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.
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?
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.
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.
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...
_@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.
@@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.
@@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.
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
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.
In table tennis, if you have a spinny rubber, as most modern players do, and your opponent uses a rubber that has no spin, you own spin comes back to you inverted. If you hit with topspin, then the return has backspin. I no longer play competitively but when I did I always asked to see my opponent's bat before the match (that is your right). The rule about the two sides of the bat having different colours (red and black mandatory) was introduced so that you can clearly see which rubber your opponent is using when hitting the ball.
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. 🤣
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."
@@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
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.
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 😊
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.
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.
@@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!
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.
The superballs from Wham-O newer than 2002 use a "new recipe" of Zectron that drop that direction change feature as well as lose 5-10% of vertical cof of restitution. I bought a couple old ones for $25+ and they work like a charm. Their path is so bizarre- for 3-4 bounces they look like a genuine "W" when spinning tangent to their direction of momentum.
@@unwaryquerier Yea, I was thinking about those balls also. I once knocked over a tray of them by accident (at a birthday party and they fell off the 10 ft high deck onto the driveway) and they bounced all over like grass hoppers where half the bounces were back towards me instead of all bouncing away as I had expected. After picking up the tray and collecting all the balls, I tossed it down again a few more times just to make sure I had seen what I thought I had seen.
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.
As an enjoyer of pool, I did not understand that sentence. Kick is normally discussed in terms of coming off rails, kicking off the rail. Chalk is "transferred to the cue ball" on a good hit, where they make firm contact (coef. of restitution = 0, in the parlance of this video (sorry, I keep using that word today)), but it's not the chalk being transferred that's the good thing, it's the English or spin you put on the ball that dictates if the cue goes where you need it to after you make your shot. Idk what you mean about contact points and other balls and changing variables. You are right that billiards has a LOT of physics in it, a lot more than most people give it credit for. You can't use much math or physics, really, it's all feel and practice.
Secondung your comment. Pool is all feel and practice. Play enough games and you just know how much to adjust a shot based on ball position and how you need to strike the ball
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).
…” 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…
@@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
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.
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.
@@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.
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.
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.
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.
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. 💨
@@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.
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!
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...)
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)
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).
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.
@@BudewFan_ if it's a fundamental force, it is conveyed by a boson... the way the electromagnetic force is carried by photons, and the strong nuclear force is carried by gluons
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.
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.
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.
3:45 One of my favorite things to do in a physics simulator as a kid (can you tell I'm a nerd) was to set the restitution value greater than 1. Pretty much no matter what else you did, everything would eventually implode, how much greater than 1 the value was would just determine how long it took.
Regarding your correction at the end: momentum and angular momentum are only conserved in a closed system. For the ball-in-a-tube to be a closed system you would have to also be accounting the momentum and angular momentum of the tube. If you treat the tube as static, you are giving it infinite inertia which I believe grants it the power to create or destroy momentum. Or alternatively you analyze the ball as a system with the tube being the outside environment, in which case momentum is not conserved, as it can enter and exit the system (of the ball) from the outside environment (of the tube).
3:20 I'm not a physicist, but I thought momentum was always conserved, and that elasticity is whether the kinetic energy is conserved or transferred into alternate forms of energy?
yeah, that was awkward. The thing is, this is not a closed system: the table or other bouncing surface can take up momentum, and since energy is p^2/2M, when you plug in M=mass of earth, the energy is irrelevant. Now if you were a physicist, you would know momentum is only conserved in systems that are invariant under translation, and a spinning ball bouncing on a table is not. (angular momentum is only conserved if the system is invariant under rotations--gravity breaks these symmetries, and with the spin coupling horizontal translation to rotations, that's broken too).
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.
Could you use your Newtonian water particles and 'visualize' with a pump how water would flow in a black hole? Both "spin suction" and with 'vertical flow' lines. Wouldn't that be fun?
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.
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.
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!
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 😁
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})
Hearing this explanation and watching a squash ball bounce and squish reminds me of my old physics teacher, Mr. T (His name was difficult for English speakers, he asked to be called that and we very happily obliged) who ran the after school squash club alongside my German teacher (whom we were generally unfairly mean to). I feel very lucky to have had them as teachers. Thank you, too!
You have to integrate, and you're screwed? Too bad you don't know another RUclips creator who specializes in Maths. Someone like that could probably help you out (unless you were trying to come up with a magic square for some reason).
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.
What a pleasant surprise. I was fidgeting with a bouncy ball at work a few days ago and started wondering this exact thing. I had a rudimentary understanding of what was happening, but these visuals help a lot. Thanks for yet another great video!
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.
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.
