Buy that special someone an AP Physics prep book, now with five-minute quizzes aligned with the exam: 5 Steps to a 5 AP Physics 1

Visit Burrito Girl's handmade ceramics shop, The Muddy Rabbit: Mugs, vases, bowls, tea bowls...

08 March 2024

AP Summer Institutes 2024 - will the new exam content and structure be discussed?

Of course it will!  

I'm doing several online and in-person P1 institutes in summer 2024 - see the sidebar to the left for details.  Please sign up!  The institute will certainly discuss content and structure changes for the 2025 exams.

What, specifically, will we do?

  • We will do a number of fluids demonstrations and lab activities, including all three major fluids topics.
  • We will do demonstrations with the three minor content changes in P1: parallel axis theorem, quantitative understanding of elliptical orbits, and center of mass location.
  • We will discuss the new exam format - though I will emphasize that in P1, preparing students for the 2025 exam format looks exactly like preparing students for the 2015-2024 exam format.
Of course, the institute will still do all the AP Summer Institute things that you expect.  I'll give an overview of the AP program, the course audit, and AP classroom.  Much more interestingly and importantly, I'll discuss give you access to my course files, problem sets, laboratory activities, quizzes, tests, and a day-by-day planner.  Teachers new to AP Physics 1 can use these verbatim to get themselves started; veterans can use the materials to supplement and inform what they already do well.

The highlight of the in-person institutes is the "studio time" in lab on the final day, in which we all work together to set up and develop laboratory exercises based on released AP questions.  You'll come away with a dozen or more pre-tested new lab ideas!  In the online institutes, which are broadcast live from my actual classroom, we'll instead do "improv time" - challenge me to set up an experiment, or to show how I use demonstrations to teach any topic on the exam.

29 February 2024

As of the 2025 AP exam revision, are Physics C mechanics and Physics C E&M two separate year long courses now? (No.)

On February 29 2024, the College Board released the course and exam descriptions for the revised version of all four AP Physics courses. You can find all the information and links at this page.  

For the AP Physics C exams, the course content will not change.  However, all AP physics exams - P1, P2, C-mechanics, and C-E&M - will be in an identical format as of the 2025 exams.  The format is, 80 minutes for 40 multiple choice questions; and 100 minutes for 4 free response questions.  That means an entire exam takes three hours.

But wait!  For decades, the two physics C courses have each had 90 minute exams, not three-hour exams, because the physics C courses have each represented a single-semester college course.  Has that changed?  

It has not.  Each of the FOUR courses now represents what is taught at the college level in a single semester.  AP Physics 1 represents the first semester of a college-level algebra-based introductory course.  AP C-E&M represents the second semester of a college-level calculus-based introductory course. And so on.

Thing is, we are teaching high school classes on a high school schedule.  The vast, vast majority of high school students taking physics for the first time should do a full year of mechanics.  This full year can be AP Physics 1; this can also be AP Physics C-mechanics for advanced students who are taking calculus.  Both cover substantially identical concepts.

For those taking a SECOND year of high level physics, well, AP Physics C-mechanics probably isn't challenging enough.  It's absolutely normal, acceptable, reasonable, typical for a student to take AP Physics 1 one year, then the combination of C-mechanics and C-E&M in their second year.  This post gives a recommended course sequence for such students.  

Me, I like to teach AP Physics 2 as my second-year high school course.  It's rich in diverse content, meaning that physics veterans won't ever say "oh, geez, not another cart on a ramp".  It's also particularly well adapted to seniors who need the course front-loaded - start with the hardest stuff like electricity and magnetism, and end with the simpler and more concrete topics like optics and thermodynamics.

But in any case, in any way you adapt the courses to your particular school ecosystem, the three-hour AP Physics C exams don't mean anything about how long you spend teaching the material.  Rather, the longer exams are a response to the fact that the pre-2025 APC exams were quite "speeded."  They were as much a test of how fast a student could do physics as how well a student could do physics.  And that's not what anyone wants to test.


