The Science of Everything Podcast - Episode 13: Newtonian Mechanics

Episode Date: January 20, 2011

An introduction to basic Newtonian Physics, including a discussion of forces, velocity, acceleration, Newton’s three laws of motion, and some common misconceptions about forces. We also discuss circular motion and conclude with a brief look at the physics of walking and driving a car.

This is the Science of Everything podcast, episode 13. And today we're talking about Newtonian mechanics. I'm your host, James Fodor. So in this podcast, we're going to look at basic Newtonian physics, including the concepts of forces, velocity, acceleration, Newton's three laws of motion, and also some common misconceptions about forces and how they behave. We'll also take a look at circular motion,

linear and angular momentum, and conclude with a brief look at some interesting applications of Newtonian physics, namely how we walk and how a car moves along a road. So, first of all, let's start with a look at some basic concepts necessary to understand Newtonian physics, things like mass, forces, position, and velocity and stuff like that. Okay, mass. In physics, mass refers to two distinct properties of matter, which have been shown experimentally to be exactly equivalent, that is inertial mass and gravitational mass. So this is quite interesting, the fact that mass, the word mass refers to actually two very distinct properties of an object,

but which happen to be exactly identical to each other. So as I said, these are inertial and gravitational mass. Now, inertial mass is a measure of an object's resistance to changing its state of motion when a force is applied. So this is what you think of when you think of an object as being heavy. A truck has a large inertial mass because it resists changes in its motion, whereas a pebble has a small inertial mass, a mass, because it's light, easy to move around, easy to change its motion. Now, the other one, gravitational mass, is the measure of the strength of an object's interaction with a gravitational field. And so you can think of the Earth as having a large gravitational mass because it exerts a large gravitational field, which, you know, attracts objects towards it and causes us to fall to the ground if we fall over.

So inertial and gravitational mass are identical. They've been measured for many different objects and they're showed to be exactly the same, but they're conceptually different, and it's actually a bit of a puzzle as to why they're exactly the same. Theoretically, they wouldn't have to be. And looking at inertial and gravitational mass and trying to explain why they are the same is one particular road of inquiry, which led Einstein to the general theory of relativity, but that's another podcast. So anyway, to recap, mass refers to the strength of interaction with the gravitational field, and the resistance to changes in motion when a force is applied.

Now, mass versus weight. Mass and weight are not the same thing. A concept you may have come across before. Mass is measured in kilograms and refers to the amount of stuff in an object. That's probably the best simple way of thinking about it. That inertial mass and gravitational mass both relate to the amount of stuff in an object, how much atoms are there or how much stuff is there. whereas weight is a property which is actually correctly measured in neutons, not kilograms or pounds,

and weight actually refers to the magnitude of the gravitational force acting upon a body. So on Earth, you know, we say I weigh X number of kilograms or X number of pounds. Correctly we should say I weigh X number of neutens, which is a measure of force. That is because weight is properly, is correctly, as I just said, the magnitude of the gravitational force acting upon us. In this case, it's the gravitational force of the Earth acting upon us, or whatever it is we're measuring the weight of. This concept is relevant because if we go up to the Moon and we stand on a scale, we find that we weigh much less less. I think it's about one-sixth of what we weigh on Earth. And the reason for that is because the gravity of the Moon is much less than that of the Earth, because the Moon is much smaller than the Earth,

or it has less mass, has less gravitational mass, and so its gravitational force is smaller, and so objects weigh less on the Moon. However, the mass of that object on the Moon is exactly the same as the mass of that object as when it's on Earth. Mass does not change from place to place, but weight does change depending on the gravitational force. So an object just in the middle of space with nothing around it has no weight because there are no gravitational forces acting upon it, but it has exactly the same mass as it would have if it was on Earth. So that's a difference between mass and weight. Okay, now there's another concept in physics called the center of mass, and this is quite important, because in physics, when we describe the motions of objects, how they move from one place to another and how forces act upon them,

we usually consider, we're usually interested in complicated objects, things like human beings, planets, buses, they're extended, complicated objects with intricate shapes, and you might think it'd be very complicated to try and analyze the motions and forces on that complicated object, given that, you know, it has bits pointing out in all directions and it's really large and so on. But actually, we can consider complicated, extended objects as being located at an exact point at their center of mass. And exactly why this works, I'll explain in a bit more detail later on this podcast, but you can think of it as that's kind of the average position of all the parts in the object, and it all averages out as if the entire object was all located at that one point in the center. Now, it's important to understand that the center of mass doesn't have to be the physical center of the object. In fact, there doesn't have to be any object there.

