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  • 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 aroundwell 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.