27 February 2024

Experimental procedures in AP physics, the redesigned free response section, and Wally the Astronaut

Wally the Astronaut, from The Physics Aviary

Above is a screenshot from the "Work to KE" simulated laboratory exercise on The Physics Aviary. In the exercise, you press start, and a fire extinguisher causes Wally the Astronaut to speed up.  You press stop, and the fire extinguisher ceases to apply a force.  Wally coasts, then passes through two photogates separated by 10 meters.  The time for Wally to cross the photogates is displayed.

You can do a thousand different sorts of classroom exercises with this single simulation.  I like to give this quiz here, go over the quiz, then have students go through this laboratory exercise. But the simulation here is so, so rich, you could do many different things.  Propose your favorite in the comments!

I was asked how I would describe* an experimental procedure on the AP physics 1 exam.  Some teachers ask their students to write a step-by-step instruction manual, including safety procedures and calculation instructions, for an in-class laboratory exercise.  Is that what the AP exam demands?  Should a procedure include calculational instructions?

*The "task verbs" on the AP physics exams will be in boldface as of the 2025 administration.

Historically, the AP readers expect students to communicate what they measured, and how they measured it.  If the experiment could in fact be done in a reasonable high school laboratory, the procedure is legit.  

The prompt on the AP exam - especially the redesigned 2025 AP exams - will be more targeted than what I often see in classroom lab handouts.  For example, the exam might write:

(a) Students are asked to take measurements to create a graph that could be used to determine the mass of Wally.  Describe an experimental procedure that the students could use to collect the data needed to determine Wally's mass. Include any steps necessary to reduce experimental uncertainty.

My response might be, "Measure the force F exerted by the fire extinguisher with a scale.  Then in each of many trials, turn off the fire extinguisher after Wally has traveled a distance d, a different distance in each trial.  Measure d; and divide the 10 m photogate distance by the time output of the photogate to find Wally's speed v."

The analysis - that is, how to do the necessary calculations - is usually in a separate lettered part of the question.  It's fine generally to write the analysis part in the same section as the procedure!  But the procedure will earn points independent of the analysis.  One being wrong or incomplete doesn't affect how the other will be scored.

Part (b) might ask about the analysis:

(b) Describe how the data collected in part (a) could be plotted to create a linear graph and how that graph would be analyzed to determine Wally's mass m.

And I'd say, "Wally's kinetic energy is equal to the work done by the fire extinguisher, .  [That first sentence is probably not necessary for credit!  But I write it so it's clear where my analysis comes from.]  Plot the work done by the fire extinguisher (Fd) on the vertical axis; plot (1/2)v^2 on the horizontal axis.  The slope will be Wally's mass."

Full credit would be earned for a more bare-bones "Plot Fd on the vertical axis, and v^2 on the horizontal.  The slope is (1/2)m."

22 February 2024

A daily quiz based on 2023 AP Physics 1 question 1 - Did you *understand* how to do the homework problem?

It's getting toward the back half of the school year in AP Physics 1.  I've made a first pass at all the major content units; we've done laboratory activities out the wazoo.  We're gearing toward one more half-length practice AP exam before spring break, and then a final half-length practice in mid April.

My students need practice doing cumulative, AP-like problems which require synthesis of multiple concepts; or which require students to choose from the entire year's menu of possible approaches.  Later on, in April and May, I'll have students do authentic AP free response questions in class practically every day, without a safety net.  We're not quite ready to take the safety net away.

No, right now, I'm assigning AP-style free response questions as collaborative out-of-class work.  Everyone is encouraged to collaborate, to seek help when they're stuck.  As long as they get to the correct answers eventually, I'm happy that they're making progress.

You have questions about this approach.  "Even the most honest, diligent students will often just do what their smart friend told them to do, Greg.  Getting done with the assignment is more important than getting it done right.  Even with the five-foot rule religiously followed, at least some students are parroting, not learning, not progressing."  

Unless there's disincentive for pure parroting.  And I don't mean grade disincentive.

The approach I use - which is absolutely not the only effective approach! - this time of year is the daily quiz based on the AP-style problem.  When students come to class, I collect their assignment.  But the first four minutes of class are basic questions about the problem they did for homework.  We trade and grade the quiz, then I collect the quiz.  