If you think of a balloon, for example, the center of mass will be somewhere in the middle of the balloon, but there wouldn't actually be any balloon there. It would just be air. but that would still be the center of mass of the balloon. Same with even a hollow concrete sphere or a box or something like that. It doesn't have to be, there doesn't have to be an actual material there. It's just spatially the average location of all the mass in the object. Similarly, if you have a really heavy end of something and a really light end of something, the center of mass is going to be biased to be more in the direction of the heavy end than the light end, or the more massive end to the less massive end.

Okay, so just remember when we talk about the motion of complex objects in physics or forces acting on those objects, we imagine as if all that force acted upon the center of mass of that object and as if the entire object was just a point located at that center of mass, which then moves about. So that should help you understand some of the examples I discuss later on. Okay, position. This is a fairly basic concept, but just to make sure you understand it, that is the spatial location of an object. Generally, it's the spatial location of the center of mass of that object, as defined by some coordinate system. Usually, we use the coordinates X, X, Y, and Z to refer to the three different coordinates in three-dimensional space.

And then in addition to position, we have the concepts of velocity and acceleration. Now, velocity refers to the rate of change in the position of an object, and acceleration refers to the rate of change of velocity. So, acceleration is, in a sense, the rate of change of the rate of change of position. It's the rate at which you are changing your changing position. Now, velocity and acceleration are both vector quantities. Now, what does that mean? A vector quantity...

first of all, we'll start with a scalar quantity, which is a scalar quantity is just ordinary numbers you're familiar with, like if I say I have six eggs. That six is a scalar quantity. It's just a number. It's just an ordinary number. A vector quantity, however, is different because it has a number and a direction associated with it.

This could be a direction in one dimension or more commonly in three dimensions, so it'd be like, you can think of it as an arrow pointing in some direction somewhere. And why do we need a direction as well as a magnitude? Well, because velocity and acceleration can be, the same value, say 10 meters per second or meters per second per second for acceleration. But that doesn't tell us everything we need to know because you could be accelerating forwards or backwards or you can be traveling to the left or to the right or up or down. You need direction

as well to specify in which direction you're traveling and in which direction you're accelerating. And velocity in acceleration don't have to be in the same direction. So, for example, suppose that you're traveling 50 kilometers per hour forwards in a car. So your velocity vector would be 50 kilometers per hour and the vector arrow would point forwards, maybe to the north if you're driving north, but say you started slowing down, you pressed on the brake and you started slowing down, your acceleration now would be some unit, I don't know, maybe 10 metres per second per second, backwards in the direction of south, in the opposite direction to which you were actually traveling. And the reason acceleration and velocity can point in opposite directions is because you're still

traveling north or forwards, but you're slowing down, you're going less for, fast in that forward direction, so you're accelerating in the opposite direction. You're accelerating backwards, if you like. Eventually, if you continue to accelerate in the opposite direction, your velocity will decrease until it reaches zero. And then if you keep accelerating in the backwards direction, then your velocity will flip and you'll start traveling south, and then your velocity acceleration will be going in the same direction. And all throughout this point, as long as your velocity is positive or negative or is non-zero, your position will be changing. So your X, Y, and Z coordinates will be changing. You're moving

through space. So anyways, that all might sound fairly obvious, but just so you understand the difference between the concept of position, which is where you are, velocity, which is how fast you're moving, and in which direction you're moving, and acceleration, which is how rapidly and in what direction you're changing your motion. So you can be accelerating really fast at a low speed, and vice versa. You can be going at a really high speed or high velocity, but not be changing your speed. So you have zero acceleration. By the way, one last thing, I'll explain the difference between velocity and speed, just in case you might be confused. Speed and velocity, you almost refer to the same thing, except that speed is a scalar quantity, whereas velocity is a vector quantity. So, for example,

