Hi everyone. Today, we are going to study about the brief concept of what's dynamics. Principles of dynamics are pretty simple, its Newton's law like most of you know. It's about how forces are back to generate the motion such as force F equals ma. Actually this concept has been covered through your high school years or even middle school years, and then your first freshmen university physics courses as well. So why do we learn again this principle of Newton's law, again in dynamics, mostly targeting for sophomore students, university students who is majoring in mechanical engineering or related topics? So I would say the reason the dynamics are different from what we have covered in high schools or the university physics is it has a little bit more intensive combinations between the university physics and the calculus, what you have learned in the first year. So what I mean by the combinations of physics and calculus is like calculus, you have covered the derivatives, integrals, or the skills about how you're handling the vector, vector products. So for example, when we learn simple concept of the Newton's law, F equals ma. When you are calculating the acceleration or even velocity, you have to take a derivative of the position vector actually, and the second derivative of positions, or the first derivative velocity to get an acceleration. When we are looking at the rotational motion, like a torque or a moment equals I Alpha kind of stuff, this is actually came from Newton's law, F equals ma and then do the cross-product of the r, both left and right hand side. So when we are handling the rotating bodies motion, we have to do some calculus under Newton's law of physics. So when you're taking the derivative of the position, it's a little bit more complicated than the rotational motion, including this Omega cross x term and same for the acceleration. When you're handling the acceleration by taking a derivative of the velocity, it's not simply just as x-double-dot, it also possess the term like Omega cross x dot, and the other terms like angular acceleration, cross repetitions and so on. So that's what we are going to cover in Chapter 2. Also, we can also do the integral for the Newton's law, like when we can do a time integral for the F equals ma on both sides, we can end it up having impulse is going to be the change for the mv, the linear momentum. So this is how we can get impulse momentum equations by integrating Newton's law over time. Similarly, when we can take the integral of the Newton's law over the displacement, what we can get is dmv dt and dx. Then if you take this term as v, we can have mv squared, which is a kinetic energy. So this is how we can get work-energy relationship. So when we are combining derivatives, integrals skills and the vector product concept, that's actually whole contents for the dynamics, what we're going to cover. So using this principle, I would like to add one more things about the importance of the practice for the dynamics. So the principles are pretty simple and interesting, like suppose you have a two balls coming towards each other and then make a collision, what's going to be the velocity after collision like a momentum? How those momentum conserved, in this case is energy conserved? Those are the concept or the principles we're going to cover during the class, which is fun and easy. However, when you are actually facing to solve the problem through the homework or an exam, sometime you will feel like, "I know the principle, but where should I start?" The kind of feeling that I have also had tens of years ago. So that's because you lack of practices. So when you actually really solve the problem, that's a really important skill that actually make the firm foundations of your principle understanding. So between the principles and practice, I would strongly recommend you to make a balance. So not only just invest in the principal, also keep practice of the problems solving. So maybe some of you have several lack of principle understandings. Like you are really good at getting the answer, getting the numbers, however, you are not really intuitively understood why this is happening and how those are happening and your answers are pretty understandable intuited by herself. So in this case, this is going to be a really good chance for you to think about why this is happening, what are the force source making those motions and so on. Ask by yourself, discuss with your peers and ask your TAs or the professors to understand the firm foundation about the principle. Also keep working on the practice. Then I'd like to give you a tip, like instead of just solving all the example problems in your textbook, of course you don't have time, I would just pick the similar problems that you have covered, just with either through the class or the sample examples. So what I mean by solve similar problems, that is, suppose you are solving the problem like a disc connected by the stream through the pulley to the other object. So you have two objects of the mass and then there is a pulley connecting these two objects through the keyboard. So what's it going to be the motion? So this is Chapter 6 level problems, but I'm just going to briefly go over the step-by-step how you can solve it, details will be covered in later. The problem first step is you have to set the coordinate and then draw the free body diagram and then draw all the forces exerted on it. Of course, there is the normal forces, I just focusing on the horizontal force part. Then you can obtain the equations of motion for linear motion and rotational motion, and then there are some unknowns. Then sometimes you can easily eliminate them by subtracting two equations and sometimes you need more information. So in this case, there is a rolling without slipping kind of condition, so that you can implement that. You can actually connect this Alpha, the angular acceleration, and then a, the linear acceleration together, so that you can actually ended up solving the acceleration term. Details will be covered in Chapter 6. So once you actually solve this problem either through the class or through the sample examples session, then just look at the textbook example problem session. Then you combine the similar setup, such as there are two masses connected by the pulley. This one is just a single mass, but instead of having other object, there is an external force P exerted. So it's pretty similar setup, same for this one. There is a one mass and then through the string there's a external force T exerted by this person. So of course a little bit of details different, but once you have solved the previous problems that, you can actually practice through the similar problem, so that you can get your own way of solving the problems in your own way of solution methodology to set it up and that could actually help you back to get the physical principle understandings. So before I end up, I'd like to briefly go over the table of contents of the textbook. There are two big parts, one covers the particle dynamics and the other covers the rigid body dynamics. This pretty much covers the topics before the mid term exam and then rigid body for the rest of the semester. So there are three chapters mainly, other than the introduction chapter, there's a particle kinematics and kinetics and between the bridges from the particle to the rigid body, there is a systems of particle chapter. For the second half, there's going to be a kinematics and kinetics of rigid bodies and then last most complicated part, not difficult but complicated part, it's a 3D dynamics of a rigid body. So it also covers kinematics and kinetics as well. Can you see some patterns of the table of contents? Yes. The kinematics chapter precedes the kinetics chapter. Kinematics of the rigid body precedes the kinetics of the rigid body, same for the 3D. So what is the relationship between the kinematics and kinetics? So basically what we want to teach you through this dynamic course is the kinetics, which is the relationship between the force and the motion. That's what it means, kinetics similar to dynamics. However, sometimes calculating the a or formulating the a is a little bit challenging or not that simple. So we have to do some preview or the how you can actually formulate the a in the previous chapter for the kinetic. So that's why you have a kinematics chapters ahead of kinetics for the particles, rigid bodies and 3D as well. So that's what we're going to cover next time. So first we're going to learn how we can describe the acceleration of the particle, especially the rotational coordinate and then we're going to learn the kinetics and same for the rigid bodies and so on. This is how the whole world contents of dynamics look like. Okay. This is it for today. So I hope you have a chance to just briefly review your textbook Chapter 1 by yourself and I'll see you next time for Chapter 2. Thank you.
