor mass is, nor energy in general, nor much of anything for that matter, it's not so surprising that we don't know exactly what momentum IS, either. we do have good ideas about it behaves, however.

Physics tends to describe what happens rather than why something happens or what something IS. As Richard Feynman is quoted as saying

Theoretical physics has given up on that

despite that fact he was quite expert at explaining g things in simple terms.

We are very lucky we have mathematics...even luckier, I think, that our universe behaves as some math indicates...

 

[DrGreg]

As force is rate of change of momentum (Newton's 2nd law), there's a simple description of momentum. It's the constant force you'd need to apply to bring an object to rest in exactly one second (assuming momentum in SI units). Or, equivalently, it's the number of seconds it would take to bring the object to rest by applying a constant force of 1 Newton.

 

[flatmaster]

As far as what it "is". I've heard momentum described as "the total amount of motion"

 

[Count Iblis]

As force is rate of change of momentum (Newton's 2nd law), there's a simple description of momentum. It's the constant force you'd need to apply to bring an object to rest in exactly one second (assuming momentum in SI units). Or, equivalently, it's the number of seconds it would take to bring the object to rest by applying a constant force of 1 Newton.

What exactly is "force" and what is "time"?

 

[DrGreg]

What exactly is "force" and what is "time"?

I refer you to post #4.

 

[Count Iblis]

Momentum is the generator of translations:

p = - i hbar d/dx ------->

d/dx = i p/hbar


psi(y) = [exp(y d/dx) psi]_{x = 0} = exp(i y p/hbar)psi(x=0)

 

[pallidin]

It is my understanding that momentum, to this day, is a mystery.

That is, the fact that a mass resists changes in velocity is well established.
The "why" however is not.

As far as I know anyway...

 

[ibcnunabit]

I don't want to know what it's like, I want to know what it IS.

On an unrelated note, I read this excerpt from a Hyperphysics article on voltage;

"Like mechanical potential energy, the zero of potential (of voltage) can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful."

What does that mean? It's really bothering me.

Momentum is best described as a mass's resistance to changes in velocity such as would result if a force were to act on it. It's a fundamental attribute of matter that you experience every time you're riding in a car and experience a hard, sharp turn. It's what makes your body want to keep going in a straight line along your previous path, but the car beneath you goes in a different direction, causing you to be pinned to the side of the car as it applies force to you, forcing you into a new path in a different direction. Is that real enough?

--Mike from Shreveport

 

[pixel01]

Momentum of a moving object is something you try to stop it. The higher the momentum it has, the harder you have to try.

 

[peteratcam]

It is probably pointless me giving my 2 cents but anyway.

p = mv is a definition of mechanical momentum, but isn't really very fundamental at all.

The canonical momentum which appears in Hamilton's equations is the mysterious one with all the links to quantum mechanics and generators of translations etc.

 

[zimbabwe]

I was trying to explain momentum to a friend and noticed that momentum is the derivative of energy in respect to velocity. Would this be a correct way to think about momentum, the rate of change of energy.

 

[tiny-tim]

I don't want to know what it's like, I want to know what it IS.

Hi user111_23!

As pixel01 says …

Momentum of a moving object is something you try to stop it. The higher the momentum it has, the harder you have to try.

It is always conserved in collisions (while kinetic energy is not),

so momentum measures the "oomph" available when something hits something else.

Momentum is a quantity which an object has when it moves.

It can transfer that quantity to another object.

That quantity is never lost, it only moves from one object to another.

It measures the ability to move another object …

the more momentum you have, the more you can move something else …

the less you have, the less you can move something else …

if you do move something else, you must give up some of your own momentum.​

On an unrelated note, I read this excerpt from a Hyperphysics article on voltage;

"Like mechanical potential energy, the zero of potential (of voltage) can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful."

What does that mean? It's really bothering me.

It's like mgh, the gravitational potential energy …

the "h" can be measured from any level (usually the most convenient one) … it's only the difference in h that matters.

Electric potential (voltage) is potential energy per electric charge (V = PE/q), and it's only the difference in V that matters.

 

[Dale]

I was trying to explain momentum to a friend and noticed that momentum is the derivative of energy in respect to velocity. Would this be a correct way to think about momentum, the rate of change of energy.

It is a little more complicated than that, but you are kind of discovering a key element of http://en.wikipedia.org/wiki/Lagrangian_mechanics" . In Lagrangian mechanics the Lagrangian has units of energy and its derivative wrt the generalized velocity is the generalized momentum.

 

[tiny-tim]

momentum is the derivative of energy in respect to velocity?

I was trying to explain momentum to a friend and noticed that momentum is the derivative of energy in respect to velocity. Would this be a correct way to think about momentum, the rate of change of energy.

Hi zimbabwe!

