I'm always surprised by how wobbly things are in slow motion. The sponsor of the video is Brilliant: Visit www.brilliant.org/stevemould to try everything they have to offer for free for a full 30 days. You’ll also get 20% off an annual premium subscription.

@MonkeyJedi99

Күн бұрын

The opening music almost made we shout "Twelve!"

@justinanderson267

Күн бұрын

Does this mean that if you threw the ball under the table, then lowered a hinge extension for the table, can you make the ball reverse direction multiple times?

@DuelScreen

Күн бұрын

You made this video because you watched Matt Parker and Grant Sanderson's recent billiards/pool video, didn't you?

@squidcaps4308

Күн бұрын

I think people would enjoy knowing how tires work, how can they produce so much grip. it is one of those mind blowing realizations that tires use static friction: the contact patch does not move relative to the ground. The tire has as much grip when the car is stationary than when it is moving (excluding some minor things). This means that the force that you need to turn the tires on the ground to make them slide, is the maximum force that can turn the car. If you push it from any direction and the tires start to slide: that is the maximum force at any speed you can use to control the car. All of the turning, accelerating etc. is done by rubber stretching and squishing, and it wanting to return back to the original shape. So, the force that moves the car forward comes from deformation of rubber, like million rubber bands stretching. The engine rotates the axle faster than the tire is rotating and this stretches the tire, rubber wants to retain its shape as it is between the ground and the wheel, and we accelerate. Slip angle as a concept.. man that has been one of the most rewarding things to learn, it was just constant "ahaa!" feeling, massive amount of rewarding chemicals floating around. It is such a simple thing that you just don't think about but... the part of the tire that contacts the ground does not move even if you are going 500kmh.

@bbgun061

Күн бұрын

I suspect that the tennis ball continues spinning in the same direction because its friction with the surface is very low. It's fuzzy, so a very small area is in contact with the surface during the bounce. That lets it simply slide along.

Are you actually sitting in the yellow chair?

@flomoose7315

Күн бұрын

I just wondered the same, after reading your comment😂🤣

@DanielFrost79

Күн бұрын

In Sweden the chair sits on you. 🤣

@nokbeen3654

Күн бұрын

It’s an ikea chair that also has a matching footstool. I think he’s sitting on that.

@pinboru_

Күн бұрын

@@nokbeen3654 Ahh, 👍 . I thought it might be green screen, but wondered why would it be green screened, and there’s shadows that show up… but without knowing about an ottoman it was messing with my brain. That helps, thanks!

@thiagorib79

Күн бұрын

'Tis a bit too far. My guess it's a chaise long 😉 I thought Ur observation concerned atoms' stuff: we never touch anything 😅👌

This video is secretly about two idiots playing pool using math, and forgetting to account for friction in their calculations 😆😆😆

@theastuteangler

Күн бұрын

classic mathematicians

@kenrickman6697

Күн бұрын

I was thinking the same thing!

@Ryan_Thompson

Күн бұрын

I was so hoping someone would have said, "oi, go grab that Parker triangle and rack 'em, Matt!"

@nurmr

Күн бұрын

I think if said mathematicians had had to apply these formulas they might still be at it, and their pool playing opponents would have conceded the game because they were all being kicked because it was closing time already.

@santiagoruiz7490

Күн бұрын

He probably just sent Matt the video and said nothing else

Tangentially related; In water polo you can bounce the ball on the surface of the water by giving it the right combination of backspin and angle of attack (otherwise it just stops dead in the water). Generally more backspin, steeper angle, more power, lower ball pressure, less textured grip on the ball increase the bounce height, but sometimes a grippy ball thrown at a low angle with a bit of sidespin can pop up just as high. I can do it instinctively but I've never quite been able to grasp how it works...

@brianhiles8164

Күн бұрын

_@NKuijlaars_ Cannot grasp the concept, you say? It is identical to the phenomenon of _skipping stones._ Plenty of blather on that topic, accessible from a Google search.

