FR1 and FR3 Solutions from the Final:

 

You have them. I've said for a long time now, go to this site:

 

 

FR1 was from the test of 2017, number 1.

FR3 was from the test of 1999, number 3.

 

You go to that year and find Scoring Guidelines to open the rubric.

 

By the way, about my posting for the solution to FR2. I'm not making any claims that "the class" did bad or good on the final. Any statement in the FR2 solution document that I made about score cutoffs or the consequences of bad FR2 preparation are statements that I've made before correcting anything. I don't know the class averages. The statements I made in the FR2 solution document are objective statements though.

 

But I do know that class was set up so that 100% of students are supposed to be familiar with FR2 and score well on that page. And I do know that not 100% of students looked at what I told them to look at to prepare for FR 2. (I know this by glancing at a few papers.) So I can say factually that this will be a problem for certain people heading in Semester 2, where differential equations will take a more central role. That's why I make the Public Service Announcement in the FR2 key.

 

I claim: follow my directions from class and a person knows FR2 well. I don't make the same claim about FR1 and FR3. On those you have to apply general principles to a less telegraphed problem. Your adaptation to that is your business. All I can do is teach the principles that you use as tools. I intend no commentary about how people score on FR1 and FR3.

 

But FR2 I telegraphed in advance many times.

 

And finally, speaking of not having FR1 and FR3 telegraphed in advance, people should have noticed by now that I sometimes intentionally rip problems for tests from this site. It's not supposed to be news by now:

 

https://apcentral.collegeboard.org/courses/ap-physics-c-mechanics/exam?course=ap-physics-c-mechanics"

  

Be ready to spend class time on physics principles as they relate to Semester 2. Conversations about what a trick it was to know something on the test will be shut down. No time for unfounded claims. It'll go without saying that all tested items had been accessible information.

 

Some necessary information for Semester 2: In the attachment that's the key to FR2. See it before Tuesday 1/23, because it does affect the first graded thing in Semester 2. Seeing the attached key is a form of HW. I'm not grading anything on 1/23, but I am on 1/25, and the key to FR2 provides important background knowledge that makes the first thing in Semester 2 familiar.

 

A healthy way to understand the final: Don't let anyone tell you how you should have scored on Free Response 1 and Free Response 3. Notice I haven't done that. It's none of my business. However, what is my business is to point out that you ARE supposed to write a relevant concept down on each item in FR1 and FR3, leaving nothing blank, because the concepts stressed were the heart of the course. But still, your willingness to do that - by listening in class and finally realizing that a test is a communication device about relevant concepts - that willingness is your decision. I will not comment on scores on FR1 or FR3.

 

FR2 is entirely different. I AM directly criticizing the act of not scoring most of the points on that. My reasons for this are well-defended, and if you don't know what those reasons are, then you must pay attention to the Public Service Announcement that I put in the attached key for FR2. And there is only one reason why I'm talking about it now at great length: It's to deliver information about Semester 2. People unaware that Free Response 2 on the final was TELEGRAPHED IN ADVANCE are going to have a problem right off the bat in semester 2 if they don't make an adjustment. Everyone needs to read this solution. (Those who didn't blow it on FR2, reading the key won't be a waste of your time, because I mention some alternative solution views.) Anyone who blew it on Free Response 2 needs to face the sobering reality that I point out in the key in the form of what I call the Public Service Announcement. The urgency of this PSA is that this type of differential equation problem isn't going away and is only going to become more central in the course. It was covered no fewer than three times in Semester 1.

 

Last healthy ideas about understanding an AP exam: The final was designed for people to have a predictable time scoring on the Free Responses. On the other hand, the multiple choice isn't supposed to be predictable. A score on it of 22 and up out of 32 is in the common 5 percentage zones in typical years. Nobody would ever be criticized for getting Multiple Choice questions wrong. The national scale is generous. It rewards quality of knowledge, concept application. I as a student never saw roughly the last 13 multiple choice questions on the AP exam I took. Aside from the fact that I wanted to see them because I liked physics, it wasn't a problem, because I did have good quality thinking on the ones I did answer. The national curve rewards that.

