Download Part 1 - How Things Work

English Wheels
Introduction
Hello, I'm Lou Bloomfield and welcome to How Things Work at the University of Virginia. Today's topic: wheels.
Wheels are so common, and have been around so long that we simply take them for granted. Not only do we avoid
reinventing them, but we avoid even thinking about them. But that may be a mistake. Their extreme commonness
makes wheels more important, not less. And giving them a little attention may save you time, money, and even
misfortune.
When they're used to propel a bicycle or car, wheels serve as yet another simple machine. Without powered
wheels, you'd have to imitate a cartoon character by churning your feet directly on the ground. But, wheels are far
more than simple machines. They also save us from the limitations of friction. Without wheels nothing would just
roll along. There would be no free-wheeling adventures and the wheels of industry would grind to a halt. In fact,
wheels are so inextricably linked to friction that the story of wheels is also the story of friction.
It's also the story of energy, but in a different way from ramps and seesaws. Ramps transform energy from one
form to another. Seesaws transfer energy from one person to another. Wheels prevent friction from wasting
energy. That is, from grinding up useful energy into countless tiny, random fragments that are then very difficult to
use. We'll examine friction and wasted energy here in the context of wheels, and then use our new-found
understanding as we continue to look at how things work.
At this point, let me have you think about a question. We won't actually ask this and answer it yet. But this is
something you might have in your mind as we continue on through this episode. Suppose you're riding a bicycle or
a car and you are stopped waiting for something. And then it's time to accelerate forward. Will you accelerate
forward fastest if you twist your wheels so hard that they begin to skid across the ground--that is, slide on the
ground, or if you twist them somewhat less hard so that they just barely avoid skidding? To help guide us through
the science of wheels we'll pursue six how and why questions.






Why does a wagon need wheels?
Why is sliding a box across the floor usually hardest at the start?
How is energy wasted as a box skids to a stop?
How do wheels help a wagon coast?
How do powered wheels propel a bicycle or car forward?
How is energy present in a wheel?
There is one video sequence for each of those questions and a summary video at the end, but now on to the first
question.
Part 1
Why does a wagon need wheels? The answer to that question is: that a wheel-less wagon would struggle against
friction whenever it moved or tried to move. The motion of an ordinary wagon, that is, one with wheels, resembles
that of a skater. When you leave them alone, they're inertial and they move according to Newton's First Law of
Motion. If they're at rest, they remain at rest. If they're in motion, they continue in motion at constant velocity.
Remove its wheels, however, and the wagon exhibits entirely different behavior. If you push it, it moves. If you
stop pushing it, it stops.
1|Page
That behavior is not the least bit surprising, but it should be disturbing. Not disturbing in the sense of call the
police or a psychiatrist, but disturbing in the sense that it goes against many of the physics concepts that I've been
talking about up until now. Why doesn't the wheel-less wagon coast when you leave it alone? The issue is this
(according to Newton's Second Law of Motion): for the wheel-less wagon to accelerate to a stop to decelerate, it
needs a net force acting on it in the direction opposite its velocity. What could possibly be exerting that force? The
answer is friction. In addition to its downward weight, a gravitational force, and the upward support force from the
sidewalk, the wheel-less wagon can experience horizontal frictional forces from the sidewalk. And it's those
frictional forces that slow the moving wheel-less wagon to a stop when you leave it alone.
The pervasive influence of these frictional forces in our world explains why early scientists and natural
philosophers didn't understand inertia and why it took the genius of Galileo and Newton to recognize inertia for
what it is. The moving wheel-less wagon doesn't slow to a stop because it lacks inertia. It slows to a stop because
it's experiencing a non-zero net force. And it, therefore, accelerates in accordance with Newton's second law,
rather than coasting according to Newton's first law. For a wagon to move according to Newton's first law, it has to
be free of net force, and thus, free of the slowing effects of friction--that's why a wagon needs wheels.
Frictional forces are exerted by surfaces on one another, and like all forces, they appear in Newton's third law
pairs. When the sidewalk exerts a friction force on the wagon, the wagon must exert a frictional force back on the
sidewalk that's equal in amount and in the opposite direction. Frictional forces act along surfaces, parallel to
surfaces, which distinguishes them from support forces. The support force that this sidewalk is exerting on the
wagon is straight up perpendicular to the horizontal sidewalk surface. Any frictional forces that the sidewalk exerts
on the wagon, however, are parallel to the surface. In this case, horizontal, so as I scoot our poor wheel-less
wagon, I feel sorry for this thing without its wheels.
As I scoot it around on the sidewalk frictional forces are pushing the wagon horizontally. At the same time, the
wagon’s frictional forces are pushing the sidewalk horizontally. (Okay it's a table but I'm calling it a sidewalk.) You'll
see the sidewalk moving, not because it fails to have forces on it, but because it's attached to the whole world,
including the camera through which you're viewing us. And so you cannot see the sidewalk’s response. But it's
there, it's just very small. So, as I scoot the wagon about, horizontal frictional forces from the sidewalk are
affecting its motion. The frictional forces between two surfaces oppose any relative motion of those two surfaces.
In other words, the frictional forces act to bring those two surfaces to the same velocity so they move together
rather than sliding across one another.
To illustrate this idea of relative velocity, let me have two surfaces that I can talk about easily: this book surface
and my hand. Right now, the two surfaces are not in relative motion because they have the same velocity. They're
both motionless, but they'll still have the same velocity if I move them steadily across, along to your left, or if I
move them steadily along to your right. There's still no relative motion. Relative motion, then, is not about
whether the book is moving, or whether my hand is moving, it's about how one is moving relative to the other.
Or, if you think in terms of perspective from the perspective of the book, technically known as “the frame of
reference of the book,” my hand appears motionless. It still appears motionless. So, if you could, imagine yourself
a tiny person (or maybe a bug) sitting on that book surface. My hand looks motionless to you no matter what I'm
doing here. But if I begin to move my hand relative to the book (like this) from the perspective of you sitting on the
book, the little person (you) go, “That hand is moving.” So this, now, is relative motion. But so is this, doesn't
matter whether the book is moving or my hand is moving: it's one as viewed from the other’s frame of reference.
So, relative-motion friction opposes relative motion. And it even opposes the start of relative motion. With that,
then let's return to the wagon on the sidewalk. Now, the sidewalk is attached to the whole earth so you're not
going to see it respond to forces. It's just going to stay put. So its velocity is zero and pretty much no matter what
we do to it, its velocity is going to stay zero. Right now, the wagon is motionless, the sidewalk is motionless, and
the two of them are not in relative motion.
2|Page
But let me start some relative motion and watch what happens: ready, get set… I started it and low and behold
this--the wagon, which was sliding toward the right, came to a stop. A frictional force from the sidewalk acted on
the wagon to slow the wagon to a stop. That frictional force in this case was to your left, correct? Let's see it again-it's a leftward frictional force. It caused a leftward acceleration of the wagon, bringing the wagon to rest. Let's
reverse the motion. I'm going to now skid the wagon to your left. Whoa, friction's smart, the frictional force of the
table on the wagon now pointed toward the right and caused a rightward acceleration of the wagon, bringing it to
a stop. So, no matter what I do with the wagon the frictional force from the sidewalk pushes on the wagon in the
direction that slows the wagon's velocity and brings the wagon's velocity to the same velocity as the table, namely
zero. So frictional forces overall, they act parallel to surfaces--that is, along the surfaces. And they act in the
direction that opposes relative motion of the two surfaces.
If the two surfaces are stopped, they are not in relative motion. That doesn't mean that frictional forces are
absent. It means that those frictional forces, if they're present, are opposing even the start of relative motion. For
example, if I give a little bit of a push to the wagon, I'm trying to get it started, and in the absence of friction, I
would be causing the wagon to undergo acceleration. But nothing happened, so a frictional force developed (a
frictional force pair actually) between the wagon and the sidewalk, causing the wagon to remain motionless.
That brings me to a question: when I hold a beverage can between two fingers, one on the right, and one on the
left, am I exerting any frictional forces on the can? And if so, in which direction do those frictional forces on the can
act? I'm exerting upward frictional forces on the can and those frictional forces are what are supporting the can’s
weight. Without those frictional forces the can would literally slip through my fingers and fall to the ground.
Since wagons move on stationary sidewalks, a wheel-less wagon is going to have serious problems with friction.
You'll have to push it hard to overcome the opposition of friction in getting the wagon started. And once it is
started, you'll still have to push it every step of the way.
