https://youtu.be/jK8VtAoAPRU
PHYS 1101: Lecture Fourteen, Part One
Welcome to Lecture 14.
This is our last content that focuses exclusively on using Newton’s Second Law. And this chapter that we’re working with, Chapter 5, is entitled “Uniform Circular Motion.” It’s nothing more than a special case of curved trajectory motion.
Here are the key points or essence behind this. I want to emphasize these so that you can appreciate that we’re not doing anything new and challenging. We’re just seeing what we’ve already done in a different context.
Here’s some main bullets you’re going to see in this lecture.
The first point is that we now know that any curved trajectory means that my acceleration can’t be zero. If I picture that curved motion as soon as the direction changes, or I speed up or slow down, I have a change in my velocity from one velocity to the next, I know that I had to have a change, a small vector delta-v, that when added to v0 gets me my next velocity.
This change in velocity we know is a good representation of what the acceleration vector looks like. So in fact usually what we do is copy that delta-v vector over to the midpoint here between these three snapshots. And we label this vector “a,” because it is a good representation of the direction the acceleration has to be.
Okay? So if my velocity changes at all — speed up, slow down or change direction, I have to have a delta-v and so I have to have acceleration. We now know with Newton’s Second Law acceleration means there must be a net force. And we further know that the direction of that net force has to agree with the direction of a.
The next conclusion to emphasize is that with curved trajectories, we’re still going to be analyzing them the same way we’ve been doing. We’re going to work with Newton’s Second Law. That’s the equation that the acceleration is equal to the sum of all of the forces but then I have to, to get the proper magnitude of acceleration, I need to divide by the mass, because a bigger object, more molecules, more mass, is going to lead to a smaller magnitude of the acceleration, a smaller numeric value, but the direction of a has to be the same as the direction of Fnet, which is the vector sum of all forces on the object.
Uniform circular motion is nothing more than a special case of a curved trajectory.
Let’s start our lecture as always with a warm up quiz question. This is a variation on one that you saw last lecture. I want you to think about it carefully, so again, I’ll give you a lot of points if you get it correct.
The only difference between this and the last quiz question from the previous lecture is that now when this hockey puck passes line one, the rocket doesn’t continuously fire and keep firing, but instead you only get a brief burst out of the rocket. This causes a brief force on the puck. And that direction of that brief force is to the right.
You need to choose from A through E the trajectory that this puck is going to follow after the rocket turns off. So imagine starting at this dashed line, the rocket has already fired briefly and it’s turned off. So what’s the right path that it takes after that?