Kinetic Energy EXPLAINED in 5 Levels - Beginner to Advanced (Classical Physics by Parth G)
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- Опубликовано: 25 июл 2024
- What is kinetic energy? How does it depend on the mass and speed of an object? And how do relativity and quantum mechanics deal with it? We'll answer all of these questions in this video, in 5 levels of difficulty.
Level 1 - Kinetic energy is the energy that an object has when it is moving. The faster it moves, the more kinetic energy it has. Energy is a quantity or number that we can assign to different parts of whatever we are studying, in order to predict how it should behave at some point in the future (based on Conservation of Energy). Kinetic energy (just like other forms of energy) is measured in Joules.
Level 2 - The formula for kinetic energy is (1/2)mv^2 where m is the mass of our object, and v is its speed. So we find that if we double an object's speed, its kinetic energy increases fourfold. If we double the mass of the object, its kinetic energy increases twofold. It's worth noting that v refers to the speed of the object, not the velocity. In other words, kinetic energy is a scalar.
Level 3 - We've mentioned the speed of an object multiple times here... but what is this speed measured relative to? Whenever we measure the speed of an object, this means the object is moving a certain distance away from some reference point, in every unit of time. From different reference frames, an object may be moving at different speeds. Therefore, these different frames may decide the object has different amounts of kinetic energy. Which is correct? The answer is all of them! Reference frames do not need to agree on how much kinetic energy an object has. As long as the total energy in each frame is conserved, that's all that matters. So to one observer an object may have no kinetic energy, while to another the same object may have kinetic energy... and this is ok!
Level 4 - In special relativity, every object has a certain amount of energy, even when at rest relative to the observer. This energy is given by the famous equation E = mc^2. However when the object is moving, the energy-mass-momentum equivalence equation (a much more complicated one) takes effect. In this video we discuss one of the basic assumptions in special relativity, that the speed of light is constant for all observers. We then also see that the kinetic energy of an object in any reference frame, is the energy it has while moving, minus the energy it had when it was stationary. Upon using a binomial expansion for small velocities, we see that the main (biggest) term of the relativistic kinetic energy equation is the same as the classical, Newtonian kinetic energy equation! However in relativity there are infinitely many terms getting smaller and smaller.
Level 5 - We've only talked about linear kinetic energy so far. We can also consider the rotational kinetic energy of an object when it is undergoing some sort of angular motion. The rotational kinetic energy depends on the angular speed of our object, and on its moment of inertia. The angular speed is simply how much angle is covered by our object per unit time. And the moment of inertia is the equivalent of mass for angular motion. Just like mass is a measure of how hard it is to move an object in a straight line, the moment of inertia is a measure of how hard it is to move it in an angular manner. The moment of inertia depends on both the mass of the object, as well as its shape.
Resources to check out:
Kinetic Energy, Conservation of Energy Different Reference Frames: en.wikipedia.org/wiki/Kinetic...
Constant Speed of Light: en.wikipedia.org/wiki/Speed_o...
Rotational Kinetic Energy: en.wikipedia.org/wiki/Rotatio...
Moment of Inertia: en.wikipedia.org/wiki/Moment_...
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Timestamps:
0:00 - Intro: Kinetic Energy by Parth G
0:31 - Level 1 - What is Kinetic Energy? How do we measure it?
1:37 - Level 2 - The Formula for Kinetic Energy EXPLAINED
3:54 - Level 3 - Kinetic Energy in different Reference Frames!
5:52 - Level 4 - How does Special Relativity deal with Kinetic Energy?
9:54 - Level 5 - Rotational Kinetic Energy, and Quantum Mechanics
12:17 - Thanks for Watching! Please Subscribe for more Fun Physics!
Hi everyone, thanks for watching! I've now made a similar video about Potential Energy (5 levels of difficulty) - check it out here: ruclips.net/video/Iu48lfJXgww/видео.html
And as always, let me know what topics you'd like me to cover in future videos :)
Might you talk about Quantus Mechanics?
