Matt & Hugh play with a Brick and derive Centripetal Acceleration

Matt and Hugh play with a tennis ball and a brick. Then they do some working out to derive the formula for the centripetal force (a = v^2/r) by differentiating some vectors.
Here are the sheet of working out: imgur.com/a/lphOr
Dr Hugh Hunt is a Senior Lecturer in Engineering at the University of Cambridge and a Fellow of Trinity College.
www.hughhunt.co.uk/
/ spinfun
This is a new video format idea, so all feedback appreciated!
(Sorry the audio goes a bit out-of-phase; fixing it for this video was beyond my current skill × time, but I'll fix it next time.)
Piano music is an original piece “The River” by Frode-5.
• The River - Original P...
All other music by Howard Carter
Design by Simon Wright
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Book: makeanddo4D.com/
Nerdy maths toys: mathsgear.co.uk/

[@sillyfly9530]

"One vector, two vector Red vector, blue vector"

[@outputcoupler7819]

My physics professor told me that if I ever used the small angle approximation in front of a mathematician, they'd cringe. Hypothesis confirmed.

[@alcesmir]

As long as you have a good motivation for it being ok, then everything is fine. This is a case where it is appropriate but where no motivation was given, hence the reaction.

[@standupmaths]

+Output Coupler I love small angle approximations, but I don't fully trust them.

[@topilinkala7651]

@@standupmaths You know that from area comparision of two tringles and a sector one gets that sin(a) < a < tan(a) when 0

[@Danicker]

@@topilinkala7651 It depends on how you use it. The key point here is that since they are differentiating, they are looking at the limit as di approaches zero, and under that limit sin theta will equal theta

[@sophieward7225]

Matt, how does it feel to step into Brady's shoes?

[@tridecalogism935]

Matte and Hue Their cousins who talk about colour.

[@williammiles9926]

+Tridecalogism *they're

[@tridecalogism935]

+William Miles No. i used their to refer to the subjects in THIS video. Otherwise i would have used they're. As in Matte and Hue are THEIR cousins.

[@robmckennie4203]

+Tridecalogism there*

[@witerabid]

+Tridecalogism weird fact: Matte is Hugh's cousin and Hue is Matt's cousin :D

[@standupmaths]

Nice one. I'll use that title if we ever do something on reflection/colour!

[@LLHLMHfilms]

Not a great explanation but a Parker square of an explanation.

[@standupmaths]

The important thing is that we gave it a go!

[@bojandimovski1504]

+standupmaths You didn't do your best of giving a go... But you gave a Parker square of a go JKing Matt you're the best keep up with the good work

[@wobblysauce]

+standupmaths Parker square + Internet.. = Fun for n-1.

[@somitomi]

+standupmaths Just out of curiosity, did you regret ever uttering the words "Parker square"?

[@dhruvgoyal7163]

Matt reacts as if he has never studied physics. :)

[@Borednesss]

You should have tried swinging the brick around instead, just to see what happens. For science =P

[@derKarl_stp]

+Boredness I knew that was coming :D

[@PhilippeAllardRousse]

That would have probably results in a tragic Parker Square.

[@ELYESSS]

+Boredness broken skulls would happen.

[@dddtl]

+Boredness Brick v. cinder block?

[@mestiarcanus]

+Boredness No lie, I had an undergrad physics prof who did that but with a heavy metal ball instead of a brick (or tennis ball). He misjudged how it would swing when he stopped and it smashed into his forehead, of course drawing blood. Thankfully there wasn't a worse injury and someone in the front row had a bandaid (bright pink to boot). It was quite the Parker Square of a demonstration.

[@JamieThelin]

good thing I can pass this off as M2 revision instead of just me procrastinating

[@NabeelFarooqui]

classic

[@NabeelFarooqui]

classic

[@James-bb5me]

classic

[@eddotron1224]

classic

[@DLMonsteer]

classic

[@Donkeyiser]

White paper? Does Brady have the brown paper trademarked or something? Surely he would let you use it if you asked..