With some napkin math i think you could calculate the e_h quite easily with only two spinning drops, and one non spinning beforehand The first non spinning is needed to have e_v, which comes easily with some basic math and by measuring the height of the bounce. The two spinning drops need to be done at different spins. Looking at the left equation at 9:16, if you have V_h, which comes from the horizontal distance of the bounce of the ball, and you have the ratio between the two samples of V_h, you can put the tqo versions of the equation together and the known ratio and solve for w_b and e_h. The two different w_b are actually connected by the same ratio factor as V_h, so it's only one variable. Now with only a ruler and some math you can get everything! EDIT: later sections reveal that e_h is just not a constant, making this pretty useless :(
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.
Iirc the coefficient of restitution measure the _energy_ retained, not the speed. A ball bouncing with a coefficient of 0.5 would retain about 71% of its speed (and bounce to 50% of its previous height).
I could have used this video like 2 months ago when I was struggling in my dynamics course. My professor never explained what the coefficient of restitution was but now it all makes sense
6:13 Re: a ball that is not able to spin, perhaps you could create this scenario by making a ball with a gyroscope inside. It would be interesting to see if the ball really bounces backwards horizontally when it strikes the surface at an oblique angle. Although you'd need an HCR close to 1 to observe that. Perhaps you'd at least be able to see the gyroball bounce directly upwards when the HCR is 0?
a really interesting video could be explaining how a cordless blind works. it’s always been really cool to me, and explanations have always been a hand-wavey “it’s under tension” loving the content recently!
11:40-12:00 - Isn't the Coefficient of Restitution dependent on the two objects colliding. So showing it acting differently with two different materials is irrelevant since you'd have two different CoRh for them. It would be more relevant if two different speeds of collision resulted in different CoR for the same ball and surface collision.
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?
3:08 : perfectly elastic just means that the total KE after is equal to the total KE before (not including thermal motion, in either case), right? This only implies having the same momentum after if the mass of the other object is infinite, right?
8:43 the equations only work for a solid ball, but tennis balls are hollow. Would that affect the conclusion of the ball having an hcr of -1 or would that be independent of the equations?
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.
The equation: Single line. The reference book for the coefficient the equation uses: Several volumes of empirically derived values with a few analytical approximations that 'sorta work' under some mostly idealized conditions that a phd went too far down the rabbit hole trying to 'tune' before realizing they were just determining the previous coefficients with extra steps.
Your video made me think of days long past when I used to play racquet ball. A friend of mine had pretty well nailed the technique of hitting the ball in such a way that the spin in the opposite direction of travel would just kill the forward momentum when it hit the back wall it would just die in the corner instead of continuing continuing on so that I could return it, the ball would just lay there like a dropped egg.
8:37 This is related to the calculations for the turntable paradox/golf ball paradox as 2/7 is from calculating the moment of inertia of a sphere, so I wonder if when calculating the HCR of a hollow ball it would be closer to 2/5, just like with those experiments?
I watch your videos, I'm from Mexico, greetings, I'm 26 and it's true that science improves the quality of life and human well-being. We must be ethically aware of the acts and actions for which science and innovation are used.
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.
The vertical CoR technically could be negative, but that would mean that the ball has broken through the surface it landed on, so in practicality it doesn't go negative very often. If you drop a bowling ball on a table and it breaks the table then the CoR relative to the bowling ball - table collision would be less than zero, but the bowling ball - floor collision wouldn't be.
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! :)
Can you do a practical science video demonstrating the chemistry math of burning fossil fuels? The weight of one liter of petrol (gasoline) and the CO2 produced by its combustion can be understood with a few calculations: 1. **Weight of One Liter of Petrol:** - Petrol has a density of approximately 0.74 to 0.76 kg/liter. For calculation purposes, let's use an average value of 0.75 kg/liter. 2. **Combustion and CO2 Production:** - The combustion of petrol is a chemical reaction primarily involving octane (C8H18) with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O). - The balanced chemical equation for the combustion of octane is: \[ 2C_8H_{18} + 25O_2 ightarrow 16CO_2 + 18H_2O \] - From this equation, we see that 2 moles of octane produce 16 moles of CO2. 3. **Molecular Weights:** - Molecular weight of octane (C8H18): \( 8 \times 12 (carbon) + 18 \times 1 (hydrogen) = 114 \) g/mol. - Molecular weight of CO2: \( 1 \times 12 (carbon) + 2 \times 16 (oxygen) = 44 \) g/mol. 4. **Calculation:** - For 1 liter of petrol, which weighs about 0.75 kg (750 grams): \[ \text{Moles of octane} = \frac{750 \text{ grams}}{114 \text{ grams/mol}} \approx 6.58 \text{ moles} \] - From the balanced equation, 2 moles of octane produce 16 moles of CO2, so 6.58 moles of octane will produce: \[ \text{Moles of CO2} = 6.58 \times \frac{16}{2} = 52.64 \text{ moles} \] - The weight of CO2 produced: \[ 52.64 \text{ moles} \times 44 \text{ grams/mol} \approx 2316.16 \text{ grams} \] Therefore, the combustion of one liter of petrol, which weighs about 0.75 kg, produces approximately 2.316 kg of CO2.