if I say I'm going 60 kilometers per hour, that's my speed, because I haven't defined which direction I'm going in. If I say I'm going 60 kilometers per hour to the west, that's my velocity, because I've added the direction. So if you have a direction, if you have that vector, that arrow pointing in which the way you're going, it's a velocity. If you don't have that, it's just speed. All right, so that's some basic concepts about mass and weight and speed velocity. Those will be necessary in understanding what I talk about. Henceforth. So let's move on to the meat of the matter, the laws of motion, Newton's three laws of motion. Okay, but before we talk about the laws themselves, I need to introduce the concept of a force. Now, I'm sure you've heard of this. In physics, a force is any

influence that influence that causes a free body, or an object of some kind, to undergo a change in speed, a change in direction, or a change in shape. So if I push my sister over, that's a force because she's changing position. If I push a compass needle from pointing east to north, that's a change in direction, so that's a force. If I push a pillow so that it's indented, it's changed its shape, so that's also a force. Any change in speed, direction or shape undergone by an object is caused by a force. Okay, now another way of looking at it, if that's a bit confusing, is that a force is some kind of pushing or pulling that acts on an object. A force is a vector quantity, so it has magnitude and direction.

So I can have a force that's pointing, pushing upwards, downwards, sideways, whatever. And it can have a magnitude. Now, force, as I said before, is measured in Newton's, named after Isaac Newton, a person who came out with all these laws. So that's why I said that weight is correctly measured in neutrons, because gravity is a force. It's something that pulls us. In this case, it pulls us downwards towards Earth.

So that's why we say that we have a weight of, like 60 newtons, because that's the amount of force that's pulling us down towards Earth. So that's a force. It's a pushing or a pulling that causes a change in shape, position, or velocity. It is important to understand that forces can act over a distance. You don't have to be touching something to exert a force on it. That's our common intuition of a force, like when we punch a wall, we have to touch it. But, for example, the force of gravity acts over space. If we get into an aircraft and then jump out, we are not touching the Earth, but we are still being pulled down towards the earth by the force of gravity. So that's clearly

forces acting at a distance. Another example is magnetism. If you hold a magnet right up close to your fridge and let it go, it will be pulled to the fridge and stick on it, even though it's not touching the fridge. So that's another example of forces acting at a distance. So objects do not have to be touching each other in order for a force to act. Now, more than one force can act on a body at the same time. In fact, this is usually the case. When this happens, what we do is calculate what's called the net force, which is the vector sum of all the forces. So first of all, just imagine that forces were scalers, so they were just simple numbers. They could be a force of 5 Newtons and a force of 3 Newtons, and maybe a force of negative 2 newtons.

So maybe that force is acting in the opposite direction to all the other ones. Now, all we do is add all those forces up and come out with the answer. So say we've got a force of gravity pulling down on something, and then maybe also, suppose we had, here's a good example, suppose we had a magnet on a attached to a metal table horizontally on the ground. So the forces acting on this magnet would be, or some of them would be the force of gravity, pulling down on the magnet, the magnetic force of the table attracting the magnet downwards, and then suppose you're also somehow pushing the magnet up, say there's a hole in the table right underneath the magnet,

and you're pushing it up right underneath that through that hole. That would be a force upward in the opposite direction. So you add all those forces up together, and whatever you come out with is the net force. and you can do exactly the same thing with vectors and the way you add vectors is a little bit complicated but you just kind of get the average direction of them all like if you have a bit to the west and a bit to the south the average vector will be southwest

you kind of need to see diagrams to see how all that works but you can add vectors as well even though their directions so anyway what we do if there are more than one force acting on the body we add up all the forces to get the net force including directions so the vector sum of all the forces and then we treat that as if that were the only force acting on the body and then it moves in that direction, or it's accelerated in that direction of that force.

And we can actually go in the opposite direction as well. If there's only one force acting on a body, we can break that up into, say a force was acting diagonally on a body, we could split that force up into a horizontal component and a vertical component, and that might make it easy to work out what's going to happen to the object. Anyway, so that's the concept of net force. Now, Newton's three laws.

