How to Succeed at Physics Without Really Trying

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.

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.

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[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

[harveyfedyk]

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

[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.

[Benjamin-novb]

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

[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.

[Dismythed]

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

[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.

[potatoesandducks]

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.

[oliverquinonez]

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

[Kram]

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.

[luckycandy]

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

[Possibleep]

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

[fusion_strike_]

Great video! Loved the Shakespeare reference 😂

[NoActuallyGo-KCUF-Yourself]

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

[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.

[badabing]

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

[slgnssp]

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)

[maxgeorge]

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?

[gotbread]

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?

[rylanschaeffer]

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