Can u do the 5 level depth video for light ? As in matter and wave nature together and also the electromagnetic radiation nature of light and also the photon nature
Hi 🇮🇳
@@YgorRichard thanks for your comment! I have a playlist on videos about Quantum Mechanics too - in fact that's what I talk about the most on here! :D ruclips.net/p/PLOlz9q28K2e4Yn2ZqbYI__dYqw5nQ9DST
I was having some problems in atomic structure , but after watching some of your videos like the one in which you talked about quantum numbers , and the Pauli exclusion theorem one ,I was able to connect things ,really thankyou sir , and can you make a video which could make us visualize or picturize an atom in some deapth , it would be really helpful 😃
keep up the good work homey and yes totally would like more of 5 level vids
homey?
I’d kinda like “five levels of math used in physics”
Could go down basic arithmetic, trigonometry, basic calculus, vector calculus, then higher level maths that are way beyond me
Geometric Algebra. Learn it. Use it. Love it.
@@Paramecium13 Hell yeah! Geometric algebra is awesome!
This is a great idea albeit it’s a bit too broad. Different areas of physics at the highest level require totally different branches of math! Someone who’s in geophysics for example would be an expert and PDEs and applied mathematics in general, while an astronomer using machine learning to classify galaxies would be an expert in statistics, data analysis, and linear algebra. So different!
The baseline of the core classes is the same I suppose, you just specialize later on.
@@Paramecium13 never heard of geometric algebra, only algebraic geometry. Can you please recommend me a book?
@@massipiero2974 personally, I read Matrix 'Gateway to Geometric Algebra, Spacetime and Spinors'. I'd also recommend the works of David Hestenes, which includes some articles he's published.
I would very much like 5 levels of voltage.That shit's crazy
seconded.
Also potentials
Isn't voltage just the difference of 2 different potentials though? With an arbitrary point chosen as a reference potential?
@@petermeter4304 yeah but you can dive into different stuff with voltage and potentials.
Like engineering and kirchoffs law with voltage
Wherease potentials are more quantum physicsy
Level 1: Voltage is just the potential difference between two points, defined as the work done to move a charge between the two points. That is, Voltage is the path integral of E along some countour often denoted gamma.
Level 2: Voltage is an example of what’s called a potential, specifically what we call a scalar potential. That is, it is a scalar field such that the physical electric field is unique up to the gradient of the scalar potential plus a constant. Voltage, although a scalar potential, isn’t the only type of potential. Other types of potentials include vector valued potentials. For example, the magnetic field is unique up to the curl of a vector field potential plus the gradient of a scalar field. The gradient of the scalar field and other constant can be arbitrary, and picking values for these quantities is called gauge theory. While it is a classical idea, it also shows up in quantum mechanics, specifically quantum field theory, where different symmetry properties are akin to picking your gauge in classical electromagnetism.
Level 3: Voltage is only really valid in the static field approximation, as we can only define a scalar potential in the countour integral of the electric field over some path is zero. However, we can modify our definition of voltage for one which is valid even when this integral, or otherwise put the curl of the electric field is nonzero. With this additional time dependence, we also need to account for the propagation delay of the field due to the finite speed of light, called the retarded time. In order to prescribe the physical electric and magnetic field from time dependent scalar and vector potentials, we use the theorem that any well behaved field can be decomposed into solenoidal and Polaroidial pieces, also called the Helmholtz theorem. From the potential formulation, we get the physical fields in electrodynamics, called the Jefimenko equations.