Part 2
Why is sliding a box across the floor usually hardest at the start? The answer to that question is that the surfaces of
the box and floor settle into one another while they're at rest, so they're particularly resistant to the start of
sliding. Friction originates in the microscopic interactions between two surfaces, and those interactions depend on
several things: on the type of surfaces involved, on how hard those surfaces are pressed against one another, and
on whether or not the surfaces are actively sliding across each other.
For the purposes of this story, I'm going to talk about a box on the floor, and the two types of forces to separate—
distinguish between the box and floor. First, is old news: support forces. When I push the box against the floor, and
try to make those two surfaces occupy the same space at the same time, they respond by developing support
forces. And like all support forces, those forces act perpendicular to the surfaces involved. So, the floor’s support
force on the box is straight up. The box's support force on the floor is straight down. So far, so good.
The frictional forces are all horizontal. All like this, these directions. And they basically originate in the tiny
structures that make up the floor's top surface, and the tiny structures that make up the box's bottom surface.
When I put these two objects on top (against one another), picture two mountain ranges: one projecting up from
the floor and the other projecting down from the box. When you set the box on the floor and try to slide the box,
well, the two mountain ranges, because they're, interdigitated like that, they press against each other with local
support forces, and that makes it difficult to start the box sliding across the floor. Once you do get the box moving
across the floor, those mountains are crashing into each other, passing through. One's going through a mountain
pass and the other--there are all kinds of collisions going on. And even some of the mountains are being broken
off. So, this leads to most of the effects that we're familiar with as friction.
Now, there's an entire field known as tribology, which deals with the interactions of two surfaces that are in
relative motion. And friction and the lubrication effects that can come in play if you put liquids in there or even
solids that have structure that allows for sliding in special ways. But, I'm going to leave all that aside and just focus
3|Page
on the simple part of friction. Which derives from these mountain range projections, basically what are known as
contact points, often between surfaces. That gives us enough to really anticipate many of the effects that you
normally see. For example, the nature of the surfaces involved matters. The rougher the surfaces are, in some
respects, the bigger the frictional effects become. Well, if you choose those mountain ranges, so that they're
pointy and tall, they dig deep into each other and they collide particularly hard against one another when you try
to slide one surface across the other. Thus, rough surfaces, sandpaper on sandpaper, experience pretty big
frictional forces. On the other hand, if you smooth off all those mountain ranges and make them casual domes, as
smooth and broad as you possibly can make them (this is at a very tiny microscopic scale), well, they can kind of
slide across one another pretty easily. It turns out that polishing surfaces (smoothing out the hills and valleys to the
extent that you possibly can) leads to relatively lower frictional effects.
You can't get rid of friction entirely because issues arise even at the atomic level of surfaces sliding across another.
But you can get the friction down significantly, and certainly the wear and tear that comes up, by smoothing out
the surface at the most microscopic possible levels. So, choosing your surface affects friction.
The second thing that affects friction is how tightly you press those surfaces together. In other words, the bigger
the support forces acting between these two surfaces, the bigger the frictional forces acting between those two
surfaces. They're not independent, even though they point in very different directions. Remember, support forces
point perpendicular to surfaces. Frictional forces are parallel to surfaces.
Well, to understand this pressure effect, think about the box sitting on the floor. The box bottom is not perfectly
smooth and neither is the floor's top. So when I set the box on the floor, the contact area is not the entire bottom
of the box. No. It's a lot of little points, contact points, where the bottom of the box is truly touching the top of the
floor. And, given the current situation, with the box sitting, pressed down only by its own weight, there might be
(just to pick a number) 1,000 contact points between the bottom of the box and the top of the table.
If I push harder on the box, I lean on it and add my own weight to what is only pushing the box against the table,
the support force is increased. The table is now pushing up extra hard on the box to support not only the box, but
me too, and it's doing that by way of more contact points. It turns out that the number of contact points between
the box and the table is approximately proportional to the support forces these two objects are exerting on one
another--this leads to two remarkable results.

First, because those contact points are themselves responsible for frictional forces, it turns out, that the
frictional forces between floor and box are proportional to this support forces between floor and box. In
other words, the harder you press those two surfaces together, the larger the frictional forces are or can
become. That's an example of what's known as Amonton's First Law of Friction, which observes that for
stiff objects like the box and floor (ones that are not liquid-like), they can't just flow into each other. The
forces of friction are proportional to the support forces, and, for most situations, that's a pretty good
approximation. Press things harder together and they are harder to slide.

The other observation that comes to this contact point idea is that the surface that you see touching the
floor isn't really the surface that is touching the floor. So, the forces of friction between this box and the
floor don't depend on the apparent contact area. It's not the whole box! So, that's actually Amonton's
second law, which says that the apparent contact area between the two objects (those surfaces) doesn't
affect friction.
For this box and floor, as for any pair of surfaces, there is what's known as a coefficient of friction, which relates
the support forces between the two surfaces to the frictional forces that are available when you try to slide those
surfaces across one another. Those coefficients of friction are typically something like .5, maybe as much as 1,
maybe a little above 1 for certain metals on metals. You can look these up. And those values are actually fairly
useful. In this case, the coefficient of friction (I measured it secretly) is about 0.3 or 0.4. Meaning that for every
Newton of support force I exert to press these surfaces together, I get about 0.3 or 0.4 Newtons of frictional force.
That's what's available to me.
4|Page
Since this is the episode on wheels, I hope you won't mind if I jump ahead a little bit to talk about a rather
important coefficient of friction--that between tire rubber and pavement. The value of that coefficient of friction is
typically in the range between about 0.6 and 1, depending on the exact circumstances. What that means is, that
for every 1 Newton of support force, pushing the tires down against the pavement, there is available about 0.6 to 1
Newton of frictional force. Well, when you're sliding a wheel-less wagon across the pavement, you want to keep
friction low, because friction's a nuisance. But when you're rolling the tires of a vehicle across the pavement, you
actually want friction between the two. Well, we'll come to that shortly in other videos, but those frictional forces
between the pavement and your tires are what allow you to speed up and slow down and turn.
You need those horizontal forces to accelerate, and if they're not there, there's no friction. You become inertial.
This is why driving on a snowy day, or sometimes on a rain-slicked highway, is treacherous. You don't have very
much frictional force available to you. And you tend to go straight at a steady pace, even when the road doesn't.
So, friction then is a good thing. And you want a lot of it. That means you want tires that grip the road well. They
have a high coefficient of friction. And also you want them pressed tightly against the road, so that there are large
support forces between the road and the tire. That brings me to a question. The heaviest component of a typical
car is its engine, and that engine is usually in front of the car, above the front wheels. That said, which of the car's
two pairs of wheels, front and back, can obtain the largest frictional forces from the pavement? It’s most
responsible for the car's horizontal accelerations, including starting and stopping. Because the car's front wheels
bear most of the car's weight, the support forces between the front tires and the pavement are very large, and
consequently, the frictional grip that those front wheels have on the pavement is also large. This is good for when
you're stopping. Those front wheels get most of that frictional force that stops the car. But it's also good when
you're starting forward from a red light.
One of the reasons why most modern cars are front wheel drive is because the excellent grip between those front
tires, pressed hard against the pavement, allows them, not only to stop the car quickly, but to pull the car forward
quickly when you start out at a green light. So, putting most of the weight on top of those front wheels means that
those front wheels are responsible for most of the car’s acceleration. So far, we know that frictional forces
between two surfaces depend on the nature of those surfaces, and on how hard they're pressed against each
other. But there's one more crucial issue: whether or not those surfaces are actively sliding across each other.
It turns out there are two main types of friction, distinguished by whether or not there's active relative motion. If
there's no relative motion--if the two surfaces are gripping each other, but they're not sliding across each other,
that's known as static friction. On the other hand, if the surfaces are cruising across each other, that's known as
dynamic or sliding friction. I prefer the latter because it tells you what's happening. You've got sliding going on.
Let's start with static frictional forces--the forces between two surfaces that are not yet moving across each other.
This box is sitting at rest on the floor, so it can experience static friction. I'm going to enhance that static friction by
pressing the box tightly against the floor with some weights, and now I'll show you the frictional force. Not directly,
because I can't get in between the floor and the box. But what I can do, is pull the box to your right with a spring
scale, and we'll see static friction from the floor fight me and try to keep that box from moving. So right now I'm
pulling with, well, 2 Newtons, 3 Newtons, 4 Newtons of force, let me pause here. I'm pulling to your right with 4
Newtons of force. And, the box isn't moving, which means, it's experiencing a net force of zero, no acceleration.
