https://youtu.be/3WfdhUHsn1k
PHYS 1101: Lecture Three, Part Eight
Last topic for our lecture has to do with motion diagrams. This is a very helpful tool to use to try to diagnose the motion and to see what we’re looking at here and to help us solve these problems. A motion diagram is going to be a way of us visualizing or recording the motion, and we’re going to restrict our focus initially here to one-dimensional motion. That means motion of something that’s moving along in a straight long. Doesn’t matter the angle of the line, but you have to imagine drawing a straight line through the path that this object took. It could be slowing down, speeding up, even turning around heading in the opposite direction, but it has to be along the line.
Here’s the main summary. These motion diagrams, they really are going to be indispensable. As you’ll see, one of the keys to this class is being able to identify acceleration, and it’s subtle. These motion diagrams will really help you out to do that.
Here’s in essence what they are. These are going to be a visual record of where this object was during the motion over some time interval, some sequence of interest. So a problem is going to describe a ball rolling down a hill or a ball being thrown up and then having it come down. So there’s going to be some well-defined scope that we’re interested in from start to finish, and it’s during that whole interval that we want to be able to picture the record of where that object was.
Okay, the key though is we’re going to imagine recording, putting a dot down on a piece of paper, a sketch, some way of recording where that object was but we have to put this mark down at equal time intervals, say once every second. By doing that, if we just glance then at the spacing between our time intervals or the spacing between these dots, that spacing alone is going to be a great visual flag to us, or key as to how fast that object was going.
So think about that for a minute and then fill in this blank. If an object is moving slow and I imagine watching it, and say it’s a person and they drop a pencil every second as they walk along. If the spacing between that pencils is short, are they going slow or fast? If the spacing between that pencils is really far apart, are they going slow or fast? So think about that for a minute.
Let me show you a quick movie that should make this clear. This movie is called Constant Velocity and it just shows a demonstration here of this glider being given an initial push and having it move back and forth. It’s on a frictionless track here, meaning there’s really no resistance to it. Once it’s given a push it really moves steadily as it goes along.
The white dots that you see there are these marks that I was talking about, equal time intervals. Let me play it again for you, that portion. So because it’s moving along at a steady pace, the spacing between these is constant. Let’s let the movie keep playing, and they are going to compare them giving it a larger push and having it speed up and go faster. Are these white dots going to be further apart or closer? Here they are. They’re giving it a larger push so it’s going faster between the two. The key here is to notice that now for that same time interval the object gets further, so our spacing between our dots gets larger.
What I want to do now is have you practice drawing your own motion diagram, and this means being able to watch the motion of something carefully and focus on the details of it. What you saw in the previous movie was this object moving back and forth, but it was moving at a steady pace. You’re going to see something now which may be speeding up or slowing down and you need to watch carefully for that. So I’m going to show you an animation and I want you to, on a piece of paper, imagine a mark at the right-most part of the motion that you see and then maybe six inches over the left-most portion of the motion.
You can back it up and watch it a few times, but when I say “start” and when I say “stop” I want you to use about seven dots to represent the motion diagram for this. So the key is going to be should these seven dots which have to represent equal time spacing for the motion that you’re seeing, would these seven dots be equally spaced, should they be getting closer together or should they be getting further apart as you watch that motion from start to finish?
So here’s the animation I’m going to show you. A white ball is going to appear here on the left and it’s going to roll up this hill, and it’s that motion of rolling up the hill that you’re going to want to focus on. So let me play this for you. I’m going to reset it and play it again. Okay, as that ball starts here and rolls up this hill until this very end point where I stopped the motion, use approximately seven dots to represent the motion diagram for this. Try your hand at that.
Okay, I recommend pausing the video here and maybe watch that a few times, and then with what you’ve drawn, your motion diagram, real briefly in three sentences or less just describe to me what your motion diagram looks like. What is the essence of it? I know it’s got seven dots. These dots should be arranged along a line, up at an angle. It should be at an angle because the motion of this ball was along this line, which is at an angle. But what should the spacing be? How should that spacing vary?
Okay, after you’ve done that, then I want you watch the movie again and draw another motion diagram. This motion diagram, it’s the same ball but now our starting point here is at the top. I’m going to hit play here, and from when I hit play, from that start until the ball disappears, focus on that motion. You’re going to draw a motion diagram for that.
