How to Succeed at Physics Without Really Trying

Units are your physics superpower! With dimensional analysis, you can get 90% of the way to the answer for many physics problems with next to no work! Get the notes for free here: courses.physicswithelliot.com...
In any given physics problem, you have a certain list of parameters at your disposal: masses, charges, lengths, and so on, and fundamental constants like G and c. And you're looking for an answer with some particular units. Dimensional analysis is a strategy to figure out how you can combine the given parameters to get the correct units of the answer you want. And often times this approach can get you 90% of the answer with minimal effort. I'll show you how to apply it to three very different problems: the period of a pendulum, the binding energy of a hydrogen atom, and the event horizon radius of a black hole.
Get the links here: www.physicswithelliot.com/dim...
More about the pendulum period: • The Trick that Makes U...
How to catch your own mistakes by checking units: • What I Wish I'd Known ...
All about pendulums: • Everything You Need To...
Tutoring inquiries: www.physicswithelliot.com/tut...
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About physics help room videos:
These are intro-level physics videos aimed at students taking their first physics classes. In each video, I'll teach you the fundamentals of a particular physics topic you're likely to meet in your first classes on mechanics and electromagnetism.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com.

[@fixed-point]

Great video. I would add that dimensional analysis can also be used for other "sanity checks" on equations. The biggest one is that it never makes sense to add two quantities that have different dimensions (or units!). Another is that exponents are always unitless (to the best of my knowledge), which means if you have a 't' up there, it better be multiplied by something with seconds in the denominator

[@PhysicswithElliot]

Thanks Aaron! Agreed!

[@MCLooyverse]

You *can* add different units together, however you know when you intend to do so. I've thought a little bit about "modular arithmetic on recipes" (what I call it. IDK if it has a name), which involves adding together butter and eggs and stuff (considered different units). In general, though, yeah, I agree. I hate the standards of economics, because they will do (1 + i)^t, and you just have to assume that it's t/year.

[@compphysgeek]

imagine exponents weren't always dimensionless. you might end up up with a quantity metres to the power of seconds for instance. what would that be?

[@James-bv4nu]

Sine, cosine, and exponential functions argument has units of radians.

[@compphysgeek]

@@James-bv4nu radians isn't really a unit. an angle is the ratio of arc length and radius, so the units are m/m = 1. Radians is just a fancy name for 1. Similar to mole, which is just a fancy name for 6.something × 10^23, or dozen, gross, etc. I still don't understand what makes a mole a fundamental unit by the way. It's just a name for a very big number.

[@harveyfedyk365]

You have to be making your Mom and Dad very proud. Great videos and this is wonderful example of the power of KZbin and Internet. It would have been great to have this “tool” when I was in university. Well done.

[@Benjamin-no1vb]

I highly appreciate the effort you put into these videos. Thank you for your important work. It helps a me a lot!

[@PhysicswithElliot]

Thanks Benjamin! Glad you're liking them!

[@sternmg]

You covered dimensional analysis well, illuminating the path from initial dimension to final ones, ruling out irrelevant ones, referenced the rigorous system of equations but also showed nice shortcuts. But a *correction request:* The SI unit symbol for "meter" (*) is "m", where _lowercase_ is significant to differentiate the symbol from _uppercase_ "M" = "Mega", the multiplicative prefix for 10^6. SI has specifics about lettercase, symbol spacing, plurals, ratios, etc., and those rules strengthen the system to be consistent and unambiguous. A rule often ignored (not in this video) is that SI unit abbreviations are _not pluralized_ when written, as that would be language-dependent. Notably, in English, appending an "s" would introduce "seconds" and thus change the dimension of the result. (*) Or rather, "metre", though that's a long-lost battle.

[@ibrahemtaha8177]

Amazing video! many thanks for sharing!

[@PhysicswithElliot]

Thanks Ibrahem!

[@MrAlRats]

All physical quantities can actually be measured using just the units of time (second) and its integer powers. Distances and time intervals between events can be measured in the same units as each other, the second. Mass, energy, momentum, temperature, acceleration, and frequency can all be measured in units of the second to the power of minus one. Angular momentum, velocity, and entropy would be dimensionless in this system of units.

[@clayton97330]

Great topic!

[@RaiyanSyazani]

Superbly done video!

[@PhysicswithElliot]

Thanks Raiyan!

[@mritunjayjha2872]

Great one👍

[@Kram1032]

Oh interesting. Somehow I never encountered that part where dimensionless quantities add the possibility of a function that depends on them, but now that you mentioned that, it's rather obvious.

[@oliverquinonez3919]

WOW. This is so simple but surprisingly powerful. I'm definitely not going to forget this one and I'm not going to forget the lesson that sometimes adding more complexity clutters your understanding. Thank you

[@PhysicswithElliot]

Glad it was helpful Oliver!

