https://youtu.be/ayeS4ggh_TA
PHYS 1101: Lecture Twenty, Part One
Welcome to Lecture 20. We’re starting Chapter 8, now. And the subject matter is called “Rotational Kinematics.” So, to give you a big picture, what we’re going to do in this chapter honestly is nothing more than the same thing we did back in Chapter 2. One-dimensional kinematics.
The only difference is that this is going to be describing an angle position of an object and how that angle position changes. And if something is winding up or winding down, that’s the analog of speeding up and slowing down. So, it might benefit you to pause the video right here and go back and look over your notes and review Chapter 2 in a little bit. You’ll see some review of that in this lecture, too.
The most challenging part to this material is you just have to memorize a new set of variables. Make flashcards, go through them. Just memorize what these variables or symbols represent and be able to recognize them in a word problem. If you can connect these variables to the physical process that’s being described in a problem, then you’re 90 percent of the way done. You’ll be using very simple equations to solve the problem, then.
Let’s start with our warm-up questions. And these all have to do with Chapter 7 and the idea of the impulse momentum theory and the momentum conservation idea. I want you to read these four problems and then just decide for yourself, just based on the description of the scenario, if the name tool that you want to start with is the impulse momentum theory. That means your starting equation is the force during this abrupt event, times the time, is equal to the impulse or the change in momentum.
This was the focus, remember, where you’d be looking at, say, one of the objects in this abrupt event. This is the scenario that you can apply in any kind of abrupt event, even if it’s not obvious that momentum conservation applies.
Momentum conservation, for two objects, was the momentum of object 1 at the beginning, plus the momentum of object 2 at the beginning. So, this is just before the event. The sum of the momentum of the two objects before. Whatever that number adds up to, then, that has to be the sum of the momentum at the end or just after the collision. That would be the momentum of object 1, final, plus the momentum of object 2, final.
The idea was that momentum conservation can clearly apply if the dominant forces that are going on during this event are only between these two objects. If that’s the case, then those forces are equal and opposite on these two objects. That’s, fundamentally, what allows us then to say that the momentum can’t change. What one loses, the other one picks up. So, that’s why this number has to add up to this at the end.
So, to decide which of these two tools you’re going to apply to these scenarios, the biggest trick is to picture these two objects or the pieces that are involved in this abrupt event. And ask yourself “Is there some large force that’s touching either one of those objects outside of or external to these forces between the objects?”
Okay, here’s my brief summary of the last lecture. We focused primarily on just the momentum conservation application in the last lecture. That’s where, as I said above, this Newton’s Third Law force pair, the action/reaction pair that’s between these objects in this event, that’s dominating what’s happening.
Then you can apply total momentum has to add up to the total momentum before and after the collision. This is true whether the collision is elastic or inelastic. Examples, if two objects stick together when they collide, that’s, in fact, called a perfectly inelastic collision.
Kinetic energy is not conserved. A lot of the kinetic energy has to go into or will go into heating up the material. If two cars collide and they stick together, a lot of that energy goes into the buckling of the metal and the deforming of cars.
Elastic collisions is the other extreme. That’s where kinetic energy is conserved. Two super-balls colliding is a good example of an elastic collision. Two billiard balls, even though they don’t seem very elastic. It turns out they are. That there’s very slight deformations that happen during the collision of two billiard balls. Whatever that deformation is, it springs back and these two balls will come back out with the same kinetic energy that you had before the collision. That’s if you add up the total final kinetic, it will equal the total initial kinetic.
So, here’s how you use it. If you have a collision and it’s purely inelastic, you’ve rationalized that the forces between these objects are what dominate. Whether it’s elastic or inelastic, you can apply momentum conservation. If the problem explicitly tells you that this is an elastic collision, then in addition to momentum conservation, energy is conserved and you can use these two equations.
But important, important safety tip. These two equations capture the essence of both momentum conservation and kinetic energy conservation. But those equations have just been algebraically rearranged into a particularly useful form.
The first one here tells you the final velocity of the first object. The second equation tells you the final velocity of the second object. These equations were derived with the assumption that the object that has been labeled “M2” is initially at rest.
That means V20 was 0. If you have an elastic collision, you will only be given a problem where one of the objects initially is at rest. And the other object comes in and plows into it or collides with it. You must label the object that initially was at rest, as “Object 2.” And then, assign your variables accordingly. Then, these two equations below here will work for you.