Someone who understood the problem, even if they had to be nudged hard in the right direction, can do the quiz just fine.  Someone who truly parroted the smart kid cannot do the quiz.

Yet!  Even the student who parroted and then flunked the quiz has made progress!  The point of the quiz isn't to play gotcha, it's to review the problem in a context in which the students will listen.  If I say "Imma go over last night's homework," no one cares.  But if I say, "here's the answer to question 1 on the quiz and how I know, now mark your classmate's paper right or wrong," I get rapt attention.

My class is contract graded, which means there's no shame for poor performance, no cookie for being perfect.  What's the incentive, then, to take the assignment and quiz seriously?  If someone does particularly poorly on the quiz or problem set, I bring them in for a consultation to redo the quiz.  I just had a student in while I was writing this post.  It took him a relatively short time to redo the problem perfectly, with clear justifications for each part (including the parts that didn't initially require justification).  He didn't get this problem at first, but the combination of attempting it for homework, trying the quiz, and grading someone else's quiz meant that he gained a serious understanding of this problem.

Your ideas are intriguing to me, and I wish to subscribe to your newsletter.  Okay, here's issue 1: a quiz based on the 2023 AP Physics 1 exam problem 1.   Notice how the quiz gets to the essence of the solution without just asking "what was the answer".  This quiz brought forth excellent questions from the class about the physics behind the original question.  It made them think!



A cart oscillates, as shown above and on the problem set last night.

1. Point A on the graph is labeled in red.  On figure 1, draw and label where the cart is located at position A.

2. Point B on the graph is labeled in blue.  On figure 1, draw and label where the cart is located at position B.

3. How is frequency related to period?

4. What is the equation for the period of an object on a spring?

5. When a block is dropped on the cart, does the frequency of oscillation increase, decrease, or stay the same?

6. When a block is dropped on the cart, does the amplitude of oscillation increase, decrease, or stay the same?

7. When a block is dropped on the cart, does the maximum potential energy of the cart-block-spring system increase, decrease, or stay the same?

8. When a block is dropped on the cart, does the maximum kinetic energy of the cart-block-spring system increase, decrease, or stay the same?

9. When a block is dropped on the cart, does the maximum speed of the cart-block-spring system increase, decrease, or stay the same?

18 January 2024

Mail Time: how do I have students describe normal and friction forces?

Vanessa asks:

How do you have students list the normal force and friction force on an object experiencing friction? Would both Fn and Ff be described as "the force of the surface on the object"?

Or do you have them specify "the normal force of the surface acting on the object" and "the friction force of the surface acting on the object"?

Just "force of track on cart" or "force of the ground on the cart" or similar, like you said.

I work so hard to get students to avoid excess language (like "the downward force of the earth pulling down on the upward moving cart") that I'd undo that work if I insisted on other language.  The simplicity helps substantially with Newton's 3rd law, for which we just switch the objects experiencing and applying the force.  

The 3rd law force pair to the friction force?  Well, friction is the force of the track on the cart, so the 3rd law pair is the force of the cart on the track.  That easy - but only if the friction force is originally written with this concise language.


04 January 2024

Mail Time: In the day-by-day plan, what are "four minute drill" and "dang fool questions"?

In my workshop materials for both conceptual physics and AP physics 1, I provide a day-by-day plan for an entire year-long physics course.  It's not that I expect teachers to follow it word for word, of course!  See, the most common questions I get at workshops are "In what order do you teach these topics?"  "What problems and labs do you assign during the momentum unit?"  "How do you review for the exam?"  and, especially, "How do you pace your course?"  Seeing the detailed list of activities and assignments that I actually used over a full school year can help teachers plan for their own classes, usually by adapting the general framework they see to their actual situation on the ground.

But, Marah wants to know: On that plan, I mention the "four minute drill".  What's that?

Here's the post about the 4-minute drill.  In 2012, this was a technique for getting my AP Physics B class to recall equations.  Nowadays, I riff off of each fact on the fact sheet.  "How do you find speed from a position time graph?"  "How do you find displacement from a position-time graph?"  And so on.  Very, very effective and fun.  I use this in all courses I teach, both conceptual and all forms of AP.