So, a static frictional force from the floor is pushing the box towards your left. Four Newtons, 5 Newtons, 6
Newtons, 7, oops. When I got to 7 Newtons, the box began to move. See right there, seven Newtons and oh, there
it goes. So, what we see then is that, that static friction is adjustable. Right now, it’s exerting zero force on the box.
The box stays at rest because of inertia alone. And I'm not pulling. But as I begin to pull to your right, static friction
begins to pull to your left with just the right amount to prevent the box from beginning to move. It's that maximum
static frictional force of about 7 and-a-half Newtons in this case, that obeys Newton’s first law of friction. It’s
proportional to the support forces between these two surfaces.
5|Page
So the harder I press these two surfaces together, the more peak static frictional force I can obtain. And, I can
show you that by adding more weight (so I'll roughly double the weight inside this box), now instead of reaching a
maximum static frictional force of 7, I ought to get somewhere up towards 14. Here we go. We're at 11, 12, 13, 14,
oh there we go. See, I pretty much doubled the static frictional force.
That brings us to sliding friction. Once static friction gives up, it allows the box to begin sliding across the floor, the
frictional force acting on the box is now the force of sliding friction exerted by the floor on the box. And that sliding
frictional force is different from the static frictional force. Let me show you.
I'm going to start with the box experiencing static friction, as it is right now, and I'm going to pull on it until it
begins to move. And once it moves, watch the force I have to exert on the box to keep the box moving at constant
velocity. I think you'll be surprised at how small that force is. So here we go. I'm going to start the box moving by
pulling harder, harder. Still not moving yet. Ready. We're at 12 Newtons. I'll get to 13, 14. Oh, there it goes, Oh,
look! Much smaller force down there in the 8, 9, 10 range.
What do we get from that? Well, once the box began to slide across the floor, the floor exerted a frictional force
on it, a sliding frictional force that was relatively small. Only 8, 9, maybe 10 Newtons, whereas when I first got the
box started, I had to overcome a static frictional force that could get as large as 14, 15 Newtons.
So, the force of sliding friction, first off, is not adjustable. It's a specific value that depends on essentially nothing
other than how hard these surfaces are pressed each other and their character, but I can't otherwise affect it. In
particular, how fast I pull the box across the floor doesn't matter, and that's an observation known as Coulomb's
Third Law. I don't know why everyone gets credit here, there, and everywhere, but that's Coulomb's Third Law of
Friction, that, once you've got sliding friction going on, the speed, with which the surfaces are sliding over each
other doesn't matter.
Here we go, I'll go fast this time, 10, 9, 10 it doesn't matter, whether I go fast or slow, I'm getting about 8, 9, 10 of
sliding friction. See there's slow, it doesn't really matter. Anyway, the force of static friction's adjustable up to a
maximum. And that maximum is quite large. The force of sliding friction is not adjustable, it's a specific value. It
always is in the direction that opposes relative motion to surfaces and it's less general than the maximum of static
friction. In other words, static friction is a stronger force. Better grip than sliding friction. And you can understand
this fairly simply in terms of the contact point, and, sort of, the interdigitation of the peaks that are acting to
support the two surfaces against each other.
When you let the box sit, and static friction can kick in, those mountain peaks up and mountain peaks down dig
into each other; grip tightly. And they're hard to get to let go. So static friction is strong up to a point, when,
eventually, it does give up. Once it gives up, and sliding friction becomes the frictional force; it's relatively weak.
Because the peaks and mountain ranges basically are moving past each other. They're already going, they don't
have time or inclination to dig into each other, settle in and grip tightly.
So in general, static friction is stronger than sliding friction. We're now ready for the question I asked you to think
about in the introduction to this episode. Will your bicycle or car accelerate forward fastest, when you twist the
wheels so hard that they begin to skid, or, if you twist them somewhat less hard so they barely avoid skidding? If
you can avoid skidding the wheels, the forward frictional force that the pavement will exert on the tires will be a
static frictional force, and that, in general, will be stronger at its peak, than any sliding frictional force you can get
from those wheels. If you do skid the wheels, well, then the frictional force from the pavement will be a sliding
frictional force, and it won't be as strong in the forward direction, and you won't accelerate as quickly. So the
strength of the frictional force is dependent on the natures of the two surfaces, on how hard they're pressed
together, and on whether or not they are actively sliding across one another. That is, whether it’s static friction or
sliding friction. But there is another important distinction between static and sliding friction. Sliding friction wastes
energy. And that's the topic for the next video.
6|Page
Part 3
How is energy wasted as a box skids to a stop? The answer to that question is that sliding friction transforms the
box's kinetic energy into thermal energy. But what is thermal energy? What sort of process carries out that
transformation? Explaining those issues is the purpose of this video. When I slide a box across the floor, something
strange happens to its energy. I do work on the box, pushing it, and it moves in the direction of my push, so I'm
transferring energy to it. It leaves my hand with that energy mostly in kinetic form, the energy of motion. But then,
it encounters the floor.
Moments after hitting the floor and sliding across it, the box is motionless. What happened to its energy? As the
first step in solving that puzzle, I'll ask you a question. When a box slides to a stop on a motionless floor, which
object does work on the other? The floor does negative work on the box, and that's it. The floor pushes the box in
the direction opposite the box's velocity. And so the box, in this case, is moving to your left as the floor is pushing
the box to your right, so the floor is pushing in the direction opposite the box's motion, so the floor does negative
work on the box. At the same time, the box is pushing on the floor but the floor doesn't move.
So, the box does no work, zero work on the floor. All that's happening then is the floor doing negative work on the
box taking energy out of the box and destroying it, getting rid of it? Well, no. The energy is still conserved and we
have to look for where that energy goes. Sliding friction can't violate the conservation of energy. The box's energy
has to remain somewhere in the universe even after it slides to a stop. What happens to that energy is that it
grounds up into tiny portions that are dispersed randomly among the particles that make up the top of the floor
and the bottom of the box. Energy is still there. It's just distributed in such tiny pieces that you don't notice it
normally, except by way of the temperature of those two objects.
To help you visualize this idea of grinding ordinary energy up into tiny random fragments, here's a series of simple
demonstrations. First, I'll roll a metal ball into a handful of other identical balls. I'll do work on the first ball when I
push it forward as it moves forward, so it will have energy in the form of kinetic energy as it rolls across the table.
When it strikes the other balls, however, its energy will be dispersed among those balls, so here we go.
So, the energy is all still there. And these guys don't roll perfectly, so they will eventually stop. But my energy put
into one ball was then dispersed among many balls. Here's the same experiment but with smaller balls and many
more of them. Let me get this guy going, ready, off it goes. The energy is still there, it's just dispersed among lots of
balls. And now, I have even tinier balls. There are hundreds of them and they're going to share the energy that I
invest in this first ball when I get it moving initially.
So, here we go. I'll start the ball rolling. It dispersed its energy among all those balls. Well, the energy is still there.
They're losing their roll after a while because things aren't perfect here. But you get the idea that, that you can
start with energy that's equivalent to work. I did work on that one ball. The ball's got that energy in the form of
kinetic energy; it can do things. But once it crashes into this myriad collection of balls, the energy is all dispersed-spread out among lots of little balls, each doing its own thing. I could keep going. I could go down to sand, I could
go down to dust, and finally, I could go down to the atoms and molecules themselves that make up materials. And
once you've dispersed the energy into that vast collection of particles, each one doing its own thing with its own
tiny dose of energy, you can't do very much with that energy. That energy now is so disordered, it's so randomized,
that you can't get it all organized again to do useful work--not directly.
This glass dish contains a very orderly arrangement of beads. All the purple beads are on one side, all the white
beads are on the other. And this kind of order doesn't happen by chance. Think of your sock drawer. If you only
have two colors of socks, purple and white, and you just dump them at random into your drawer, you don't end up
like this. It's all mixed up. You have to sort them to end up like this.
So, this arrangement is not a chance arrangement. And it's not forbidden, strictly speaking. The, the laws of
probability make it extremely unlikely. It could, in principle, happen. But in practice, it's so unlikely you never ever
have it happen by chance. I sorted these before filming this and I don't want to mix them up very often because
I'm going to have to sort them again. I'm not going to be able to sort them just by chance. I'll show you.