[@RexGalilae]

Brady bros. have copyrighted the paper

[@rrni2343]

There should be a crossover series with numberphile and sixty symbols where the physicists and the mathematicians talk about how the formulas in physics are derived. In short as a uni student, and as a general science enthusiast I find this video to be superb, and you should, if you can, do more of them.

[@jonathanCRoberts]

Your pronunciation of centripetal is a classic #parkersquare.

[@otakuribo]

... which you could try yourself by filling in the hashtag to form a 3x3 magic square; perhaps of square numbers. You might not succeed, but that shouldn't stop you from giving it a go.

[@Libya4LY]

That small angle approximation is quite the #ParkerSquare

[@witerabid]

+Libya4LY Well... Physics... ;)

[@standupmaths]

This may be the best use of #ParkerSquare yet.

[@erickcapitanio1957]

not really if you consider it infinitesimal

[@ObjectsInMotion]

If we are talking about infinitesimal angles, sin(x) is _exactly_ x.

[@disnerdforever]

That was a really nice circle he drew freehand 😳

[@Exaskryz]

+disnerdforever It was practically the opposite of a #Parkersquare

[@lanceraltria]

@@Exaskryz a #Huntcircle it is then

[@OneShotAwayy]

An amazing idea for a video series! Everyone enjoys physics demonstrations / toys. Plus the explanation side of things is great info! Loving it! Keep it up

[@mwffu2b]

Rather than "Tennis ball holds brick," it'd be better to say "Brick holds tennis ball (in orbit)."

[@bencesarosi7718]

Well, since every action has an equal and opposite reaction... :)

[@stickmandaninacan]

is that a Parker Brick?

[@JanStrojil]

I loved it, I definitely want to see more (and I don't care how much if at all it overlaps with numberphile). Hugh is great, bring him back for more!

[@cjp21211]

I just want to give thanks to your videos matt, I love math and physics (I'm not particularly skilled) but learning a bunch of equations and explanations just leave me so hungry... may seem childish but I'm the kind of person that really wants to figure these things out myself or at least be able to apply it to something by myself. you show that you can do just that. and you don't need a laboratory or abundance of resources. just whatever you have at hand and a good imagination. thanks matt

[@samhadley5608]

Can't believe this came out same day I learnt about it in school! Great video, would love more of these!!

[@semiawesomatic6064]

*DO MORE VIDEOS LIKE THIS PLEASE* Im a physics nerd and just now starting to get into all the mathematics like this. took me until my sophmore year in high school to start calculus but its really awesome to me to see these derivations and playing with your things!

[@Hecatonicosachoron]

Aah, finally a popular youtube video with a nice and simple derivations. Derivations and proofs make me very happy.

[@PassiveMarmelade]

Very good vidéo ! I love your new format ! Thank you very much !

[@TheTrevorS1]

Great video, it is so nice to know that I am not the only one who gets excited over vectors!

[@benstannard3574]

This video made me happy - What a wonderful derivation!

[@lawrencecalablaster568]

I really like this new format & show. Please please please make this a thing :)

[@standupmaths]

+Lawrence Calablaster I have a few more videos planned. And based on the response, it should be come a regular video.

[@lawrencecalablaster568]

standupmaths Awwwwwww yeah! :)

[@kathrynblodgett1969]

Matt, your channel is amazing. I barely made it through high school algebra, but watching your videos is actually helping me understand. Half way through his little diagrams, I realized I understood what he was talking about and what he was trying to achieve. I don't even attempt your little puzzle challenges. Trying to find an equation to solve the puzzle is just over my head. And I don't think I will ever USE those equations, but it's nice to not feel as if you stopped speaking english 15 minutes ago. LOL Good day Sir.

[@standupmaths]

Glad you enjoy them! Understanding everything isn't even the point: it's enjoying the process of finding things out. You're doing that perfectly!