[@NovaWarrior77]

fantastic video

[@sergiolucas38]

very good video, your didactic is amazing :)

[@fusion_strike_3384]

Great video! Loved the Shakespeare reference 😂

[@paologat]

Dimensional analysis is a great tool but not failproof. For example in quantum electrodynamics the fine structure constant alpha (about 1/137) and its powers play a fundamental role- and, being dimensionless, the right power to use cannot be inferred by dimensional analysis. Same goes with E/kT in statistical mechanics: dimensional analysis can’t tell apart the classical, Bose-Einstein and Fermi distributions. But if in some way you can set up a situation where the adimensional constants cancel out (e.g. the ratio of periods of two pendulums) then dimensional analysis gives its best.

[@PhysicswithElliot]

Yep I talk a little bit about the fine structure corrections in the notes! Will hopefully discuss it more in future videos

[@potatoesandducks958]

But what if the constant contains units? For example, Coulomb's Law. If you are trying to find the variables needed to find F, using dimensional analysis, you might think charge doesn't matter, or that charge needs to be divided by another charge.

[@TheGuruNetOn]

Round hole requires round peg. Ideas is to fashion a key from things at hand. Now how do we manipulate what we have to get what we require? Reverse engineering/working backwards from the solution to the problem statement. Works better combined with pincer movement ie digging backwards and forwards between 2 ends of the tunnel. What's important is to stay in alignment.

[@johnchristian5027]

nice little video

[@Possibleep]

Mol is my favorite SI unit, it's a pure number and yet it's also a unit measure - what the heck?!

[@TIO540S1]

Yes!

[@erikev]

Great videos. Could you tell us what drawing tool you use? Neat how lines etc are corrected. Is that automagically?

[@PhysicswithElliot]

Keynote, Procreate, and Final Cut Pro mainly!

[@Dismythed]

To say that this video's title is misleading is an understatement cubed.

[@ayhamhalalsheh221]

Wonderful

[@PhysicswithElliot]

Thanks Ayham!

[@shatandv]

Thanks for the video, Elliot! A small question on the parameters of our equation. As someone who is just learning physics, how would I understand which parameters I even have in the equation? Right now I'm not sure which ones I have and which of them are even relevant to a problem.

[@PhysicswithElliot]

In general, that depends on the type of problem and what level of approximation you're using to try to understand it! For example, when I talked about the Hydrogen atom here I ignored both the speed of light c and the proton mass. But both of those can be incorporated into the calculation of the binding energy and give small (but very interesting) corrections to the formula I gave you. If we're talking about something like a homework problem though, I would write down symbols for all the numbers that you're given (like masses of particles, charges, lengths of ropes, spring constants, and so on). Then think about what kind of problem it is, and write down any appropriate constants (like little g for a projectile motion problem, Coulomb's constant for an electricity problem, big G for a gravity problem, and so on). Then apply dimensional analysis to your list of parameters. Most importantly, after you do your actual calculation, check that your answer has the right units. If it doesn't then you know you've made a mistake somewhere along the way!

[@shatandv]

@@PhysicswithElliot Thanks, Elliot! That sounds useful

[@RickyMud]

Wasn’t dirac the one that was famous for his dimensional analysis and order of magnitude estimations

[@maxgeorge1463]

I haven't taken a course in physics in my life. I'm taking ap physics e&m next year. Should I be understanding such topics before I start next year?

[@ram-my6fl]

you are the G.O.A.T elliott

[@PhysicswithElliot]

Thanks ram!

[@luckycandy4823]

Don't know about the second problem, but the black hole radius is more a classical mechanics problem then general relativity, all we have to do is write the escape velocity of the star, and see when it equals c

[@PhysicswithElliot]

It's true that the Newtonian escape velocity exceeds the speed of light when a star or planet is squished inside 2GM/c^2. But Newtonian gravity doesn't predict black holes---as far as Newton is concerned you could strap a rocket to your object and launch it past the horizon!

[@user-sl6gn1ss8p]

I'm not sure whether the fact the answer is exact is a coincidence or something more (and the factors and their exponents are pretty much a given either way), I think it's good question. I don't the classical approach would hold for more complex scenarios though, so if this is more than coincidence, it could be seen as an approximation which holds for the simplest sense, maybe? Like maybe the symmetries and assumptions that go into the Schwarzschild metric are still "isomorphic" to plain old euclidean space for this purpose or something? (really just at the wall throwing stuff I don't quite understand here : p)

[@samicalvo4560]

Hello Elliot (or if anyone knows), could you tell me which app do you use for writing your diagrams and so on? Thank you!

[@PhysicswithElliot]

Keynote, Procreate, and Final Cut Pro mainly

[@NoActuallyGo-KCUF-Yourself]

If you don't know what to do, do whatever it takes for the units to match.

[@fungkeat9272]

Can I know what animation software you used, the animation is simple and beautiful

[@PhysicswithElliot]

Keynote mainly!

[@gotbread2]

I wonder... while the angle is dimensionless, it is different from other dimensionless numbers. If we add on the "made up" unit of radians, (or use radians instead of degrees in the first place), would we get that 2*pi factor?