7|Page
Ready? Here we go, I'm going to mix them. I'm not looking. Yay, and viola, all scrambled. Can I sort them by stirring
again? They're still messed up. It's hopeless. Once you've let the randomness in, and you've evolved to a more
disorderly arrangement, there's no undoing it. The laws of probability are against you. If all this talk about
probability brings to mind gambling, you're thinking along the right path. There's a reason why you’re not likely to
win the lottery even once, and why no one ever wins the lottery a thousand times in a row, although it’s
technically possible. It's so unbelievably unlikely that it simply never happens. This glass dish now contains about
50 dice and they're all ones.
Do you think that happened by chance? Let's see if I give this a shake, what happens to this orderly arrangement of
dice? Here we go! Oh, look, it's not all ones anymore. What do you think? What about if I show you another shake
and see what you think of this. All ones. Wow, I'm pretty tricky! That outcome is so fantastically unlikely that you
know I reversed the video, I cheated. Once I disordered the dice, there was no simple way back. In all of these
demonstrations, the Laws of Motion, Newton's Laws, have been silent. Those laws deal only with things like forces
and accelerations and they have nothing to say about the return of order from disorder. The demonstrations,
therefore, have been all about probability instead.
This brings me to a question about a familiar nursery rhyme: Humpty Dumpty. Spoiler alert: Humpty Dumpty is an
egg. Humpty Dumpty has a great fall and he breaks. And according to the rhyme, all the king's horses and all the
king's men couldn't put Humpty together again. So, the question is this, if dropping Humpty once broke him, why
won't dropping him again reassemble him? Dropping Humpty Dumpty a second time wouldn't reassemble him
because it's simply too unlikely. The Laws of Motion will allow for that reassembly of all the yolk and all the white
and all the shell pieces, all move just right, following the Laws of Motion and the forces and accelerations and all
that, Humpty will reassemble. The odds of that happening are just fantastically small. It never ever, ever happens.
So, poor Humpty is out of commission here, not because the Laws of Motion forbid it, but because the Laws of
Probability do so.
So, sliding friction takes the energy of one or 2 large objects, say, the box and the floor. And grinds up that energy
into tiny random portions that are then dispersed among the particles that make up those two objects. Ordered
energy, that is, energy that could easily do work has become disordered energy, energy that can't do work very
easily. It's a one-way street, and there's no simple route back. How do we know that this disordered energy even
exists though, and what role does it play in our lives? It's known as thermal energy, the disordered energy
associated with temperature. Sliding friction increases the temperature of the surfaces as they slide across one
another.
You could observe this effect fairly simply just by rubbing your hands together. If you press your hands tightly
together and slide them across one another, you'll feel your skin getting warmer. Your muscles are doing work on
your hands. Pushing them in the direction that they move and sliding friction between your skin is grinding that
work up into tiny pieces, thermal energy, that's still in your skin, and you feel warmer. Now, some people may be
able to start a fire simply by rubbing two sticks together. That is, using the sliding friction between those sticks to
turn enough ordered energy into thermal energy to heat the surfaces of the sticks until they ignite. I'm not one of
those people; I can't pull off that trick. However, with some help, I can make wood rubbing against wood start a
fire.
And what I've got now is a jig that holds a round wooden peg, a piece of dowel about that long and about half an
inch in diameter. And it's pressed between two pieces of wood so it sits in sockets in those two pieces of wood.
And I'm going to spin that peg using a bow, an archery bow, and I've wrapped the bowstring once around the peg
so that it grabs the peg using static friction, actually. And as I push the bow toward you and away from you, the
peg will spin and its surface will rub against the wood at the other ends of the socket.
So, here we go. I'm going to begin moving the peg using the bow. I hope you can see all the smoke. I can get it to
the point where it will ignite, probably with a little help from tinder, something that really burns easily. But the
basic idea is here. I got that wood so hot that it's smoking vigorously and it is therefore possible to start a fire by
8|Page
rubbing wood against wood and using sliding friction to turn ordered energy into thermal energy. We've seen that
sliding friction grinds up energy. It turns useful ordered energy than much less useful thermal energy. But sliding
friction also grinds up the surfaces themselves. It wears them out. That wear isn't very noticeable when you simply
rub your hands against one another but you do notice it in the sole of your shoes after months of scuffing them on
the pavement. And those soles wear the surfaces they scuff against.
Take a look at an old stone staircase--one that has handled many feet for many years--and you'll see wear. Sliding
friction can even wear out steel. This is a piece of tool steel, a metal so hard that it can cut nearly any other metal.
The machine has shaped the tool steel by wearing it away. They use a grinder too and sliding friction to take away
parts of the material and give it shape. Now, this grinder will spin the wheels very fast so that their surfaces will
move past and slide against the tool steel at hundreds of miles an hour. And they'll wear away that metal rather
quickly. Here we go. It takes a few seconds for the grinder to get up to speed. I've started it spinning. There it is, up
to speed. And now, I'll take the piece of tool steel, and put it against the, the fast moving surface. It's cutting away
the metal and shooting sparks. So, as you can see, you can shape the metal using sliding friction. This is also now
getting very hot, so that's why I stopped. I normally would cool it off periodically in water, but I did a little bit of
shaping, and cut away a little metal using sliding friction.
Sliding friction wastes energy and wears out surfaces, but what about static friction? In principle, static friction
wastes no energy and causes no wear. When the surfaces don't slide across one another, static friction instead
transfers energy perfectly from one surface to the other. For example, if I push on this box, and try to get it sliding,
but don't, so it doesn't actually slide at all, there's no energy transfer at all between the box and the floor. In fact,
the two objects do no work on one another either positive or negative because neither one moves a distance.
So, there were forces between the box and the floor, but that's it. No distance traveled and therefore, no work
done, no energy wasted. Another example is when I lift a beverage can in the usual manner. I just used a static
frictional force to lift the can. You know it's a static frictional force because it's an upward force. I'm supporting the
can's weight as it moves upward, and for our force to be upward--exerted by my finger on the can, that has to be a
frictional force. It's parallel to the surface of the can. If there were no friction, the can would slip right through my
fingers to the ground. So, I exerted an upward frictional force, a static frictional force on the can, as the can moved
upward. I did work on the can. At the same time, the can did negative work on me. It pushed my fingers downward
as my fingers moved upward. That's negative work. And the amount of negative work the can did on me is exactly
equal to the amount of positive work I did on it.
Overall, static friction perfectly moved energy from me to the can and didn't waste any of it. On the way down,
static friction moves energy from the can back to me, again, no waste. So, there's a pretty clear distinction
between the world of static friction and the world of sliding friction. Static friction wastes no energy and causes no
wear. Sliding friction, on the other hand, does waste energy and does cause wear. Well, this episode is about
wheels. And the purpose of wheels is to avoid wasting energy and wearing out surfaces. So, the problem that
wheels solve is not static friction; the problem is sliding friction. And wheels, it turns out, get rid of sliding friction
but keep all the good features of static friction. And that's what we'll see in the next video.
Part 4
How do wheels help a wagon coast? The answer to that question is: the wheels eliminate sliding friction between
the wagon and the ground. I worded that answer carefully because wheels eliminate only sliding friction. And even
then, they only eliminate sliding friction between the wagon and the ground. Those details are important, and my
goal for this video is to explain why. When you’re trying to move a wagon down the sidewalk you want it to be able
to coast indefinitely. In other words, you want to avoid wasting any energy, and you want to avoid wearing out the
wagon on the sidewalk. So those two problems are associated only with sliding friction--that's what you want to
avoid--sliding friction.
Static friction isn't necessarily a problem. So long as it doesn't prevent the wagon from moving on the sidewalk.
One solution to this this problem, that is one way to get rid of sliding friction between the wagon and the sidewalk
9|Page
allowing the wagon to coast and not waste any energy or wearing anything out, is to use rollers. So let's start with
that approach. So, before we put in wheels, let's put in rollers. If I set the wagon not directly on the sidewalk, but
on these metal rods, watch what happens. All of a sudden, it can coast, perfectly. Wow. I haven't eliminated
friction altogether, but I have eliminated sliding friction.
Those rollers are doing what I call touch and release in terms of their contact to both the sidewalk and the wagon.