[@joao6723]

"Ok, let's come over here where we have more space... I'm a bit worried of that close to your cabinet" *Approaches the piano with the brick*

[@NaN0s7]

I've been waiting for this explanation for a very long time

[@Holobrine]

That's the wrong color of paper.

[@H0A0B123]

+Holobrine But its ratio is radical 2, so I forgive them.

[@RandomNullpointer]

You took me back to my school days :) thanks, Matt!

[@djmintyfreshful]

I was looking for this video for the rotating unit vector bit!

[@Noremaad]

Aaaand I can officially say that a brick on a string was the most fascinating and educational thing I've seen in some time. Never considered centripetal force as a vertical torque. Not sure what the practical applications would be, but I'm not a physicist engineering solutions to problems with strange properties of matter. Excellent demonstration, though.

[@hazzmando]

I love it. More of these please

[@MrBallinmangosocks]

Love the combination of mathematics and physics. Would love to see more like this.

[@CarterColeisInfamous]

i love this series

[@superj1e2z6]

I'm lacking my parker square fix.

[@fanthomans2]

I want more of these. I learned these at the university, still I find it fascinating. :)

[@PhilippeAllardRousse]

I liked the format.

[@Laborejo]

Will we see Brady as a guest explaining math stuff to us?

[@jasonh8353]

It's nice to see this written out and how it all comes together. My question is what about the rope and the rigid pipe you're holding? And for that matter what about gravity on the tennis ball? How much extra velocity does the tennis ball need to start moving the brick vs holding the brick in place considering the forces holding the rope more rigid at a right angle and the forces the rope applies to the pipe

[@pantherof7]

I love this, please do more proofs and derivations.

[@pasinduruwanthadharmaratne4443]

That was beautiful!

[@TheHamoodz]

Right after my dynamics exam is done I get to see a cool video about dynamics. I feel like you should've asked Mr. Hugh to explain the sin(theta) = theta for small theta thing as it was one of the most mind blowing and insanely useful things in that course.

[@standupmaths]

+TheHamoodz I have been planning to do a video on small angle approximations for a while. You are right: they are amazingly useful.

[@gabrielnorris8014]

The math on that worked out really nicely.

[@OhhBabyATriple]

great video. should definitely do more videos with Hugh

[@Iliffe1992]

@standupmaths I was wondering how would you work out the net force in the z direction that the rope feels as you are spinning the tennis ball.

[@Pehr81]

I like the phasing sound effect you've used for this video

[@standupmaths]

+Pehr Meldert Yes, that is my bad audio editing. It will be fixed next time!

[@Arkhanno]

Jeez, I can't believe you Parker. There was obviously a long, thick string holding that brick up. Seriously, though I really enjoyed this. I hope there's more!

[@oldcowbb]

prepare for parker square comment

[@grahamrich9956]

Your comment forgot the word "a" in between "for" and "Parker". What a Parker Square.

[@SlipperyTeeth]

+Graham Rich Actually he forgot an "s" at the end of "comment". What a Parker Square of a correction!

[@standupmaths]

This is my life now.

[@grahamrich9956]

+standupmaths Yup!

[@grahamrich9956]

Phoenix Fire Both would work.

[@arsenelupin123]

The whole time I couldn't help staring at all the fragile and valuable things in the background that could get shattered.

[@TheMajorJF]

I was fun seeing Matt Parker actually learning as the video went on.

[@jamesn7173]

Nice video! So we can use this to determine the minimum speed (rev/s) at any particular r value of the rope that will provide sufficient force to stop the brick from falling? To do this we would also need the force exerted by the brick and where the equilibrium lays?

[@standupmaths]

+James N Yes! There is enough detail in the video to be able to estimate all of those numbers and check if it works.

[@TheApostleofRock]

I really do think that the intro to this show is among the best of any show

[@valwold3567]

The lack of mathematical rigor with the differentials kind of made this video a Parker Square of an explanation of centripetal force. However, it was a pretty good attempt.

