one of them glued like this and the other one glued like this

so this one I can balance very carefully like this

on a support

whereas the other one I have really no chance of balancing

it's very unstable

so you might have the impression that this one

is the stable one and this one is the unstable one

because this bulges out and

and hugs whatever supported standing on

with this is well, going to tip.

Let's do the dynamic

version of the experiment so this is an

inclined plane and we'll try to let this roll down the slope.

here we go. And it rolls down

and rolls all the way down very happily.

next, this one. let's try to make it roll down the slope and

when I do that, oops, it went off the rails

oops, however hard I tried to center it, it really

doesn't want to go all the way down it's

very very difficult

almost made it, but not quite it doesn't

why is this such a good roller all the way down

and why is this such an unstable roller?

the difference is very interesting and

it has to do with one of the most

fundamental if simplest ideas in science

and engineering which really is at the

heart of today's technology called

the stability and instability. let's first look at

this one.

well as long as I can center this thing

exactly in the middle

well thats fine goes straight down, rolls straight down, there

is no problem there. But, you know in nature

you always make mistakes so there is

some error initial error. let's see if it has

erred slightly to the left like this so

it's now deviated slightly to the left.

in that case you see

this thing is going to be supported on

the left the rail here and on the right

rail here that is on the left

it's rolling on effectively a wheel that

has a large radius over here it's

effectively rolling on the wheel that has

small radius so you have a large wheel

on the side and small wheel on this side

and you know what they're going to do

going to start deviating rightward in

other words in such a way as to cancel

the initial error to the left so this is

a restoring mechanism or an automatic

correction mechanism whenever there is a

slight deviation to the left, the system

automatically corrects itself by going

right and if it deviates a little bit to the right

into the same thing the other way around

you start automatically going to the

left so there's an automatic correction

mechanism and that's why it's so stable just wrong

(Brady) Why, professor? Why can't the big one roll along slowly

and what's the physical thing that happens?

Aha, because if you have a

small wheel on the side a large wheel on

the side and if they roll both at the

same time you see the per same amount of

angular roll the smaller one will advance a small

distance and large one advance a large

distance so you see this one goes a

little but it this one goes large so it starts curving in this

direction and if you have a small one on

this side and large one on this side, it's the other way and starts curving

on this side, so whichever side is smaller that side is

the side toward which the whole thing

starts reeling

(Brady) it's because they're connected, isn't it

Yeah they are connected. That's right.

ok so that's why this thing is such a

stable roller because whenever there is

an initial error which is inevitable

automatically is correcting its course

so why it's wobbling around the center

it can still go down in contrast this

is a disaster because again you know if

you can if you can at all center it in the

middle there is no problem to roll straight down but

that's only the ideal scenario in

practice there's always initial error let's

as before assume that there is a slight error to

the left but then you see the left part

of this object is supported here on the

rail so it's rolling on a small wheel

whereas the right part is supported here

which is rolling on a large wheel so

whenever it's deviating slightly to the

left you have a small wheel on the left

and a large wheel on the right and you know what those

wheels will do they'll start moving

towards left so if there is an initial left error

there will be a tendency to start going even

further left so the error grows and grows

and goes out of control

and eventually of course the whole thing

moves off the rails so there is a mechanism

which is opposite to what we had before

that is, whenever there is a small initial error which is

inevitable there is some mechanism

a devilish mechanism that makes the error grow and

grow and that is called an instability

and in general in abstract terms

whenever there is a system that we want

to control or something that nature

gives and you know there are some

initial errors in the positioning well if

the error has a tendency to diminish

there's an automatic correction mechanism

that system is stable and if the error

tends to grow and goes out of control

that's the unstable mechanism and that is why this can

hardly go down the slope whereas this is very very

stable thing that keeps going down

(Brady) Professor, anyone watching is immediately right now

is going to start thinking about trains maybe. How does a train wheel work?

So, if a train is going straight there is no problem

but suppose it wants to round the corner

and it has the wheel that say on this

side and the outside wheel on this side

and they are connected. As it goes around the corner

the distance that this outer wheel has to travel is

actually longer than the distance this inner wheel

has to travel so there's a

problem because they are rotating at the

same rate

one of them must skid and that's a very

bad the situation so they cannot both roll

because the distances are different

so how do you correct for this effect as

long as the wheels are connected it

seems to be completely insurmountable as a

difficulty but today is a really nice

mechanism here is what you should do: effectively

you should put this kind of design on

the pair of rails you see so when it wants

to go around the corner the centrifugal

force make this go slightly outside but

that's very good news because as long as

it's on the outside that part of the wheel

becomes effectively larger and this part effectively smaller so the

distances that they travel are ultimately

adjusted and indeed the outer wheel does travel

the longer distance and the inner wheel a short distance and

because the wheels radii are different

and of course in real train

wheels it doesn't look

like that but actually the designs kind

of look like this cross-section and this

is sitting on the rail like this and

this is sitting on the rail like this

so as the wobbles left and right the

effective wheel size varies and that

automatically adjust for the unstable

rounding of corners its radial on the

full thing. And by the way if you designed

the wheels in this fashion that would be

really a disaster train that

immediately come off the rails just as this

couldn't go down the slope.

I wonder if I can actually make it

go down all the way. AHAHA -- the first time.

[laughing]

You've just undone

all that math there

one way to do it, is from my point of view, the right hand and pull it

over and then do this which produces

a perpendicular knot.