Momentum isn't the rate of change of kinetic energy, that would be dKE/dt.

As you pointed out to your friend, momentum is dKE/dv.

This is because of Newtonian relativity … the laws of physics are the same for any inertial observer (ie a non-rotating observer with uniform velocity).

So if your friend has velocity a with respect to you, and if you say that

∑m_iu_i² = ∑M_iv_i²,​

then your friend says that

∑m_i(u_i - a)² = ∑M_i(v_i - a)².​

Subtracting, gives (∑m_i - ∑M_i)a² = 2(∑m_iu_i - ∑M_iv_i).a,

which since it's true for any a means that each bracket is zero …

so from KE = constant and mass = constant (first bracket), we get momentum = constant (second bracket).

Alternatively, if we differentiate ∑m_i(u_i - a)² = ∑M_i(v_i - a)² wrt your friend's velocity in any direction (by choosing a component of a and varying it), we get the same result: the component of momentum in any direction is constant.

The same happens in relativity … instead of speed |u|, we use the "rapidity" λ, defined by speed = tanhλ, so that KE = mcoshλ and momentum = msinhλ …

then, in one dimension for simplicity, your friend says that KE = ∑m_icosh(λ_i - α), and momentum = ∑m_isinh(µ_i - α), so dKE/dα = momentum and d(momentum)/dα = KE.

 

[danielatha4]

Here's some fun thinking... maybe...

If F=ma is the time derivative of P=mv then there must exist the integral of p or mv

?=mx, therefore momentum is the rate at which a body of mass finally comes to a given point, or position, in space?...

Humor me

 

[danielatha4]

To Zimbabwe, I also noticed that momentum is the derivative of Kinetic Energy with respect to velocity.

As a body of mass' velocity increases (it accelerates) it's energy goes up, along with it becoming harder to stop?

 

[ZirkMan]

I'm just formulating a theory where every fundamental property is expressed in terms of energy (you cannot get more fundamental than that ;).

In this way momentum is simply a relative velocity x quantity of energy.

Inertia is a macroworld phenomenon related to not-immediate transfer rate of energy. You cannot simply immediately transfer energy from one macro-energy-object to another.

If you try to stop a flying ball by applying energy from your hand the energy from your hand cannot get immediately to all energy objects in the ball. So they will continue on their way until the energy from your hand reaches them (by propagation in the ball energy-mater medium) and only after that they will change their energy to either stop or change direction. This time-delay in energy transfer is sometimes referred to as a consequence of momentum but its cause is actually the same as the cause of inertia.

 

[milford30]

I think you'll have to expect to be disappointed. Suppose someone answers you. You can then point at the answer and say, "Yes, but what IS it?" Eventually you can reach a point where all that can be said is how "it" behaves.

agreed, same as asking what is mass, time, space :P

 

[HallsofIvy]

Physics, like any science, relys upon observation and experimentation. Any physical quantity is defined by telling how to measure it or calculate it from measurements. In other words, momentum is defined by "p= mv".

 

[Dale]

I'm just formulating a theory where every fundamental property is expressed in terms of energy (you cannot get more fundamental than that ;)

Have you studied the Lagrangian and Hamiltonian formulations of classical mechanics? It sounds like they have already done what you are talking about.

Btw, this is not the place for personal theories.

 

[ZirkMan]

Have you studied the Lagrangian and Hamiltonian formulations of classical mechanics? It sounds like they have already done what you are talking about.

No, but thank you for pointing me there.

Btw, this is not the place for personal theories.

There was nothing speculative or personal in my explanation of momentum and inertia, I hope.

 

[sponsoredwalk]

Although the original question was asked about 7-8 months ago, I don't see any reason not to add some visual aids to this heated debate.

First, a nice 6 minute illustration http://www.youtube.com/watch?v=T9lehHxv-C8&feature=channel full of hockey players hitting each other and that oh-so famous puck on the ice that never seems to feel any friction in a physics book.

Then, we'll get a bit crazier and watch the boys down at the pool hall http://video.google.com/videoplay?docid=-6424932573390409362#docid=-1865978801687874664 .
Some of the quips by the narrator have enough oomph to make you LOL & you'll never forget Chalky's Billiard bar :tongue2:
Some nice history on Descartes and Bruno mixed into the equation make p=mv unforgettable.

