字幕表 動画を再生する 英語字幕をプリント Hello Ding-a-lings. My name is Michale Stevens and you are here just in time for another episode of Michael's Toys. Have you ever spun a penny? It's amazing. Watch this. As the penny comes to a stop it's wobble will become more and more vigorous. That's what you're hearing but its spin will decrease. Watch how Abraham Lincoln spins slower and slower and slower. Of course a penny will not spin forever here in the real world because air resistance, friction, vibration, all those kinds of things rob it of energy and it eventually runs out and lays flat right down there on the table. But how long can a coin spin for? Well, in 1990 Joseph Bendik invented Euler's disk. It's a spinning course. Of course the coin in this case is a very large and heavy steel disk. There are no batteries here. There's no magnets. Nothing like that. It's just a piece of metal spinning on a mirror but the design is pretty much a trade secret but watch how well this spins. Your ready? Here we go. Euler's disk. Quite phenomenal. The disk spins because that's what I made it do at first but then it begins precessing because of gravity. Precession is a change in the orientation of an object's rotational access. As far Euler's disk goes, precession works like this. When I first spin the disk, it spins around a vertical access that runs through this, whoa! We're not ready for the tilting yet. It spins around an access like this right? But unless I spin it perfectly such that it never tilts, it will eventually tilt and then gravity will do it work and gravity causes that access of rotation to precess like this so we've got a disk spinning this way and then all of a sudden its rotation begins pointing all around in a circle. Ahh yeah, I'm actually getting pretty good at doing precession with just my hands. A little precession puppeteering, you're welcome. Now the reason Euler's disk spins for so long is that its spin's specifically designed to lose energy as slowly as possible. Now we don't know exactly how the inventor did this because like I said, it's kept as a trade secret. Only one company sells this toy but you can tell that the mass of the disk matters. If it was lighter it wouldn't have as much inertia and air resistance and friction, that kind of stuff would take more of its motion away more quickly. But if it was too heavy. If it was heavier than this it might have more of an issue with greater friction and deformation of the base of itself because of its weight and that would rob energy from it. It also has this interesting curve on one side and that's the side that you want it to roll along. The way that curve works as opposed to the sharp corner on the other side must help the disk lose less energy as its angle to the table changes. The final result is phenomenal. In many ways Euler's disk operates like a gyroscope. It's why it precesses and it's why it doesn't just flop over like that. So let's take a look at a gyroscope but first let's talk about precession. What is it? Well, it we imagine that this baseball is a satellite orbiting around the Earth and that the satellite's orbit is somewhat like this, sort of around the ecliptic, perfect. Now what happens if, while it's orbiting in this horizontal plane I come in and I push it down? I apply a force, a quick little impulse, boom, right there, to the satellite. What will happen? Will it get hit by the force and go straight down? No. The acceleration induced by my impulse will just combine with the velocity the ball already has in the horizontal plane. So we have this kind of motion. The motion from my force going down and we'll wind up with a combination, a sort of diagonal motion. That means that the ball will when struck, let me use this hand, the ball when struck, BOOM! Will start orbiting like this and what is in relation to us sort of a diagonal orbit. Now this is really really interesting because it means that the effect of my force which is pushing down is not felt within the line of that force but instead is seen 90 degrees ahead in the original rotation. Take a look at my favorite demonstration of this happening. I just love to play with this as like a fidget toy. Little disk of cardboard and a pencil. If the disk is not spinning and I blow here on this side that's near me it tilts down. The part that I blow on is pushed down. It's pretty obvious especially if you've seen my episode on spinning in which I literally do this same demonstration but watch what happens when I get the disk rotating and I do the same thing. I blow on the back. It tilts to the right. Keep in mind that the disk is spinning when looked at from above clockwise. And just like what I was saying with the orbiting satellite, the effect of my force, my air blowing down on the disk here is seen 90 degrees ahead in the rotation so instead of the disk going down here it goes down 90 degrees ahead. That's because the acceleration from my breath combines with the velocity all the mass of the disk already has. If I blow here, tilts to the right. If I spin the disk counterclockwise it should tilt to the left. Pretty awesome right? So this is where gyroscopic stability and precession come from. Now watch what happens if I always blow on the side of the disk that is down. The lowest part of the disk. It precesses. Its access of rotation moves around. This is exactly what happens in a gyroscope. Of course its not breath moving around. It's just gravity constantly putting a torque on the object according to how it's oriented. Let me show you what I mean. Here's a gyroscope which consists of just a spinning disk on an axel surrounded by a cage so that it can be held and manipulated and the effects of rotation can be felt. If the disk is not rotating and you balance it on its axel it falls off. But if the disk is spinning you're going to see the same behavior you saw form this cardboard disk. It'll balance but because no one's perfect there will always be just a tiny amount of skewness that causes a torque from gravity. Gravity operates from the center of gravity of this top which is well let's just assume it's pretty much right there in the middle but the base is exerting a normal force like this. Those two forces are not in line so we get a torque right? Rotation. Well if gravity starts pushing this way what's going to happen? We know that that effect of gravity will be seen 90 degrees ahead in the rotation so the disk is rotation clockwise when seen from above. A