My name is Professor Bill Heitbrank. I'm substituting for Professor Dennen today. I'm really happy to be able to do this. This is a great topic that he's given me. So what I'm going to talk to you about is rotational motion.

What we'll do today will be mostly qualitative, but it's really wonderful because rotational motion is analogous to all the different things that you've been learning throughout the quarter and will get tested on next week. So this will be a great review and at the same time there's a lot of fun demonstrations that go with it. So just to get started, when we consider

Dennen called it linear motion, but the more general term is translational motion because of course you can move in three different directions. I can go back and forth, I can go sideways, I can go up and down, so you can move in those three different directions. So let's just kind of review symbols

that go with these different terms that you've already learned involving translation. So you should have learned about position, velocity, acceleration, mass, force, momentum, kinetic energy work in Newton's second law already. So for position, what would be a typical symbol for position? X. And then we would have different directions so we could have more than that.

For velocity, the symbol usually is v. And you'll remember that in general, v position is a vector, velocity is a vector because it can have different directions. If you just choose one component of the velocity, it's related to the change in position in a certain amount of time.

A delta x, delta t. Acceleration, the symbol for acceleration is a. It's also a vector quantity because it can be in different directions. A component of acceleration in a particular direction is the change in what? Change in velocity in that direction

with respect to time. Then we have mass. That one's easy. The symbol for mass is You've got to play with me. Sorry. Learning is a participatory sport. Mass is m.

Force, symbol, f. Should I put a vector over m? No, because it's a scalar. But force is a vector so I put a vector over that. Momentum, symbol, p. And it's equal to what? Mass times velocity. It's a vector quantity. Mass is a scalar but velocity

is a vector. That makes it a vector. Kinetic energy, formula, one half m v squared. Work, formula w equals, remember this? Did you do work?

What is it? Force over distance. So I push on something and I move it a certain distance in the same direction as the force. That's the work. So it's force times distance. Say if the distance is in the x direction we can call it x. And Newton's second law of course is f equals wait, you're not playing. Newton's second law is f equals

ma. Okay. Now we have all of these things have exact analogs in rotational motion. And so that's what we're going to go through in today's lecture. First of all, kinematics, which means how you describe motion, has analogs to this.

So for position, instead of this, for rotation, this is an angle that we choose. And it's actually three dimensional as well because you can rotate in three different directions. But I'll just call my angle theta here.

And then of course there could be other angles. To prove to you that there are three different directions for rotation, of course I can go this way. Now the way we describe the direction for rotation is to use the right hand rule. So if you take your fingers and have them curl in the direction that the object is spinning,

your thumb will point along the axis. So if I'm going like this, the direction for the axis is up. So that's one dimension. But of course I can do angles in other directions. So I can go side to side. So the direction

for that will be, it's either this way or that way. And similarly, I can somersault. And so if I do right hand rule for that, I get that it's this way. Like that. So there's the three dimensions for angle. Okay, now velocity, for velocity

we have the angular velocity. It's also a vector quantity because it can go in any of the three directions. For today's lecture we'll focus on just one. It has its own symbol. Its symbol is

the lower case Greek letter omega. And it is equal to, now it's analogous to this. So we look up here. Position is like x. Angle is like this. So I'm going to have delta what? Over delta t. This is going to be the change in the angle

in a certain amount of time is the angular velocity. So if you think about clock hands, they go by. You know the second hand has a relatively high angular velocity. The minute hand has a slow angular velocity because it changes angle slowly in time. For acceleration, we have angular acceleration.

It has its own symbol. We use the Greek letter alpha. Once again, it truly is a vector quantity because you can be accelerating an angle in three dimensions. But for simplicity, we won't do that. So we consider that angular acceleration is going to be the change in angular velocity

in a certain amount of time. So it's delta omega in a given amount of time. Like that. And then our last quantity, which I'm running out of room in front of my table here for, is, oh, so those are our things for

rotational, whoops. You can just see the very bottom of this screen. There's the alpha equals the change in omega in a certain amount of time. Now, whoops, so that's how we describe kinematics. If we want to think about

describing motion, the term for that is dynamics. And so for dynamics, then we have a quantity called the mass. For angular motion, for rotation, we have something that is called so mass could also be thought of inertia. It's how