 

The in-class test ended up being out of 73 instead of 75. The key to FR2 explains why. It's fairly minor (but annoying to me). You don't need to worry about it, but there is physics to learn in the reason why, so please read it.

 

Based on 73, the AP score cutoffs are as follows:

 

On the national scale the year this test was given, the lowest 5 was 53 of 90. Percentagewise, this is 42.99 out of 73. That makes the cutoff score 43 on the final for a 5.

 

On the national scale, the lowest 4 was 42 of 90. Percentagewise, this is 34.07 out of 73. That makes the cutoff score 35 on the final for a 4. It will not be 34. I announced in December that these generous 3, 4, and 5 scores would be cutoffs and not rounded values. A 4 score must be no lower than 46.67%, AKA 34.07 out of 73. The score of 34 does not exceed that threshold. 35 is the lowest 4.

 

On the national scale, the lowest 3 was 33 of 90. Percentagewise, this is 26.77 out of 73. That makes the cutoff score 27 on the final for a 3.

 

To yet again point out one of the several ways that I telegraphed FR2 in advance, I am yet again attaching the notes called Resistance ODE Summary. Still needed for Semester 2.

 

Let me remind you that Resistance ODE Summary is very thorough. You should review it again. And now. When that's done, here's an opportunity to see if you came away with strong enough language to adapt to what I asked on the 2015 FR2 problem. When this was asked in 2015, a lot of people earned 100% on it, or close to that, and a lot of people earned like 3/15 on it, with very few grades in the middle. The key talks about that.

 

The key was a discussion with people in 2015. But as it's posted here, I break in a couple times and say, "hey if you're reading this in 2018..."

 

The final statements in the key talk about what people are to expect in Semester 2. That was written as a notice to people in 2015, and it's neither negative nor positive. The principles are the same now, but I didn't specifically write the end bullet points for the 2018 students. I did, however, leave them in the key document, because it's stuff that's useful for you to know: things about what a person's mindset should be when approaching tests.

 

The third FR on the final is going to be this very same topic, so prep and review for that the same way.

 

And the second FR is going to be about Separation of Variables and motion through resistive medium. So prepare to be solid on a big chunk of the final.

 

I have a very busy weekend of work, but if I have time, I'll post a typed form of the rotation test rubric.

 

It was agreed that I'd devote time to go over the 1993 Multiple Choice Mechanics Sample Final on Friday, January 12, and the only way to make that happen is that a person must sit for 45 uninterrupted minutes at home between now and Friday and take the 1993 exam like it's a real test. (That means at a desk, with scratch paper for solving, and all that.) Then when you're done, use the key and see how many you got right. If you left some questions unanswered in the 45 minutes, and then want to take more time to do some of them before looking at their answers, that's up to you. This mock-testing and answer-correcting procedure has to happen individually before 8 AM on Friday. DO NOT SIT AND DO THE TEST IN STUDY GROUPS AS YOUR FIRST RUN-THROUGH OF SUCH A TEST. That defeats the purpose. You have plenty of other problems for that.

 

People who show up on Friday as if they will do the 45 minute mock test sitting in my classroom during Period 4 will not be catered to. I'm not devoting those 45 minutes of class time. I'll be set up to show best solutions methods (with efficiency being one goal) of the things that people say they want seen from already having been through them at home. When 1993 is exhausted, people can move onto other years if they want to.

 

I posted the 1993 exam (with all the others and their keys) awhile ago, and here it is attached again. And its key. Do it like a test as if it counted. Moving on...

 

The last useful rotation solution page I made for you is called Cranking Out The Compound Pendulum Collision Answer. You've had access to that for awhile as well. It comes after Notes Part 6. I instructed people to go through that problem now as the document presents it, and I showed the visual in class today. I did just find and correct one typo in it (an exponent of 2 I forgot to write), so I'm re-attaching the document here, corrected. I also refined some of the explanations, but briefly. The document is improved. It's the highest level problem I have in rotation.

 

The Derivatives Quiz from ancient days is being re-offered this Friday at lunch. So anyone who wants to may come and take another Derivative Quiz, and people will get to keep the higher of their two grades on the two quizzes. The given functions will be different, but will involve similar decision-making.

 

Aside from Mock Final Exam questions you want to bring up, the remainder of the semester is tying lab loose ends, and we'll also have the rotation quiz at 8 AM Friday, and that will end within 20 minutes.