To show you, let me get a larger roller. As I roll this beverage can along the sidewalk, it's landing on the sidewalk. It
drops itself onto the sidewalk and lifts off. Touch and release. At no time does it ever skid or slide across the
surface. So there's no sliding friction there. But there is static friction. So, at any given moment, if I, if I grab the can
and try to scoot it along the surface, I'm now being opposed by the forces of static friction between the sidewalk
and the can. They're fighting me. And up to a certain point, they will continue to do that until finally I overwhelm
them and cause the can to skid or slide. But, as long as those forces are small, static friction remains, and the can
rolls. And it rolls along that surface without wasting any energy and without wearing out the can surface or the
sidewalk surface. Similarly, the same thing can go on for the wagon. I can roll the wagon on that beverage can and
the can is touching and releasing the bottom of the wagon. It’s only static friction.
Well, the can's too big for this activity. And the rollers, as I've got them, are better. But they're now doing touch
and release to both the sidewalk and to the bottom of the wagon. And they're allowing the wagon to move
perfectly. That is, to coast perfectly because there's no energy being wasted. The rollers are experiencing static
friction and nothing else. Static friction is actually a good thing for rollers. Without it, there will be no tendency for
the rollers to move with the wagon. For example, I have the wagon here at rest on rollers that are at rest. And if I
move the wagon abruptly to your right, and there's no static friction, the wagon will just leave the rollers behind.
They're inertial, after all, so they don't accelerate with the wagon.
With static friction, which is specifically between the bottom of the wagon and the top of the rollers, the rollers do
undergo an acceleration to the right as the wagon undergoes an acceleration to the right. And they move to some
extent with the wagon. I say to some extent, because the rollers don't accelerate as fast as the wagon does. They
actually travel at half the speed of the wagon. And that's sort of a geometry thought problem. That those rollers
are interacting, not just with the moving wagon bottom, but they're also interacting with the motionless sidewalk
top.
And they average the two velocities: the velocity of the moving wagon and the velocity of the motionless sidewalk.
So they travel not as fast as the wagon; not as slow as the sidewalk. They travel halfway in between. And that's a
problem for rollers. They don't keep up with the wagon, they travel at half the wagon’s speed and roll out from
behind the wagon. If you want to use rollers with the wagon, you can do it, and you will waste essentially zero
energy. Rollers are perfect.
Within the limits of the imperfect world, rollers experience no sliding friction, waste no energy, cost no wear.
They're great, except they shoot out the back all the time. So, you need three rollers at a minimum. And you have
to keep replacing rollers. Every time one roller shoots out the back, you have another one to put in front. And you
can keep recycling them over and over. As you roll it along, you have to just keep on moving the roller from the
back of the wagon to the front of the wagon, back of the wagon to the front of the wagon, and so on.
Well, this is kind of a nuisance even for a wagon. And it's certainly a problem in an automobile traveling 60 miles
an hour down the highway. If you want to be cycling rollers from the back of your car to the front of your car at 60
miles an hour on the highway, more power to you. Not a great solution. A better solution is to go to wheels. And
so, I'm going to get rid of the rollers and the wagon that has no wheels, and switch to a wagon with wheels. I have
the luxury of two wagons. Woo hoo. And this wagon, now, because it's on wheels, takes its rolling surfaces with it.
The bottoms of those wheels are still doing the touch and release trick I mentioned earlier. They land and leave,
touch and release. And they experience, essentially, no sliding friction--just static friction. That's great, there's no
rubbing, no wasted energy at the bottom surfaces of the wheels. And there's no wear in principle, at the bottom of
the surface of the wheels and the top of the pavement, the top of that sidewalk.
10 | P a g e
This is a great solution. Is there any problem at all? Yes there's still sliding friction around. Where? The sliding
friction is hiding from view. It's not between the wheels and the pavement or the sidewalk. It's in what's known as
the hub of the wheel. Where the wheel attaches to the wagon is a portion of the wheel known as the hub, and it's
suspended in an axle. So that the axle passes through the hub, and in that little area where the axle sits and the
hub grabs it, they're rubbing. There is sliding going on as the wheel turns. If the wheel still experiences sliding
friction in its hub and axle, what's the point of wheels? It turns out that the consequences of that sliding friction
between the hub and the axle are much less than the consequences of sliding friction between either the wheel
and the pavement, or the bottom of the wagon and the pavement.
That's a matter of work and energy. The diameter of the axle is very small, and so its circumference is small, which
means that every full rotation of the wheel only slides the hub across the axle a short distance. It's sliding against
the force of sliding friction. So, this is wasted energy. But since the distance is small, the work done against sliding
friction is small. So, yes, a rotating wheel on a fixed axle does waste energy because of sliding friction, but not very
much. And the narrower that axle is, the smaller the hub, the less energy is wasted. That's good as long as the axle
can tolerate, use a narrow enough axle and still tolerate both the wear and the weight of the wagon. And there's
some compromise made then, between making the axle so skinny that it wastes almost no energy, but it breaks or
wears out and making it so fat that it never wears out but it, but it causes a lot of energy waste.
Well, another helping thing here is to add axle grease between the hub and the axle. It's called axle grease for a
reason. It's a lubricant that sits between the motionless axle and the turning hub, and tries to reduce sliding
friction. And the wear that occurs and the energy waste that occurs.
It's time for a question about wheels. But I'm going to ask that question in a context that is very different from
wagons and bicycles and automobiles. After all, wheels and wheel-like components are common in the objects
around us, including objects that don't use their wheels to travel from place to place. The context for my question
is mechanical time-keepers, such as this antique carriage clock, and this modern mechanical wristwatch.
Mechanical clocks and wristwatches contain many wheel-like components. And those wheels, I'll just call them
wheels, are suspended in tiny polished axles that rotate in tiny polished cups that are made from jewels, like ruby
and sapphire. We can actually see those in this watch. We'll take a close look at how this watch is operating and
you'll be able to see its tiny little rubies. So my question then is this, why does that suspension technique, namely
tiny polished axles rotating in tiny polished jewel cups, allow the rotating components in one of these mechanical
time keepers to waste almost no energy and work consistently for years? As the axle turns in its tiny jeweled cup, it
does slide across the cup's surface, and therefore, does experience sliding friction. However, the distance traveled
by that tiny narrow little axle as the wheel-like component rotates is very small, and therefore, the work done
against the force of sliding friction is minuscule.
Remember, work is the product of force times the distance traveled in the direction of the force. And although the
sliding frictional force is there, the distance traveled by the axle against that sliding frictional force is very, very
small. So, the wheel-like component wastes very little energy. Moreover, the axle, which is typically a polished
piece of metal, and the cup, which is a polished jewel, has that pairing, has a very small coefficient of friction.
Unlike rubber on pavement, for example, metal on ruby or sapphire has a small coefficient of friction.
Finally, the two polished surfaces, the jewel and this polished piece of metal, they're so smooth that they don't
have serious collision problems as they slide across each other. And they experience almost zero wear. Therefore,
this wheel-like component can go round and round and round for years, decades, or even centuries, with almost
zero wear. And that's why one of these clocks or watches can keep on ticking for a very long time.
But there's actually a better solution to this friction problem in the hub axle system. The solution is to insert a
bearing between the axle and the hub. And that bearing is our old friend, the roller. Instead of loose rollers, where
have I put them? The loose rollers, we put the rollers in a loop and mount them to form what's known as a roller
bearing. It consists of a bunch of rollers very loosely held in a frame, known as a cage, and we insert this. We put it
on the axle like that and into the hub, which I don't have here, but the hub we grab it on the outside. And it's the
11 | P a g e
rollers again. They do touch and release, as the wheel rolls turns around the fixed axle. Those rollers do touch and
release both on the axle and on the inside of the wheel's hub and there's no sliding at all, and therefore, no energy
wasted at all.
What's more, the rollers travel all the way around the axle and they recycle automatically. So, roller bearings and
their cousin ball bearings, where the roller is replaced by just a round sphere of metal or something other, some
other hard substance. They cycle perfectly, they roll pure static friction, and they waste no energy. And so our
world, basically, runs on bearings like this. Things that turn typically have these inserted to get rid of even the small
sliding friction that would otherwise appear between an axle and a hub.
Here's another roller bearing with a built-in hub. There are the rollers sitting in the hub, and if you insert an axle in
here and turn the axle, the rollers go round and round, only static friction, no sliding. This is a ball bearing. It has a
hub and it has a cylinder to hold the axle in the middle. And as you turn the axle, the balls roll. And I know it's a ball
bearing because this guy can be rotated, so that you can actually see the balls. There they are. Those are the balls
that roll between the outer cylinder and the inner cylinder, and ensure that there is no sliding friction, just static
friction as the balls touch and release. Alas, my little wagon doesn't have any fancy bearings between its wheel
hubs and its axles. And that's why, as I roll the wagon back and forth, it has a lot of squeaking. That's sliding friction
between the wheels and the axles and other components of the engine. And I could probably get rid of that with a
little bit of oil or grease. Another day.