[@nic5146]

I think it's more that since the period is independent of degrees or radians, there's nowhere for the angle to "fit" into the relation using dimensional analysis

[@PretTy_Fish]

Radian and degree are dimensionless units, with radian defined as the unit one. In terms of dimensional analysis, the angle is actually not different from any other numbers, just that it has a purpose in equations. Also as shown in the video, he did describe that there could be another factor depending on the angle (which becomes prominent when the angle is large), but neither that nor the 2*pi factor could come from simply performing the dimensional analysis, as they are dimensionless factors.

[@PhysicswithElliot]

Try making yourself a pendulum out of a piece of string and a little weight! Then time out a few oscillations with a stopwatch and divide by the number of oscillations to get your measurement of the period. Compare to 2\pi \sqrt{l/g} to convince yourself whether that 2\pi should be there or not!

[@ccdavis94303]

Plank would be proud of you.

[@badabing3391]

i did this way too much to avoid thinking too hard on some intro level concepts, this might bite me later

[@nHans]

So when we eventually adopt Planck Units, will it become easier to work with equations, or more confusing?

[@PhysicswithElliot]

It makes formulas a lot simpler to not have factors of hbar and c all over the place. But you can always put them back when necessary!

[@carultch]

It would make things a lot harder for run-of-the-mill problems that take place at the human scale. You'd have scientific notation in every common measurement you can see with your own eyes.

[@pdfgovardhanb8093]

Nice

[@rylanschaeffer3248]

Does this strategy always work? Are there notable examples in which it fails?

[@PhysicswithElliot]

It definitely has limitations. Understanding how the initial angle of the pendulum enters the period formula is one example. Another example is any time you have two parameters with the same units in a problem, like two masses m_1 and m_2, say, you can form their ratio, which is unitless. Then any function f(m_1/m_2) is allowed on the grounds of dimensional analysis alone. In the hydrogen atom example in the video I'm ignoring relativistic corrections that depend on the speed of light c. Once you add c to the list of parameters you can form a unitless combination ke^2/(hbar c) called the fine structure constant, and dimensional analysis doesn't tell you how the energy depends on this parameter. That leads to small, but measurable and very interesting, corrections to the energy formula.

[@ulissemini5492]

3:35 If theta is unitless can't we multiply by any function of theta without changing the units? how do we know theta isn't in the answer? edit: haha you answered my question later on, this is what I get for pausing :D

[@ulissemini5492]

oh I guess possible dependence on theta is included in the "proportional to" notation, I guess it makes sense since theta_0 is a constant - and for this specific problem it happens that the proportionality constant is not dependent on theta_0

[@user-sl6gn1ss8p]

A minor nitpick, but the video didn't show that "if such a critical radius were to exist, it would have to take [the shown form] based on dimensional analysis", but that a solution depending in all of and only those dimensional constants, parameters and variables would have to take that form if it were to exist (really nice video tho)

[@thedoublehelix5661]

It also assumed the units are combined in a "simple" way

[@user-sl6gn1ss8p]

@@thedoublehelix5661 what do you mean?

[@thedoublehelix5661]

@@user-sl6gn1ss8p there are typically a lot of assumptions when doing dimensional analysis like "exponents have to be dimensionless"

[@CoreyChambersLA]

Clickbait does not pay.

[@frnoor7001]

Investing subscribe to this channel because I wanna watch it grow

[@rodrigoappendino]

3:08 Isn't radians a unit?

[@PhysicswithElliot]

It's a ratio of lengths (arc length divided by radius), so no not really

[@Grizzly01]

Yes, it is a unit (an SI derived unit), but it is dimensionless, which is what Elliot should have said for θ∘ rather than 'unitless'.

[@ONRIPRESENCE]

Funny thing is, I have a friend named Elliot (Tanner) who is also a physicist. He is 13 years old, doing his PhD in high energy physics :D

[@ONRIPRESENCE]

He finished his BS in physics last year.

[@ShanBojack]

13yrs old?!

[@hooya27]

42 may be the answer, but without units, it is meaningless.

[@nHans]

🤣 I always love a well-timed reference to the Guide. However, in the interest of accuracy, I'm compelled to point out that according to the Guide, it's meaningless as an answer because we don't know what's the question. It has nothing to do with units. As you know, we do have very meaningful dimensionless constants such as 1/137, 10⁻¹²² and so on.

[@hooya27]

E=mc^2 seems trivially obvious once you do the dimensional analysis. Maybe that's why he didn't get the Nobel for something so simple!

[@carultch]

That formula is an oversimplification of his work anyway. It's like people knowing Euler for e^(i*pi) + 1 = 0, when it is much more useful to know his full formula of e^(i*theta) = cos(theta) + i*sin(theta).

[@bitterbob30]

The background on this video is very distracting.

[@spencergee6948]

I'm sorry but physics describes the workings of the Universe. You have to try. Believe me.

[@andaeh]

Coulomb is not a SI unit. Ampere is.

[@Musician-Songwriter]

1:44 H bar, ℏ, is Planck's "Reduced" constant or the Dirac Constant, equal to the constant divided by 2π