@NKuijlaars

Күн бұрын

@@brianhiles8164Firstly, by grasp I meant being able to control it based on my understanding of the physics, and vice versa, but that just doesn't really work here. When skipping stones the side spin is only for stability (?) and there is no backspin, but with a ball stability isn't really relevant (?) and the ball *cannot* bounce without backspin. The ball is also capable of bouncing out of the water with a steeper angle than it was thrown which makes me think it's more of a restitution problem. My apologies for daring to think there might be an interesting little nugget of physics in the mechanism here.

@brianhiles8164

Күн бұрын

​@@NKuijlaars Obviously, you have a “sufficient“ technical background, that you are both _able_ to be fascinated by the nuances and intricacies of the physics involved, and just as importantly have a _discrimination_ of when you have indeed “wrapped your mind around“ an understanding of the problem. This is key. On more than one occasion, I have purposefully _not_ remanded my understanding to an expert, that I have forced myself to figure out a given mystery myself. As an aside, though, in the matter of _restitution_ being the prevalent phenomenon of a Newtonian liquid: If I understand the context of your observation, angle-of-attack is predominantly a function of the forward momentum of the rock inducing an inclined plane of the “sticky“ water surface to then be “launching“ it upwards, converting some of the forward momentum to an upward trajectory -- thus the “skipping“. However, in the matter of providing the “real world“ model of rock skipping: In general, I understand now that you are advanced beyond its intended purpose.

@jamesmccann531

Күн бұрын

I would think it would be quite similar to the bouncing bomb used in WW2, as that was a cylindrical shape given backspin and forward speed to make it skip over the surface of the water. Iirc, they also tested spherical bombs

@bobstr6224

13 сағат бұрын

As a polo goalie the bounce shot is my worst nightmare, impossible to predict

When I was a little kid I once saw my dad throw a hula hoop he'd put backspin on, and when it hit the lawn edge-on the hula hoop rolled back to him, and I realized right then and there that, despite what everyone had told me, magic was real, and my dad was a wizard. It was the only explanation. 🤣

@mailleweaver

Күн бұрын

When I was a kid, my dad told me that if I could salt a bird's tail then I could catch it. I got excited and took a fish net and a salt shaker in hand and went stalking birds. Never did catch anything. It was only years later that I realized that if I was sneaky enough to get close enough to salt the tail then I could indeed catch the bird, but the salt had nothing to do with it. He might as well have said, "If you can catch a bird then you can catch a bird."

@giovane_Diaz

Күн бұрын

​​@@mailleweaveryeah, but where is the fun? the best phrases are those that seem absurd, but still carry the truth underneath. your dad got it well to push you to keep going

@DennisKovacich

Күн бұрын

Gee, my dad told me that toilet paper was getting really expensive, so we had to start conserving it by using both sides.

@deltamico

Күн бұрын

Just fold it

@0neIntangible

Күн бұрын

@@mailleweaver Up for a Snipe hunt, anyone?

“How could you work out the area under graph that’s infinitely thin and infinitely tall?” Laughs in Dirac Delta

@SteveMould

Күн бұрын

The original script had that it but it got cut!

@ersetzbar.

Күн бұрын

Thats 1 way of describing an area

@tissuepaper9962

Күн бұрын

​@@SteveMouldI imagine that was the bit that got replaced with "well actually 0*inf _is_ defined in this case because it's a limit but we're really getting into the weeds here". Probably a good call to cut out the rigorous definitions, especially since the video was really about how we can *avoid* having to work with delta functions directly.

@Luke-mr4ew

Күн бұрын

​@@SteveMould Was it cut? Or did it become an infinitely informative segment with zero duration?

@asmithgames5926

Күн бұрын

You use take a limit as t (time) approaches zero. (I had to derive these physics myself (without taking spin into account) for a high school senior capstone project I was writing a Pool game in C.

Some of my favorite undergrad physics problems involved the physics of collisions. Here's a neat one: A solid ball sits on a frictionless plane, subject to a standard gravitational field. It is struck with an impulse 'I' from a direction horizontal to the plane and in line with the center of the ball. Where does the impulse need to be directed so that the ball rolls with zero slippage? The answer, it turns out, is 3/5D (3/5 the way up on the ball.) I use this fact when breaking a racked set of pool balls. It really makes for a solid break.