This is interesting as someone that grew up playing tennis at a decent level. In a way, some of this becomes intuitive after dealing with the physics a lot. I also played table tennis in college and that game is entirely spin based. I think Steven would love looking at ping pong balls and how the spin’s effect differs on the playing surface (hard and stiff) and the paddles themselves (sticky rubber with a foam layer underneath that creates give or “dwell time”). Note that really cheap paddles are basically useless and would be boring for physics analysis because they don’t have the tacky rubber or a foam layer underneath. In college I often practiced and played with a guy that had traditional tacky rubber on his forehand, but the other side had a long “pips out” surface. Imagine the kind of stippled bumps on a cheap paddle, but they are elongated into almost short strands of rubber instead of just small bumps. Like you gave a buzz cut to a Koosh ball. This created all sorts of wild effects that would be awesome to analyze the physics of. Sometimes the ball could be hit to him with tons of spin and come back looking like slice but moving like a knuckleball in baseball. The extreme “dwell time” as the pips formed an elastic cushion could give paradoxical effects. Sometimes absorbing incoming spin so that the spin on the ball before the collision seemed to have no effect on the outcome, yet also sometimes I guess the pips “bouncing back” gave more elastic energy to the ball’s rotation and it would seem to magically gain inordinate amounts of spin/rotational velocity. It was wild to play against as in table tennis everything is about spin and really the physics at play, so something that seems to break physics itself will quickly break your brain and game when opposing it. Sorry for the Ted talk comment, and I know Steve won’t likely see this, but it is perfectly up his alley to look in/explain the physics involved and use his skills analyzing some different slo-mo interactions to present both the seemingly paradoxical effects and why it actually makes sense once you understand what is truly going on!
Had an idea that I think you could answer, where is the center of gravity for a slinky going down stairs. Does it pass in a straight line or bob up and down? You’re the only RUclipsr that can help my mind visualize this. 🙏🏼
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"
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 :)
Great video! I have been wondering for ages why, in tennis, a GROUNDSTROKE topspin ball bounces higher than a non-spinning ball, whereas in the case of a topspin LOB, the ball accelerates horizontally after the bounce!? Thanks to you I've just understood (at last) that's because the trajectory of the latter is much more vertical (incidence angle closer to 0) and thus the static friction has more time to kick in. Same phenomenon with a backspin OFFENSIVE low ball (e.g. Federer's slice backhands, especially on slippery surfaces like GreenSet or grass) which bounces lower, versus a backspin DROP SHOT which can stop its horizontal momentum after bouncing (or even bounce backwards). Thank you for this aha moment!
So many variables. The makeup of the ball and the surface it is striking plus the surface of both. Added to that is the angle the ball strikes the surface and the rate and direction of spin. In games like snooker there is at least one constant. The makeup and surface of the ball. The variables are direction and speed of strike plus direction and speed of spin. And variables in cushion rebound.
Linear momentum is a vector and angular momentum is a pseudo vector. Yes, very complex. But the video is excellent and I have watched it more than once because it is so good.
Here’s some questions: how do ceiling fans, floor fans, and a/c units work? Do ceiling fans cool by pushing air down or drawing heat up? Is it a myth that the rotation of a ceiling fan should be clockwise in winter and counterclockwise in summer? Is it smart to have a fleet of small floor fans distributing cool air from an a/c unit around the house, or does this only localize the cool air to one room by drawing warm air to that area?-or, is this the exact same thing as distributing cooler air throughout the house? (These questions are highly salient to me now as I live in an apartment with very limited a/c, and am desperately trying to dial in my cooling system before the summer heat really sets in.) . . . I thought you might be the perfect person to ask, Steve. ☺️
Ceiling fans promote convective cooling, so their effectiveness depends on humidity. If the wet bulb temp is above 35°C they're basically useless and you need air conditioning to not die. You can measure that with a WBGT thermometer; that also takes radiant heat into account and hence gives you some safety buffer before temperatures really get lethal. That said, ceiling fans are in fact slightly suboptimal because they actually oppose the direction of natural convection, since hot air naturally wants to rise. There was a TV show which reversed the direction of a classroom's ceiling fans to draw air up instead of down and the students reported the room to be more comfortable as a result. Not sure how you're gonna do that though. The truly optional solution here would be to use a HVLS fan, but it'll be a big ask to fit that in a home. But the same concept applies: aim for large, slow blades to create laminar rather than turbulent flow for maximum efficiency, and ceiling fans are pretty much the best house-sized version of that. Maybe go for the quietest industrial fans you can find if ceiling fans aren't quite enough? P.S. Wet bulb temp is the lowest temperature you can reach by evaporative cooling (ie sweating), and it's typically lower than ambient temperature unless you have 100% humidity. The air temperature can be well above that and still be easily survivable if it's dry and you have enough water around you to drink, which is why deserts are generally survivable as long as you have a reliable water source. It takes really crazy conditions to get a lethal wet bulb temperature, the only place that really sees that regularly is Qatar, because the Persian Gulf's water is pretty much boxed in by geography and becomes really hot, bathing the whole place in hot and humid air. You literally need to air condition the streets there to survive!