Marah's next question: What is this "Dang Fool Questions" class?  

Dang Fool Questions in AP Physics are generally the last day before an exam, or before The Exam.  I go through all the topics on the AP exam (linked is the 2015 AP Physics 1 version, you can still use it for P1 but cut the waves and electricity stuff) as fast as I can, in about 10 minutes of riffing.  Then I ask for questions.  They're "Dang Fool" questions because I say no judgment, ask whatever is on your mind, even if it's the simplest or most obvious thing in the universe, I'll answer patiently and kindly, no worries. Usually the questions I get are things they've encountered in the past but are worried they won't remember how to approach.  

Like, "How would you approach a flying pig-style problem?"  "It looks to me like forces and circular motion... so that means we use the force approach:  free body, components, N2L... where acceleration is v^2/r to the center."  "What are the typical things where you can't use kinematics, again?"  "Anything without constant acceleration.  The canonical situations are, object moving on a spring, object swinging on a string, or cart on a curved track.  In those cases, the free body diagram changes throughout the motion; so you can't use kinematics.  Make an energy bar chart instead."


02 January 2024

How do you teach students to use simple scales for graphs?

From a physics teacher message board:

This topic recently came up on a Facebook group: Some students when plotting graphs will choose an axis scale that uses every line-division, but in turn makes the scale difficult to use and read when plotting points and calculating slopes, etc.

I agreed with most responses that say the student deserves full credit. But I also agree that the scaling makes the graph difficult to use when plotting points and calculating slopes. I always tell my students to select a scale that uses at least 50% of each axis AND is easy to use for plotting points and reading values. However, I have struggled to teaching students HOW to do this. I would appreciate any help or suggestions of exercises or teaching strategies that can reliably help students choose good scales that are easy to use and that work for a variety of graph paper types.

These recommended scaling instructions are exactly what I give my students.  Using 50% of the available grid space on each axis earns full credit for every AP physics rubric I've ever seen.  As for getting students to actually use simple and appropriate scales... as with so much of physics teaching, I think we have to let students mess up, then explain the better approach when the context for that advice is exactly right.

It doesn't matter what I say before we start a lab - no one is listening then.  Nor is anyone listening when we have finished an experiment and are ready to move on.  Just as when teaching Newton's Third Law, there's no One Weird Trick for perfect comprehension.  Rather, the best you can do is fight a year-long war of attrition.  Each time just one more student gets the idea of scaling experimental graphs, rejoice; then hope another student comes on board next week.  

I usually have the conversation about scaling at two key moments in the course of an experiment.  And I design the general approach to full-on graphical analysis laboratory exercises so these two moments are likely to happen.

(1) Data collection: All data is required to go on a graph as it is collected, though it's fine to first take one or two data points for the purpose of estimating the overall scale.  And yes, I have to holler and cajole and (figuratively) poke students until they actually follow this requirement.  But as I'm moving from group to group checking their graphs, I'll often see a graph as you describe - with each line-division representing 3.67 m/s, or 0.13 N, or something similarly silly.  Such a group is generally behind others, perhaps a bit frustrated, possibly arguing with one another.  That means they're ready to listen.  

"Hey, can you tell me what x and y axis values this dot (I point at the graph randomly) represents?  Yeah, it's tough to figure out, isn't it.  But what if you rescaled so that instead of the graph going up exactly to 0.82 N at the top, the top line were 1.0 N, or 1.2 N, or 1.25 N or something like that that's easy to deal with?  Take a look here (where I do a simple rescale on a draft piece of paper, and graph a data point easily)."  Generally at least someone in the group says "oh!" and does the rescale.  

"But Greg, only that one student understood - the other group members will make the same mistake again."  Yup, very likely.  My responses are, (1) see above about the war of attrition; and, 

(2) Analysis:  I only ask for one experimental graph per group.  If the fastest grapher (or the only person in the group who is any good at all at graphing) makes this initial graph, that's fine.  But the next part of the experiment generally requires students to linearize their graph, and then to use the slope of a best-fit line to determine an unknown quantity.  And for the linearization and analysis, each student must make their own graph individually.  They all take pictures of their group's data table, but then they graph the data by themselves.  Collaboration according to the five-foot rule is acceptable, which explicitly means students can't just copy other students' work.  They can talk, they can look, but they have to *do* the scaling and the plotting by themselves.