@HiddenLemur

Күн бұрын

Applied physics is so much easier to grasp. Thank you for sharing this, I enjoyed the problem and the lesson feels intuitive when applied to a pool ball 😊

@MrScorpianwarrior

Күн бұрын

Huh. This is information that will stick at the back of my mind until one day I can use it.

@halisidrysdale

Күн бұрын

Even knowing this information, I know that I'll remain unable to play pool any better :D Fantastic insight, thank you :)

@thisscreensucks

Күн бұрын

If the impulse is horizontal to the plane, and also hit the ball in line with its center, how could it strike the ball anywhere except the center? To hit the center of the ball 3/5 of the way up the ball it needs to be angled down towards the table.

@Chokluss

Күн бұрын

now try to figure where is 3/5 on the ball

Years ago I noticed that 'power-balls' (a very popular 1970s toy) a high density plastic ball with a very high coefficient of restitution would jump backward and forward - reversing direction and spin on each bounce because their elasticity worked rotationally as well as vertically, hence the 'can't bounce a ball off the bottom of a table without it coming back' paradox in the opening few seconds of the video. Fascinating stuff physics.

10:49 - 12:12 perfectly sums up why billiards games are so tricky. Kick which is when the chalk that was transferred to the cue ball is perfectly positioned so that it's at the contact point with another ball, changing the variables. Billiards and curling keep physicist up at night.

Steve can answer ANY physics question we throw at him, and provide high quality demonstrations and footage to show it. What a legend

@pvic6959

Күн бұрын

throw at him? with what velocity and spin?

@reidflemingworldstoughestm1394

Күн бұрын

Great. Imma ask him if gravity is a fundamental force that is carried by bosons, or a downstream effect that arises from more basic elements of the universe.

i love wham-o 1965 super balls. they (or imitations) are the only ones that spins the opposite direction each time

Would love to see how a golf ball interacts with a club face. There’s so much compression of both the ball and face, with such a soft cover on higher-end balls.

@dannymac6368

Күн бұрын

Edit: compression on metal woods (Driver, 3-wood, fairway metal)…though the interaction with a grooved iron or wedge would be just as interesting.

@dannymac6368

Күн бұрын

I wonder if manufacturers of clubs can limit the horizontal COR while maintaining vertical/neutral COR. Low-spin (but non-zero) on a driver is typically ideal, but is typically modified through a difference in swing path and face angle, since you normally hit a stationary target in golf. All bets are off if it’s a links course in Scotland, you may need to hit a moving ball. 💨

@A1BASE

Күн бұрын

@@dannymac6368 I'm more interested in the compression of irons and wedges. Longer woods you're getting most of the compression of the ball on the clubface and the elasticity of the face itself. With an iron (particularly some of the newer hollow distance irons) you'll have similar face and ball compression (just less), but also the compression of the ball against the ground. And those two compressive forces are in different directions.

@ianmanning4062

Күн бұрын

Smarter every day has a video with slow mo footage of golf balls colliding with things! I don't recall if a golf club was used, but they definitely have some cool footage!

Now explain flubber

This actually explains a weird thing I noticed as a kid when I played with bouncy balls and tossed them with some back spin, where it would be spinning slower after it bounced and sometimes even slowly spun in the opposite direction from before. If I remember correctly it usually happened on surfaces with high friction like concrete, and now it makes sense where that force reversing the spin direction comes from.

I've actually been wondering about this forever, thank you for making this video!

Steve's videos are the best. Don't ever change your format, man.

Fascinating topic. I always love the surprise in what you choose to talk about in every new video Steve.

Always answering questions I didn’t ask but I’m glad you did

I can't belive he forgot about Tau Day. I thought he was a real tau fan.

@CeeJMantis

Күн бұрын

Tauists aren't Pi-ous. He needn't be advocating for Tau all the time. He has a family and such. Besides, tau as a circle constant speaks for itself

@reidflemingworldstoughestm1394

Күн бұрын

Being a Tau fan is the real reason he has more subscribers than that Matt guy. Tauists are just a better class of people.