 

I don't have any new concepts to highlight unless you want me to address the Parallel Axis Theorem (for calculating moments of inertia) in person. If you don't ask for that, it means you let the textbook take care of it, which is crystal clear. But you do have to know the Parallel Axis Theorem.

 

And finally, I made yet another mistake. I spoke loosely when I said "Smells Like Teen Spirit", yet I know that's from 1991 and not 1993. I should have said "Heat-shaped Box."

 

The thing on the board called "Proof of Why the Two Cat Methods are the Same" is a very big deal, and I had left you to fill it in. If you didn't, or did it wrong, you missed the point. Not many people asked about it. That could either be good or bad. The document "Proofs of Energy Methods" states again what those blanks were to fill in and why they mattered.

 

I've attached the speed answers to 12.1 (with a GREAT Star Wars reference). Make sure you do WS 12.1 on your own before looking at those answers. I explained in class the specific way you'll be graded on 12.1 as HW. The original WS 12.1 document was sent in December.

 

The grading technique of HW 12.1 (Rolling Things) will be linked to the Rotation Quiz that occurs on Wednesday. That quiz has been listed on the Study Guide, and be aware that I have stuck with the Study Guide. With that in mind, I've now covered and shown examples of all the types of problems that are reinforced by Problems 1 through 11 from the Supplementary Problem sheet. Last week through now are the times when I should be seeing people coming to me specifically with questions on those 11 problems. If not, it means, you're setting them up yourself and working to the final listed answers (in brackets at the end of each problem) successfully. And you'd be used to such techniques during testing. Maybe I'll have time to post even more solution notes to some of them like I have, but I'm not sure if I will. You should be coming to me if you need to. Unit 12 SP's are attached here again, because why not?

 

The end of "Proofs of Energy Methods in Rotation" includes a typed version of what's in the handwritten Mallet Problem alternative methods that I handed out today. Note: in the Mallet Problem, the handle's mass has always been (0.5)M. In class today I labeled the handle mass's wrong in a hand-written handout diagram. All algebraic answers have been consistent with the handle's mass being (0.5)M, and the original Mallet Sheet had (0.5)M as the mass. Nothing has changed, even though I originally labeled it wrong on the handwritten document. Change the handwritten document if it doesn't say (0.5)M.

 

Attached is a reposting of the original Mallet Problem but with Answers to 1 and 2 at the bottom of the page. Just in case anyone was ever unclear about what its final answers were supposed to be. This might be overkill, but I want one of its answers loudly stated since some of the learning depends on getting that same answer but from a different point of view (in the last few lines of "Proofs of Energy Methods in Rotation".)

 

I've attached the answers to today's 5-question Homework check. "Readiing Check Answers..."

 

Notes Part 6: Do them now if you haven't. They're great. They finish the unit, and thanks to Liam being the Human Gyroscope, you know enough about angular momentum to tear through Notes Part 6 now. They very carefully help with SP-14 actually. I just re-read them, and I really like them. A Mr. Warren of the past did well writing them. If you disagree, tell Mr. Warren of the present. I re-attached Notes Part 6 here for a dumb reason: the ones I posted for you before say "Part 5" in the title even though the file name is Part 6. Part 6 is correct, and the title in the file is now corrected, so if you haven't already printed them, there you go.

 

MISTAKE CORRECTION: Since mid-December, the file called Unit 12 Solving Strategies has been in your possession. It's a great, informative file. But as of 9 PM on 1/6, I have corrected two mistakes in it: when in error, it referenced "Rotation Notes Part 4". That should have said "Rotation Notes Part 5". It's now corrected. Also, when in error, it referenced "Rotation Notes Part 5" in an effort to give advice on SP's 12 through 16. It should have said "Rotation Notes Part 6" there. That too is now corrected. (What happened was I made my notes a little better and renumbered some this year.) The corrected Unit 12 Solving Strategies is now attached here, as of 9 PM, 1/6.

 

(Cat Problem Document has been here since Thurs. 1/4. I added one more answer to the end of it on Saturday 1/6. Mallet Problem is now written in Word and attached, identical to how it was on the board in class. Mallet Problem came before Cat Problem. If I attach anything else after Cat Problem on 1/6, it won't be discussion-y, mostly algebra-advice-y on doing solution steps on the SP's.)