Level 4: The idea that the Laplacian of your voltage or scalar potential is proportional to your charge density in electrostatics is no accident. In elementary Newtonian mechanics, we may also define a scalar valued potential field analogous to the voltage scalar field in electrostatics. For it too, it’s laplacian is proportional to mass density, and from first year calculus that 2nd derivatives are related to curvature. However, what is the physical intuition behind curvature here? This is actually crucial for general relativity, where from the elementary idea of voltage from electrostatics, this becomes the time piece of what’s called the metric tensor field. The information contained in the curvature of the metric tensor field can be found under the principle of general covariance, where we refine what we mean by derivative such that it is covariant. The laplacian of the time piece of the metric tensor then becomes two covariant derivatives of the metric, a physical quantity called the Riemman curvature tensor. This is a matrix with 256 components telling you how curved a surface is. From this quantity, we can eliminate certain redundant pieces of information in the tensor to construct the Ricci tensor. By requiring that this coordinate dependent derivative or covariant derivative vanishes, we can construct a quantity with the Ricci tensor which vanishes, specifically the Ricci tensor minus one half times the metric tensor times the Ricci scalar, which is a doubly contracted Riemman tensor. A priori, we know that curvature of the manifold is related to its mass-energy content, expressed via the energy momentum tensor which is also covariantly conserved. By equating this quantities by requiring they are covariantly conserved, and requiring that in the weak field limit of the fields we get Newtonian Mechanics, we can derive the field equations of general relativity, all inherently based upon the idea of a voltage or scalar potential in classical electromagnetism.
Level 5: ???
He did it. The madlad did it, there's a video on potentials out
It's actually insane how good you are at explaining complex topics. I never feel "burned out" from watching your videos
Thank you for the kind words!
Me, controlling my urge to crack a joke on complex numbers
@@ParthGChannel
Kinetic energy was defined long before the theory of relativity. It is defined from energy conservation law. Using definition of work W we obtain:
W= ∫ F•dr =∫m•a•dr = m∫ (dv/dt)•dr=
m•∫ (dr/dt)•dv=∫ m•v•dv =
Δ(1/2•m• v²)=ΔK
Also potential is defined from work:
W=∫ F•dr=-∫ (dU/dr)•dr=-∫ dU=-ΔU.
So ΔK+ΔU=W-W=0 energy conservation law only applies for conservative forces in which F=-dU/dr.
For example gravity potential energy: ΔU=-∫m•a•dr=-∫m•g•dr=-Δ(m•g•h)=-ΔK.
Student of physics level.
This video was amazing! It's basically a video introduction to roughly everything about kinetic energy, and even its formulas, yet explained so simply and teaching so many, so many new things! I'd love to see more of these!!!
I’d love to see the symmetry vs conservation topic presented this way. I wished there was a simplified scenario where conservation of energy could follow from a given symmetry.
Level 6 : Energy is the conserved quantity associated to time-translation invariance. Very much like Momentum is
associated to space-translation invariance. Those invariances are always there for a given system : You get the same results from doing the exact same experiment today or tomorrow (time translation), and likewise you get
the same resultsfrom doing the exact same experiment in Paris or London (space translation). Note here that by "exact same experiment" I mean you are able to reproduce exactly all conditions releveant to the experiment about the system and its environment.
If you want to learn more details, lookup about Lagrangian/Hamiltonian mechanics and Noether's Theorem.
Cheers !
I definitely enjoyed the 5 levels video. Please keep using this structure. It really helps build an intuition for the concepts from low to high level.
Another very interesting video. Well done. I liked the idea of explaining the concept and equations in levels.
More videos like this would be of much help, sir.
Thank you.
love your 5 levels explanatory methodology here and elsewhere - it's a brilliant way to seamlessly develop a student's understanding - please do keep these coming Parth
I always liked the mathematical explanation of why the 1/2 factor occurs in this formula when you calculate the line integral ∫ F • dr
Kinetic energy was defined long before the theory of relativity. It is defined from energy conservation law. Using definition of work W we obtain:
W= ∫ F•dr =∫m•a•dr = m∫ (dv/dt)•dr=
m•∫ (dr/dt)•dv=∫ m•v•dv =
Δ(1/2•m• v²)=ΔK
Also potential is defined from work:
W=∫ F•dr=-∫ (dU/dr)•dr=-∫ dU=-ΔU.
So ΔK+ΔU=W-W=0 energy conservation law only applies for conservative forces in which F=-dU/dr.
For example gravity potential energy: ΔU=-∫m•a•dr=-∫m•g•dr=-Δ(m•g•h)=-ΔK.
More of these! This was an excellent gauge of my own level of understanding as an undergrad who is generally unsure of "where" I am!
I also got a lot of help. By the way I am a high schooler. I knew 1st 3 levels and the rotational part of level 5 in detail.