Don't worry too much about the actual numbers of these laws. Those are kind of arbitrary, but I'll just do them in order for the sake of... making it easier. The first, Newton's first law of motion is that if the total net force on an object is zero, its center of mass continues in the same state of motion. So to put that into a phrase that's easy to understand, if the total net force on an object is zero, so there are no net force, there's no net force acting on an object. Remember, this is only net force that's important. So you could have heaps of forces acting on an object, but if they all sum to zero, if they all cancel out, so there's zero net

force, then that object will continue in the same state of motion as it was before. And the same state of motion means just a constant velocity. So it won't change direction or it won't change speed. It will stay at the same speed going in the same direction when zero net forces are acting upon it. And as I said before, if the object is a complex extended one, it's the center of mass of that object that actually continues in the same state of motion. We imagine this is the whole object will concentrated there. A good example is, if you go and go and like to the case where we jump out of a plane, at first the force of gravity will act to accelerate you towards the ground. You'll speed up, but as you speed up, the force of air friction,

which acts in the opposite direction to gravity, it acts upwards, gets greater and greater, until air friction and gravity cancel each other out, the net force is acting on you, are therefore zero, and you stop accelerating. But you don't stop moving, you just stop accelerating. You are still traveling in a fairly rapid velocity towards the ground, but you are no longer accelerating because of the zero net force, and so your state of motion stays constant. And when that happens, by the way, when a falling object reaches that circumstances called terminal velocity, the final velocity you reach. Okay, that's Newton's first law, and now Newton's second law of motion, is that the body, I'm sorry, a body of mass, M, subject to a force

F undergoes an acceleration A that has the same direction as the force, and a magnitude that is directly proportional to the force and inversely proportional to the mass. Okay, that may sound like a load of gobbledygook, but it's the simple equation F equals MA. The force exerted on an object will be equal to the mass of the object, the subject of the force, multiplied by the acceleration that that object experiences. So a small force acting on a big object will produce a small acceleration of that object. Similarly, a large force acting on a small object will produce a large acceleration, or a large force acting on a medium-sized object will produce a medium-sized acceleration. The basic point is that for a given force, the mass and the

acceleration of the object are inversely related. The bigger the mass, the less acceleration and vice versa. So if, and this concept is fairly intuitive, if I want to push a truck up the hill, I need a lot more people to help me than if I were just pushing a small car up the hill, because a truck has a lot more mass, and so you need to exert a lot more force on it to get the same acceleration. Okay, that's the second law. Now, Newton's third law. Forces always occur in equal and opposite pairs. is the classic, every action has an equal and opposite reaction. That's a bit of a misleading statement though, because it's not so much an action is not really a defined constant in physics. A better way of saying would be every force has an equal and opposite force. So a good example of this is if I am

driving a truck and I hit a mosquito on my windshield. Now, when that occurs, both the mosquito and the truck are traveling at some speed, and they both have a mass, so they both exert a force on each other. The question is which force is greater? The force of the truck on the mosquito or the force of the mosquito on the truck. The actual answer is that the two forces are exactly the same in magnitude, but opposite in direction. Obviously, the opposite in direction, because the truck exerts a force forward in the direction it's traveling in the direction of the mosquito. Mosquito exerts a force on the truck, opposite to the direction in which the truck is traveling, because they're traveling at 9 perpendicular to each other and hitting each other. That's easy to understand,

but why are the forces the same size? Well, the reason is that's just how the universe works, that if two objects sort of collide with each other or interact with each other, they will both exert exactly the same magnitude force on each other. What's different, though, is the masses of the two objects. So remember from Newton's second law that a given force acting on an object of small mass produces a large acceleration, whereas if a given force acts on an object of large mass produces a small acceleration. The mosquito has a much, much smaller mass than the truck. So because the forces are the same, the acceleration on the truck is virtually nil, the acceleration on the mosquito is so large that mosquito gets squashed. That's the difference. So the difference is actually

the masses of the mosquito versus truck and not the forces that are acting. The forces are the same. Remember, however, that these forces that go in the pair, they act on different objects. They don't both act on the truck or both act on the mosquito. One force acts on the mosquito, one, and the other force acts on the truck. That's important to understand. Okay, so those are Newton's three laws. Just to recap, the first law is the law of inertia, that if the total net force on an object is zero, it stays at a constant velocity. The second law is F equals MA, the force equals a mass on an object times the acceleration of that object. And the third law is that forces always occur in equal and opposite pairs, although those forces will act on different objects.

So now I'll look at what force is not, or some misconceptions about forces. Now, many of these misconceptions, I think, arise from the sort of sloppy way we use the word force in ordinary conversation. When we're using the word in physics, however, we have to be very careful and only use it in the correct context. So force is not a property of an object. Force occurs or refers to the interaction between two objects, when one object collides with another or when an object with mass comes close enough to the earth to be affected by its gravity.