 

Mallet Problem and Cat Problem attachments make sure you are aware of the main idea of Thursday's Problems from the board. It will have some solving tips, but more importantly tie everything together with the main idea. In blue ink on the side board was something I'm calling The Mallet Problem. Everyone was to have done it, because I pointed it out. Where I wrote in blue in it, "4. Compare the meaning of this to the I.P. Problem", and "5. Compare to Cat Problem", I now want to make sure that those were not just weird cryptic comments. Everything is tied together well if you paid attention and pay attention to the attachments. In class, I did state what the Cat Problem would be. It's now attached.

 

"IP Problem" refers to the animation of the spinning propeller blade whose answer was 8 radians. Why was that so important as an introduction of certain kinematics equations? If you're paying attention to details in BOTH The Cat Problem and The Mallet Problem, you'll find out. If you don't find out why they are connected to the IP Propeller problem, then you speak up in class.

 

The Mallet Problem had 5 items, was up for an hour, everyone was supposed to solve its first two questions. Those who didn't missed something very important, but I know a lot of people did, because I had conversations with people about it. I wrote it there for a big reason. I also clearly wrote its solution steps by the end of the period, saying "you fill in these blanks to complete the algebraic follow-through". The Mallet Problem's actual final answers are now given in the last page of the Cat Problem document attached. If you did neglect The Mallet Problem in class thus far, its full description, with diagram, is now available in Word form and attached as well, so catching up should be simple.

 

It's very important to take The Cat Problem as a quick practice quiz, and then read its key. And then at the end of its key, you'll see how it connects to the Mallet Problem, whose answers will be stated. And then an enormous connection will be made. I specifically designed January 4's class to set up for that connection. And all the seeds got planted as I intended (as long as you did the Mallet Problem). It's up to you to harvest the crops.

 

The 3rd, 4th, and 5th questions of the Mallet Problem were very conceptual, are the most important thing, and their content is handled on the last page of the Cat Problem. Questions about this most important content are highly expected on Monday, January 8.

 

If you're extremely busy in all of your classes and this Cat Problem/Mallet Problem comparison were the only thing you focused on before 1/8, that wouldn't be the worst thing. Better if you have time to use some of my final exam practice stuff as well, but of course we know that the rest of life can eat into our precious physics time, so I'm posting this to help you know the best priorities in my stuff - the good bang for the buck in rotation right now. I hope this posting has helped with that.

 

This posting of rotation Unit Documents have been here since mid-December. This entire posting is not new. I'm just bumping it up as a reminder.

 

MISTAKE CORRECTION: Since mid-December, the file called Unit 12 Solving Strategies has been in your possession. It's a great, informative file. But as of 9 PM on 1/6, I have corrected two mistakes in it: when in error, it referenced "Rotation Notes Part 4". That should have said "Rotation Notes Part 5". It's now corrected. Also, when in error, it referenced "Rotation Notes Part 5" in an effort to give advice on SP's 12 through 16. It should have said "Rotation Notes Part 6" there. That too is now corrected. (What happened was I made my notes a little better and renumbered some this year.) The corrected Unit 12 Solving Strategies is now attached here, as of 9 PM, 1/6.

 

Notice as of Saturday 1/6: Everything after this paragraph was posted mid-December. I'm reminding you on Saturday 1/6, you need to have worked through my notes at least through Parts 5 and 5A by now, and ideally you should be finishing all of my notes through Part 6. (If I write them and give them, it always goes without saying that you become aware of their contents as soon as possible.) I've covered in class the ideas that are handled in Notes 5 and 5A. It's always your job to know what things are in the notes so that YOU can be the most intelligent person about when to use them. For example, by being aware of what's in 5 and 5A (torque), since I gave them early, you then know that their topics (torque) came up big in class, and through that, you were signaled that you're behind if you haven't completed 5 and 5A. People who don't use my notes before 1/8 and then act like stuff is hard on that day should at least know how they got into that state. (The topics of Notes Part 6 (angular momentum) haven't been stated in class yet, but that's no reason to not work ahead.)

