[MUSIC] Hi everyone. Today, we are going to study about the brief concept of what's dynamics? Principles of dynamics are pretty simple, it's Newton's law, like most of you know. It's about how forces are back to generate the motions, 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 freshman 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 and 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 products. So, for example, when we learn simple concept or the Newton's law F equals ma, when you're calculating the acceleration or even velocity, you have to take a derivative of the positions, vector actually and the second derivative petitions or the first derivative velocity to get an acceleration. When we are looking at the rotational motion, like a torque or the moment equals I(alpha), kind of stuff. This actually came from Newton's law F equals ma and then do the cross product of the r both left and right hand side. Okay, so when we are handling the rotating body's motion, we have to do some calculus on the Newton's law of the physics. So when you're texting taking the derivative of the position, it's a little bit more complicated with the rotational motion, including this omega x 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 possessed the term like omega x X-dot and the other terms like angular acceleration x the petitions and so on. So that's what we are going to cover in chapter two. 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 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 an integral of the Newton's Law over the displacement, what we can get is d(mv), dt and dx and then if you take this term as v, what we can have is mv square, which is a kinetic energy. So this is how we can get work-energy as a relationship. So when we are combining derivatives, integrals skills and the vector product concept, that's actually whole contents for the dynamics, what we are going to cover. So using the six principle, I would like to add one more thing about the importance of the practice for the dynamics. So the principles are pretty simple and interesting, like, suppose you have two balls coming toward each other and then make a collision. What's going to be the velocity after collision, like a momentum? How is momentum conserved and in this case is energy conserved? Those are the concept of the principles, what 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 the exam, sometimes you will feel like, I know the principal, 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 principal understanding. So between the principles and practice I would strongly recommend you to make a balance. So not only just understand the principle, also keep practice of the problemsolving. So, maybe some of you have sort of lack of principal understandings. Like you are really good at getting the answer, getting the numbers, however, you have not really intuitively understood, why this is happening and how those are happening and the your answers are pretty understandable, intuitive by yourself. 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 making those motions, and so on? Ask by yourself, discuss your peers and ask your TA's or the professor's to understand that firm foundations about the principle. Also keep working on the practice and then I'd like to give you a tip, instead of just solving all the example problems on your textbook, of course, you don't have time, I would just pick the similar problems, that what you have covered. Just do it either for the class or the sample examples. So what I mean by solve similar problems, that is, suppose that you are solving the problem, like a disk, connected by the string through the pulley to the other object. Okay, so you have two objects of the mass and then there is a pulley connecting these two objects through the keyboard. So what's going to be the motion? So this is kind of chapter six 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 the later. The third favorite first step is you have to set it up the coordinate and then draw the free body diagram and then draw all the forces exerting on it. Of course, there is the normal forces, I just am focusing on the horizontal force part. And then you can obtain the equations of motion for linear motion and the rotational motion and then there are some unknowns, okay. And then sometimes you can easily eliminate them by subtracting 2 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 it. You can actually connect this alpha, the angular acceleration and then a, the linear acceleration together, so that you can actually end up solving the acceleration term. Details will be covered in chapter six. So once you actually solve this problem, either through the class or through the sample example session, then just look at the textbook example problem session and then you can find a similar setup, such as, there are two masses are connected by the pulley, okay. This one is a just a single Mass, but instead of having other object, there is an external force P exerted. So it's a pretty similar set up, same for this one. There is a one mass and then through the string, there's an external force T exerted by this person. So, of course there are similar detail, a little bit of detail is different, but once you have solved the previous problem set you can actually practice it through the similar problems, so that you can get your own way of solving the problems in your own way of solution methodology, to be set it up and that could actually help you back to get the physical principle understandings. Okay? 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 a rigid body dynamics. And then this pretty much covers the topics before the midterm 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 system of particle chapter, okay? And for the second half, there's going to be kinematics and kinetics of the rigid bodies and then last, most complicated part, not difficult, but complicated part, it's a 3-D dynamics of the rigid bodies. So it also covers kinematics and kinetics as well. Can you see some patterns of the table contents? Yes, the kinematics chapter precedes the kinetics chapter. Kinematics of the rigid body precedes the kinetics of the rigid body, same for the 3-D. 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 how you can actually formulate the a in the previous chapter for the kinetics. So that's why you have a kinematics chapters ahead of kinetics, for the particles, rigid bodies and 3-D as well. So that's what we are going to cover next time. So first, we are going to learn how we can describe the acceleration of the particle, especially the rotational coordinate. And then we are going to learn the kinetics and same for the rigid bodies and so on, okay? This is how the overall 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 one by yourself. And I'll see you next time for chapter two. Thank you.