torque this way will manifest as motion this way. 90 degrees ahead of the rotation but look what's happening now. Now because the center of gravity is here and the base is sort of in front of the center of gravity from my perspective, the torque is now going to move the gyroscope down this way if it weren't spinning but it is so now gravity's effect is seen 90 degrees ahead of the rotateon here. So the gyroscope tilts that way. Now the torque operates like this which means its effect will be seen 90 degrees ahead this way. So it'll tilt like this and all of a sudden we've got ourselves a gyroscope that just doesn't fall over. Instead it precesses. Alright let's see this in action. I'm gonna take a string and poke it through a hole in the axel of the gyroscope. This end is a little sharper. Ow. Okay perfect. Now I'm going to turn the gyroscope and wind the string around that axel. Perfect. When I pull the string while holding the cage not the disk. The disk will spin up really quickly and it's going to be spinning clockwise when seen from above. But I think I'm gonna turn it over so that the notched side which is for balancing on the string is not the one on the base. So the disk will be spinning counterclockwise which means we should see counterclockwise precession. Here we go. I'm holding the cage, pulling the string, turning the gyroscope over, and tada! It appears to be defying gravity but in reality all it's doing is taking the effect of gravity and constantly relocating it around in a circle so gravity never has time to fully topple the thing over. But as the disk slows down due to friction and air resistance and vibration, gravity torque becomes a larger part of the influence, the velocity, every piece of mass on that disk has and the precession becomes greater and greater. As you can see the precession is much more dramatic now and the gyroscope will continue lowering and the precession will speed up until the gyroscope is no longer able to stay up and it falls down to the ground. It's pretty dang amazing. Spinning objects can behave quite unintuitively. And what is Euler's disk but a spinning disk? Well a few other things. Euler's disk has no axel and there's no cage to hold it. So when it precesses instead of moving around like this balanced on the edge of a spoke here, it just sticks one of its edges right down on a surface which means that because of Euler's disk's precession it also rolls. One of the edges is in contact with the surface as it precesses. And there's a relationship between the speed of precession, the angle the disk is at, and how quickly it spins. That relationship is caused by the fact that the higher the greater the angle between the disk and the table, the smaller the circle is that the disk rolls around due to its precession. Once the disk is really low like this as it precesses the edge touching the table traces out a circle that's much closer in size to the circumference of the disk itself. At the limit when the disk is flat on the table the edge of the disk touching the table is touching a circle with the same circumference but up here it's really tiny. You can observe this effect yourself. I'm gonna use a roll of tape because this is really nice and easy to see. If we mark off a line on the circumference right here, perfect, and then we carefully roll without slipping the ring of tape around a circle we can see that if that circle is a lot smaller than the circumference after rolling all the way around will still have some space left if we roll in this direction across that part of the tape we won't come back to the purple line that I've drawn if we started there. So it will appear as though the ring is spinning. Watch this. I'll start with the line on the ground and then I'm going to roll not slide but roll the tape around a little tiny circle. And look at that. I've completed one precession but where's the purple line. It's not down there anymore. Now it's all the way up here. The disk has spun quite a bit but if the disk's angle with the table is really shallow like that then a rotation takes us around…well a precession takes us almost all the way around the circumference and when we get back the line has only moved a little bit. The disk has only spun a little bit so that's why the spinning penny sounds more and more vigorous. That's because the precessions' making that sound even though Abraham Lincoln himself or the tail side appears to be spinning even more slowly. Both of those are true. The disk is spinning more slowly but precessing more quickly. But wait hold on hold on. Why does the rate of precession increase. Well just like as we mentioned with the gyroscope the spinning of the disk slows down due to friction which means that gravitational torque becomes a larger proportion of the effect on all the mass. But also as the disk loses to gravity and drops down and the angle between the disk and the table gets smaller the moment arm that gravity acts on gets longer. You can think of the disk like a lever right? When it's really steep like this it's pivoting from a point, I'll use the pencil to point it's pivoting from a point right here and it's being pushed down from the center of mass basically like right there. But as the disk obtains a shallower and shallower angle the distance from the pivot point to the center of gravity increases and gravity operates more perpendicularly to that lever arm. It's the difference between using a crowbar like this and pushing down like that and pushing like this. You're gonna get more leverage this way. For that reason gravity's torque increases as the disk loses it's height. And precession increases in rate. Okay I think you guys are ready to see a magic trick that I learned from the Pillowcase of Terror. You ready? So here we are with just a regular old penny. In fact the very same penny that was in my mouth just moments ago. But watch. Corn cob. Whoa! Amazing right? But of course this isn't a real penny. You couldn't spend this in a store. If you want something of true value try this one. Cob corn. Curiosity Box 12. Now shipping. We only have a few of these units left but it's amazing. The stuff inside here is basically a mystery but a few spoilers. The deck of cards that we specially designed are in here. I tweeted about those earlier. And this shirt. This is the shirt in the next box. It works in very cool ways with the red blue 3D glasses. Now Euler's disk and the gyroscope are not in this box.