Students come and show me each step in their analysis, including the linearized graph.  When someone shows me a graph with inefficient scaling, the time is right to have a conversation.  Usually, if the scale is awkward, the data isn't quite plotted correctly; and even if the data is technically correct, they can't answer the "what x and y values does this dot represent?" question quickly.  Either way, I explain how an easy-to-read scale avoids these issues, I suggest a simpler scale... and I ask the student to redo the graph.

Here's where my approach differs significantly from what you're probably seeing on Facebook.  You're right that on an AP exam, a graph done correctly but with suboptimal scaling will earn full credit.  Thing is, my laboratory is emphatically NOT an AP exam.  It's a studio, a place for practice, collaboration, and learning.  The point of plotting data points isn't to earn points.  

Generally, a student sighs, goes back and replots their graph, and finds the new graph much easier.  Aha!  I can rejoice over this student's progress.  Sometimes they got help from a friend to do the rescale.  That's fine, too - because they have to physically create the graph by themselves, they also see for themselves the elegance and utility of a simple scale.  

Very occasionally, a student might try to argue that they don't need to rescale.  I say only very occasionally, because I'm not taking off points, I'm not docking a grade, I'm just asking the student to redo the graph, the same way an art teacher might ask their student to mount their painting to a more attractive frame before the big art show.  The only thing this student has lost is some time.  So such a student generally gets a sympathetic smile from me along with a firm, "I'm sorry you have to regraph, I know it's a pain in the butt, but it's gotta be done."  

(And if a student were to become hostile, the problem is beyond one of whether the graph is acceptable or not.  Passive-aggressive or actual-aggressive argument-for-the-sake-of-argument is unacceptable in the classroom, whether we're talking about scaling graphs, using free body diagrams correctly, or starting a justification with a fact of physics.  Culture building from day one of the class means that generally students listen rather than lawyer up.) 

This student who feels like they have "wasted" their time with a badly-scaled graph usually doesn't make that mistake again!  Lost time matters to students in a way that grades do not.  I cannot recall having this conversation about proper graph scaling in the analysis section of a lab twice in a year with the same student.   

Because my students have been graphing large data sets by hand all year, when the AP exam asks them to graph 5 or 6 data points, they practically laugh at the simplicity.  The large amount of in-class time spent on experimental graphs pays off in that moment. 

30 December 2023

Addressing AI use for school assignments - *It's not about AI!*

"I don't understand why using AI for assignments isn't allowed.  AI is a tool, right, like a phone or a computer?"  Peter made this comment in authentic good faith.  The tone was curious.  Peter, my student, wasn't being performative, or jockeying for social capital - no other students were even around.  He honestly wanted to know my thoughts.  And so I answered honestly and openly.

"I guess it depends on the purpose of the assignment," I told Peter.  "I agree, AI is a tool, a robot.  Would you use a robot to vacuum your floors?"

"Well, yes," he said.  "That's what a roomba is."

"Right," I said.  "Because the purpose of vacuuming floors is to have a clean floor."

I followed up.  "Would you use a robot to lift weights for you when the team goes to the weight room?"

"Of course not!  That's dumb," he said.

"Why is that dumb?"

"Because the purpose of weightlifting is to build muscles, not just to raise and lower a dumbbell."  Peter's eyes widened a bit.  "Oh, I get it.  That makes more sense now."

My analogy here is not likely novel or interesting to people reading this blog.  Conversations in which I explain simple ideas to teenagers are commonplace.  I mean, I teach 9th grade.  I'm used to student puzzlement about things that are obvious to me, things beyond Newton's third law.  For example, I had to explain the meaning of the word "sacred" the other day.  The student newspaper, edited by a senior, referenced "the Beatles rock musician John Lennon," which still provoked the question "what's a Beatle?"

