Do all forms of energy fall under 'kinetic' and 'potential'?

[Obliv]

I know that energy is recognized through motion. Even in the mass-energy equivalence a velocity is present even though it is a rest-energy (Not really sure if this would count as a potential energy since there is no 'field' of acceleration that the mass is in)

So does kinetic and potential energy make up all other forms of energy by definition?
also as a side tangent: it is described here https://en.wikipedia.org/wiki/Time_in_physics that time is used to derive kinetic energy. I tried defining $$v = dx$$ without respect to time
$$\frac{dv}{dv}{v} = dx$$
$$\frac{dv}{dx}v = dv$$
$$m\int{a}dx = m\int{v\frac{dv}{dx}dx} = m\int{v}{dv} = m\frac{v^2}{2} + C$$
actually it might be easier to just say $$a = dv$$ therefore
$$m\int{a}{dx} = m\int{dv}{v} = m\frac{v^2}{2} + C$$
How come I can define energy in terms of position but it says time is used to derive energy?

 

[Khashishi]

Potential energy is pretty much defined as any energy that isn't kinetic, so yeah.

Your math makes no sense. What is this

v=dx

supposed to mean? In normal calculus, a differential like dx only has meaning when it can be divided by another differential, like dx/dt.

 

[Obliv]

Potential energy is pretty much defined as any energy that isn't kinetic, so yeah.

Your math makes no sense. What is this

supposed to mean? In normal calculus, a differential like dx only has meaning when it can be divided by another differential, like dx/dt.

can't you just say velocity is defined as the change in position? Like $a = db$?

okay i just realized how stupid that suggestion was. if v = dx then it's just $v = \Delta x$ which makes even less sense when you say $a = \Delta V$ lol.. it would just be geometry at that point

 

[Khashishi]

Change in position over what?

 

[Obliv]

Well I got this response: "The "fundamental" definition of energy is that energy is that it is the conserved charge associated to time translations by Noether's[/PLAIN] theorem, and it knows no different "kinds" of energy." – ACuriousMind On stack exchange and was wondering if anyone could explain in layman's terms what he means? If not, any explanation that i correct will suffice.

 

[anorlunda]

So does kinetic and potential energy make up all other forms of energy by definition?

Electromagnetic energy, heat, chemical energy, nuclear energy, blah blah blah.

 

[Obliv]

Electromagnetic energy, heat, chemical energy, nuclear energy, blah blah blah.

Thermal energy can be described as the individual kinetic energies of particles. I haven't studied chemical/nuclear/E&M so you'll have to let me know how this energy is different from KE&PE. Rather, you could explain where the energy comes from and I'll hopefully be able to understand if this is related to KE/PE

 

[anorlunda]

I haven't studied chemical/nuclear/E&M so you'll have to let me know how this energy is different from KE&PE

Just think of a photon, whose energy is proportional to its frequency and nothing else.

 

[Obliv]

Just think of a photon, whose energy is proportional to its frequency and nothing else.

isn't it

where the velocity of light is involved?

 

[Khashishi]

In physics, the major terms like energy and temperature are defined in different ways depending on context. Most of the time, the definitions agree. But there can be subtle differences. For a system described in an inertial reference frame, Noether's theorem gives you a conserved quantity for time-invariance which happens to be the same as energy. But in a rotating frame, or something else weird, you won't get energy.

Propagating electromagnetic waves are considered kinetic energy. Non-propagating electromagnetism (like the field surrounding an electron) is potential energy. Heat can be both kinetic and potential. Chemical and nuclear are potential energy.

 

[Obliv]

In physics, the major terms like energy and temperature are defined in different ways depending on context. Most of the time, the definitions agree. But there can be subtle differences. For a system described in an inertial reference frame, Noether's theorem gives you a conserved quantity for time-invariance which happens to be the same as energy. But in a rotating frame, or something else weird, you won't get energy.

Propagating electromagnetic waves are considered kinetic energy. Non-propagating electromagnetism (like the field surrounding an electron) is potential energy. Heat can be both kinetic and potential. Chemical and nuclear are potential energy.

I'll keep that in mind, thanks. Do you know what kind of knowledge is useful/necessary in understanding Noether's theorem?

 

[Khashishi]

You should probably know the Hamiltonian formulation of classical mechanics (sometimes called Hamiltonian mechanics).

 

[anorlunda]

isn't it

where the velocity of light is involved?

Yes, where frequency is $1/\lambda$. But kinetic energy varies with $velocity^2$. The speed of light c is constant. Changing frequency changes photon energy without changing c.

In addition, a photon has no rest mass, so an expression like $mv^2$ can't be used to describe a photon energy.

 

[Obliv]

Yes, where frequency is $1/\lambda$. But kinetic energy varies with $velocity^2$. The speed of light c is constant. Changing frequency changes photon energy without changing c.

In addition, a photon has no rest mass, so an expression like $mv^2$ can't be used to describe a photon energy.

I don't really have the knowledge to be saying this since I haven't studied beyond classical mechanics. But, https://en.wikipedia.org/wiki/Kinetic_energy What I meant by kinetic energy was simply the energy due to motion of an object with 'mass' and I say it with '' because I have no idea how to describe photons if they are massless.

So, for an object in classical mechanics this is related by $\frac{mv^2}{2}$ and this is not always the case later on. An object with momentum must have kinetic energy in classical mechanics. Whether this is true or not entirely, I will have to learn.