if something's light, it has little inertia, it doesn't resist changes in motion very much. If it's heavy, or it has big mass, it has higher inertia. So the term for rotation is called rotational inertia, and it has a symbol

capital I, like that, is rotational inertia. And what is rotational inertia? Well rotational inertia does depend on mass, just like ordinary translational inertia does, but it also depends

on how far away from the axis the object is. So if we consider this, for example, here is an object that will have some rotational inertia, and it's moving this way, so the axis that we're interested in is the one coming out, like that. When it's set up like

this, it has relatively large rotational inertia. If I give it a little hit, it doesn't rotate very readily because it has relatively large rotational inertia. But with the same mass, if I bring the masses in close, then it will have a lot less rotational inertia. The rotational inertia

actually depends on distance squared from the axis. So you can get really big changes. I give it the same kind of hit, and it rotates much more readily. It has much less resistance to the change in motion. So it will pick up the motion very readily. In fact, we can actually do a more quantitative comparison

with this. And I understand that you learned about torques before, right? Did you learn about torques? Torques are what? Force times, remember this? Lever arm. Right, it's like the force times lever arm. So, a torque here, I can actually apply a torque to this thing. I've got a little wheel here

in the middle, and I'm going to apply a force, which is going to be the weight on this. So this is going to be mg, it's going to tug on this thing. And then there's a little wheel, and is there a torque on this system? The answer is yes, because the weight doesn't go right through the middle here. It's off to the side,

so there's a little lever arm that's like that big, that's going to pull on this thing. And so when I let it go, right now, well first let me set it up so that the rotational inertia is big, then when I apply a torque to this system, it will

be, it won't rotate that fast because it has big rotational inertia. So let me try it. Here we go. I did this before. Okay, there it is. So it's pulling and it's applying a torque. Actually it's accelerating, it's gaining angular acceleration because it's getting more and more torque. And then it switched over. Okay, now let's try the same thing again, but make the rotational

inertia tiny. So I do that by putting the mass close to the axis. I've got to get this wound back up. How do I do that? Wind it back up.

Okay, and get ready to apply my torque. Saying torque is a lever arm and the weight is the same, so force times lever arm is the same. Ready, set, go. Okay, oh it spins much faster now because it has far less rotational inertia. That make sense?

Yeah. Okay, so that's about rotational inertia. You can see it in barbells here as like in the picture. Okay, we know about force. The thing that's analogous for force is torque. So torque, just like forces are what makes things move when you want to translate them,

torques are what make things rotate. So if you apply torque you tend to rotate things. Symbol for that is tau. It's a vector quantity in general. And you learned before that it is the lever arm crossed with the force

that's applied to it. So just as a reminder, here's a slide that shows torque. You want to apply a torque to this bolt in order to turn it. So you can apply a certain force which is supplied by your muscles of your arm. If you don't have the force

cross product optimized, you apply less torque. You can get more torque by optimizing it so that r cross f is at its maximum magnitude. That will turn the thing better. But if you need any more, you can make the lever arm longer by putting a pipe on top of your wrench and then you can turn a tough bolt like that.

So that's a torque is r cross f reminder. Okay, and then we still have momentum and kinetic energy. So for momentum we have p. In the absence, if you don't have any external,

when is momentum conserved? When you don't have any external forces. That's an isolated system. So there's a similar kind of thing for something that's called angular momentum. Angular momentum

capital symbol L. And actually you can figure out by analogy what L is. L is going to be what's my analog to mass to m? Analogous to mass is rotational inertia.

I and then what's analogous to b? Omega is analogous. That's a velocity, angular velocity. So that's what angular momentum is. Looks like that. You can do the same thing for kinetic energy. There's kinetic energy if something is rotating away, it has

kinetic energy. Let me take this weight off. If this thing's rotating it has kinetic energy associated with that motion. We can describe it in terms of that. So this is still kinetic energy again. The formula for it is one half. What goes with m? You've got to play with me. One half

I and then what goes with v squared? Omega squared. So what the kinetic energy is, work there's still going to be work. So what's the analog of force? The analog of force is you're not with me or you just don't want to play?

The analog of force is torque so it's tau and the analog of position is angle. So it's like that. So if I want to do work on a bicycle wheel

I will want to apply a torque to it. So I apply a torque by applying a force this way so that r cross f will apply a torque to it and I can do it over a tiny angle

and I won't do a lot of work and it won't have a lot of kinetic energy. I can apply that same magnitude of torque over a bigger angle, torque over a bigger angle and it spins faster. I do more work on the object because I push it further just like in translational motion. So it gains more energy and then it has more kinetic energy as it spins around.