[@Dr.1.]

can I just say that his(Hugh) handwriting is so elegant

[@HariPrasadindependantphysicist]

We need a Boomerang video!

[@raykent3211]

seconded!

[@BrutalToad]

that was a wonderful derivation

[@thesimen13]

We need some brown paper

[@yizelindbizle]

This is the guy who interviewed me for engineering at Trinity, he has so many boomerangs xD

[@standupmaths]

+George Wills In the background you can see Hugh's "interview in progress" sign as he was doing more interviews when I was visiting.

[@yizelindbizle]

I think i was quite lucky in having him as one of my interviewers, he is a pretty funny guy perhaps the engineering equivalent of "standupmaths"! (He even has a obsession equivalent of yours for Pi. Boomerangs). Shame i didn't know you were about during interviews, would have been pretty cool to meet you and perhaps see what a mathematician would have made of the engineering entrance paper for Trinity.

[@christianvikkels4801]

Hey Matt! I'm a 14 years old boy from Denmark and I really love your videos! I've just bought your book and It's pretty cool. Thank you very much for all of your work. Today I've played with some logarithmic paper. What about making a video about that? Just an idear... //Christian Vikkelsø

[@SoulSukkur]

I came to see some working out, and not ONE bicep curl

[@standupmaths]

Never skip log day.

[@johnox2226]

standupmaths 1:51 Best Parker dodge ever!!

[@Cromeman82]

Lots of brain muscles exercised though :)

[@brcoutme]

They did play with a tennis ball and a brick though, seems like something you might do in a gym class. Also they talked about how heavy the brick was, so all that lifting has to count for something.

[@SimonClarkstone]

There are many more things you can differentiate than just vectors. I remember this video from a while ago called "Beautiful Differentiation" vimeo.com/6622658 I had to watch it slowly to follow it all. One of the strangest things to differentiate (brought up by an audience member at the end of that) is data structures, giving you a things called a "zipper". For example, differentiating a singly-linked list w.r.t its elements gives you the pointer-reversal trick for traversing such lists.

[@Mystery_Biscuits]

You should combine this style of video with your "Matt explains" videos. It would be awesome. Great vid as always :)

[@standupmaths]

+Cardude 2015 Yes, that is a very good suggestion. I will also try to do more Matt Explains videos.

[@Mystery_Biscuits]

+standupmaths thanks, I look forward to it. For a Matt explains video, could you talk about derivatives please. I loved both your parabola videos but I didn't get that bit. Thanks :)

[@Mystery_Biscuits]

Wow, this is history right here. I’m currently in my final semester of my 4 year MMathPhys degree course. How time flies 😅

[@birdy_coolbeans]

I'm glad the brick is clearly labeled as such.

[@raykent3211]

The brick is producing the centripetal force, not the ball. The ball is trying to flee from the centre along a tangent. This "tendency" has a vector component which can be called centrifugal. For the string to be in equilibrium it must have equal and opposite forces at the ends. The brick is exerting the centripetal one, the inertia of the ball is exerting the.... anti-centripetal force? (note the minus sign hastily inserted near the end!). I like Matt pretending to be horrified at the word centrifugal, it's a touch of humour, but centrifugal force is not the only fictive force that can be used to simplify explanations, there's also the "force of gravity", for example. I'm off to get my blood sample centrifuged, er sorry, centripeted? How would that explanation go?

[@bolinkd]

I would have loved to see some calculations for how long r would need to be, or the velocity of the ball in order to hold up a mass of a certain weight.

[@tov5490]

Hey Matt! Love your videos. Got a question, though. Is the audio coming from both cameras? There's a slight echo in Hugh's voice. Maybe it's just the recording, though.

[@danthebat666]

They are each wearing a mic, and sat close enough that both mics pick up both voices, but at slightly different times, at 2 to 3ms difference.