To get mixed in with the math at a basic level + problems to practice on, we'll head over to Salman Khan @ khanacademy ala youtube to try out our newfound skills manipulating p=mv

Then, we'll take a trip down to the atomic scale and learn why this concept of momentum is a concept we may never be able to pin into one single place, http://www.youtube.com/watch?v=EnAbKLtbeGE&feature=related , but must rely on probabilities of this momentums location :tongue2:

 

[Rasalhague]

The first definition I learned was

$$(1) \enspace m\textbf{v}.$$

Then I read that a more general definition is used in relativity, which approximates to the first definition at low speeds.

$$(2) \enspace \frac{m_0 \,v}{\sqrt{1-\left ( \frac{v}{c} \right )^2}},$$

where $m_0$ is the mass as measured in a coordinate system in which the object isn't moving. Very soon afterwards, often on the same page, I'd find textbooks would start talking about the momentum of a pulse of light, which they said was massless. The following relation is said to hold in general:

$$(3) \enspace E^2 = \left ( pc \right )^2 + \left ( mc^2 \right )^2,$$

which, setting $m=0$, gives

$$(4) \enspace E = pc$$

for the momentum of a massless particle. Wikipedia is typical in announcing, after the fact, that "this relativistic energy-momentum relationship", i.e. equation (3), "holds even for massless particles such as photons", when neither of the previous definitions were said not to hold for massless particles! This momentum for massless particles is given here as a scalar, but I suppose it can be treated as a 3-vector if given the direction of motion of the photon.

I'm intrigued by the statemen in the Wikipedia article that that in curved spacetime, momentum isn't defined. I'll bear that in mind for when I've learned enough to have more context.

I haven't studied any quantum mechanics yet, but it seems there's a different definition of momentum there, which has been mentioned in this thread. I wonder what its relationship is to the other definitions. Elementary textbooks give the equation

$$(5) \enspace p = \frac{h}{\lambda},$$

for the momentum of a photon ($h$ being Planck's constant, and $\lambda]$ wavelength), but this can be derived from (3) and the equation for the energy of a photon, so isn't a new definition.

I've also briefly looked at the very basics of Hamiltonian mechanics, which seems to have more abstract definition of momentum. I hope to explore that more fully. Does the Hamiltonian definition work as a more general way of expressing the particular definitions used in classical, relativistic and quantum meachanics?

 

[andert]

My preferred way to think of momentum is as part of the stress-energy-momentum tensor which is a covariance matrix that becomes diagonal (assuming an orthogonal coordinate system) when the observer and the object are at rest with respect to one another. Momentum forms the time-space components (assuming a symmetric tensor) of the tensor. So we can think of momentum of a massive particle as the flux of its internal energy in the observer's frame. This means that momentum depends on the relative frames of the observer and the object, i.e. it depends on your state of motion.

A fascinating fact is that momentum is conserved in every reference frame even though it changes (covaries) from frame to frame, i.e. in the absence of forces $$\partial_\mu T^{\mu\nu} = 0$$ where, e.g., $$T^{\mu\nu}=mu^\mu u^\nu$$ is the stress-energy-momentum tensor of a basic particle. This is quite different from other properties of particles. For example, for electric current, $$\partial_\mu J^{\mu} = 0$$. There's no second Lorentz index on the current. So while the conservation of the stress-energy-momentum tensor says that a Lorentz 4-vector, $$\partial_\mu u^\mu (mu^\nu)$$, is conserved in an arbitrary frame, the conservation of the electric current only says that a scalar, the rest charge, q, is conserved in every frame.

 

[jtbell]

$$(2) \enspace \frac{m_0}{\sqrt{1-\left ( \frac{v}{c} \right )^2}},$$

Correction:

$$(2) \enspace \frac{m_0 v}{\sqrt{1-\left ( \frac{v}{c} \right )^2}}$$

 

[Rasalhague]

My preferred way to think of momentum is as part of the stress-energy-momentum tensor which is a covariance matrix that becomes diagonal (assuming an orthogonal coordinate system) when the observer and the object are at rest with respect to one another. Momentum forms the time-space components (assuming a symmetric tensor) of the tensor. So we can think of momentum of a massive particle as the flux of its internal energy in the observer's frame. This means that momentum depends on the relative frames of the observer and the object, i.e. it depends on your state of motion.

Is the quantity you call "momentum" that labelled "momentum density" on the diagram at the top right of this page, rather than "energy flux", the name they give to the time-space components? (Not that that affects the numbers if it's symmetric.)

If there was only one particle and it was at rest with respect to the "observer" (i.e. reference frame), would all the components vanish except $T_{00}$?

 

[danielatha4]

Momentum can be thought of as the rate at which an object comes to rest at its center of mass.

 

[Galap]

I don't want to know what it's like, I want to know what it IS.

On an unrelated note, I read this excerpt from a Hyperphysics article on voltage;

"Like mechanical potential energy, the zero of potential (of voltage) can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful."

What does that mean? It's really bothering me.

Momentum ends up being the quantity that is physically 'real' or 'meaningful', as it is conserved in all frames of reference in both relativity and QM. Both mass and velocity (the components that classically make up momentum) are not conserved and are interchangeable, etc. It is a measure in a way of how much stuff there is in a system.