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.
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.
My fvourite coefficient that we used frequently in uni is the gant coefficient, used in scattering. Professors used to say "it's between 1 and 10 so we assume 2 on average". Physics is much more approximation and simplification than people think
Hey there really love your videos and make awesome content Just had a request for you man Recently I was trying to make a hidden storage for a PS5 like a pop up drawer which comes out with a press of a button but was not able to find any reliable info Would be great if you could show a step by step video about it keeping it in mind that it cost the bare minimum 🙏🙏
I'm always surprised by how wobbly things are in slow motion.
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The opening music almost made we shout "Twelve!"
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?
You made this video because you watched Matt Parker and Grant Sanderson's recent billiards/pool video, didn't you?
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.
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.
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...
_@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.
@@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.
@@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.
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
As a polo goalie the bounce shot is my worst nightmare, impossible to predict
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.
hello (i play too!)
In table tennis, if you have a spinny rubber, as most modern players do, and your opponent uses a rubber that has no spin, you own spin comes back to you inverted. If you hit with topspin, then the return has backspin. I no longer play competitively but when I did I always asked to see my opponent's bat before the match (that is your right). The rule about the two sides of the bat having different colours (red and black mandatory) was introduced so that you can clearly see which rubber your opponent is using when hitting the ball.
@@trapkat8213oh huh TIL the colours on ping pong paddles are used to actually convey information among the pros. Which one is which if I may ask?
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. 🤣
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."
@@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
Gee, my dad told me that toilet paper was getting really expensive, so we had to start conserving it by using both sides.
Just fold it
@@mailleweaver Up for a Snipe hunt, anyone?
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.
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 😊
Huh. This is information that will stick at the back of my mind until one day I can use it.
Even knowing this information, I know that I'll remain unable to play pool any better :D
Fantastic insight, thank you :)
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.
now try to figure where is 3/5 on the ball
This video is secretly about two idiots playing pool using math, and forgetting to account for friction in their calculations 😆😆😆
classic mathematicians
I was thinking the same thing!
I was so hoping someone would have said, "oi, go grab that Parker triangle and rack 'em, Matt!"
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.
He probably just sent Matt the video and said nothing else
Are you actually sitting in the yellow chair?
I just wondered the same, after reading your comment😂🤣
In Sweden the chair sits on you.
🤣
It’s an ikea chair that also has a matching footstool. I think he’s sitting on that.
@@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!
'Tis a bit too far. My guess it's a chaise long 😉
I thought Ur observation concerned atoms' stuff: we never touch anything 😅👌
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.
The superballs from Wham-O newer than 2002 use a "new recipe" of Zectron that drop that direction change feature as well as lose 5-10% of vertical cof of restitution. I bought a couple old ones for $25+ and they work like a charm. Their path is so bizarre- for 3-4 bounces they look like a genuine "W" when spinning tangent to their direction of momentum.
@@unwaryquerier Yea, I was thinking about those balls also. I once knocked over a tray of them by accident (at a birthday party and they fell off the 10 ft high deck onto the driveway) and they bounced all over like grass hoppers where half the bounces were back towards me instead of all bouncing away as I had expected. After picking up the tray and collecting all the balls, I tossed it down again a few more times just to make sure I had seen what I thought I had seen.
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.
As an enjoyer of pool, I did not understand that sentence. Kick is normally discussed in terms of coming off rails, kicking off the rail. Chalk is "transferred to the cue ball" on a good hit, where they make firm contact (coef. of restitution = 0, in the parlance of this video (sorry, I keep using that word today)), but it's not the chalk being transferred that's the good thing, it's the English or spin you put on the ball that dictates if the cue goes where you need it to after you make your shot. Idk what you mean about contact points and other balls and changing variables. You are right that billiards has a LOT of physics in it, a lot more than most people give it credit for. You can't use much math or physics, really, it's all feel and practice.