So force refers to an interaction. It's not possessed by an object in isolation. An object doesn't have force. If an object was just sitting by itself in a completely empty universe, there would be no forces, because there would be nothing to interact with. So force is not like mass.

Objects possess mass as a property. Force is not a property. An object doesn't have force. Okay. Second point. Force is not a measure of an object's motion. You shouldn't say a train comes down the hill with great force. Motion can be described in terms of velocity and speed, and also momentum, which I'll

talk about later on, but not unfortunate. So objects don't move with great force. That's just an incorrect use of the term. Force is also not energy. You can't store force and you can't use up force. Indeed, it actually kind of is the other way around. energy is sort of like the ability to generate a force. So if you've run out of energy, you can't generate any more force.

Like maybe if your car has run out of petrol, that means it's run out of energy, and so it cannot generate the forces necessary to get it moving. But the car doesn't run out of force. That's an incorrect way of using the word. Force also does not require motion. You are presumably either standing or sitting at the moment, or possibly lying down, but either way, the force of the ground or the chair or the bed is acting upwards on you, whilst at the same time you are exerting a force on the chair or the

bed or the ground. So forces are acting, but there's no motion occurring because the forces balance each other out. The force of the chair exerts on you is equal to the force that you exert on the chair and so on. So you don't need motion for forces. And the final misconception is that forces have no perpendicular effects. Now what does that mean? Well, perpendicular just means it right angles to something. So when a force acts on an object, it has no effect on any motion of the that object that is perpendicular to the force. So the classic example of this is comparing a bullet that is dropped, that you're holding at the normal height you would hold the gun and you drop the bullet, and at the same time you fire a bullet from that gun, which of these two bullets that dropped

or the fired bullet will hit the ground first? The answer, as you may have guessed, is that they hit the ground at exactly the same time. And why is that? Well, because the force that causes the bullets to accelerate towards the ground is the force of gravity acting upon them and pulling them down. that force is acting completely perpendicularly to the horizontal motion of the bullet that's fired, being shot horizontally perpendicular, sorry, parallel to the ground. The point is that the force of gravity has no perpendicular effect. It only pulls that shooting bullet downwards. It doesn't change the sideways motion at all.

So the bullet that's been shot travels a good horizontal distance before it hits the ground, but it will hit the ground at the exact same moment that the dropped bullet does. Okay, so having dispelled some misconceptions about forces, now I want to look at the different types of forces that exist. In fact, there are many different types of forces, and they can be categorized in different ways. But here I just want to look at some ones that are particularly relevant, I think, to a beginning understanding of Newtonian mechanics. One is the concept of a normal force. Now, this is a bit of a strange word, but a normal force is just the support force exerted upon an object that is in contact with another object. So if you place a book on a table, that book, the force that stops the book from falling through the table is called the normal force.

It's the normal force that the table exerts on the book. And the normal force always acts perpendicularly to the surface that the object is resting upon. Now, the reason for the normal force is because of the repulsion between the electrons in the atoms around the two objects. So remember from my episode about the atom that atoms are surrounded by a negatively charged, electrons, those electrons in the book come into close contact with the electrons in, say, the table, and repel each other, and that generates the normal force. And yeah, so that's the actual reason why you don't fall through the floor. It's because your feet basically are being repelled by the electrons in the floor, and that's referred to as the normal force, and an act in opposite direction to

gravity. And that leads me on to a second kind of force, which is gravitational forces, the attractive force between two objects possessing mass. All objects in the universe that have mass are attracted gravitationally to each other. So you are gravitationally attracted to your iPod or MP3 player or computer that is playing this podcast at the moment, but the force is so small that it's almost impossible to detect it. In fact, even the best laboratories have trouble detecting the gravitational forces between ordinary objects. Gravity is generally, therefore, only noticeable on the scale of astronomical objects like planets and stars. Friction is another type of force, and it refers to the resistance to the relative motion between

solid surfaces or fluid layers or other material elements that are sliding against each other. So there are two main ways of thinking about friction. One way is you can think about it is that it's caused by roughness, kind of like sandpaper, and that if you zoomed into the surfaces of two objects that are being moved past each other, think of, I don't know, a piece of furniture being pushed across the floor. You could think of that these two surfaces are both bumpy and jagged at an atomic level or at a microscopic level, not an atomic level. So as you push it sideways, the object kind of rides up, the rides up and then falls down into the grooves of the floor and then rides up again. And you can imagine that that going up and down and bumping and