Before I leave this wagon though, I want to talk a little bit about the type of wheel it uses. It uses what's known as
a free wheel: a wheel that turns essentially freely and that the wagon doesn't try to control. The wagon doesn't
exert torques on the wheel deliberately to make the wheel spin. So, what makes the wheel spin? It turns out that
the source of the torque that causes the wheels to begin rotating, to undergo angular acceleration, is static friction
between the bottom of the wheels and the top of the sidewalk.
When the wagon is just motionless on the sidewalk, its wheels are motionless. Both they're not translating and
they're not rotating. Everything is totally at rest. But if I pull the wagon to your right, the wheels begin to rotate.
And they rotate because static friction, a static friction force from the pavement on the wheel pushes the bottom
of the wheel to your left. That force is there because the static friction is trying to prevent the wheel from skidding
on the sidewalk. Let me go back here. If the wheel skids on the sidewalk, like, I'll hold it and drag it. Well, static
friction doesn't like this, actually becomes sliding friction. So, static friction is trying to prevent that sliding process.
And it does that by trying to keep the bottom of the wheel at the same velocity as the top of the sidewalk, namely
zero. So, as the wagon accelerates to your right, the, the sidewalk exerts a leftward static frictional force on the
bottom of the wheel to keep the bottom of the wheel motionless. And that force, exerted as it, at a lever arm from
the center of rotation of the wheel, namely the middle of the axle, produces a torque on the wheel and causes the
wheel to undergo angular acceleration.
So, it's a little bit of a complicated story. But as I pull the wagon to the right and cause the wagon to undergo
normal acceleration, static friction from the pavement, the sidewalk, exerts a leftward frictional force of static
friction on the bottom of the wheel that produces a torque on the wheel. That causes the wheel to undergo
angular acceleration, and that angular acceleration is toward me, away from you. And the wheel begins to spin.
Free wheels turn because of static friction, but not all wheels are free wheels. The rear wheel of your bicycle turns
because you're pedaling the bicycle. And it's called a powered wheel because you're providing it with power.
Powered wheels are the focus of the next video.
Part 5
How do powered wheels propel a bicycle or car forward? The answer to that question is that the ground exerts a
forward static frictional force on each powered wheel and thereby pushes the entire bicycle or car forward. In the
previous video, however, I pointed out that the ground exerts static frictional forces on free wheels as well. So,
what could be different between free wheels and powered wheels?
12 | P a g e
To explain that, let me start by re-examining free wheels. When you pull a wagon forward so that it accelerates
forward, the bottoms of its wheels are threatening to slide forward relative to the ground. And static friction acts
to prevent that sliding. It pushes the bottoms of the wheels backward, and that backwards force of static friction,
the bottoms of the wheels, has two effects. First, it produces torques on the wheels that cause those wheels to
begin their spin, to roll. And when I pull the wagon forward and its wheels roll, that's because of static friction with
the ground. But second, those backward frictional forces on the bottoms of the wheels affect the entire wagon.
And, you have to pull a little extra hard, and do a little extra work to get the wagon up to speed because its
spinning wheels are carrying extra kinetic energy. Something we'll explain in the next video.
The key point here is that the ground pushes free wheels backward as their vehicle accelerates forward. In contrast
the ground pushes power wheels forward as their vehicle accelerates forward. To explain that observation I need a
powered wheel. Wagons don't normally have powered wheels so I have to add one and here it is. It's a cordless
electric drill with a big rubber stopper. And when I turn on the drill it twists the rubber stopper and the stopper
begins to spin. Well, in the language of physics, the drill exerts a torque on the rubber stopper and causes the
rubber stopper to undergo angular acceleration. If I press this stopper against the sidewalk, the stopper becomes a
powered wheel and it propels the vehicle attached to it forward. At present, the vehicle it's going to power and
propel is me. And when I turn on the drill, it pulls me forward.
Now where does this come from? It comes from the fact that if I were to spin the wheel above the sidewalk here.
The bottom of the wheel will move in the backward direction relative to the sidewalk. And once I touch the two
surfaces together and static friction appears, it's going to fight that relative motion. It does not want the bottom of
the wheel moving backward. And therefore it will push the bottom of that wheel forward to oppose sliding and try
to keep those two surfaces at the same velocity. That forward force on the bottom of the powered wheel has two
effects. Does that sound familiar?


One effect of that forward static frictional force on the bottom of the wheel is to produce a second torque
on the wheel that opposes the drill torque. It acts to slow the angular acceleration of that wheel. It fights
the drill. That's one effect of that forward frictional force on the bottom of the wheel.
The second effect is a forward force on the entire vehicle. It causes the entire vehicle to accelerate
forward, namely me. Whoa! Off we go.
So, a powered wheel obtains a forward static frictional force from the sidewalk that propels the vehicle forward.
Well, I don't make a very good vehicle. So, what could we do better? Well, I have a big wagon. I have a powered
wheel. Let's go on a road trip. Here we go, powered wheel on a wagon. Full speed ahead, yeah. That worked out
pretty well, and I'm still in one piece.
It's time for a question related to powered wheels. At a track and field competition the runners in a 100 meter
sprint start that race with their feet pressed against the nearly vertical surfaces of starting blocks. And they're
wearing spikes that project into the track as they run. Why are the starting blocks and spikes important to the
runners in a 100-meter sprint?
Speaker 1: To win a sprint like this, the runner wants to accelerate forward as rapidly as possible, and may well be
accelerating even as the runner crosses the finish line. At the start of the race, the runner has to be motionless
before the gun goes off, so the runner has... feet pressed against these nearly vertical surfaces of the starting
blocks. When the gun goes off, the runner pushes back hard on the starting blocks with support forces. Your
surfaces, these two surfaces, are attempting to occupy the same space at the same time. So as the runner's foot
pushes back on the starting blocks hard, the starting blocks respond by pushing forward on the runner's feet hard.
And that helps the runner get started from the moment the gun goes off. Once the runner loses contact with the
starting blocks, however, all they have to push against is the horizontal track surface. So to get a forward force out
of a horizontal surface, you need friction, and ideally, static friction.
So, having spikes on your shoes as a runner allows you to get better traction. That’s a higher maximum static
frictional force out of the track. So with those spikes digging into the track, you can get forward forces that are
13 | P a g e
enormous on a human scale. And accelerate forward at a dramatic rate. And so the best sprinters obtain very large
support forces out of the starting blocks. And then maintain their acceleration by getting very large forward
frictional forces of static friction toward the finish line. And they may well still be picking up speed in the forward
direction as they cross the finish line. I've talked a lot about powered wheels, but I've never actually defined the
term "power."
People often use the words power and energy interchangeably. But they're actually different, though related,
physical quantities. Energy is the conserved quantity of doing. And power is the rate at which energy, that
conserved quantity, is transferred from one object to another. In more official language, energy is the capacity to
do work and power is the rate at which that work is being done.
To shed more light on this relationship between energy and power, let's revisit the energy/money analogy. Just as
energy is the conserved quantity of doing, money is the conserved quantity of spending. If you have energy, you
can do work. If you have money, you can spend. Spending transfers money. Just as doing work transfers energy.
When you buy something, you spend a specific amount of money. Similarly, when you complete some mechanical
task, you do a specific amount of work.
Money and spending are measured in your local currency, which might be dollars, Euros, or something else. Energy
and work are measured in the SI unit of energy: the joule. But there are other units. What about when you rent
something? You're not buying it outright all at once. You're paying for it steadily over time. Rather than a one-time
transfer of money, there is a sustained flow of money. A dollar, a dollar, a dollar, and like rent salaries wages
subscriptions are also these sustained flows of money. And you usually measure them in your local currency
divided by a unit of time, for example, dollars per hour, or euros per year, or bots per day, or rupees per month.
Analogously, when you're peddling your bicycle, you're providing a sustained flow of energy to the bicycle's
powered wheel. The rate at which energy is flowing, that is, the work you do per unit of time, is the power you're
providing. A typical bicyclist transfers an energy of 100 Joules to the powered wheel in a time of one second
corresponding to a power of 100 joules per second. The SI unit of power is the joule per second, which is so
important that it has its own name. It's called the Watt. A typical bicyclist provides a power of 100 watts to the
bicycle’s powered wheel or 100 jewels per second. There are other units of power but they're all related to watts.