Secondung your comment. Pool is all feel and practice. Play enough games and you just know how much to adjust a shot based on ball position and how you need to strike the ball
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).
…” 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…
@@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
@@ernestgalvan9037 Sliding is motion constrained to a contact surface.
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.
Definitely a great thing to consider. Because walking on slippery ice is hard.
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.
"bzzzthwip" is spot on. I knew there had to be a word for it.
IMAGINE GETTING 69 LIKES.
“How could you work out the area under graph that’s infinitely thin and infinitely tall?”
Laughs in Dirac Delta
The original script had that it but it got cut!
Thats 1 way of describing an area
@@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.
@@SteveMould Was it cut? Or did it become an infinitely informative segment with zero duration?
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.
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.
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.
Edit: compression on metal woods (Driver, 3-wood, fairway metal)…though the interaction with a grooved iron or wedge would be just as interesting.
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. 💨
@@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.
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!
I'd love to know the physical properties that attracts a golf ball to trees and bunkers and repels them from the hole
WOW! This was the nicest, clearest and most objective masterclass on collisions I've ever watched!!
Very fine work, Steve!
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...)
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)
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).
1:34 This is the right response, anytime you need to use integrals in physics
1:34 "We're screwed, basically"
- Steve Mould, 2024
Out of context, but still highly relevant.
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.
Steve can answer ANY physics question we throw at him, and provide high quality demonstrations and footage to show it. What a legend
throw at him? with what velocity and spin?
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.
@@reidflemingworldstoughestm1394it’s a more fundamental force, it results from the way space bends around big stuff, no carrying particle whatsoever
@@BudewFan_ if it's a fundamental force, it is conveyed by a boson... the way the electromagnetic force is carried by photons, and the strong nuclear force is carried by gluons
@@reidflemingworldstoughestm1394 He's got balls to do 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.
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.
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.
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.
@@JP_Hatecrewneed to get checkered balls popular, so we can get better slow-mo footage of their spin
@@giovane_Diaz great idea!
@@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.
Also, the ball being hollow means spin is more important.
3:45 One of my favorite things to do in a physics simulator as a kid (can you tell I'm a nerd) was to set the restitution value greater than 1. Pretty much no matter what else you did, everything would eventually implode, how much greater than 1 the value was would just determine how long it took.
Regarding your correction at the end: momentum and angular momentum are only conserved in a closed system. For the ball-in-a-tube to be a closed system you would have to also be accounting the momentum and angular momentum of the tube. If you treat the tube as static, you are giving it infinite inertia which I believe grants it the power to create or destroy momentum. Or alternatively you analyze the ball as a system with the tube being the outside environment, in which case momentum is not conserved, as it can enter and exit the system (of the ball) from the outside environment (of the tube).
quantititivley 5:10
3:20 I'm not a physicist, but I thought momentum was always conserved, and that elasticity is whether the kinetic energy is conserved or transferred into alternate forms of energy?
yeah, that was awkward. The thing is, this is not a closed system: the table or other bouncing surface can take up momentum, and since energy is p^2/2M, when you plug in M=mass of earth, the energy is irrelevant.
Now if you were a physicist, you would know momentum is only conserved in systems that are invariant under translation, and a spinning ball bouncing on a table is not. (angular momentum is only conserved if the system is invariant under rotations--gravity breaks these symmetries, and with the spin coupling horizontal translation to rotations, that's broken too).
Slow motion shots are so fascinating!
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.
Could you use your Newtonian water particles and 'visualize' with a pump how water would flow in a black hole?
Both "spin suction" and with 'vertical flow' lines.
Wouldn't that be fun?
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.
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.
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!
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 😁
I thought the same thing, but in different lines, like, "squash and stretch" animation principle. Amazing!
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})
Hearing this explanation and watching a squash ball bounce and squish reminds me of my old physics teacher, Mr. T (His name was difficult for English speakers, he asked to be called that and we very happily obliged) who ran the after school squash club alongside my German teacher (whom we were generally unfairly mean to). I feel very lucky to have had them as teachers.
Thank you, too!
"I'll be abbreviating it to HCR"
Immediately says the whole phrase again 😂
You have to integrate, and you're screwed? Too bad you don't know another RUclips creator who specializes in Maths. Someone like that could probably help you out (unless you were trying to come up with a magic square for some reason).
I'm not going to have some Parker Integration on this channel.