@shandybasshead

Күн бұрын

Hawk Tau

@lfvanheijkamp

Күн бұрын

​@@shandybassheadComing full circle

Try doing the same study for table tennis. Show why "long pips" are kinda unpredictable compared to an inverted rubber, when doing top or backspin.

@JP_Hatecrew

Күн бұрын

Screw pips. I want to see a super slow mo of the chinese. I want to see what they are doing, how long the ball stays really on the rubber and how spin is created.

@giovane_Diaz

Күн бұрын

​@@JP_Hatecrewneed to get checkered balls popular, so we can get better slow-mo footage of their spin

@JP_Hatecrew

Күн бұрын

@@giovane_Diaz great idea!

@alexanderdickens2517

11 сағат бұрын

@@JP_Hatecrew there's a video Fang Bo made, i believe, where he analyzes the rotational speed of Xu Xin's forehand on a slowmo cam.

WOW! This was the nicest, clearest and most objective masterclass on collisions I've ever watched!! Very fine work, Steve!

1:34 "We're screwed, basically" - Steve Mould, 2024

@BrianSantero

12 сағат бұрын

Out of context, but still highly relevant.

Slow motion shots are so fascinating!

Thank you Steve. This video cleared many doubts, including how a cricket ball works differently for spin bowlers.

Ever play around with a superball on a gymnasium floor? The way spin interacts with the bounces will really surprise you at first. Back when I was a kid, you could get superballs in various sizes. The ones that were about the size of a tennis ball, those were the best. Easily could make one bounce over a two-story house. (and put someone's windows out, maybe that's why they are hard to find now...)

@johnflorian6745

Күн бұрын

I remember having one of those! My brother became a licensed hot-air balloon pilot in that same "era" and the first time he was able to take me up was the last day I saw that ball. Worth it, but now I miss that crazy thing!!! (The ball, of course. lol)

@geoffbuss3699

22 сағат бұрын

We had an egg-shaped superball which provided much dangerous fun on a squash court. Give it a good belt, cover your head and duck and wait for the pain. (Extra points if you hit the duck).

I swear that since I grew up geeking out over all kinds of activities It helped me master the art of back spin & all the ways u can utilize it

I studied angular momentum a few weeks ago and that is a very fun case scenario to test some equations! Thanks!!

Thanks for making content like this

You are a marvelous teacher for many !

awesome, i've been wondering about this for the last nine days.

Brilliant Steve! Liked and subscribed.

Thanks for another great video. I appreciate them! 🙂

Bravo! Nice analysis of what happens when a rotating object contacts a surface. Also nice would be the effects of top spin or back spin on aerodynamic lift.

Hi @SteveMould, I'm not a scientist by any mention of the subject, I'm actually an illustration student. but whenever i picture this i imagine the ball as bendy lines or sticks coming from the centre of the ball (like a hedgehog or a sea urchin) and whenever the ball is spining and catches the table, the the point of contact is where the sticks stop moving but everything else keeps moving until it snaps back (like a mouse trap or a bow or something along those lines) idk it might not make any sense to anyone else but it does to me. anyways, love the videos, you always make my day a bit more interesting 😁

@AAChaveiro

Күн бұрын

I thought the same thing, but in different lines, like, "squash and stretch" animation principle. Amazing!

1:34 This is the right response, anytime you need to use integrals in physics

Interesting. Thanks for making it simple. Cheers 🍷

Now you've got me thinking about how the dambusters worked. Great video

Steve really making the most about the bouncing ball under a table idea haha, cool vid!

One small but important thing I would change about the way you talk about this: "friction always acts in the opposite direction to the direction of motion." I *would not* use the word motion here. The motion of the ball is downwards, but friction doesn't point upwards. Friction doesn't oppose motion, friction opposes *sliding.* Using the word motion here makes it hard for people to understand how friction can actually make things move (like how we walk or cars drive, friction actually pushes us forwards because our legs/wheels are trying to slide backwards).