So that's that one and then we have Newton's laws which are actually analogs for all of Newton's laws as well. I forgot to mention this. So rotational inertia depends on the direction of the motion. We have the three

different directions in general and so if we choose this particular axis, if I put on the left hand case I got my mass close to the axis so that has relatively low rotational inertia. In the right hand case I got my mass far as possible from the axis so that has large rotational inertia.

Oh, so here's a clicker question. Hopefully I can get the technology to work. Do I just click this? Is that what I do? Oh, it's working.

Just do the first one. Which position has the largest rotational inertia? Okay, are you done? Okay, so now I stop it, right? Which one? Does this display your answers?

Okay, so 67% of you are brilliant and I don't know what to say about the rest of you. Okay, so the correct answer for the largest rotational inertia is B because that's just like the picture I showed you before. The body has as much mass as possible away from the rotation

axis which is this turntable in the middle. Just without doing the clicker. Which one's the smallest? D because that's the one where the person's got as much mass as possible. The other ones are intermediate. Actually C is from largest to smallest. B is largest. C is next because there's more mass in a leg than there is in an arm.

C is next. A is next because the arms are still farther away and D is the smallest like that. Okay, so that's the idea behind rotational inertia. Now what?

B was the answer, okay. Now, Newton's laws are analogous for both translational and rotational motion. First of all, what's Newton's first? Somebody raise their hand for me. What's Newton's first law? Let me do fill in the blank again since number one. I used to use candy to motivate people to talk when I did physics three.

Newton's first. An object in motion tends to stay in motion. An object that's stationary tends to stay in motion. And as long as there's no force, that's what happens. Okay, so we have an analog for that for rotational motion. If an object is

rotating, it keeps rotating. So here's my wheel. It got going. There's no torque done to it. Now, of course, these things have very good bearings that are really good, so there isn't very much torque associated with the bearings or energy dissipation associated with that. So Newton's first

is it likes to keep rotating. If it's stationary, it likes to stay stationary. I mean, that's it. It's just like Newton's first for translational motion. Newton's second, we already talked about this one. Newton's second is F equals ma, so Newton's second is like that.

The analog is torque is rotational inertia times angular acceleration. And I kind of already demonstrated this. I applied a constant torque before and I changed the rotational inertia. So when the rotational

inertia was small, then the angular acceleration was you with me? For the same torque, if the rotational inertia is small, the angular acceleration is large and vice versa. Now, of course, we can do the same thing where we can have a certain rotational inertia and then apply different

torques. So I apply one torque and the angular acceleration is pretty small. I hit it with a bigger torque and of course the angular acceleration is bigger. So that's just the same as what it is in Newton's law where you have the factor acceleration, mass and force coming into play.

Now, Newton's third, it's often quoted this way. For every action, there's a UA action. Another way of saying it is that forces come in action-reaction pairs. So I push on the floor, the floor pushes on me.

So actually if you want to jump higher, it seems counterintuitive until you understand Newton's third law. If you want to jump higher, you push harder on the floor. Right? Because that makes the floor push harder back at you through Newton's third law. So they come in action-reaction pairs. Well, that's the way it is for rotation too. Torques come in action-

reaction pairs. So if I apply a torque to this object, it applies a torque. Bill applies torque to Rod, Rod applies torque to Bill, trying to make me go the opposite direction. So here's a, oh, I forgot about this. This was

back to Newton's second, just in a practical example of this. Torque equals rotational inertia times angular acceleration. So if you're running, when you run, you swing your legs back and forth in periodic angular motion. So when the leg is out straight,

it has relatively large rotational inertia. If you bend it, it's closer to the axis of rotation. It has less rotational inertia. So if you want to go faster, after a while you have trouble doing, you know, if you try to run like this, it's hard. You bend your legs to make your rotational inertia, and then you can get more angular acceleration.

So that's the idea behind one of the applications of Newton's second as applied to rotation. Now here's action-reaction pairs. So when a person is up in the air, they're an isolated system, and there's

no torques on them. So this athlete is jumping up in the air, swinging with their arm. Because they're an isolated system, the torque applied to make the arm swing by the body, the arm gives an equal and opposite torque on the lower body to make it rotate the opposite direction.