@@SteveMouldway to *stand up* to the *maths* !
@@SteveMould I'm both sad that he won't be here, and happy that you're having a jab at him! 🤣
Matt is more for Math. For Physics, call over Dianna Cowern. (Physics Girl) =)
@@SteveMouldMatt is more for Math. For Physics, call over Dianna Cowern. (Physics Girl) =)
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.
What a pleasant surprise. I was fidgeting with a bouncy ball at work a few days ago and started wondering this exact thing. I had a rudimentary understanding of what was happening, but these visuals help a lot. Thanks for yet another great video!
Steve is always so real and doesn't use rendered simulations. I respect it so much
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.
You are a marvelous teacher for many !
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.
That's the Magnus effect and Steve has already done that one
With some napkin math i think you could calculate the e_h quite easily with only two spinning drops, and one non spinning beforehand
The first non spinning is needed to have e_v, which comes easily with some basic math and by measuring the height of the bounce.
The two spinning drops need to be done at different spins.
Looking at the left equation at 9:16, if you have V_h, which comes from the horizontal distance of the bounce of the ball, and you have the ratio between the two samples of V_h, you can put the tqo versions of the equation together and the known ratio and solve for w_b and e_h. The two different w_b are actually connected by the same ratio factor as V_h, so it's only one variable.
Now with only a ruler and some math you can get everything!
EDIT: later sections reveal that e_h is just not a constant, making this pretty useless :(
You know, I always thought mechanics was boring and solved physics but Steve always manages to bring back some weird stuff.
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.
Iirc the coefficient of restitution measure the _energy_ retained, not the speed. A ball bouncing with a coefficient of 0.5 would retain about 71% of its speed (and bounce to 50% of its previous height).
I could have used this video like 2 months ago when I was struggling in my dynamics course. My professor never explained what the coefficient of restitution was but now it all makes sense
10:37 when you store footage for 1000 years and dig it up so you don't have to ruin another sheet of paper XD
6:13 Re: a ball that is not able to spin, perhaps you could create this scenario by making a ball with a gyroscope inside. It would be interesting to see if the ball really bounces backwards horizontally when it strikes the surface at an oblique angle.
Although you'd need an HCR close to 1 to observe that. Perhaps you'd at least be able to see the gyroball bounce directly upwards when the HCR is 0?
Fascinating topic.
I always love the surprise in what you choose to talk about in every new video Steve.
a really interesting video could be explaining how a cordless blind works. it’s always been really cool to me, and explanations have always been a hand-wavey “it’s under tension”
loving the content recently!
6:02 this concept of the ball springing back the way it came blew my mind!
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
Always answering questions I didn’t ask but I’m glad you did
Thanks for not using a clickbait style text or thumbnail.
1:07 bro that is so mesmerising to watch
11:40-12:00 - Isn't the Coefficient of Restitution dependent on the two objects colliding. So showing it acting differently with two different materials is irrelevant since you'd have two different CoRh for them. It would be more relevant if two different speeds of collision resulted in different CoR for the same ball and surface collision.
Gyro zepplie at 12:12
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?
3:08 : perfectly elastic just means that the total KE after is equal to the total KE before (not including thermal motion, in either case), right? This only implies having the same momentum after if the mass of the other object is infinite, right?
Thank you Steve. This video cleared many doubts, including how a cricket ball works differently for spin bowlers.
I love this guy. He explains some of these topics in a way most can understand
8:43 the equations only work for a solid ball, but tennis balls are hollow. Would that affect the conclusion of the ball having an hcr of -1 or would that be independent of the equations?
awesome, i've been wondering about this for the last nine days.
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.
The equation:
Single line.
The reference book for the coefficient the equation uses:
Several volumes of empirically derived values with a few analytical approximations that 'sorta work' under some mostly idealized conditions that a phd went too far down the rabbit hole trying to 'tune' before realizing they were just determining the previous coefficients with extra steps.
Your video made me think of days long past when I used to play racquet ball. A friend of mine had pretty well nailed the technique of hitting the ball in such a way that the spin in the opposite direction of travel would just kill the forward momentum when it hit the back wall it would just die in the corner instead of continuing continuing on so that I could return it, the ball would just lay there like a dropped egg.
Now I can fully understand Kyiora's insane backspin pass thank you steve 🙏
8:37 This is related to the calculations for the turntable paradox/golf ball paradox as 2/7 is from calculating the moment of inertia of a sphere, so I wonder if when calculating the HCR of a hollow ball it would be closer to 2/5, just like with those experiments?
I watch your videos, I'm from Mexico, greetings, I'm 26 and it's true that science improves the quality of life and human well-being. We must be ethically aware of the acts and actions for which science and innovation are used.