@ernestgalvan9037

Күн бұрын

…” Friction doesn’t oppose motion, friction opposes sliding “… So, you are saying that “sliding” is not “motion”, or that “motion” is not “sliding”.. ??? And here I always thought that ‘sliding’ involved something ‘moving’… Well slap my hide and snap my suspenders.. I learned something new today…

@SirPhysics

Күн бұрын

@@ernestgalvan9037 I am saying, quite clearly despite your apparent inability to understand, that motion is a broader category and sliding is a particular type. Friction is concerned only with sliding. When you walk, you are moving forward but your foot would be sliding backwards along the ground, so friction pushes you forwards because friction doesn't give a shit about how your body is moving, only how your foot would slide

@veikkoimmonen7300

Күн бұрын

@@ernestgalvan9037 Sliding is motion constrained to a contact surface.

@victormarcoara5876

Күн бұрын

Friction occurs with air as well, an that is against the direction of motion. Unless you are only talking about things moving over a surface you're technically wrong.

@zeroinfinity5864

Күн бұрын

Definitely a great thing to consider. Because walking on slippery ice is hard.

hey in this video you leaned way more into the difficult to explain physics in natural language that you tend to oversimplifly for the sake of the general public's understanding (explaining limits and the hcr parts for example) and I think this is kind of refreshing! I know this should not be the rule rather than the exception for your kind of content but its cool once in a while, puts the viewer mind to work a bit, you know? gives context that some things can be hard to understand at first but once you get the principles involved than you are set to understand the rest. A nice teacher walks together with his students through the path of understanding, thank you for showing us that im almost every video, but specially in this one for me :)

The "steel ball dropped on an anvil" experiment demonstrates just how short collision times can be in a fun way --- the ball bounces many times, each one a little lower (and thus taking a bit less time) than the one before, until it goes "tap tap tap taptap taptaptap bzzzthwip!" meaning that at the end it's bouncing thousands of times per second, and the time the two surfaces are in contact must be a fraction of a millisecond.

@geoffbuss3699

22 сағат бұрын

"bzzzthwip" is spot on. I knew there had to be a word for it.

I love how you go into so much detail, just for fun. But now I am curious, how this changes with wet balls and surfaces. Now with the EC going on, wet footballs and how they get incredibly unpredictable under these conditions, come to mind.

Magnificent video Steve! You revealed many of the exact points I wish I had learned in school 50 years ago. You gave me heaps of ah-ha moments and cleared so many confusions in me. I could watch your videos all day. Brilliant! :)

Thanks Steve!

Please do more on this topic? - and completely nerd out for us.

Funny to watch a video of something I kind of learnt inherently, from playing with bouncy balls (which reverse when spun because of the friction) and also pool, where you learn to account for the gripping effect on rebound shots.

Thats an amazing series!

Finally understood what impulse is, thanks!

Another great video about a surprisingly complicated physics problem. I need to watch it again when I am not sleepy. The one thing that I missed in the video was the interaction between the spinning ball and the air, but I understand that is a completely different story that is better to ignore for the bouncing ball problem.

@alopexlagopus1488

Күн бұрын

That's the Magnus effect and Steve has already done that one

When you have a negative vertical coefficient of restitution, that would probably suggest that the projectile is passing through the target. Bullets have a negative vertical coefficient of restitution against soft materials.

@defalt8558

Күн бұрын

I don't think it works like that. The coefficient of restitution is based on an assumption, and in that assumption the surface against which the projectile bounces is unbreakable and immovable. If a bullet collided with such an object, it would probably bounce but absorb most of the energy, having a really low coefficient of restitution.

Great video!!

I’m always grateful for your willingness to share your thoughts and talents with the world. MKBHD recently posted a video about how the tech on a golf course can track a ball at the moment it is hit. I’m curious if math that plays into this conversation.

Your final conclusion is what I came to after a brief think, that each form of momentum is its own dimension, since objects can move with multiple degrees of freedom. It was also very use to reduce the values to 1-0 or 1-0-1. That reminded me of Planck's use of arbitrary values for things like speed, temperature, etc.

Thanks for this.