So you get this action-reaction kind of pair for torques. And this is very important, particularly in athletics involving gymnastics and things like that. Okay, so this is our summary. We already have this up on the board, but this is just a nice PowerPoint. You have our different

things that we have and how we have these analogs between all of these different quantities. Okay, so let's do another clicker question. See how you're doing. Oh, I was going to demonstrate this first. So you can wait a minute if you want. Let's pretend that I'm

playing baseball, and there's a really good fastball pitcher against me. So they throw it, and the ball's already in the catcher's mitt by the time I swing. What do I do? Well, I actually will choke up, and then the next pitch comes.

Now I'm able to get around it by the time the pitch gets there. Because I only have a fixed amount of time to judge whether the ball's going to be a ball or strike. Okay, now go ahead. A is supposed to

be rotating, not rotating. Just in case you were wondering. Okay, let's stop. The correct answer

is 77% is correct. Yay, majority rules this time. So this is an example. This is actually just like the running example. Newton's second law. So I'm rotating this object. If the rotation

axis is at the end here. Some people are talking and it's that's rude. Thanks. So if the rotation axis is here, it puts the mass farther away from the rotation axis, and so you get more rotational inertia.

If I put, actually, you wouldn't choke up this pitch, but if you do this, you put the mass as close as you possibly could to the rotation axis. You minimize how far all of it is, and this is the easiest to rotate. I mean, you can usually try this yourself. You feel it very readily with your hands, so this is much easier to rotate because it has less rotational inertia. Now the way this applies to Newton's second

is in order to catch up with the fastball, which is going to come in a finite amount of time, I need to get my, I need to have significant angular acceleration because I'm starting from no rotation, and then I'm trying to get up to high rotation when I hit it. So I need a lot of angular acceleration since my body is only so strong

I wish that I could apply more torque, but I have limited amount of torque that I can apply so I'm only so strong for torque. The best way to get more angular acceleration is to reduce I, thereby increasing alpha, the angular acceleration. So B was correct.

There it is. Okay, now this is too easy, sorry. And never mind that B that's highlighted by red.

For some reason, I actually don't like a lot of Microsoft products, but somehow I couldn't get that B to not be red. Okay, once again the majority is right. It is I omega. First of all, let's remember about momentum, just translational momentum. P equals

mv. So now we need something that's analogous to m, what's analogous to m is the rotational inertia is analogous to just the ordinary inertia and what's analogous to v is the angular velocity. So we need I omega is the correct answer there.

Not that. Rotational inertia times angular velocity is the correct answer. Okay, now I'm going to do a demonstration.

And this is the way it's going to work. So this thing has good bearings so it doesn't apply for around this axis, it's got a little bit of torque to it, but not very much. So when I stand on this I'm going to pretty much be an isolated system. Remember for

conservation of momentum, the condition for conservation of momentum was no external forces. The condition for conservation of angular momentum is no external torques. Because torques are analogous to

forces. So no external forces, I mean torques. So once I stand on this thing I can be in an isolated system with no external torques. That will mean that angular momentum will be conserved. Now what I'm going to do is I'm going to

take this and I'm going to enhance my rotational inertia by holding these weights out and then of course that means I can adjust my rotational inertia dramatically. Because I can pull the weights in towards the axis which makes the rotational inertia small. Or I can put them far away from the axis which makes the rotational inertia large.

So I'll be spinning on there and then I'll pull the weights in and what is going to happen? So let's try a little prediction.

Now you predict that it's B I spin faster. They all said because angular momentum is conserved which is a basic assumption that we're going to make. So now let's try it and see. We make hypotheses in science and then we check them out and you're going to help me a little. Don't spin me very fast at first. You're just going to give me a little spin.

Yeah, that's good. Okay, we can try a little faster. Go ahead.

So the idea is that you can see why I was happy to substitute for this particular lecture and that's really fun.

Just as an aside, the department now has this little seat so you sit on the seat which makes it all safe. I don't like that. I like the thrill of knowing that you're going to kill yourself. So I spin faster because angular momentum is conserved but this

really shows it more. The idea is that I times omega is the same. So in this case the one on the left I is big but omega is small and the one on the right I is small but omega is big. In both cases the L is the same. So that's what we just saw in that demonstration.