Could you tell me how much does one learn in undergrad?
@@rikthecuber In my experience, these levels are all still in the scope of undergrad, but there will be additional detail: you will learn some more problem-solving techniques, ways to reframe problems or express them differently, and how to view models as a set of working assumptions rather than absolute laws
Just exactly what I needed. Excellent format and exceptionally clear.
This video was really lot of fun, i hope you do more of these, i suggest you do a video about the notion of dimension in different levels of difficulty, would be interesting, it s done before but i wanna see you do it your own way
Love how you make these concepts so clear!
Parth love you, you are making great videos. Keep up making.
Brillant, loved it, and thanks. I would like to hear you discuss quasi-particles, E = hf, and the confusing notion of where exactly is the energy assigned.
Cleared all my doubts related to KE. Make more such videos 👍
Bro you speak so concisely and clearly about KE - a mark of a high level understanding. An important idea that I didn't think about is the idea from level 1 that energy is a number that allow description of what an object is doing or will do. I didn't ever really think about this, I just took the formulae and applied them using conservation of energy. Thank you for giving me this new understanding.
I'm in love with the way you explain things. It's so buttery and easy to digest. Thanks for the great vids!
This is really good, keep it up!
Clicked video after notification with KE max
This some bomb ass physics content right here... looking forward to your future videos
Informative and easy to understand.
Very interesting. Thank you very much
Amazing work!!
Loved it as Usual.
woooow amazing !!! I love you !! good job, bravo !!
keep this kind of video, i loved it
Awesome explanation!
Fun. Thanks for posting. Liked and shared.
Mind blowing brother🤯🙌, love your content💯❤️
Fantastic video
Gold. Sweet work bruh
This video is Amazing!you made me understand more about this topic than my high school books.
🙏🙏🙏🙏🙏🙏 Thank you so much sir now I finally got the proper explanation of energy please make such more videos of trigonometric ratios of obtuse angles, it would be such a big help.
Excellent presentation skills
That's amazing please keep us up with 5 levels of physics
great video
great explaination
Hai dear Parth!
You're doing great with these concepts. I request you to explain about Gibbs free energy.
I am still 15 yrs old and I understood QUANTUM MECHANICS by watching ur videos
Love from INDIA
Woah I absolutely needed to understand this, now that I know it I feel much relieved 😭😭😭
Very clear explanation
I would say just one thing - Never stop making these videos.
Now that's the kind of video i like👍👍👍
Excellent overview. Wonder what the historical development was that led to the 1/2 factor in the expression.
More! Cover EVERYTHING!
@Parth G, please bring in the concept of electricity and how is it related to tensors and all that stuff!
Exceptional. I expect some treatment on transistor as a switch
Please continue this 5 level series.
you are a good teacher.
Please make a vedio like this more about one concept at different levels in deep🙏🙏
Subscribed.
Talk about Boundary Layer Theory next.
It'll be super interesting to see how you talk about BLT in Level 5. xD
I feel lucky to understand it all
Is mass and velocity are directly proportional when density is same or constant?
Hi Parth G,
About the different Reference Frames, at 5:43 you say:
"What really matter is how this energy changes" -- I like this approach, but I'd need a littlebit more explanation, for example:
If a 1000kgs car goes with 10 m/s then if it wants to accelerate by 10 m/s to reach the speed 20 m/s, it needs 150 kj energy to speed up, because this is the kinetic energy change it have to deal with.
If the same car wants to accelerate from 0 m/s to 10 m/s, it needs only 50 kj, because the change in kinetic energy from 0 to 10 m/s is less in this case, since the square of the speed in smaller absolute values matter less, than in bigger absolute values.
And here is the seemingly problematic contradiction with different frame of references.
In the first scenario, if we are sitting in another car and go paralelly with the same speed as the first car, 10 m/s, then from our point of view the first car needs to consume only 50 kj energy, since from our reference it accelerates from 0 to 10 m/s.
Can you please describe this seemingly contradicting energy change differences in an intuitive way?
Thank you
This is a very good point, which require introducing a bit more details.