I was literally thinking about this concept this afternoon lol that's crazy

Regarding the simplification that we take the center point as a parameter, could also use dynamic formulas to capture this center position accurately relative to deformation on impact. As I understand it (which might also be incorrect of course), keeping this point static will essentially give a built in threshold for the actual usefulness of the equation at different scaling. As of course mapping this deformation would be most precise, though that might be done for simple systems by continuously tracking the distance of the center point to the edges of the shape in turn taking into account mass distribution. This would be a pretty intuitive way to represent the forces (at least for visualization purposes) and how the change of position of the center of mass works in tandem with angular directions and applied force(s) on impact and otherwise.

Wow thank you so much for this, and specifically how in depth! It's eerily timely for me as I'm making this physics-based video game where you shoot pinballs around. I realized that so many of my assumptions about how physics works just isn't accurate. Spin turns out to be the biggest area of confusion. Like, I always expected that if you spin a ball and roll it, it should proceed in a curve and that doesn't seem to be the case at all. I bought some pinballs to see for myself, and I'm struck by how much the density of the ball changes small things, e.g. like in your video how it changes the collision time.

As someone who's gotten really into table tennis, one of the interesting facets of the sport is that the players effectively get to choose their coefficient of horizontal restitution via their equipment choice. We can't change the ball, but generally attacking-style players tend to choose gippy rubbers and thick, springy sponges on their paddles to maximize thier spin (aka maximize their coefficient), while defensive players tend to choose less grippy pips-out rubbers and a thin sponge to minimize the impact of the opponent's spin on their bounce angle (aka, minimize their coefficient), while actually preserving the spin of their opponent. Thanks for this video, it has given me a lot to think about with my game and technique as well.

Though it is the case that linear momentum and angular momentum are conserved independently of eachother, I think your correction may need to be qualified a bit. Linear and angular momentum are conserved, but that's because the earth takes the ball's linear momentum and gives the ball some of its angular momentum, but the ball doesn't gain energy from the earth. We see linear momentum "converted" to angular momentum when a non-spinning ball hits a wall at an angle. The linear kinetic energy of the ball must decrease because the rotating kinetic energy of the ball increased and the only source of energy is the ball. In this case "converted to" means something more like "allowed for the formation of" which is a common understanding of converted. e.g. "plants convert light into food" when really the food is not made of the light, but the decrease of light made energy available for the food to form.

Fascinating and insightful video, thank you! One small comment, though: I don't agree with the statement that the difference between kinetic and static friction is responsible or necessary for the collisions to often give a horizontal restitution coefficient near zero. I think this is rather due to the fact that the tangential force is always dissipative (in particular always antiparallel to the direction of motion). So given enough contact time, the slip velocity is bound to approach zero.

6:02 this concept of the ball springing back the way it came blew my mind!

Awesome video! Can you do electron spin next?

Now I can fully understand Kyiora's insane backspin pass thank you steve 🙏

I wish this video existed when I was learning about momentum in highschool physics, as it would have given me a much better foundation of understanding. Momentum and impulses were first explained to me as an instantaneous collision and left at that, the instructor ignored the integral bit. I really needed the integral explanation because I intuitively knew there must be an integral, without it the math didn't make sense and I always ended up with 0 time = infinite force = error.

Kudos to you for trying to explain the Dirac delta to the general public!

Perfect timing

Can you please make a part 2 of this where you mess around with some Ping Pong or even just spinning a basketball or bouncy ball as fast as you can in weird ways to see all the unique behavior you can get. It's fun to see all the crazy angles and behavior you can get to happen

Can you please do a video about spin in table tennis? It's cool to see in a bouncy ball, but I'd love to get a much more detailed 2d visual of how the rubber pips deform in a table tennis sponge and why that may affect the angle the ball returns at or the amount of spin in the returned ball vs the total returned kinetic energy, etc.

Thanks for not using a clickbait style text or thumbnail.

3:45 The coefficient of restitution is essential to answering the age old "unstoppable force vs. immovable object" question, which can be modeled as a collision between two objects of infinite mass. If the coefficient if restitution in this scenario is not 1, there is a tendency for the collision to be quite destructive.

