Lowest N required for a 5 is 49

Lowest N required for a 4 is 38

Lowest N required for a 3 is 30

 

N = MC + FR1 + FR2 + FR3

 

The highest these components could be are as follows:

 

N-Max = 35 + 15 + 15 + 15

 

This scale information is posted here Friday afternoon, 1/18, just prior to my grading the tests. Therefore, this is not a curve. It is a preset scale that matches the percentages in the nation that determined 3's, 4's, and 5's the year that this particular AP exam was given.

 

Question: In Supplementary Problem 12, study the diagram now, as the dart gets closer and closer before hitting the wheel, how do you express the angular momentum?

 

Related question: How will you handle the fact that the radius vector in L keeps getting shorter and the angle between the radius vector and v keeps changing. Do not scroll down until you have fully tried this on your own. You were supposed to give it effort in class and then want to check in with me about the answer before leaving today. Only one person asked specifically about it.

 

 

 

 

 

 

 

 

 

 

 

Pre-collision, the angular momentum can't be changing. Handling the cross-product correctly reveals that the value of L is mv times a constant length. That constant length is the distance between the horizontal diameter of the circle and the line of motion along which the dart's velocity is aligned. This distance is Rsin(theta), where theta is as defined as in the diagram. This theta is constant, NOT changing.

 

So the angular momentum pre-collision is mvRsing(theta). That means this quantity is equivalent to the wheel/dart's angular momentum post-collision.

 

Any student who did not figure this out or who is not willing to figure this out has another option: they can do my Notes Part 6. Those who do none of the three things above will be choosing to fail on a required topic in the course.

 

Notes Part 6 contain more than just this one concept. Everyone is expected to have used them by now. Those who wait are those who act like physics is complicated and they do this to themselves by simply refusing to assimilate the vocabulary in a timely way.

 

Done correctly, the answer is 1.70 rev. I made one typo on the board when I wrote that alpha equals 0.25 s^-2 times t. I misremembered things. That was actually the torque's expression. Alpha has a different coefficient times t.

 

It's perfectly well done in the attachment, which is why I don't stress over little typos on the board, and why I tell you not to photograph the board. This is because I know that I always back everything up with thorough notes. I try not to write typos on the board, but I also don't hold myself to perfection. So as I've said over and over, you are supposed to be a critical reader of the board and tell me if I have a little careless answer like the one I mentioned above. Either way, the notes posted will have it correct, and I eventually correct myself.

 

Bonus item in this attachment. A solution that predicts how fast a bike will move from knowledge of the gear one is in and radius of the circle on which the foot moves when pedaling.

 

These are unique and necessary. They don't teach anything new. They apply the last topic, Conservation of Angular Momentum. They do a lot to show what this conservation looks like on paper so that a solver could write similar stuff on Supplementary Problems 12 through 16.

 

You might wonder, "Where are Notes parts 1 through 5?" There are old notesets 1 through 5. But their content isn't unique. It's all been covered, mostly through the Supplementary Problems and the labwork. But Notes Part 6 are different. I think a person needs Part 6's topic in written form like I've provided.

 

But here also are Notes Part 5 anyway.

 

(This is the last topic. Nothing new in these notes, it is just illustration of how angular momentum conservation looks on paper when it gets applied. You might be wondering, "Which were Notes Parts 1 through 5?" The things that would have been in Notes 1 through 5 have all been covered. I might still post the old notes 1 through 5, but this year I did things in different order, so I don't think they are necessary, because their content has been covered in the labwork and the Supplementary Problem-set and its solution notes. But Notes Part 6 are different; everyone needs to see what's in Notes Part 6.)

 

Notes Part 6 will help with the Supplementary Problems 12 through 16.

 

In the problem on the front board labeled "93 AP Test", #3. I wrote the final answer on the board as:

 

square root of (3g/L).

 

But Matthew Tsai caught my mistake. The valid answer is:

 

square root of (3g/2L)

 

 

I had solved it as if the beam were going to end vertical, like in the recent experiment. But the accurate solution needed the instantaneous angular speed at the instant when the rod was angled such that its body made a 30 degree angle relative to the horizon. Thank you, Matt Tsai.

 

Most of your Final Exam info will come from these online postings. I mentioned this in class. I'm not planning on repeating much of this information by talking about it. Read what I post.

 

"Resistance ODE Summary" is meant to be very powerful, because I already told everyone the topic of Free Response Problem 2 on the final. The document "Resistance ODE Summary" can only be beneficial to people who use it with at least one full week of questioning time available in the classes before the final exam. The document requires you to respond to things and form your own questions based on critical thinking, and then I expect to hear those questions from vocal students in Period 6 classes as early as January 10, 2019. There will not be much time left between January 10 and the final exam date.

 

People who plan to ignore my advice about preparing for FR#2: Since I can't talk you out of your ways, it would be wise to do things your way in a forum that isn't graded. So that's what the 2015 and 2018 sample documents are for. So if you plan to not prepare ahead of time, see what it feels like on 2015 first, then 2018 and get yelled at by their keys. Keep in mind, last year, I offered the 2015 one ahead of time to 2018 students, just like I'm doing now. And then a lot of people did precisely what they're supposed to do and aced it. And the rest pretty much got zero/15 on the FR2 problem, because they didn't listen to me regarding preparation. So it starts to become comical to read these keys. You have two years' worth now. Again, don't take from them that "everyone blew it". That's by no means true. The truth is the scores were A's and F's, and the only way to be in the A's is to specifically prepare. And all tools have been provided.

 

Here's why the keys are comical: they're preachy. Yet those who need to be preached to probably aren't reading the preachy document. So why do I bother? Well, there is another reason I post them in an effort to point out the importance of differential equations. Speaking the language of differential equations is what FR2 is largely about. What's going to happen in Semester 2? A LOT of differential equations. Those who want to have an easier time in Semester 2 must prepare themselves well for Free Response Problem 2 on the final.

 

Note: I can make infinite variations in the way I ask the questions of FR2. Those who prepare by learning the concepts and the physics will handle anything. Those who only "learn" the mathematical forms will be prepared for nothing.

 

You may enter for credit. Boats that make it across the pool will get an A in an optional gradebook column that will be about 7% of the semester. Boats that win heats or the whole thing will earn greater than 100%.

 

Restrictions: Cardboard only. Duct tape on one side only. Largest boat size is 6'x4'x3'. Team sizes are 4 or fewer.

 

Note: a good boat with a bad paddle doesn't do well. (At least in the race; it can make it across the pool.)