The change in kinetic energy in a given reference frame is the same at first order is a more precise
statement : you actually take the derivative of the kinetic energy with respect to the change in speed
(which you should note gives the formula for the momentum, this is why we rather use momentum
than speed. Momentum is a conserved quantity, not speed.)
This is only true for an infinitesimal change in speed which happen in an infinitesimal amount of time.
Indeed, you will not be able to change speed instantly, you cannot have infinite acceleration.
Now you have to consider how much time you need to accelerate to reach a desired speed from your
starting speed, as well as the amount of acceleration you provide, via applying a force (ie. F=ma).
The total amount of energy change over a period of time during which you are accelerating with respect
to a given frame now needs to be computed as an integral of the infinitesimal energy change over that period
of time.
In your example, in the case of both frame, you require the same energy change to provide the same
acceleration (F=ma) as a force that would be applied over an infinitesimal period of time,
but you would have to apply the force longer in the case of the moving frame which indeed requires
more energy, which will be reflected in Newton's formula as an additional acceleration term.
Lastly, if you are really serious about it, you need to use Lorentz transformations from special relativity
to properly combine velocities and use the special relativity formula for kinetic energy.
I love this video
Liked and shared.
Great
Pls make a video like this on Potential Energy.
Can you make a video on electricity, explaining what voltage,current, potential,emf, potential differences are and how they depend.
Nice liked video
can you make a five lelvel video on momentum
wow there's so much stuff I don't know that is pretty cool
Sir why don't you make proper full course videos like of relitivity,quantum l,optics etc
As your conveying method is fantastic we can actually understand you
Nice
Sir pls make a video on kinematics tips and tricks
Great video! You did a wonderful job explaining kinetic energy all the way from PHY 101 up to Relatavity!
One question: Is there a sign error inside of the square-root @8:51? Should that be addition instead of subtraction?
I think so
Thank you, and ah yes great spot - it should be a plus, not a minus :)
hey can you please explain why regardless of the reference frame or velocity of the observer, light is always measured to be c ms⁻¹ and not otherwise!!
Nice video, maybe in the third level you can use an argument like "If a mass m, with initial velocity v is thrown upwards how much kinetic energy it has at the beginning?"
Now you use conservation of energy to show that
K=mg y_f
Where y_f is the maximum height reached which can be worked out from the equation of a uniformely accelerated motion
y(t) =vt-1/2 gt²
Which has a maximum for t_M=v/g
y(t_M) =v²/2g
So that kinetic energy is given by
K=mg v²/2g=1/2mv²
We can do a similar derivation in the case of a mass on a plane with friction and using the fact that the work of friction is equal to the loss of energy
Hey parth I wanted to know what it really means to understand a concept or idea , does it mean being able to infer or deduce it using more fundamental idea or being able to form a picture or kind of metal model if so than of what accuracy. Btw great video as always. ❤️
A good way to test if you understand an idea is to see if you can explain it to someone else
You didn't ask me, but I think your question is interesting. I think the best way we can measure understanding is to test "your" model of the concept that you build as you gain more knowledge and solve more problems. When I say "model," I mean the way that you approach problems with respect to a concept and how you envision the concept can change over time or in different circumstances. Over time, your model should become more consistent with scientific principles and theoretical & experimental evidence. If your model contradicts those things, that could be a sign that your model is incomplete (and therefore you need more information to better understand), but more excitingly, it could mean that your model explains what's happening even better than the accepted model!
Science is all about refining accepted models into better approximations of the real world, so best practice is to try and generate your own from the ground up and continually take them as far as they can until they either break or represent a new discovery!
I'm not sure if this answers your question, but this is how I think about understanding--it's my model of learning & understanding ;)
Cheers
@@lattice737 great advise 🙂😄
Is it same energy/ mass of two object where one weighs 40 kg and the v is 10 km/h and the other object weighs 80 kg and the v is 5 km/h then?.
5 levels of symmetry would be interesting, eg visual intuition of what a symmetry is, using symmetry to simplifying problems, thinking of symmetry in terms of groups/ transformations, noether's theorem, spontaneous symmetry breaking
8:20 p is 0 at rest so root over m^2c^4 =mc^2?
hi could you make such video on entropy
Where you do this animations? :)
amazin!'