It would be great if you could share the sources you used for this video, for further exploration. Thanks, and btw great explanation.

I like thinking about how a spin affects an impact by imagining that rather than spinning, its being dropped without spin onto an angled surface. Really what's happening when a ball is spinning is that when it impacts the surface, one side of the ball is hitting with more force than the other side which can be emulated by simply angling the impact surface (IE changing the "time" component of the impulse to mimic an otherwise different force component- resulting in the different shape same area sort of thing you mentioned at the start of the video). Naturally, the side that hits "harder" (or longer) is going to bounce back harder/sooner than the other and thus the spin is based on some ratio/proportion of the two modified by all the nitty gritty details like elasticity and friction.

GOD DAM I love your videos! ❤

I like to separate momentum (M) and vectors (V) in my head. they're always paired up though (MV or VM, depending on which is more important at the moment). "Spin" can be described as a straight line vector that's *parallel* to the surface of a sphere (the simplest spinny shape) and tangential to it (only touching at one, infinitely tiny point). I like to imagine that it is an arrow, pointing in the direction of the spin. I visualize it as being longer, the faster the spin is, and/or that there's a color change (like white for slowest, black for fastest spin, or vice versa, or maybe stoplight or flame colors). The former is more convenient for visualizing one object, making it's arrow longer with speed, and the latter is better for several in proximity as it's just a color change. I then imagine that arrow being infinitely repeated for every iota of the surface of the sphere on the plane of spin, giving you a perfect circle outlined with a "vector shell" that's thicker the faster it's spinning, or just a different color. Every tangent point on that circumference acts like a fireball on the end of a catapult arm that's attached to the Rotational Axis at the Center of Mass of the ball. If the arm released it, it would fly away in a _straight line_ that was _tangential_ to the fmr circumference. _That's_ the Vector, and how far it flies will be based on how fast it was spinning: aka, it's momentum. A ball can have 3 such spins; one for each of the 3 axis A, B, C, that correspond to the 3 _dimensional axis_ X,Y, Z. If it moves along an axis, it's "Translational" (T-axis), and if it spins around it, it's a _rotational axis_ (R-axis). Spinning on all 3 axis AND flying along on a T-axis is how you get a high score on a skating game like Tony Hawk or SSX 🤣 really crazy spins are very possible. It can *simultaneously* have a "translational Vector" with it's _own_ momentum. Unlike those above, however, this one is NOT tangential to the circumference, but _perpendicular_ to it and originating at the Center of the Sphere, it's Center of Mass/balance. ALL that is to say; when a spinning object hits a surface, it is *all* of those vectors *interracting with eachother, *and* the surface in all those ways at the same time. but with a Single Plane of Rotation around One R-Axis and ONE direction of travel on the T-axis, you can more easily predict the "Equal and opposite reaction", modified by Coefficient of Friction (or "bite" as I like to call it) of these disparate vectors interacting with the surface AND levering against each-other via the "catapult arms"

You know, I always thought mechanics was boring and solved physics but Steve always manages to bring back some weird stuff.

I loved playing with my Whamo Superball in the 1960s. I could throw it with enough backward top spin that it would bounce back to me instead of forward. Of course I got in trouble for bouncing it under the dining table. Thanks for the explaining the physics of my fun.

This is making me wonder about Spin of Fermions and bosons. I'm not sure if they are just useful conventions, or if there is related spin mechanics to be realized in the quantum world. Eitherway Such an incredible and insightful video! really appreciate the breakdown!

Love the HTML shout out.

Hey @SteveMould - have you tried testing a big solid rubber ball - like the dog chewing toys? The effect is quite interesting as the ball goes back em forth due to the spin changing direction, quite like your ball under the table experiment.

This one will be awesome

When I was a kid I used to spin a basketball on my finger then drop it. I was always fascinated when the ball would bounce and invert the rotation of the spin (clockwise would turn to anti-clockwise etc). I wonder how a rotation around a pole perpendicular to the surface like this would work, and I'd love to see the mechanics of this scenario in slo-mo.

that was really cool

Now this vid will live rent free in my mind whenever I play table tennis

It would be interesting to see an analysis of the effect of different tennis court surfaces. Pethaps for Wimbledon next year??

i always think about this when i play basketball. when you shot the ball you always try to give it a spin so it can bounce back to you. its great to see the physics behind it.

