 Hi, I'm Zor. Welcome to Unizor Education. Today's lecture will be about the force, acceleration and inertial mass of the objects. Now this is the first lecture of a new section called Dynamics. That's part of the part called Mechanics in the Physics 14 course. The course is presented on Unizor.com website. I suggest you to watch this lecture and all others from the website. The website is free and there are no advertisements, but there are very detailed notes for each lecture. And this lecture is one of those where the notes are important because I'm trying to explain certain concepts. Now I can find some words as right now as I'm talking, but at the same time I found might be slightly different words when I was writing the comments for this lecture. So I think both are very beneficial for you if you will compare them. So we start Dynamics. Kinematics we have finished. That part actually has the exams as well, if you want to take them. I do suggest you to take them. And now back to Dynamics. Now as I basically said a few times, the prerequisite to the entire Physics 14 course is knowing your math, especially vectors and calculus derivatives. All this is presented in another course on the same website called Maths 14. So I suggest you to go to this particular course again. It's free for all, but in any case I kind of assume that the concepts of vectors and derivatives are pretty much comfortable for you. Now I always have a problem explaining certain basic concepts which are not really properly defined but understood intuitively and for instance force for instance or mass. But I would like to approach these concepts as logically as possible, as rigorously as possible. Now I'm actually borrowing this from Mathematics that certain concepts are basic, so basic that they are not really defined by anything which is more basic than themselves. And examples for instance in geometry a concept of a point or a straight line. They are not really defined as object but they are defined by their properties which we are accepting as axioms. So I think this is a very interesting approach which was definitely beneficial in Maths and I will use it wherever it's necessary in Physics as well. We already had concepts like space and time for instance which we kind of accepted without proper definition. However, even if we don't really define exactly what space is, we can always introduce a system of coordinates and we can always associate position in space with certain numerical triplet x, y, and z coordinates and also we don't really define what time is, I don't know, it's part philosophy and more than physics I guess, but we can measure time, we have the clocks. So here again I will approach the concept of a force from the perspective of the properties of the force. Now let me recall the law of inertia. Now we already mentioned that law when we were talking about kinematics and this law states that the object continues the state of rest or uniform motion with the constant velocity vector. Unless acted upon it by certain external unbalanced forces. Now at that time I really did not define what what forces is and now we are in the position when we're talking about the forces and that's exactly what I would like to connect together the force and the law of inertia. So the law of inertia says that the body will continue to be at rest or in uniform motion unless some forces exist, which means that force is anything which is changing this state of rest or state of uniform motion. So that's exactly what probably can be put into rigorous approach to the concept of force. I don't know what force in general is, I cannot point to something and say this is the force and this is not the force. However I can say that if there is an object and it's moving and at some time and it's moving with uniform velocity vector and at some time it changes either the speed going in the same direction or it's changing the direction so the vector of velocity is changing. That means that there is a force. Basically I'm defining the force not by concretely stating okay if I'm pushing this that's the force if earth attracts a stone which is falling down that's the force or electricity attracts plus to minus attract to each other. So I'm not really doing all this enumerating all the different forces that are too numerous to enumerate. I'm just saying that whenever you have something which is moving uniformly and then all of a sudden it's changing it means that some force acted upon it. Okay now we have defined the force by its property to change from uniform motion or from the state of rest to some non-uniform motion. So there is some change in the velocity vector maybe it used to be zero now it's not zero now if it used to be some constant the vector like this and now it will turn that's all manifestation of some force. The force is defined by its property now we want to measure the force right and here we have a problem let's just assume that we have an example of the force for instance my efforts when I'm pushing a chair let's say I can feel what kind of an effort I'm actually exhorting so I'm exhorting certain effort and the chair is moved now if I will take instead of a chair I will try to move a large sofa and I will really push it with exactly the same effort as I feel the same effort well I'm sure we all know that the sofa might maybe will not move at all or will move much slower or to a shorter distance etc so what does it signify well first of all it signifies that acceleration which I have actually caused by moving a standing stool chair or pushing the sofa I'm causing acceleration so there is acceleration in both cases but it's different although my force which I have exhorted is exactly the same I feel it's the same effort I'm pushing the chair and the same way I'm pushing the sofa results are different so what we have actually come up with the following statement that although force is actually causing acceleration of the object this force is applied against or applied to different objects behave differently they change their vector of velocity but they change differently acceleration is different now obviously acceleration exists in both cases because it was used to be like state of rest and now it's state of motion whatever the speed is it's definitely change in velocity vector it used to be zero now it's not zero all right so we have come up with a very important statement that force by itself the same force applied to different objects results in different acceleration so I cannot really measure the force by the acceleration and we wanted to measure quantitatively the force I mean it would be great if all the objects whenever I'm pushing with the same effort with the same force will will act the same way and I will measure acceleration and that would be the result of my force okay so we can't do it so what can we do well we can do basically the following very kind of obvious we will introduce another parameter which we will call inertial mass or simply mass I will probably use the word mass without the word inertial although it's implied and whenever in the future we will learn something about gravity it will be gravitational mass but right now the word mass means inertial mass this is the characteristic of the object since the same force results in different accelerations with different objects what I'm saying is I'm introduced a concept of mass I'm saying that the chair has one mass and the sofa has another mass and these characteristics of these objects together with the force define acceleration so we have a characteristic of the force and we have a characteristic of the object these together force and the mass they define acceleration completely so if one object let's say a chair moves really far and fast when I'm pushing it with some effort and the sofa moves slower and shorter distance that means they have different masses okay great so I have a concept of force and I have a concept of mass and I know that the force the mass and acceleration are related to each other question is how well next lecture will be about the laws of Newton and there will be a second Newton's law about this about quantitative relationship but that's not exactly what I would like to talk right now about I would like to know how to measure if I more I can measure acceleration right because acceleration is just a second