Here’s what this motion looks like. Let me play that again for you. Your motion diagram would start now. So maybe back that up a couple times and watch that carefully. Draw that motion diagram and then your next lecture quiz question is another text box where I want you just very briefly, in three sentences or less, to describe how this motion diagram is either different or similar to the previous one. In fact, there are features that are similar to the one you drew before and there are features that are different. Ask yourself what those are, what they would be.
The next question I have for you, it’s another quiz question, question number 11. I’ll give everybody 3 points just for answering. So just pause the video here for a minute and just looking at this motion diagram I’ve drawn to the right, ask yourself is this object moving to the right, to the left, or can you tell?
Well, if you think about that your first inclination, because we’re all programmed to read from left to right, is to imagine that this an object that started here, moved to the right. It must be slowing down because these spots are getting closer together. But that’s an assumption that you don’t necessarily know, that it went from left to right. It easily could have gone from right off to the left.
There’s no way in a motion diagram that’s just dots like that that indicate the time sequence of when this occurred. So technically the right answer to this is you really can’t tell. How would you indicate this? Well, one thing you can do is number them. That would tell somebody the time sequence.
Another handy way to do it is to use an arrow. Let me show you what I mean. We’re going to use these arrows between our dots because with one symbol, that arrow can represent two things: certainly, the direction that it was going, which will tell you the sequence of events, the time sequence, and also the length of these arrows will capture the physical spacing between these dots. That’s going to give us a very strong visual of the velocity.
In other words, say you went up to this motion diagram and I sketched in arrows between these dots. Let me make these arrows here consistent with the choice I made there. Let’s just assume it went from left to right. So the number sequence indicated that, but just as easily if I erase these numbers, I have the same information now. The arrow has to represent the direction it went, so this had to have occurred earlier in time than this last.
For this object, the spacing got larger, meaning this object was able to move further between the time intervals. It started to go faster. So the length of this indicates how fast it’s going. Slow here, faster here. These arrows are going to be a great representation of the velocity vector for this object.
That’s the definition of velocity. We’ll get to that more in the next lecture, but technically the velocity is a vector, the magnitude is the speed. It has to tell us at that instant how fast it’s going, so many miles per hour or meters per second, and the direction of this vector will always point in the direction that the object is headed at that instant. So we’re going to do that. To our motion diagrams we’re going to add arrows between all the points and the direction is going to convey the proper time sequence, the direction the object was headed and the relative size will tell us if the object is speeding up or slowing down.
Here’s a summary statement for you and then here’s a quiz question for you. See if you understand that concept. The 1 and 2 indicates the time sequence of these two spots in a motion diagram. What’s the right velocity vector for that object? Okay, this bullet is going to represent a key, key, key point to the entire class. In fact, I’m going to get out my yellow marker to highlight it.
We’re going to get the hang of drawing these motion diagrams, putting in these velocity vectors, and the whole point to these motion diagrams is to get us to slow down and really look at the velocity of this object and ask ourselves, is the velocity of that object changing? Yes or no? If it is changing, we’re going to emphasize again and again, we’re going to learn that that means the object has to be undergoing acceleration. That’s an important distinction in this class, whether an object is accelerating or not. You’ll hear a lot more about that later.
So what I have for you here at the end of the lecture is a handful of quiz questions that just have you practicing a bit more with this idea of motion diagrams. What I’m showing you is the motion diagrams of two objects, object A on the top, B on the bottom, and these are taken simultaneously. So the motion of these two objects is happening at the same time. It’s from instant 1 to instant 6. You can imagine that the clock starts here and these are one-second time intervals showing you the position of these objects.
So here’s your first question. We’re now up to quiz question 13. For objects A and B, did the two of them start at the same location?
The next question: which object is going fastest initially?
The next question: is either object accelerating? Can you tell from those motion diagrams?
The very last question for this lecture is just bonus points. I’ll just give you 3 points for giving me your opinion. I’m showing you here off to the right three different motion diagrams. In fact, I’m drawing the whole object here at different snapshots. Let’s just assume that these objects are all moving to the right. The boy on the skateboard, the girl running. The time sequence goes from left to right.
From what you know about motion coming into the class, what’s your opinion, what’s critical to the fundamental ideas of motion? Is it the difference between 1 and 2, the difference between 2 and 3, or are the differences between 1, 2 and 3 equally important? Just give me your opinion.
That then brings us to the end of lecture three. There’s a lecture quiz that goes along with this. There are 16 questions on that and those are due, well, forget it.