Great deep dive. Now do the same for the "knuckleball" in baseball and "floater serve" in volleyball.

A fun thing is to drop a basketball vertically with it spinning on its vertical axis. As it presses against the ground during the bounce, the rubber grips and the spinning energy gets converted into an elastic twist. As the ball bounces back the stored elastic energy is converted back into a spin in the opposite direction.

Hey Steve, thanks for this video, as a ping pong king I love backspin.

Loved the tangent joke! :)

I found this interesting because for the last dozen years or so I’ve been experimenting with a golf swing based around Ben Hogan’s grip and ‘waggle’ action which I realized can create a huge increase in club head mass acceleration with very little effort just before impact with the ball, and if gripped so the wrist joints lock up and slow down the club head just the compressed ball releases causes it to release off the face faster than in a conventional ‘sweeping’ swing where the club head is still accelerating as it picks up and releases the ball. I don’t understand the physics well enough to explain it mathematically but observation and intuition tell me that the hammer like waggle action with the wrist increases the velocity of the club head more than the conventional sweep and the abrupt arresting action with the wrists slowing down the club head results in higher velocity when the ball leaves the face which must be related to the rate of restitution of the ball. The wrist action I’m referring to is the same used to crack the tip of a whip past the sound barrier or cast with a fly rod, rapidly snapping the wrist from maxed out ‘thumbs up’ radial deviation “lag” to maxed out ‘thumbs down’ unlar deviation release. In a conventional golf swing that pulling of arms and wrists and club straight does not occur until well into the finish. The difference with respect to the ball between the swings is in a conventional swing the club head velocity is still increasing the entire time it takes for the previously static mass of the ball to compress then releases. The swing I’m using is more like a car which accelerates from 60-100mph pushing the occupant back in an elastic seat cushion, and then just as it reaches max. velocity of 100 mph the brakes are slammed on firing them through the windshield if not wearing a seat belt. Ben Hogan was actually in an accident like that in 1948 when his car hit a Greyhound Bus head-on trying to pass another car on a foggy night. Compared to a conventional constantly accelerating swing I get much greater ball speed by using the ‘hammer down and hit the brakes’ swing strategy but how does the physics and math explain it?

2:50 Indeed, when something is "undefined" in maths it usually means that it is undefined *on its own* because it can give different values depending on the context in which it comes up (usually due to it being a limit of two functions which give different results). E.g. 1/x as x-->0 goes to +inf, while 1/-x as x-->0 goes to -inf, even though both tend towards 1/0. Hence 1/0 is undefined if you use it on its own, since it can be either +/- inf depending on context.

Always been mildly fascinated by ball bouncing and particularly the effect of the surface it is bouncing on, and particularly the hardness of those surfaces. I used to have a conservatory with a ceramic tile floor, the tiles were so hard / stiff that a ping pong ball actually couldn’t bounce in it, the ball would just crack or buckle instantly.

I saw what you did there discussing tangents in your tangent.

12:12 Yes, I did wonder. Thanks for showing.

If you're interested in the whole static/dynamic friction relationship, it's worth exploring the exception to the rule - rubber! Tyres specifically, experience a greater dynamic friction than static friction. It's referred to as the slip ratio or slip angle depending on the circumstance, and it's the core principle behind why cars drive the way they do. For anybody that works in vehicle dynamics or any kind of racing, it's the whole reason the career exists!

This is wonderful. And as a bonus, we now know never to use a and b for (respectively) after and before :)

2:44 - That's the point of the Dirac delta function - helping find the area of a sudden infinity. In this case F(t) = -m*g + 2*m*v_{collision} * δ(t-t_{collision})

This analysis also applies to rotating car wheels. The same kind of deformations apply and can be calculated with Pacejka's "magic formula" for tires.

Good video

This is one of the best story arcs on the internet