 

The book Chapters are 10 and 11. The way I name the units in my curriculum are Unit 11 (Rotational Kinematics) and Unit 12 (Rotational Dynamics)

 

Rotational Kinematics = learning how to relate alpha to omega to theta

Rotational Dymanic = learning to use Newton's Laws to model forces AND NOW Torques and to deal with centers of mass and moments of inertia and to factor such things into familiar conservation laws, only now with allowance for rotational KE. Also, a new conservation law becomes important: conservation of angular momentum.

 

None of the following are required to be used before January 2, but I know some people will appreciate seeing the terrain ahead of time. I will cover the concepts in all of these things in the classes of January 2 and 4. Then we have a weekend. Then we have the 8th. Then 10th is test.

 

The order of the attachments is very important to heed:

Objectives - inventory of required concepts

Rotation Analogs - access this early

Notes 5 and 5A - have to come after the 4 and 4A you already did, but before the rest below.

SP's - a redundant electronic copy of the hard copy I already gave you

Unit 12 Solving Strategies - notes that reference specific SP's

Worksheet 12.1 - Rolling Races - that will also be the last semester experiment

Worksheet 12.2 - Reviews Notes 3, 4, 5, 5A, and reviews the whole semester

Conservation of Angular Momentum = Notes 6 = deep into the unit. Handled in class late January 4

Cranking Out The Compound Pendulum Collision Answer = unit mastery problem

 

Since the last document on the list above references a unit mastery problem to test yourself, don't look at that document's contents until I've introduced the problem in class. The document in this attachment gives away the answer to the problem, so it's to be used when you're ready for it, but you gotta see the problem first. I attached it prematurely, but I did it so that people who wanted to could see the picture of the things we have left to do.

 

 

 

Anything on this site that says "Due January 8", READ IT and take action. I've been doing additions and updates to all such postings throughout the night of January 6. Most of the content in such postings is old news that's been posted for awhile, but my January 6 additions are supposed to be helpful bits of new answers and reminders.

 

One such reminder:

I'm reminding you on Saturday 1/6, you need to have worked through my notes at least through Parts 5 and 5A by now, and ideally you should be finishing all of my notes through Part 6. (If I write them and give them, it always goes without saying that you become aware of their contents as soon as possible.) I've covered in class the ideas that are handled in Notes 5 and 5A. It's always your job to know what things are in the notes so that YOU can be the most intelligent person about when to use them. For example, by being aware of what's in 5 and 5A (torque), since I gave them early, you then know that their topics (torque) came up big in class, and through that, you were signaled that you're behind if you haven't completed 5 and 5A. People who don't use my notes before 1/8 and then act like stuff is hard on that day should at least know how they got into that state. (The topics of Notes Part 6 (angular momentum) haven't been stated in class yet, but that's no reason to not work ahead.)

 

Good quality control on my part: I have two ways of calculating the moment of inertia, and they are represented by Columns B and O in this spreadsheet. Column O matches the formulation that I put into the Notes 4A, and I just added it. Column B pre-existed the Notes 4A before I ever wrote those, and I know that Column B is accurately formulated.

 

Since I made a geometric representation error in Notes 4A, I wanted to make sure that this mistake didn't pollute other things in the document. The document culminates in some algebraic expressions, one of which is the moment of inertia formulation that is in Column O of the spreadsheet. By putting Column O in the spreadsheet and looking to see that its results match those of Column B (which I already knew were accurate) I reassure myself that Page 4 of Notes 4A gives a robust and accurate moment of inertia formulation. (You can also check it by the theoretical integral, which I did, but I could make a math mistake there too.) I'm confident that the moment of inertia part of Notes 4A, Page 4, is unaffected by the geometric representation error that I wrote on the first page. (And I'll next check that the other part of Notes 4A, Page 4, are also unaffected.)

 

For future reference, it's good for you to know the name of the trick that is the basis of the moment of inertia that's in column B. That trick is called The Parallel Axis Theorem. It's part of your required reading, and this is a good chance to see it in action and less abstract.

 

Summary: Column O is more directly from first principles and integration. Column B reveals a nice shortcut that is harder to prove.

 

I hope you make good use of this spreadsheet.