[@standupmaths]

+Tov Rex It was my inability to edit the audio correctly and match the two microphone recordings. But I'll try to fix it next time!

[@victorfloresmeyer804]

There should be more videos like this one. Proper maths! love all of matt's videos though.

[@fiftyfat]

I think rope/tube friction at the top end of the tube plays a big role, but still cool ! =) I should try this with a smooth tube that has a filet at the top end, too bad it's too late for me to do it with the students. Great video !

[@JacobShepley]

:D :D :D will you be doing more videos with Hugh or other engineers and deriving mechanics?

[@standupmaths]

That's the plan. Hugh and I are pretty-much just going to work through that cabinet of stuff you can see in the background.

[@alcesmir]

+standupmaths Is this the expert you were/are going to do a follow up about the Euler disk with?

[@andresfernando3342]

BEST VIDEO EVER

[@draenthor4621]

I found the camera angles to be a bit of a parker square at times, but overall great video; it's nice to see some physics stuff from time to time.

[@standupmaths]

+Draenthor Magewater Yes: the camera set-up was far from ideal. But I gave it a go. Classic #parkersquare

[@zilo500]

this is really interesting, makes me wonder if this could be used to make something fly. like a flying mace.

[@victorribera5796]

i love he puts the vector sign as a underline

[@otakuribo]

Pleeeease tell me that boomerang collection features in a future episode! :D Also, requisite Parker Square joke. :p Congratulations on achieving official meme status

[@danielortega2441]

Vector deferential... Always heard if it.. Finally saw it..... Great video....

[@5eurosenelsuelo]

What a nice experiment

[@AaronHollander314]

Could you spin the ball fast enough to raise the brick up? And how much is friction of the rope against the rod playing in holding up the brick?

[@carultch]

Answer to the first question: yes. When m*v^2/r of the tennis ball exceeds the weight of the brick, the brick will rise. The r-value will decrease as the brick rises, so eventually, they will settle on an equilibrium position where the tension in the string equals the weight of the brick, and also equals mass*centripetal acceleration of the tennis ball. Answer to the second question: friction is involved. Look up the Capstan equation, and you can calculate just how much of a role friction can play. It is possible to get the tennis ball to exactly the right speed, where it balances the weight of the brick and the friction is zero, but thanks to friction, there is a much greater tolerance on the range of speeds of the ball.

[@ianwalker6546]

Really enjoyed the pace of this - just slightly quicker for those of us who have no problem following along with algebra. And practical derivation of classical mechanics formulae never get old. Maybe you could do an entirely experimental set of SI units......although the gray might be a little dangerous

[@jackie2877]

Good job hitting yourself with the tennis ball, classic #parkersquare

[@MichaelWarman]

I was quite surprised this didn't feature a calculation of how long the rope has to be above the pole and/or how fast the ball has to spin for some assumed weights, etc.

[@evilcam]

Every physics classroom in the world should have that ball and brick toy. That is a great physical example of acceleration increasing mass. You get this cool derivative out of it, plus a bunch of other ones, like an example of the Heisenberg Uncertainty Principle, easy to demonstrate right in front of everyone.

[@evildude109]

+evilcam wut

[@edskev7696]

+evildude109 *whisper* just smile politely and nod...

[@alcesmir]

+evilcam "acceleration increasing mass" That's not even remotely true.

[@evildude109]

I suppose it depends really, whether that acceleration is in the same direction as velocity or the opposite direction.

[@edskev7696]

+evildude109 except that this is all done using classical mechanics, and einstinian relativity has a negligeable effect. The mass increase of the tennis ball is basically nothing and most certainly is less than the mass of the brick (by many orders of magnitude...)

[@campshay19]

i loved this

[@acronis011]

At 5:30 it is not a small angle approx. the vector goes around in a circle so the arc length is the radius times the angle in radians.