So why do I relay my conversation about AI?  Well, because it's not only about AI.  AI is just the bogeyman of the day.*

*To paraphrase Neil DeGrasse Tyson, who was totally speaking tongue-in-cheek:  AI has been all around us for years.  It's only become a "problem" since humanities professors realized it could write students' papers for them.

The idea of a school assignment as authentic practice, in the same category as sports conditioning or musical scales, was foreign to Peter.  He had always thought of schoolwork as a chore, as a means to an end.  Get these answers right by any means necessary.  

Before you harumph at Peter, consider typical middle school or elementary school culture.  How often do you hear about parents who do their kids' homework for them?*  Even in 1983, a quick look around my class's "visual aids" would show twenty professional-level works of art, and two thrown together with watercolors and rubber bands.  Twice (in the 1990s) I took jobs tutoring middle school students.  Twice the parents stopped calling me when they realized that I wasn't just giving the student answers, and that I wasn't making myself available on short notice when said student forgot they had a major assignment due the next day.

*Well, the parents SAY "I never do my kids' homework for them!  But I always check it over to be sure their answers are correct.  If they're confused and I don't know how to help them, I ask my spouse.  Boy, do I hate it when a class covers material that we don't know about!"

Worse, my experience - in both public and Catholic school - was that teachers praised the students who produced high-end projects with, shall we say, heavy adult influence.  And the few of us with projects that looked like they were fully created by a middle schooler were either shamed or pitied.

I've often addressed assemblages of middle school parents who are considering sending their kid to my high school.  They ask, "what can we do to help our child be ready for the rigors of high school academics?"  My answer is always, "Make them do their homework on their own.  Don't help, check, read over, or discuss their assignments at all, ever.  Allow them to fail - and then let them recover.  Then they will know their successes are truly their own, not due to a 'support network.'"  

This response never fails to produce surprised looks.  Not hostile looks, as the parents are asking the question authentically and are willingly listening to the answer of an "expert".  It seems, from the reaction and the follow-up conversations, that most parents had simply never thought about the developmental purpose of authentic schoolwork.  

Just as Peter hadn't.

24 December 2023

Joe Hicks, "in my judgment"

I attended the Harry Wendelstedt Professional Baseball Umpiring School in 2008, on school sabbatical.  For those readers who were not obsessed with national league baseball in the 1980s, Harry Wendelstedt was one of the best-known and most-respected* major league umpires during his 33 year career.  He was a very old man that year when I met him at the school.

*Respected, yes; but Wendelstedt wasn't God.  Doug Harvey was.

Toward the end of the five-week program, I asked some folks back home in central Virginia how I might get into umpiring at the high school level, now that I had serious training.  They told me to call local umpire supervisor Joe Hicks, a name I recognized.  I called.  I told the man on the phone with the Virginia down-home drawl that I was currently at the Wendelstedt school, and that I was interested in doing some umpiring when I returned.

"Oh, Harry!" Joe said.  "How's old Harry doing?  Tell him I said hi.  Oh, and we'll put you on our schedule this spring."  Okay.  That conversation went more easily, and more interestingly, than I anticipated.

Joe Hicks died last week, age 91.  At his funeral, no shortage of folks discussed Joe's friendliness, his kindness, his willingness to assume good faith of others and to offer help to those in need.  And yes, they discussed his baseball prowess.  They told of Joe helping his grandsons with their hitting when they asked.  They told how when Joe, age 70, was handed a bat during a game of stickball on the beach, his one swing ended the game - he hit a beach house that had been out of range for all others.  Joe was a small-town guy who became famous, yet remained humble, who never used his status for self-aggrandizement.  

I first met Joe and his umpiring partner Alex Smith in the early 2000s when I was coaching JV baseball.  They called virtually every game on campus, JV or varsity.  After the game, they would invariably head to our boarding school's dining hall for dinner.  I found out later that Joe deliberately assigned himself to Woodberry games because we were the only school who offered a free meal to go along with the $50 game check.  

I'd occasionally sit with Joe and Alex.  We'd talk baseball, and baseball umpiring.  Even before my foray to umpire school, I had a reputation on campus as a baseball rules expert; but here were two folks who were truly expert, and who were excited to teach me things.  Joe never let on about his history in the major leagues.  Alex let a couple things slip, bragging about how Joe had played for Casey Stengel, or how Joe had hit a walk-off home run off of Don Larson in the Polo Grounds.  Joe just said, "well, I did, but we didn't call it a 'walk-off' in those days."  