dragging would cause a lot of friction, of resistance to motion. That's one way of thinking about friction. But however, friction also occurs between completely smooth objects, at least some completely smooth objects, like plates of metal. The reason for this kind of friction is the attractive force between objects, sorry, between atoms, or particularly between molecules and other types of materials. Now, before I said that electrons in two atoms repel each other, and that is generally the case, but in other circumstances you can have slight charges

upon the electron clouds around different atoms or molecules, and they can attract each other, forming some kind of chemical bond. Recall the podcast that we did on chemical bonding. And when this occurs, the objects can momentarily stick together, and it requires a force to sort of pull them apart again, and break those bonds and prevent the sticking. So friction can be thought as both roughness and stickiness, and stickiness referring to at the molecular atomic level.

And, okay, so now there are actually two different types of friction, static friction and kinetic friction, or dynamic friction, it's also called. Static friction occurs between surfaces that are not sliding relative to each other. Now, the size of static friction, first of all, the direction of static friction always acts, in fact, any type of friction always acts in the opposite direction than which an object is being pushed. So if you're pushing an object horizontally across the floor, friction will act in the opposite direction to that force,

sort of pushing backwards and making it harder for you to push. The size of the static friction, however, depends upon the size of the force that's being exerted on that object, or particularly the horizontal force. So as you exert more force upon an object that you're trying to push, the static friction force actually increases. And you can think of this as being caused by greater stickiness or greater roughness between the surfaces. The more you push, the more this stickiness or roughness sort of has an impact, and therefore the greater the static friction is.

However, the static friction force has a maximum value. If the force you're applying exceeds this maximum value, the object will start to move. You'll break those temporary bonds or get out of the grooves that you're in and break that static friction and the object will start moving. Once the object is in motion, static friction completely goes away because the objects are moving. It's not static anymore. And instead what you get is called kinetic friction or dynamic friction, the other kind of friction that I mentioned, which goes between two objects that are moving or sliding relative to each other.

Now, kinetic friction is usually less than static friction. So remember, static friction has a maximum value. Kinetic friction is usually less than that, maximum value, but still can be significant. And it generally does not depend upon the speed that you're pushing the object relative to each other. relative to each other. Friction, however, both types of friction do increase with the downward force on an object. And that kind of makes sense. If you are pushing down on something as you're trying to push it horizontally, so you're kind of pushing it down and forwards, that's much harder than if you sort of squat down and push all of your, use all of your energy to push horizontally. And that's because for two reasons. One,

the horizontal force that you're exerting is greater because you're not wasting energy pushing it down on it. But secondly, the friction force is actually less because you're not exerting a downward force. force on the object in addition to your horizontal force. And that's also why heavier objects tend to have more friction. It's because the object, the force of gravity is acting, it has a larger force of gravity acting on that heavier object, and then so the normal force acting on the object from the ground is also larger, and so you get a larger frictional force. Friction also occurs in fluids, and that's manifested in resistance to flowing. It's also called viscosity. That can be thought of as caused by the bonding between the molecules or atoms in the substance.

Honey is a classic example of a very viscous fluid, so there's a lot of friction in there, lots of bonding between the molecules, and so it's hard for it to flow, hard for the molecules and fluid layers to move past each other. Water is a good example of something that doesn't have very much friction. It can flow fairly easily. A final type of force I want to talk about is tension. Tension is the magnitude of the pulling force

exerted by something like a string or a cable or a chain. It's the opposite of compression. So compression when you push something together, tension when you sort of pull something apart. Ropes under tension, sort of, you can think of tension not as exactly a force, but more as of a means of transmitting forces. So, for example, if you're pulling a heavy object by a rope, one way of thinking of it is that you're applying a force to the rope, which then tenses, so undergoes tension, and then, as a result of being tense, the rope is tense, that rope then exerts a force on the heavy object. And so you exert a force on the rope, rope exerts a force on the heavy object. and the heavy object then moves. Of course it will also work in the opposite way, because we know from Newton's second law that you always have, or third law,

I can never remember the numbers, an equal-on-opposite reaction, so as you exert a force on the rope causing tension, the rope also exerts a force on you, making it difficult for you to pull it along, and so on. And tension, the mechanism of that is changing the tauntness or the length of the atomic bonds between atoms and molecules. So you can think of it as like the atoms are moving a little bit further apart, and that causes the material to become harder, and also a bit longer and it tenses up.