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.
The vertical CoR technically could be negative, but that would mean that the ball has broken through the surface it landed on, so in practicality it doesn't go negative very often. If you drop a bowling ball on a table and it breaks the table then the CoR relative to the bowling ball - table collision would be less than zero, but the bowling ball - floor collision wouldn't be.
Now you've got me thinking about how the dambusters worked. Great video
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! :)
Can you do a practical science video demonstrating the chemistry math of burning fossil fuels?
The weight of one liter of petrol (gasoline) and the CO2 produced by its combustion can be understood with a few calculations:
1. **Weight of One Liter of Petrol:**
- Petrol has a density of approximately 0.74 to 0.76 kg/liter. For calculation purposes, let's use an average value of 0.75 kg/liter.
2. **Combustion and CO2 Production:**
- The combustion of petrol is a chemical reaction primarily involving octane (C8H18) with oxygen (O2) to produce carbon dioxide (CO2) and water (H2O).
- The balanced chemical equation for the combustion of octane is:
\[ 2C_8H_{18} + 25O_2
ightarrow 16CO_2 + 18H_2O \]
- From this equation, we see that 2 moles of octane produce 16 moles of CO2.
3. **Molecular Weights:**
- Molecular weight of octane (C8H18): \( 8 \times 12 (carbon) + 18 \times 1 (hydrogen) = 114 \) g/mol.
- Molecular weight of CO2: \( 1 \times 12 (carbon) + 2 \times 16 (oxygen) = 44 \) g/mol.
4. **Calculation:**
- For 1 liter of petrol, which weighs about 0.75 kg (750 grams):
\[ \text{Moles of octane} = \frac{750 \text{ grams}}{114 \text{ grams/mol}} \approx 6.58 \text{ moles} \]
- From the balanced equation, 2 moles of octane produce 16 moles of CO2, so 6.58 moles of octane will produce:
\[ \text{Moles of CO2} = 6.58 \times \frac{16}{2} = 52.64 \text{ moles} \]
- The weight of CO2 produced:
\[ 52.64 \text{ moles} \times 44 \text{ grams/mol} \approx 2316.16 \text{ grams} \]
Therefore, the combustion of one liter of petrol, which weighs about 0.75 kg, produces approximately 2.316 kg of CO2.
This is interesting as someone that grew up playing tennis at a decent level. In a way, some of this becomes intuitive after dealing with the physics a lot. I also played table tennis in college and that game is entirely spin based. I think Steven would love looking at ping pong balls and how the spin’s effect differs on the playing surface (hard and stiff) and the paddles themselves (sticky rubber with a foam layer underneath that creates give or “dwell time”). Note that really cheap paddles are basically useless and would be boring for physics analysis because they don’t have the tacky rubber or a foam layer underneath. In college I often practiced and played with a guy that had traditional tacky rubber on his forehand, but the other side had a long “pips out” surface. Imagine the kind of stippled bumps on a cheap paddle, but they are elongated into almost short strands of rubber instead of just small bumps. Like you gave a buzz cut to a Koosh ball. This created all sorts of wild effects that would be awesome to analyze the physics of. Sometimes the ball could be hit to him with tons of spin and come back looking like slice but moving like a knuckleball in baseball. The extreme “dwell time” as the pips formed an elastic cushion could give paradoxical effects. Sometimes absorbing incoming spin so that the spin on the ball before the collision seemed to have no effect on the outcome, yet also sometimes I guess the pips “bouncing back” gave more elastic energy to the ball’s rotation and it would seem to magically gain inordinate amounts of spin/rotational velocity. It was wild to play against as in table tennis everything is about spin and really the physics at play, so something that seems to break physics itself will quickly break your brain and game when opposing it. Sorry for the Ted talk comment, and I know Steve won’t likely see this, but it is perfectly up his alley to look in/explain the physics involved and use his skills analyzing some different slo-mo interactions to present both the seemingly paradoxical effects and why it actually makes sense once you understand what is truly going on!
Oh no, apparently wrote “Steven” in that post and my mobile YT site won’t let me edit it.
"the force must be infinite"
Me: I bet they don't like infinity......
"and in physics we generally don't like infinity"
CALLED IT!
I love understanding what's happening before the explanations because of “Technische Mechanik 3“. Those 60h of studying in a week were worth it.
Had an idea that I think you could answer, where is the center of gravity for a slinky going down stairs. Does it pass in a straight line or bob up and down? You’re the only RUclipsr that can help my mind visualize this. 🙏🏼
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"
Kudos to you for trying to explain the Dirac delta to the general public!
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 :)
Great video!