This should remind you, did Dennen fire off the liquid nitrogen cannon for you? I was sure he had because that's like the best demo we've got in our arsenal. Pun intended I guess. So the idea behind that is that's an isolated system. There's no external forces.

It has no momentum initially so the momentum this way from the cannon has to equal the momentum that way from the cannon ball or in our case a plastic bottle. The cannon ball has small mass but huge V. This one has big mass but

little v and the two momenta equal each other. So it's the same kind of thing where you can trade off mass or velocity but the two are comparable, are equal to each other because of this conservation property. Another thing that happens when I pull my arms is

is that the kinetic energy increases. That's not obvious right now so I'm going to show you some math to show that that's the case. This we've decided for sure. Angle momentum is conserved. So think of one as when my arms are out. So when my arms are out, I1 is big. When my arms are in

I2 is small and correspondingly omega 1 is small when my arms are out and it's big when my arms are in. Now we can just solve this to figure out what's going to happen to omega 2 and in fact omega 2 is whatever my initial speed was times the ratio

of the rotational inertia when my arms are out to rotational inertia when my arms are in. Just in terms of the experiment, why did I add masses, why did I hold those weights in my arms? Which factor here was I changing?

I was changing I1. I was trying to make I1 big to start with because my arms aren't actually a very big part of my total weight. By getting weights out there too then I can make big change in rotational inertia. And then of course I asked what's your name?

I asked Arash not to give me a very big push to start with. So what did I want to minimize? That was omega 1. His push that he gave me at the beginning was omega 1. Now how does the change in energy work? Well, you remember that kinetic energy for translation is one half mv squared so our analogous thing is one half i omega squared.

Here we can just write down a formula for what the initial kinetic energy is and then let's compare how much kinetic energy we have after I pull my arms in. That's governed by the same formula. So now what I want to do is use this formula up here, substitute in for omega 2 so I do that. Omega 2 is I1 over I2 omega 1

square that and what I get from that is after I do the algebra I end up with I1 squared over I2 times omega 1 squared. Then I remember that one half I1 omega 1 squared is the initial kinetic energy so I find that the kinetic energy with the arms pulled in

is actually altered by this same factor as the velocity is, I1 over I2. Now if you want to give something kinetic energy, what do you have to do to give it kinetic energy? You do have to apply a force, that's true.

Well actually no, you don't have to apply a force necessarily. Do I do work on the podium right now? Am I applying a force to the podium? So you have to do work. It has to be force times distance. I said that my kinetic energy increased when I came in. There must have been some work

done on the rotating body for that to be true. And indeed there is what there is. As I'm spinning around, by Newton's first law, did you do circular motion?

For circular motion, do you remember what direction the acceleration is if something is going in circular motion? It's called centripetal acceleration. Did you hear that? It's centripetal acceleration and it points in towards the center.

So we often call, they're called so in order for this object to go around in a circle, there has to be a centripetal force that's pulling in towards the center and the object if left to its own devices would like fly off the other way. So what I have to do is, you know this from experience, if you're spinning around, the weights want to go like that. So what I have to do

is I have to do work to pull the weights in. So that's force that I do over distance and where does that energy come out? It goes into the system of the rotating body and I have more kinetic energy than I had before.

So that's the basic idea here. Centripetal force supplied by the skater is radially inward. The motion of the weighted arms is also inward so the workforce times distance is positive. That work done by the athlete comes from where? The work done by the athlete comes from where? Gannon was also trying to

encourage you to think about total system and the whole system is isolated here. So I do work what's the reservoir of work that I call upon in order to be able to pull those weights in?

Breakfast, right? Lunch. I mean it's chemical energy. I'm converting chemical energy into mechanical energy in order to do that work. Question?

No, but then you wouldn't be isolated anymore. It's a more complicated system to analyze in that case. No, that's true. You wouldn't necessarily spin. I mean we could actually try it.

So just spin me. Ok, now I'm going to hand off the weights. Ok, now hand it back to me. Oh, see I spun up some because of my own rotational inertia. Oh, it didn't work. Never mind. Because I forgot that I have rotational inertia in my arms.

But basically you can take them away, put them back and there was no work done during that time and I'll still be going at omega, the initial omega. If I should have kept my arms out and had him put them in my pockets then it would have worked. So that's our answer to that one. Ok, so here's another one.