[@stephenbeck7222]

+acronis011 I think you have to constrain it to small angles (since we're taking the derivative after all, which is the limit as dx or dtheta in this case goes to zero) because otherwise the direction of that small vector would not be directly perpendicular to vector i, so you would have to split it into component parts and mess up the neatness of the calculation.

[@acronis011]

+Stephen Beck yeah but the useful consequence is not that that "sinx" will be "x" but the arc length will be equal to the length of the vector of difference. But im just heckling :)

[@celtgunn9775]

Matt, you had far too much fun with that brick & tennis ball. I hope you made yourself one of those at home. 😉👍

[@jamespklett]

Awesome !!

[@ilmansonic]

This was a bit hard to follow, since I haven't done any calculus courses. I have some basic idea of what's going on, but the entire dx/dt thing confuses me. Any idea where I can catch up with derivatives at least, so that I can follow this video properly? I've tried Khan Academy's calculus lessons, but they really failed to engage me and as a result I don't remember a thing.

[@ElementOfAdventure82]

Most of the things you learn are from a friend that wants to show you something cool.

[@PassionPopsicle]

I'm just so damn happy that #ParkerSquare is already a thing. The internet is a magical place indeed. Yay!

[@hi10drakk]

I remember such a problem on the cover page of Irodov's book - Problems in general Physics back when I was preparing for IIT JEE

[@joebert7255]

loved it

[@brianb2308]

Parker square! I did a lab with that exact setup lol. Nice video

[@MSRChurch]

Very nice video showing the application of maths in real world solutions. I have one recommendation that the maths could be gone through a little bit slower though just so that it's easier to follow

[@standupmaths]

+Matthew Church It is a difficult balance to get the speed just right. But I've made the notes available so people can follow along! imgur.com/a/lphOr

[@superjugy]

What you derived was not the force but the acceleration, the force would just be that times mass so F = mv^2/r. More importantly since the system is in balance, that means M1g = M2v^2/r. from there you get that the tangential speed at which you need to drive M2 to lift M1 is v = sqrt(M1gr/M2). If you want it in terms of w instead you get M1g = M2(wr)^2/r. thus w = sqrt(M1g/M2r).

[@panonymous9659]

I believe it's much easier if you'd do it with exponents. Position is r * exp(angle * i), or r * exp(omega * t * i) -> velocity is the derivative over t, so r * omega * i * exp(omega * t * i), or r * omega * i * position, and as we know, a multiplication with i is a 90 degree change of direction, so it checks out. Acceleration is the derivative of the velocity, so r * omega^2 * i^2 * exp(omega * t * i), or -r * omega^2 * position, which is exactly your solution, but without approximating.

[@panonymous9659]

I made a few mistakes, in the beginning I defined position with the radius and angle, but after that I forgot to remove the 'r's, which makes 'position' only the angle, or a unit vector. It still holds however.

[@nujuat]

We did this experiment in year 11 physics - that was fun :)

[@whyando]

Nice to see you at trinity, I'm a maths student here!

[@standupmaths]

+whyando Fantastic! Say hello if you ever see me walking around.

[@thomasoulton1855]

quite a nice video

[@c9593469]

why there is no mentioning of f=ma and of the tension in the string, now the math part and the ball vs brick part just looks unconnected

[@donegal79]

i genuinely hope that you never have to explain a concept to anyone.

[@fakjbf3129]

I like seeing Matt get confused for a second and then realizing what it means. It makes me feel much better that he isn't able to instantly look at an equation and immediately understand everything about it, it makes him much more human. Plus I don't then feel bad when I have to pause and consider for a few seconds myself.

[@standupmaths]

+Fakjbf Mathematics is all about the joy of thinking about things until they eventually make sense.

[@sidraket]

So this is how they built the pyramids

[@grahamrich9956]

Pretty much. Thankfully, the guy they had swinging didn't Parker Square it.

[@inescapablestud]

+Graham Rich Never go full Parker Square

[@grahamrich9956]

inescapablestud It's pretty bad, eh?