What is the difference between conserved momentum and potential energy?

[genome66]

I recently came upon an article describing conserved momentum, and from what I got about the subject; it would seem that it is (for the most part) the equivalent of potential energy. Is this true, because it seems like there must be a difference between the two?

 

[Mr Vibrating]

Yes, conserved momentum can be considered an energy form, either potential or kinetic depending on your reference frame.

For example a flywheel is a store of PE (albeit somewhat confusingly in the form of KE as angular momentum) that can be used to perform work, upon which point it'll become KE again as it tranfers, etc.

The amount of energy is defined by the mass times the speed - or in the flywheel case the moment of inertia vs rpm.

Other examples of PE stored as conserved momentum would be current in a superconductor (additionally the conserved motion of the electrons would turn a superconducting ring into a permanent magnet, one way of illustrating that an ordinary fridge magnet's field is a product of the conserved angular momentum of the material's unpaired electrons!), or the arcing of electricity across a broken contact (again it's the momentum of the electron mass that carries it through space), or indeed the heat stored in a thermos flask.. essentially the conserved momentum of the food's molecules.

Some physicists even consider CoM to be more fundamental than CoE itself... they're intricately related, although still distinct in practice.

ETA: just remembered, it's also the solution to Feynman's paradox! (the rotating disc one)

 

[tiny-tim]

welcome to pf!

hi genome66! welcome to pf!

I recently came upon an article describing conserved momentum, and from what I got about the subject; it would seem that it is (for the most part) the equivalent of potential energy. Is this true, because it seems like there must be a difference between the two?

no, this is rubbish …

momentum and energy are completely different

momentum (and angular momentum) is conserved in every collision, mechanical energy isn't

no equivalence at all

 

[Dale]

Adding to what tiny-tim said, if you have a Lagrangian which is symmetric in space and time then the space symmetry gives the conservation of momentum and the time symmetry gives the conservation of energy.

 

[genome66]

Tiny Tim, I understand how conservation of momentum can't be compared to Kenetic energy; but couldn't the conservation of momentum, of an object with the net force of zero, be compared to the kenetic energy that an object has at rest?

-thanks for the welcome by the way :)

 

[tiny-tim]

hi genome66!

… couldn't the conservation of momentum, of an object with the net force of zero, be compared to the kenetic energy that an object has at rest?

i don't get it …

if the net force is zero, then nothing will happen …

there's no "before" and "after" to be compared, so conservation doesn't come into it

 

[Mr Vibrating]

hi genome66! welcome to pf!


no, this is rubbish …

momentum and energy are completely different

momentum (and angular momentum) is conserved in every collision, mechanical energy isn't

no equivalence at all

Seems like a ropey distinction between mechanical energy and momentum, ie. ommiting thermal exchange.. In reality mechanical KE and momentum are one and the same thing and equal to mechanical PE.

p=mv and mass in kg times velocity in m/s equals our energy in Joules..

In inelastic collisions the momentum is carried off by phonons etc., but the total momentum of the system (including the immediate environment) is conserved. There is ultimately no distinction between momentum and mechanical energy... it's all Newtonian energy, force x displacement.. and it's all conserved. Mostly.

 

[Doc Al]

In reality mechanical KE and momentum are one and the same thing and equal to mechanical PE.

Not in this reality.

p=mv and mass in kg times velocity in m/s equals our energy in Joules..

No. The units of momentum are kg-m/s, whereas the units of energy are kg-m²/s². Big difference!

 

[Mr Vibrating]

Not in this reality.


No. The units of momentum are kg-m/s, whereas the units of energy are kg-m²/s². Big difference!

Pedantry's great until we start missing the wood for the trees... the OP question refers to the equivalence of the energy forms not the dimensions of the units..

If something has momentum relative to us then it has energy, as a product of its mass and speed!

High speed flywheels have even been developed as energy storage for satelites for instance

http://en.wikipedia.org/wiki/Flywheel_energy_storage

The black box system is essentially no different to a spring or cell, it's stored KE or PE depending on the viewpoint.

 

[Doc Al]

Pedantry's great until we start missing the wood for the trees...

Pedantry? We're talking basic physics here!

the OP question refers to the equivalence of the energy forms not the dimensions of the units..

Nonetheless, your response was incorrect. How is that helpful?

If something has momentum relative to us then it has energy, as a product of its mass and speed!

Energy is not the product of mass and speed.

High speed flywheels have even been developed as energy storage for satelites for instance

So?

 

[AlephZero]

lol alright meant function of but regardless, it's patently clear what the OP means by 'conserved momentum' and it certainly IS a form of energy..

It might be clear to you, but it certainly isn't clear to me, and I 've used these concepts just about every working day for the last 30 years or so.

At the least, the OP (and perhaps you also) need to learn the correct terminology to describe what he/she is talking about. That isn't pedantry, it's an essential part of learning any subject.

"Conservation of momentum" is a technical term in mechanics which doesn't mean the same as "storing momentum" (which is probably what the OP really meant). Even if we are talking about "storing momentum", two objects with the same amount of momentum can have different amounts of energy, so the supposed "equivalence" is arm-waving, not physics.

 

[genome66]

To tell the truth, when I said Conservation of momentum, i meant the most absolute basic meaning of the term (basically High School Physics meaning), I meant what I asked, all i wanted to know is, is there any similarity between conservation of momentum and potential energy, in any possible situation/scenario? If so post it and explain the link between the two.

 

[Mr Vibrating]

Ignore the pedants, couldn't get a straight answer out of 'em if you tried...

You said "conserved momentum" as in a conserved quantity of momentum.

Conservation of momentum (CoM) is a fundamental conservation law, energy is the potential to perform work.

If there is non-zero momentum between two bodies then by definition there is energy between them. I spend a lot of time playing in traffic and can confirm this to be true.

I gave a good few examples above, a flywheel is prolly the clearest one tho.. esentially because momentum IS conserved, so is mechanical energy, and the amount of energy depends on the relative momentum of the bodies in question.

 

[K^2]

Ignore the pedants, couldn't get a straight answer out of 'em if you tried...

That's not an excuse to say something that is wrong just to make it sound simple.

To actually make a connection between momentum and energy, you have to go to relativity and translational symmetries of space-time. If the person is studying classical mechanics, you'd only be filling said person's head with nonsense.

As far as classical mechanics goes, no, these are two completely different and unrelated concepts. Energy is ability to do work. Momentum is ability to transfer impulse. One is force over distance, the other is force over time.

 

[tiny-tim]

As far as classical mechanics goes, no, these are two completely different and unrelated concepts. Energy is ability to do work. Momentum is ability to transfer impulse. One is force over distance, the other is force over time.

Exactly.

 

[Dougggggg]

As far as classical mechanics goes, no, these are two completely different and unrelated concepts. Energy is ability to do work. Momentum is ability to transfer impulse. One is force over distance, the other is force over time.

That is the most clearly defined difference between the two that I have heard.

If you have taken Calculus then this can help with understanding quite a bit.

Impluse, which is change in moment, is equal to the integral of the force with respect to time. Work, which is also equal to the change in KE, is the integral of the force with respect to displacement.