I'm going to do another experiment. What I'm going to do here is I'm going to be up here again and I'm going to have these bags out and I'll be spinning and then at some point I'm just going to let the bags go. And the question is when I let go of the bags, what are they going to do?

Ok, so let's get your hypotheses for this. Ok, we have some mixed opinions here. The majority think it's C, but there's a substantial number that think it's B and some who think it's A. Ok, so what

is the key issue in thinking about this? This is back to actually Newton's first law kind of thing. Because once I let go of the bags there is one force still on them. What force is still on the bags once I let go of them?

Gravity. So that's why they will fall down because of gravity. But let's not worry about that direction right now. That's this way. Now if we think about the other part, when I let go now there's no force on them. So what should they do? They should keep going

if we're just talking about the view from above, they should just keep going in a straight line the way that they were going. Right? What way are they going? They're going in circular motion, so what way are they going? Do you remember about circular motion? Which way the velocity goes? The velocity goes, here's looking down from above, the velocity is

tangent to the circle. So I should let go and they should just fly out. B is the one that your intuition grabs on but is not right. There's no force spiraling around on them. So this is back to

one of the trick questions for Newton's first that often comes up on tests. Where you don't, it doesn't care. Once it lets go the thing just flies in the direction it wants to go. So let's see if it actually works as claimed.

I guess I want a decent velocity this time so we can see something. Okay, that's good. And let's see, you should be looking from above but we'll see what happens. Did it work? Okay. Alright. They move in a straight line away from me as they fall down in the direction

that they were going. Ah, okay. So we have time for another one. So the way this one works, this is another really cool conservation of momentum demonstration.

So, of angular momentum demonstration. Okay, so this wheel has angular momentum because it has a certain amount of rotational inertia and it has angular speed. So that's I times omega means that it has a certain amount of angular

okay, so take it like this from above and I get on here and I want to be stationary to start. Here, let me stop myself. Okay, good. I'm almost stationary. Now, somehow I've got to take

this from you. Okay, here we go. So now what I want to do is, right now, what's my net angular momentum? There's no net angular momentum in this system right? So what's going to happen if I flip this thing over?

Isn't physics cool? That's what you're supposed to say. Yes, Professor Heidrich, it's cool. Okay, thank you.

Okay, let's understand how this works. Okay, so we set it up so L sub B stands

for the angular momentum of the wheel. Now, did I have any angular momentum to start with? No, because we arranged it so I was standing still. So the one on the left is our initial condition, like this. Now, when I flip the wheel over, angular momentum is a vector

and it has a direction to it. Now the wheel's spinning the opposite way. So by the right hand rule, now L B is pointing down. But we know by conservation of angular momentum that the sum of these two things has to add up to what we had initially, because the system is an isolated one.

And so, since this flipped down this thing has to turn, which is the angular momentum of the man has to turn out to be twice the magnitude of the initial angular momentum of the bicycle wheel.

Does that make sense? Do you understand this? You could make almost something very similar to this for linear momentum and have it be like on one of your exams. So that's pretty cool. Okay, what else do we have? Ah, here's another thing. We talk about conservation of momentum and here's

a question that often comes up. If you start an object up, I didn't prove this to you, but there's no torques on a falling body in the absence of appreciable wind resistance. So if you have a body and it's isolated and it doesn't have any angular momentum to begin with,

can it turn? It has no angular momentum to start with, which means omega is equal to zero, so can it turn? So you might think no, and that's the correct answer if you have a rigid body, but if you have a body that can bend, you can use

this Newton's third law of torques thing in order to turn one part of your body while the other part is turning, and then once you stop moving, then you're back to no net angular momentum but you get one part to rotate one way and the other part to rotate the other way and it works out. Now of course the most famous example of this is not the one that

mine's going to be pathetic because I'm not very good at it, but the most famous example of this is if you drop a rabbit or a cat upside down, will they land on their feet? And the answer is yes, they definitely land on their feet. They can do it, they start with no angular momentum, but they have very flexible bodies and they have these things where they counter rotate

one way and the other part rotates the other way and eventually they get their feet facing the ground and they land on the ground. Now I can show you I can show you sort of a crummy version of this because I'm not nearly as agile as a cat. First you've got to start with no momentum.

So if you rotate your upper body it will move your lower body. So you can do it like that. You can do it. You like that? That is pathetic.