So that's some different types of forces and hopefully you've got a bit of an understanding about tension, friction and stuff like that. Now I want to have a look at circular motion, which refers to rotation along a circle or around a circle. Now there are two different types of circular motion. There's rotation around a center of... around the object's center of mass.

So you can think of a merry-go-round, for example. The object's rotating, or the rotation of the earth, which causes the day-night cycle. It's the object moving around, rotating about its centre of axis. It's a central axis, which will generally be at the centre of mass. The other type of circular motion is rotation around another object. So an example of that is the Earth rotating around, the Earth orbiting around the Sun. They're fundamentally the same sort of thing, but just to clarify,

that there are two different types. They can be occurring at the same time, like the Earth is rotating about its axis at the same time as it's orbiting around the sun. Now, the key thing to understand with circular motion is that although the velocity of the object may be constant, excuse me, the speed of the object may be constant. The velocity cannot be constant. Why is that? Because the direction, as the object moves around in its circular pattern, the direction has to be changing, kind of by definition of what a circle is. And if the direction of motion is changing, velocity is also changing because it's a vector quantity. And in order to get a changing velocity, you have to have an acceleration. Remember from Newton's Law of Inertia, the only way to change

velocity is to have a non-zero net force acting upon the object. And, When you have a force, you also have an acceleration from Newton's other law, F equals M.A. And so we call this force necessary to maintain circular motion the centripetal force. Centripetal means inward pulling. And centripetal force is the opposite of a centrifugal force, which you may have heard of before. Centrifugal force is not actually a force as such. It's the apparent force that kind of makes it seem like objects are being flung off outwards away from their circular motion. It's not really a force because actually what the objects is trying to do is just keep going.

or what the object is tending to do is keep going in a straight line in the direction it was originally traveling. You're, in order to maintain a circular motion, you have to exert a centripetal force, pulling it inwards along the radius of the circle around which the object is traveling, and that force acts in the opposite direction to the centrifugal force, and so it makes it seem like there's a force pulling it away, but in fact it's not. You're exerting the force inwards. So as I said before, centripetal force has to act along the radius of the circle around which the object is moving. So think of it, if you're swinging a rock around you on a string, the

centripetal force is the tension force on the string that pulls inwards towards you and keeps the rock moving around. What that force actually does, it doesn't change the speed of the rock, or whatever the object is, but it's continually changing the direction of the rocks, of the velocity of the rock, so so that it continues around the circle. If you let go and stop accelerating that rock around the circle, it will just fly off in a straight line and go off in some other direction. So rotation is described in a very similar way to linear motion, or motion in a straight line, but instead of just velocity and acceleration and displacement,

we have angular displacement, angular velocity and angular acceleration. The only real different series, instead of using like meters or kilometers or something to measure distance or how far we've traveled, we use degrees or the proportion of the circumference around a circle that the object has passed. But it's basically the same. Same concept, just it's circular, not linear. Another interesting difference, though, of, for example, angular velocity compared to linear velocity, or ordinary velocity, is that it's not just equal to V,

so that's your traditional speed and direction, but it's actually V divided by R, which is the radius, or the distance between the point around which you're orbiting and the object itself, the radius of that circle. So, angular velocity, to repeat, is V, linear velocity, or the equivalent of that divided by R, the radius, which means that the smaller the axis of rotation, so the closer you are orbiting around that object,

so think of it as your rock on a string, the smaller the length of that string, the higher the angular velocity, and therefore the greater the force that you'll have to exert to maintain that velocity, that angular velocity. And the reason angular velocity increases with a smaller radius is because you can think of it as at the same speed,

but with less smaller circle, more rotations can be performed in a given time. angular velocity kind of measures the number of rotations in a certain time, and so less circumference means more rotations, and so greater angular velocity. Similarly, the size of angular acceleration is also dependent upon both the speed of travel and the radius of the turn. So the smaller the radius of the turn, the more rapidly one must accelerate in order to make that turn, and so greater force is required. So you can see this when you're driving a car. If you're trying to turn, that's an angular acceleration, you're trying to change your angular velocity. You're sort of turning around a