For example one horsepower is equal to about 750 watts. A serious bicyclist can provide about 750 watts or 1
horsepower to the power wheel of a bicycle--at least for a short period of time.
To help you distinguish between energy and power and jewels and watts, let me ask you a question. If your toaster
is labeled as using 1,000 watts, how much energy does that toaster consume in 1 hour? A toaster that consumes
power steadily at a rate of 1,000 watts, that is, 1,000 joules per second will consume 1,000 joules in one second,
2,000 joules in two seconds, 3,000 joules in three seconds--and in an hour (which corresponds to 3,600 seconds)
that toaster will consume 3.6 million joules of energy coming in the form of electricity. So, 3,000, 3.6 million joules
is kind of an awkward number to talk about, so it has another name, it's called a kilowatt hour. So when you see
written on a power bill, electric power bill for example, that you have consumed energy in total of one kilowatt
hour. That's 3.6 million joules of energy--the energy that would be consumed by a 1,000 watt device like a toaster,
in the course of a single hour.
Powered wheels are rotating objects. And the work that's done on them is done in the context of rotation. That's
an interesting complication: rotary work. We've seen that you can do work on a translating object by pushing it
and having it move in the direction of your push. You exert a force on it, and it moves a distance in the direction of
that force. But what about a rotating object? It turns out, that you do work on a rotating object by twisting it, and
having it turn in the direction of your twist. You exert torque on it, that's twist, and it rotates through an angle in
the direction of that torque. For example, when I spin this bicycle wheel, I do work on it. I exerted torque on it, I'm
going to twist it, and it rotates in an angle in the direction of my torque. My torque was toward you and it rotated
toward you. I'm transferring energy to it and you can see that energy because it's moving; it's got kinetic energy.
Getting the units right when doing work in a rotational context is a bit tricky. You have to be careful to choose the
correct units when measuring angles. Those angles should be measured in radians, the natural unit of angle.
14 | P a g e
As a reminder, one full rotation like this is two pi radians, where pi (π) is the mathematical constant. It's
approximately equal to 3.14159—so two pi radians is about six and a quarter. That means if I rotate this wheel all
the way around, that was about six and a quarter radians. Well, if you choose that unit to measure your angles in
and you use the SI unit for the torques you exert, you end up with the SI units of energy when you figure out how
much work you've done. So, for example, if I exert a torque of one SI unit, which is one Newton meter -- that's the
unit of torque -- on this wheel as it rotates through an angle of one radian in the direction of my torque. I'm going
to rotate it like that towards you. And it's going to turn toward you.
So I'm going to follow all the rules. So here you go, about. I'm going to exert a torque of about one Newton meter.
And I'm going to do it as the wheel rotates through one radian. So I've got to go from about here to about there,
that's about a radian. Here we go. Ready, get set, okay. I did about one Newton meter times one radian, one joule
of work on the wheel. So I transferred about one joule of energy to the wheel. And that was the goal here. For a
powered wheel, like my drill-powered rubber stopper here, the rotary work is done at a steady rate. So the drill is
providing rotary power to the wheel.
Before I show you how to calculate power in a rotating system, let me show you how to calculate power in a
translating system, this wagon. If I push the wagon, and it moves steadily in the direction of my push, I'm providing
it with power. And the amount of power I'm providing it with is the work I do on it per second. In this case that’s
the force I exert on the wagon times the distance it travels in the direction of that force per second. Well, the
distance it travels in the direction of my force per second is its velocity. At least the part of the velocity that is in
the direction of my force. So, the amount of power I'm providing this translating object, the wagon, is simply the
force I exert on it times its velocity, where we're only considering the part of velocity that's in the direction of my
force.
That's the power in a translating object. Now, we can return to the power in a rotating object. That rotary power is
the rotary work the drill does on the wheel, per second, which is the torque that the rotary drill exerts on the
wheel times the angle through which the wheel rotates per second. That angle through which it rotates per second
- that part, is just the wheel's angular velocity. So in short, the rotary power the drill provides to its wheel is the
torque it exerts on the wheel times the wheel's angular velocity, the angle through which it rotates each second
with all of the directions done properly.
If some of these details about rotary work are too complicated to follow, don't worry about them. The take-away
message is that if you twist something and it turns in the direction of your twist, you're doing work on it--and
transferring energy to it. And if you twist it and it keeps moving. You twist you know, twist and it steadies, rrrrrrrr,
and then you're providing it with rotary power. When you do rotary work on a wheel, you give it energy. We'll look
at what becomes that energy in the next video.
Part 6
How is energy present in a wheel? The answer to that question is that the wheel has kinetic energy in both its
translational and rotational motions. It can have other forms of energy. Such as gravitational potential energy if it's
high in the air. Or nuclear energy if it’s made out of uranium, but the energy I have in mind here is kinetic energy,
energy of motion. And, as I'm about to explain, a spinning wheel on a vehicle carries an especially large amount of
kinetic energy. Let's start by looking at the kinetic energy the wheel carries in its translational motion. That is, the
kinetic energy that's associated with the wheel's velocity. We can determine that kinetic energy by calculating the
amount of work we would have to do on the wheel to bring it from rest to its current velocity.
So, we'll start with the wheel at rest. We'll push on it as it begins to pick up speed and move in our direction, and
we'll keep pushing until it's moving at the final velocity. If we know how much work we did, we know how much
energy we've invested in that wheel. And therefore, we know its kinetic energy. That's the program here. So,
rather than doing that calculation completely, which is more complicated than is appropriate for this course, I'm
going to explain the most important issues. To make these observations, I need a wheel that can translate without
15 | P a g e
rotating and without friction. So I don't want to have that wheel…, yeah it's translating, but it's also rotating, that
just complicates the story. So I can't make this wheel translate without making it rotate. I have friction otherwise.
So what I'm going to use is this wheel which is actually a toy puck that rides on a little cushion of air. It's a
miniature hovercraft. The cushion of air is created by a battery-powered fan so when I turn it on, it rides essentially
without any important friction. And if I start it from rest and do work on it like this, it carries that work with it as
kinetic energy. Nonetheless, it's a wheel. Off it goes, right? I don't have to roll it through to get the friction less
effect. So, first observation to make using this interesting little wheel is that the direction of the final velocity I end
up with doesn't matter. It takes just as much work to go from rest to moving to your right at a certain speed as it
does to go from rest to moving to your left at a certain speed or toward you at a certain speed.
The kinetic energy of this wheel, then, doesn't depend on the direction of its velocity. It depends only on the
amount of its velocity, which is speed. So it's important that kinetic energy doesn't depend on the direction of
motion. I've called energy the conserve quantity of doing because it's about doing work, not about moving. In the
episode on bumper cars, we will encounter the conserved quantity of moving--a physical quantity officially known
as momentum, since momentum is all about moving--going somewhere in a particular direction. It does depend
on a direction. But energy has no direction, and no dependence on the direction of motion.

So far, we know that the kinetic energy of a wheel depends on its speed.

Second important observation is the kinetic energy of a wheel is proportional to its mass. How can I show
you that? Well, I have one wheel and a second wheel. Isn't this great? These are two identical wheels. And
if it takes one unit of work to get that wheel moving to the right at certain speed, how much work do you
think to get two wheels move from rest to moving at that speed? It takes twice as much work. Each wheel
takes one unit or work. Boof, off they go. So, without further ado it's pretty clear that kinetic energy, the
kinetic energy of a wheel or any other object is proportional to its mass.

My third important observation is that the work required to bring a motionless wheel up to its final speed
is proportional to that speed squared. That's a rather startling observation. It means that if I double the
final speed of the wheel, say from this to this, twice the speed, one quadruple the kinetic energy. That’s a
huge increase in kinetic energy.
Now, rather than going into all the details behind that relationship, I'll show you the basic issues behind it. First,
let's look at how the, the wheel's velocity evolves over time if I exert a steady force on the wheel. So, I'm going to
push it with a constant force. It accelerates at a constant rate. The acceleration is constant. And so its velocity
increases steadily. And basically, then the velocity is proportional to the time over which I've been pushing it. If I
double the time over which I push it, I double its velocity. That doubling is not going to work for work. Watch what
happens to the energy I invest in that wheel as time goes on. Once again I'm going to push it with a steady force
and it’s gone to a steady acceleration. But as it accelerates it travels faster and faster. So I have to chase it.
