# What is exact definition of potential energy if all forms of energy except kinetic comes under potential energy? [duplicate]

I need to know the exact meaning of potential energy. I AM confused what it actually means.They say all types of energy comes under 2 types kinetic and potential so what is potential energy then?

• There's no precise definition as such, but kinetic energy is the one that comes from variations in time, for eg. velocity $v$. Mar 16 '19 at 8:36
• "they" are wrong. Mar 16 '19 at 9:31
– user225609
Mar 16 '19 at 9:46
• Possible duplicate of What is potential energy truly? Mar 16 '19 at 10:11
• @Jasper I would argue that is a form of kinetic energy, although this statement has to be understood in the context of special relativity. But since the tags on the question just deal with Newtonian mechanics, I would say EM waves are off the table here anyway. Or I guess if you want to we say that we are only using Newtonian mechanics, so EM radiation is a separate energy not explained in our framework. We can both be right I guess based on the tags here :) Mar 16 '19 at 11:08

The main point about energy is that it is a single-number property (in technical language, a scalar rather than a vector) that is conserved overall in any isolated system.

I will distinguish between kinetic energy, internal energy and potential energy.

Kinetic energy is a property that can be directly attributed to or associated with a single body, and is connected to its motion. It is, though, a relative property, in that its value will depend on what frame of reference has been adopted.

Internal energy is energy stored inside a body. It could for example be stored in the form of elastic energy inside a spring, which ultimately comes from a combination of molecular vibrations and field energy in the electromagnetic fields between the molecules. One can include relativistic rest mass energy as a form of internal energy.

Potential energy is not a property of any single body in quite the same way as either kinetic or internal energy. It is rather a way of keeping track of interaction energies, and usually it quantifies the amount of energy that is in fact located in a field. For example, when two like charges are pushed close to one another, the energy provided by the forces that pushed them together is stored in their joint electromagnetic field. It is called field energy, which is the form that internal energy takes when it is stored in a field such as electric field. Similarly, when we lift an object, the energy we provide is stored in the gravitational field. What happens is that when the object is lifted up, the size of the joint gravitational field of that object and the Earth together is very slightly increased in some regions and decreased in others, with a net result that the integral over volume of the square of the field strength has gone up.

At the fundamental level, then, we can say that we don't need to consider potential energy at all, as long as we include kinetic energy and field energy. Sometimes people will call field energy by the name potential energy, which I guess is ok as long as they know what they are doing. Internal energy is the sum of all the kinetic energy and rest mass energy and field energy of the parts of a body.

In the case of gravity there are further subtleties that come in when one considers general relativity, but in ordinary conditions (the weak field limit) you do not need to worry about that.

• But at the fundamental level internal energy is still potential energy. It still arises through interactions of conservative forces. But I do thing the distinction is relevant. Internal energy is from interactions between objects within the system. Your potential energy category is due to interactions between the system and external forces. I think it is misleading though to say that internal energy is not potential energy. Mar 16 '19 at 10:47
• I added the penultimate paragraph in response to this. Still not perfect without writing a long essay, but there you go. I hope people read the comments! Mar 16 '19 at 11:18
• Yeah ok I guess that's fine. I think really this all comes down to nitpicky definitions that ultimately don't change the physics. I don't think the statement "energy is either kinetic or potential" really has any truth value associated with it. It just depends on your definitions. Mar 16 '19 at 11:21
• I agree with both you and Aaron. I would only point out that whereas the kinetic energy of an object as a whole, which is based on the velocity of its center of mass, depends on the frame of reference in which it is measured, whereas the kinetic energy component of the internal energy (average kinetic energy of the atoms/molecules) does not. The temperature of the object does not change depending on the velocity of the object. Similarly for potential energy. Mar 16 '19 at 14:58
• Sir i cant understand why u thought a person who dont know potential energy will know about field and all that @AndrewSteane
– user225609
Mar 16 '19 at 15:05

You may understand potential energy in classical mechanics as stored work, where work is defined as $$W = \int_{\cal C} \vec{F}\cdot d\vec{s}.$$ Here, the force $$\vec{F}$$ is to be understood as a conservative force, in contrast to a dissipative force (such as a frictional force) acting on a body. The force acts along curve $${\cal C}$$.

A conservative force is one for which the value of the above integral depends only on the endpoints of the curve $$\cal C$$, but not on its shape in-between.

In this sense, also kinetic energy can be understood as a form of stored work (acceleration work), but we have the special term kinetic energy for it.

• So does the energy in a rotating flywheel count as 'stored work'? Mar 16 '19 at 11:24
• @EmilioPisanty: Sure, why not? You have to invest work to make it rotate. Mar 16 '19 at 12:11
• @Emilio's point is that such energy is universally binned as kinetic. And indeed to take an object with no kinetic energy and give it some you have to perform work on it. That's the exact content of the work-energy theorem. Mar 16 '19 at 16:23
• @dmckee: I do not disagree with any of that. Is this not exactly, what I said in my answer? We have a special name for work stored in the motion of an object. I think I do not get your point. Mar 16 '19 at 18:14