circle. As you do that, you need to exert a force, and that force is in the form of frictional forces acting between the tires and the road. At a given speed, your angular acceleration will be determined by how sharply you're turning. The more sharply you're trying to turn, the more you must accelerate. And the more you have to accelerate, the greater the force is required, because obviously the mass of your car doesn't change. So if F equals MA, you need a bigger acceleration, you need a bigger force. And if you can't, and that force comes from, as I said, the frictional forces between tyres and road, and that force, as I said before, has a maximum value. Now, one thing that is a bit confusing, just to take a step backwards

in the physics of driving, is that the frictional forces between your tire and the road are not actually dynamic frictional forces. They're not sliding frictional forces. They're actually static frictional forces. That may seem a bit counterintuitive because clearly the car's moving. The key point is, though, that the tire is not moving relative to the road, or it's not sliding relative to the road. It's sort of one part of the tire is rolling such that it moves away from the road and the other part is rolling onto the road, but it's not sliding relative to the road, and that's what's crucial. So the friction is actually static friction between tire and road. Now, why is that important? It means that static friction has a maximum value. Once you exceed

that maximum value, you start sliding, and this is what happens when your tire skid. When will you start sliding? Well, it's when forces, the forces acting on the car, exceed the level, the maximum level of static friction. You'll start sliding. And when does that happen? Well, it's just when forces get too great. And that can happen if you're trying to accelerate too fast. That can occur in a linear acceleration, but it can also occur in an angular acceleration.

If you're trying to make a very sharp turn, you need to have a very, you're changing your angular velocity a lot because it's a very small circle. Therefore, you need a large force. So therefore, you need a large acceleration, angular acceleration. To get that large angular acceleration, you need a large force from F equals M.A. to get that large force, you're aware of your engine,

and the result of that large force is potentially that you exceed the static frictional force between tire and road. When that happens, you start sliding, your tire starts sliding along the road, no longer rolling along them. When that happens, the frictional force goes down, because remember, the sliding frictional force

is generally lower than the static frictional force between tire and road, and when that happens, you actually get less force than you originally had. And so your attempt to increase your force is actually backfired, because now you're sliding and you have less force, and so you can't turn as sharply as you want to, and moreover, you've lost control of your car because you're now sliding.

And that's one way that car accidents can happen. Basically, you're trying to turn too sharply, you lose control of the car. It's all about angular acceleration, angular momentum, forces and, and alike. One last thing, I wanted to talk about the physics of walking. I've already discussed the physics of driving. The physics of walking are actually fairly simple. The basic point is that we, obviously, we lift up our feet and place them down again, but what allows us to move forwards is the frictional force between our feet and the ground.

Once again, this is a static frictional force because our feet are not sliding along the ground. We're not in roller skates here, I'm making that assumption, we're just walking. So because of that static frictional force, what we do with our muscles is that we apply a force acting backwards, sort of in a diagonally downwards along our legs, so backwards and downwards. We apply that force with push on the ground, and so the ground pushes back on us, owing to that static frictional force between foot and ground, and we take advantage of that push from the ground to help us sort of lunge forward.

It's not so badly coordinated, as obviously as I'm describing it, but that's the basic idea. We push off from one foot, and then we use that forward motion so gained from the ground to help us land on the other foot, which we place then forward, and then we go through the process again. Of course, we need to be able to use our muscles and tendons and so on to do that as well.

But the basic idea is that we push on the ground, then the ground pushes back on us. We take advantage of that and move forward. This becomes plainly evident if you try and walk in, in a slippery ice, for example, there's very little static friction between your feet and the ice. So no matter how hard you push, the ground doesn't push back, and so you just slip and fall over. So that's about all I wanted to cover today. In another podcast, we'll talk about momentum and angular momentum, which I didn't have time to cover today, and also some other interesting concepts like energy and work.

But those, today I've discussed the basics of Newtonian mechanics, forces, mass and circular motion and velocity. So hopefully that was of use to you. Now, if you found this podcast interesting, I'd appreciate a review on iTunes. I have one review so far. More would be very helpful. And of course, please spread the word about this podcast to friends, family or anyone you want to really. I'd love to have more listeners. if you would like to give me feedback on things to improve or episodes you'd like or whatever else,

please send that to my email address, Fods12 at gmail.com. That's FODS-12 at gmail.com. Thanks for listening and I'll speak to you next time.