Level 6 would be the noether theorem and invariance of time translation right?
Hi! Why you don't said bout integrals of movement and lagrangian function?
Please do a Explain video for the Lagrangian L=T - V (KE-PE). What does it mean? Why does it work? Thanks.
There is a form of kinetic energy that isn't reference frame dependent, and is arguably more directly useful, which is the kinetic energy between two objects, or the difference in the total referential kinetic energy in the two objects from their current state to the state they would be in after a fully inelastic collision. I say this is more directly useful because it also represents the maximum extractable kinetic energy when only considering those two objects.
How does this fit into general relativity? I know energy, momentum and pressure are the source of gravitational fields in GR, but kinetic energy and momentum are relative. Does this mean different observers disagree about how much spacetime is curved, because they disagree on what the source of the gravitational field is? That doesn't quite sit well with me because of black holes. Let's say a massive object was travelling close to the speed of light in my reference frame, but you're flying alongside it, stationary relative to it. I see it as having momentum and kinetic energy, you don't. So that implies its gravity would be stronger for me than for you - perhaps strong enough to be a black hole in my reference frame but not yours? That doesn't sound right...
In GR, I think the answer is that you have coordinate independence so the way you represent the energy content of spacetime, via the energy momentum tensor is coordinate independent. That means you can transform to a different reference frame traveling at a different velocity than me, but we both measure the same curvature of spacetime (I believe this is called general covariance).
In SR, I think this is analogous to saying that you can define your mass to be invariant under Lorentz transformations (m^2=E^2 - p^2 in natural units). This gets rid of the weird idea of relativistic mass saying that you somehow get more massive as you can kinetic energy. For a video showing why this interpretation is flawed, see Sean Carroll's video: ruclips.net/video/n_yx_BrdRF8/видео.html&ab_channel=2veritasium
@@chrisallen9509 So basically, even if energy and momentum themselves differ in different reference frames, they combine in such a way to make a tensor that's the same in all reference frames?
@@kafuuchino3236 Yes pretty much, this is why tensors are so useful since they take things which might look completely different in different coordinate systems (e.g. Newton's 2nd law in spherical coordinates vs. Cartesian) and show that the underlying physics is the same.
You should do hawking radiation!!!!
E=√p²c²+m²c⁴ and p=mu as object is in rest. Since u=0 then p=m*0, hence initial momentum is 0. So E=√0*c²+m²c⁴, hence E=mc² :)
Potential energy also please!
as the kinetic energy of a system is relativistic because of the speed, similarly is the force on a system relativistic because acceleration also depends on the frame of reference
Really loved it . The most important thing in this video is not really Kinetic Energy (for me😂😂)LOL , It is understanding of moment of inertia. Now I have a more intutive way of thinking moment of inertia. Any way I really loved it . Can you write book for quantum mechanics for newbies? btw Your videos are awesome.
Ok... I've recently been told the following question is much deeper than it seems. I would love a 5 levels explanation to this question: Why can visible light pass easily through a quarter inch thick pane of glass, but not through a quarter inch thick wood plank?
I would say that the pane of glass probably has a very regular geometric crystalline structure that allows most of the photons to pass through unobstructed whereas the wood structure is probably more disordered and tangled up so to speak so more photons hit and bounce off rather than pass through
No mention of temperature?
So, what is really energy? Does it really exist? Or is a product of our measures?
It would be interesting with potential energy
Maybe 5 levels of gravity? Great video btw
It missed talk about the relation with kinetic energy and the temperature of the system in thermodynamics and statistical mechanics
de brogile equation five levels please
5 levels of Lagrangian, pls
Great format on the 5 levels. I’d like to see it applied to EM induction
5 levels of Quantum Field Theory or some of that Standard Model stuff.
How about 5 levels of angular momentum
So. .if I move my arm twice as fast when scrubbing something I'm using 4 times more energy?
yes!
8 times faster = 64 times more energy and so on…