# Types of energy

Green dwarf
TL;DR Summary
Are there three types of energy - kinetic, potential and mass?
I am planning to teach a school astronomy group about energy. Most people seem to accept that there are two types:
kinetic energy, resulting from movement;
potential energy, resulting from position in a force field with a potential gradient (convertible to KE if the object is allowed to move down the potential gradient).
But I'm not sure where the rest-mass energy of a particle fits. Is it one of these or a third type?

Gold Member
No, you can think of mass as a kind of potential energy.

Homework Helper
Gold Member
Unlike kinetic energy and potential energy, the energy associated with rest mass is frame-independent.

For elementary particles, a change in rest-mass usually corresponds to a change in the identity of the elementary particle.

Homework Helper
Gold Member
2022 Award
Summary: Are there three types of energy - kinetic, potential and mass?

I am planning to teach a school astronomy group about energy. Most people seem to accept that there are two types:
kinetic energy, resulting from movement;
potential energy, resulting from position in a force field with a potential gradient (convertible to KE if the object is allowed to move down the potential gradient).
But I'm not sure where the rest-mass energy of a particle fits. Is it one of these or a third type?
You could check out the Science Asylum:

Green dwarf
Demystifier says: No, you can think of mass as a kind of potential energy. Though I'm not sure of the reasoning behind that.
robphy seems to imply that mass is neither KE nor PE.
The video suggested by PeroK includes a diagram showing rest energy as KE+PE, though it doesn't explain that.
Hoping for a bit more insight.

Green dwarf
You want insight, I'll give you insight!

https://www.feynmanlectures.caltech.edu/I_04.html
Thanks PeroK. I read through the article, but the only mention of mass energy was this: Finally, associated with the relativity theory, there is a modification of the laws of kinetic energy, or whatever you wish to call it, so that kinetic energy is combined with another thing called mass energy. An object has energy from its sheer existence.
It says mass energy is another thing, but I still don't know whether it is KE, PE or neither of these.

Homework Helper
Gold Member
2022 Award
It says mass energy is another thing, but I still don't know whether it is KE, PE or neither of these.
At an introductory level it is neither of these. The energy of a free particle in Newtonian mechanics is all kinetic ##\frac 1 2 m v^2##. In the theory of relativity the energy of a free particle is given by:
$$E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - \frac{v^2}{c^2}}}$$If we take ##mc^2## to be the rest energy of the particle, then the Kinetic Energy is given by:
$$KE = (\gamma - 1) mc^2$$You can then use a binomial expansion to show that for ##v## much less than ##c## we recover the Newtonian approximation:
$$KE \approx \frac 1 2 mv^2$$

Last edited:
Mentor
Is it even valuable to rigidly classify energy into kinetic, potential, etc.? What is that classification actually going to be used for?

Vanadium 50, DrClaude, Ibix and 1 other person
2022 Award
I'd be inclined to agree with Dale's view here - what's the point of classification? What are you hoping to achieve by grouping different kinds of energy this way?

Consider heat energy. I can certainly see it as a potential energy in the sense that how much heat a thing has limits the mechanical work I can get out of it, and once it's gone it's gone much like the chemical potential in a battery. But fundamentally heat is the kinetic, rotational, vibrational, etc energy of molecules, so it's all about motion. So which of your classes it belongs to probably depends how I'm thinking about it.

If you're wedded to your classification I'd just say some things don't fit neatly into classes, even in a fundamental science like physics.

Staff Emeritus
Is it even valuable to rigidly classify energy into kinetic, potential, etc.?
"All science is either physics or stamp collecting" - Ernest Rutherford,

berkeman
Mentor
Is it even valuable to rigidly classify energy into kinetic, potential, etc.?
It's not (which of course is the point of Dale's rhetorical question).

We make the classification because it is useful for specific classes of problems. For example, the potential/kinetic classification is used when we're analyzing the behavior of objects moving under the influence of conservative forces and the heat/mechanical classification is useful in some thermodynamics problems.

Green dwarf
Thank you everyone. Being a science teacher and not a physicist, I have been influenced by science textbooks for school kids which tend to classify energy, though I have never been quite comfortable with the classifications offered. Hence my initial question.

It's actually quite a novel idea to me that any classification of energy types is somewhat arbitrary and different classifications would be useful for different purposes.
Teaching kids from 11 to 18 years old though, I do feel that some sort of classification makes energy easier to grasp in that it sorts it into bite-sized chunks. But, knowing that classifications are somewhat arbitrary, I am now quite happy to use a three-way classification into kinetic, potential and rest-mass.

I have included this idea in a PowerPoint at www.csf.canterburydarkside.com/Energy.pptx in case anyone is interested in having a look.

PeroK
Homework Helper
Gold Member
But, knowing that classifications are somewhat arbitrary, I am now quite happy to use a three-way classification into kinetic, potential and rest-mass.
But it's actually not arbitrary.
They are well defined in physics. If one neglects the definitions, then they may seem arbitrary.

In order of fundamental importance...

From a relativistic viewpoint,
mass-energy is an observer-independent energy associated with the rest mass of a particle.

Kinetic energy is the energy of motion
associated with the work-energy theorem... and it is frame dependent.

Potential energy is the energy of configuration,
associated with a special type of work that
only depends on the endpoints (and not the path).

Consider heat energy.

Recall that heat energy is a transfer of energy due to a difference of temperatures,
without a change in configuration. When there is a change in configuration, then
work has been done.

Last edited:
PeroK