I have been wondering for ages why, in tennis, a GROUNDSTROKE topspin ball bounces higher than a non-spinning ball, whereas in the case of a topspin LOB, the ball accelerates horizontally after the bounce!? Thanks to you I've just understood (at last) that's because the trajectory of the latter is much more vertical (incidence angle closer to 0) and thus the static friction has more time to kick in.
Same phenomenon with a backspin OFFENSIVE low ball (e.g. Federer's slice backhands, especially on slippery surfaces like GreenSet or grass) which bounces lower, versus a backspin DROP SHOT which can stop its horizontal momentum after bouncing (or even bounce backwards).
Thank you for this aha moment!
I studied angular momentum a few weeks ago and that is a very fun case scenario to test some equations! Thanks!!
05:00 can somebody explain why the torque/twisting motion is said to be clockwise? for my brain its just twisting it to the left, not clockwise.
So many variables. The makeup of the ball and the surface it is striking plus the surface of both. Added to that is the angle the ball strikes the surface and the rate and direction of spin. In games like snooker there is at least one constant. The makeup and surface of the ball. The variables are direction and speed of strike plus direction and speed of spin. And variables in cushion rebound.
Linear momentum is a vector and angular momentum is a pseudo vector. Yes, very complex.
But the video is excellent and I have watched it more than once because it is so good.
Here’s some questions: how do ceiling fans, floor fans, and a/c units work? Do ceiling fans cool by pushing air down or drawing heat up? Is it a myth that the rotation of a ceiling fan should be clockwise in winter and counterclockwise in summer? Is it smart to have a fleet of small floor fans distributing cool air from an a/c unit around the house, or does this only localize the cool air to one room by drawing warm air to that area?-or, is this the exact same thing as distributing cooler air throughout the house? (These questions are highly salient to me now as I live in an apartment with very limited a/c, and am desperately trying to dial in my cooling system before the summer heat really sets in.) . . . I thought you might be the perfect person to ask, Steve. ☺️
Ceiling fans promote convective cooling, so their effectiveness depends on humidity. If the wet bulb temp is above 35°C they're basically useless and you need air conditioning to not die. You can measure that with a WBGT thermometer; that also takes radiant heat into account and hence gives you some safety buffer before temperatures really get lethal.
That said, ceiling fans are in fact slightly suboptimal because they actually oppose the direction of natural convection, since hot air naturally wants to rise. There was a TV show which reversed the direction of a classroom's ceiling fans to draw air up instead of down and the students reported the room to be more comfortable as a result. Not sure how you're gonna do that though. The truly optional solution here would be to use a HVLS fan, but it'll be a big ask to fit that in a home. But the same concept applies: aim for large, slow blades to create laminar rather than turbulent flow for maximum efficiency, and ceiling fans are pretty much the best house-sized version of that. Maybe go for the quietest industrial fans you can find if ceiling fans aren't quite enough?
P.S. Wet bulb temp is the lowest temperature you can reach by evaporative cooling (ie sweating), and it's typically lower than ambient temperature unless you have 100% humidity. The air temperature can be well above that and still be easily survivable if it's dry and you have enough water around you to drink, which is why deserts are generally survivable as long as you have a reliable water source. It takes really crazy conditions to get a lethal wet bulb temperature, the only place that really sees that regularly is Qatar, because the Persian Gulf's water is pretty much boxed in by geography and becomes really hot, bathing the whole place in hot and humid air. You literally need to air condition the streets there to survive!
I can't belive he forgot about Tau Day. I thought he was a real tau fan.
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
Being a Tau fan is the real reason he has more subscribers than that Matt guy. Tauists are just a better class of people.
Hawk Tau
@@shandybassheadComing full circle
What if the ball is a particle, eg. a photon? Can a particle be spun like a ball then bounced to a surface and have a non-ordinary return angle? 🤩
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.
4:20 - That is an awesome piece of footage. It doesn't look real. I love the jiggle as the ball exits to the left.
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.
My fvourite coefficient that we used frequently in uni is the gant coefficient, used in scattering. Professors used to say "it's between 1 and 10 so we assume 2 on average". Physics is much more approximation and simplification than people think
Steve really making the most about the bouncing ball under a table idea haha, cool vid!
Now explain flubber
Flabber is highly classified.
Damn, I am old enough to get the reference.
Hey there really love your videos and make awesome content
Just had a request for you man
Recently I was trying to make a hidden storage for a PS5 like a pop up drawer which comes out with a press of a button but was not able to find any reliable info
Would be great if you could show a step by step video about it keeping it in mind that it cost the bare minimum 🙏🙏
Whatever the subject, these are always well researched and superbly presented videos. Many thanks!!