At first it’s easy to push on it, but then it goes faster and faster. I have to move faster and faster--it’s moving faster
and faster. The distance it travels with each new portion of time each new second is bigger than during the
previous second. While the work I'm doing is equal to the force size times the distance it travels. During the first
second it doesn't travel very far. So I don't do very much work on it. But the second second, it travels farther. The
third second it travels father still. With each passing second, I'm doing more work on it than the previous second.
That means that although its speed and velocity are increasing in proportion to the time over which I push it, the
work I'm doing is skyrocketing. It's going faster and faster. I could chase after this poor wheel and push and push
and push longer and longer distances. So, that's the origin of this explosion in energy that occurs as the puck's
speed and velocity increase.
So when all the dust settles and the calculation is done in its full glory, it turns out that the kinetic energy that the
wheel has by virtue of its velocity: that is, kinetic energy associated with translational motion alone, that kinetic
16 | P a g e
energy is equal to one half the wheel's mass times the square of its speed. That's the final story. And that's true of
any translating object.
When I begin to move to your right or to your left, remember direction doesn't matter, my kinetic energy at any
moment is ½ my mass times my speed squared. I happen to be a complicated, moveable, you know, shape
changeable object. So in my translational motion you really would concentrate that on my center of mass. And
how is my center of mass moving? And take one half of my total mass and multiply it by the square of the speed of
my center of mass.
Well, this observation that kinetic energy increases in proportion to the square of speed, goes a long way to
explaining why high speeds are potentially so hazardous. If you compare two identical cars, one traveling 60 miles
an hour (which is essentially the same as 100 kilometers an hour) to a second car that's traveling only half that fast,
30 miles an hour (50 kilometers per hour) they're different by a factor of two in speed and velocity, but they're
different by a factor of four in kinetic energy. That faster moving car carries four times as much kinetic energy in its
translational motion as the slower moving car. And that explains why collisions that occur at those high speeds are
a problem and modern cars are designed to dissipate that enormous excess in energy, in this case in the form of
kinetic energy. They dissipate both by grinding it up in part into thermal energy and in part into the deformation
and destruction of safety zones in the car--portions of the car that are intended to have work done on them during
collisions and to absorb that energy in a way that's safe.
It's time for a question. A ten year old child, who is a good baseball pitcher, can throw the baseball at 50 miles an
hour as a fastball (that's about 80 kilometers an hour) but it takes a world class professional pitcher to throw a
fastball that travels 100 miles an hour or 160 kilometers an hour. Compare the kinetic energies in those two
pitches. The faster moving baseball is carrying four times as much kinetic energy with it, even though it's only
traveling twice as fast. That enormous increase in kinetic energy explains why it's so hard to throw 100mph fast
ball and why only a few people have been able to do it. Moreover, they throw that ball in a shorter period of time
than a person throws a 50mph fastball. They're pouring four times the energy into it, in roughly half the time,
which involves a much more rapid transfer of energy, that is, more power. Throwing a 100 mile an hour fastball
requires something like eight times as much mechanical power as throwing a 50 mile an hour fastball.
Now let's look at the kinetic energy associated with the wheel's rotational motion. That kinetic energy is the work
it takes to bring the motionless wheel up to its final angular velocity. The rotational story will be almost exactly the
same as the translational story. But this time, I'm going to do rotational work by exerting a torque on the wall as it
rotates through an angle. Well, as before, as with a translational story, I'm not going to do everything. I'm going to
look instead at some important observations. And the first of those (there's three of them again):
 The first observation is that the direction of angular velocity doesn't matter, whether I spin it from my
perspective route you know clockwise or counterclockwise, that's, this is rotation down. This is rotation
up. It doesn't matter. I do the same work spinning it this way as spinning it this way. So, what matters is
not angular velocity, the whole thing, but rather angular speed. The amount part of angular velocity, the
direction part of directional velocity, is not important. Because once again, energy is about doing, not
about moving, direction doesn't matter.
 Second observation: this one is about rotational mass. It turns out that the kinetic energy associated with
rotation in a wheel is proportional to the wheel's rotational mass. To show you that, I'm going to get my
second wheel. So here we have a second wheel, same as the first, but instead of moving around
separately, I'm going to sit this wheel on top of the first wheel. Well, if it took me one unit of work to get
this guy spinning like that, it's going to take two units of work to get this stack, if I can do it, spinning like
that. Basically, the amount of work I have to do rotationally, to get one of these wheels spinning is
proportional to its rotational mass. If I double the rotational mass, it takes twice as much work. Ten times
the rotational mass? Ten times the work. We know now that the kinetic energy in an object’s rotational
motion is proportional to its rotational mass.
 The third part, the tough one, is how the kinetic energy in the rotational motion of the wheel depends on
angular speed and once again that kinetic energy is proportional to angular speed squared for the same
reason, if I exert a steady torque on this wheel it undergoes angular acceleration steadily, constant
17 | P a g e
angular acceleration. And it spins faster and faster and faster, so its angular velocity is then proportional
to how long I twist it, the amount of time over which I twist it. If I twist it twice as long it ends up spinning
at twice the angular velocity.
But the work I do doesn't go up proportionately with time for exactly the same reason that we saw with
translational motion. As I spin this little guy, I exert a torque on it, a constant torque, and it undergoes a major
acceleration. It goes faster and faster. The work that I'm doing depends on the angle through which it rotates. It's
the torque I exert times the angle through which it rotates. And as it picks up angular speed it rotates farther and
farther with each additional second. So I'm chasing it around in a circle. The first second it doesn't turn very far,
and I do relatively little work on it. The second it turns farther and I do more work on it. Third second, farther still,
and so on, I'm chasing it around the circle. So the energy, the work I have to do on it skyrockets and so does its
kinetic energy.
The kinetic energy in a wheel's rotational motion turns out to be equal to one half the wheel's rotational mass
times the square of its angular speed. Fast-spinning wheels can therefore carry enormous kinetic energies, even
when they're rotating in place. The wheels on a moving vehicle however are translating and rotating at the same
time. What about their kinetic energies? It turns out that those kinetic energies add up. When your bicycle is
moving forward, each wheel has translational kinetic energy associated with the velocity of its center of mass. And
rotational kinetic energy associated with its angular velocity about its center of mass. That double dose of kinetic
energy distinguishes the wheels from the rest of the bicycle.
Bicycle wheels carry more kinetic energy per kilogram than any other part of the bicycle. Since you have to provide
that energy as work when you peddle the bicycle forward from rest, the wheels make your job more difficult.
Similarly, the bicycle's brakes have to get rid of that extra energy when they slow the bicycle to a stop. And,
because of these effects (extra energy in, extra energy out) in the wheels, those wheels are generally designed
very carefully to reduce both their masses and their rotational masses. Replacing a solid rubber tire with an airfilled pneumatic one not only reduces the wheel's weight, so it's easier to lift and carry uphill--it also reduces the
wheel's mass and rotational mass, and thus reduces the kinetic energy that the wheel carries as it moves.
Summary
Without wheels, a wagon would experience sliding friction as it moved across the sidewalk. That sliding friction
would grind up the wagon's ordered energy into thermal energy. And wear out both the bottom of the wagon and
the top of the sidewalk. Adding wheels doesn't eliminate all friction, but it does eliminate sliding friction between
the wagon and the sidewalk. In a normal situation, the wagon's wheels and the sidewalk experience only static
friction, this touch-and-release stuff. And static friction doesn't waste energy, although sliding friction still occurs
between each wheel's hub and axle. They don't waste much energy because the hub and axle don't move very far
relative to one another. And the work done against sliding friction in that hub and axle is quite small. Even that
sliding friction can be eliminated by inserting roller bearings or ball bearings between the hub and axle.
When you pull a wagon forward, the sidewalk exerts static frictional forces on the wagon's free wheels. And those
static frictional forces produce torques of the wheels that cause them to undergo angular acceleration and begin
to turn. In contrast, when you pedal a bicycle, you are exerting a torque on that powered rear wheel. Causing the
sidewalk to exert a forward static frictional force on that powered wheel propels the entire bicycle forward. Once
the wagon or bicycle is moving and its wheels are rotating and translating, those wheels have kinetic energy in
both their translational motion--and in their rotational motion. So, they have more than their fair share of kinetic
energy. In the context of wheels, we've examined frictional forces and their effects on motion. We’ve seen how
ordered energy can be ground into thermal energy. And we've developed strategies to minimize the waste of
energy by way of static friction. We'll use those concepts often now as we continue to study how things work.
18 | P a g e