derivative from the position so if I measure my position as a function of time I can have the first and the second derivatives and the second derivatives derivative will give me the acceleration at any moment of time so I have instantaneous position instantaneous velocity vector which is the first derivative and instantaneous acceleration vector it's all vectors right in three-dimensional words okay so I know how to measure acceleration but I don't know how to measure mass and they don't know how to measure the force so I have to introduce something some some technique which will allow me to measure these things and then I can think about how to combine them together into some kind of a formula like the second law of Newton okay so how can we measure two out of three things you see if I have some kind of functional dependency between these two things if I know the function and I know how to measure x I can obviously measure the y however now I have two different parameters I have acceleration which is some kind of a function of the force and the mass and I don't know neither of these all right we actually can do something and here is the way how I suggest to to build our measurement theory measurement techniques now I do not know how to measure yet but I know how to answer the question are these two forces the same or different how can I do it well let's take one particular object I will apply one force against it and then another force against it if the results acceleration of this object are the same it means the forces are the same so I have to repeat experiment with two different forces but under all other conditions which are exactly the same the same object the same surrounding the same whatever location so if my two forces result in the same acceleration for this one and only object these two forces are the same so I can answer the question are these forces the same or not now experiment shows that if two forces are the same for one object they are the same for another object so there are no other characteristics than the object itself and basically it's mass which we don't know yet but anyway I can answer the question about sameness of the forces okay can I answer the question about sameness of the masses of two different objects the answer is yes because I will take one and only force I will put one object against this force and see how it moves and then they take another object against exactly the same force and they know how this moves if the movements are the same acceleration resulting in this action are the same that means the objects have the same mass the same important physical characteristics which is kind of a measure of inertia of this object or measure of resistance of this object to change its position under the action of the of the force so the mass is basically a measurement of how responsive the object is to the force and experiments show that the larger the bigger the heavier objects are less responsive to the force all right but that's besides the point but anyway now I can determine are the masses two of two different objects the same I just apply the same force and see if there is the same result that actually is a very important notion which we have right now because what we do is we will introduce a unit of mass first and it can be anything I can take any particular object and say okay the mass of this object is the unit so what people actually did they took the a small cylinder of platinum and iridium alloy which weighs approximately the same as a cubicle decimeter of water like one liter of water more or less the same weight on the surface of the earth doesn't really matter how we obtain this it happened to be more or less equal to this and that was obviously the original idea but it's completely irrelevant to our theory our rigorous theory so we took this object this platinum iridium cylinder and say this is the unit of mass which means this particular object will help us to measure mass of any other object so here is one kilogram that's the name of the unit of mass so we have this cylinder here now what we are saying is we can introduce the measurement of the force if the force acting on this one kilogram platinum iridium cylinder cause one meter per second square acceleration so this is the mass this is acceleration caused by this force now this is the unit of acceleration in system c right system international then I'm saying that this is a unit of measurement of any force and it's called Newton obviously after Sir Isaac Newton so the force is measured in in new tones and what I'm saying is that if I have this my cylinder platinum iridium cylinder which way which has a mass of one kilogram by definition so we just by definition took the cylinder and say this is one kilogram this is the unit of mass so if I am causing this particular object the acceleration of one meter per second square it means my force is equal to one Newton by value by magnitude but force is actually a vector and we are assuming that the direction of this vector is exactly the same as direction of acceleration it it's causing so the force is a vector which is directed towards the vector of acceleration it causes and we can measure it if it's one kilogram object and one meter per second square acceleration that's one Newton okay that's one Newton how about 10 Newtons very easily if I will take the same object of one kilogram and I will obtain 10 meters per seconds that would be 10 Newtons so that's how we measure so I can basically have any acceleration I can measure acceleration of this particular object and say that this is in Newtons measure of my my force so I can measure the force by how the force is acting upon this particular cylinder made of platinum and iridium now I have already told you that any other object which has exactly the same mass would have exactly the same acceleration again that's the experimental fact so it doesn't really matter what kind of a object this is whether it's this particular cylinder which is basically stored somewhere in in Paris if I'm not mistaken or any other object which has exactly the same mass and we know how to determine whether it has the same mass or not right so right doesn't really what kind of an object as long as it has the mass of one kilogram the same as that cylinder in Paris right okay so now we can measure the force now knowing the force I can actually measure the mass of any object for instance if I am acting with the force of one Newton on some unknown mass and I have acceleration k a not just k if acceleration is equal to k meters per second and this is the force of one Newton acting upon this particular object so instead of one meter per second I have k meter per second well the object obviously is well consider well if k is big positive number so I have a bigger acceleration with the same force well it means my object is well smaller has less mass it has less resistance to the force and the measure of resistance to the force is the mass so I'm saying that my mass by definition again I'm basically defining this is equal to one over k kilogram so if the force acts and it has let's say 25 meter per second second square result it means my object is 125 so a kilogram and vice versa if my acceleration is equal to half of the meter by second square then my mass is two kilograms so that's how I measure masses and I measure forces so again first I just by definition decided what's my unit of measurement of the mass then I can measure all the forces and knowing all the forces I can actually measure any other measure the mass of any other object by basically checking how it moves under certain force well this is how I introduce these three main concepts in dynamics the force the acceleration and the inertial mass or just masses we are seeing right now that was the purpose of my lecture to introduce you from the intuitive understanding of this concept the the theory behind it or how you can rigorously build your physical theory where you have the units of measurements you have definitions you have properties and you have the relationship between them well that's all I wanted to say today I do recommend you to read the notes for this lecture again it explains more or less the same thing but it's like a textbook it has maybe slightly different presentation etc that's it for today thank you very much and good luck