Joe welcomed me into the local association for the 2008 season.  He made sure I had a well-seasoned and supportive partner for my first-ever game.  After that game, Joe called me up to ask me how it went.  "Well, I didn't do anything crazy-bad, but I'm not happy with calling balls and strikes.  I know I missed two curve balls that dropped in for strikes."

"You only missed two pitches in the whole game?  I mean, that's great work!  You got hundreds right, then," he said.  Well done, Joe - being kind, building up the first-time umpire's confidence.  

What sticks with me about my umpiring conversations with Joe is how he taught me, and all umpires in the association, to handle conflict.  Again and again, an umpire would describe a tough situation they* had encountered; and Joe would recommend starting the explanation with a folksy, "coach, in my judgment..." 

* No, not necessarily "he".  Joe's association, in 2008, was the most diverse group of umpires I'd seen.  At umpire school, of 120 trainee umpires from all over the western hemisphere, 119 were white-looking folks, including one woman.  In Charlottesville, there were men of multiple colors, and many racially diverse women.  That's more usual in 2023, but Joe had reached across racial and gender lines before that was common in the hidebound world of umpires.

Joe's thesis was, the umpire is there for the express purpose of making judgments.  If the umpire sticks to that purpose, a coach has little room for argument.  An emphatic "I'm telling you, your runner was out" as a statement of fact practically demands the angry coach to riposte, "no he wasn't!"  But a calm "coach, in my judgment, the catcher put the tag on before the runner touched the plate" has a disarming quality.  Sure, the coach can give his version of events... but rather than emotionally charged statements of conflicting facts, the discussion becomes one of conflicting judgment.  And the umpire is the one paid to use their judgment to keep the game moving.  

I've used Joe's phrase - even his intonation! - "in my judgment," hundreds of time since 2008.  And only occasionally on the baseball field.  Usually, I'm discussing a student's placement (or lack of placement) in an advanced science course.  Or a failing student's plan to improve.  Or my observations of an interpersonal conflict on dorm.  Or a disciplinary matter at boarding school.  Or a problem I've graded.  "In my judgment, this response does not state that acceleration, not velocity, is to the left, and so does not earn the point."  I'm employed by my school precisely for my experience in putting forth this sort of physics judgment.  The 14 year old responding "well, in *my* judgment, it does" sounds silly.    

I miss you, Joe.  Rest in peace.





23 December 2023

Center of mass calculations for AP Physics 1

The revisions to the AP Physics exams for 2025 are imminent.  I've posted about the formatting changes, which are truly no big deal for physics 1/2, and are so, so welcome in physics C.  (Doubling the time available for the exam, but not doubling the length of the exam, will allow students the time they need to approach complicated questions.)

The *content* changes are nonexistent in physics C. In P1, most folks are focused on the major change that adds fluid mechanics.  But what about the minor changes to P1?  They're there, too: the parallel axis theorem, quantitative questions about gravitational potential energy in orbits, and calculations with center of mass.

So what is there to know about center of mass quantitatively in AP Physics 1?

First of all, the conceptual treatment of center of mass motion that's already covered on this exam won't go away.  We still need to understand that the center of mass of a system obeys Newton's laws - with no unbalanced external force, the center of mass moves in a straight line at constant speed; with an unbalanced external force F, the acceleration of the center of mass is F/M where M is the system mass.

Then, the conceptual understanding of the location of a system's center of mass still is relevant.  For a symmetric object, the center of mass is in the, um, center.  For two equal-mass objects, the center of mass is right in between.  And for two unequal-mass objects, the center of mass is closer to the larger-mass object.

The new stuff is based on calculating the position of the center of mass using the equation m1x1 + m2x2 = Mtotal(xcm).  No, please don't write this equation using the notation from the updated official equation sheet, with summation notation!  Your students don't know what that ziggy-zaggy capital E is; and why is there an i in there?  We have to know about imaginary numbers now?!, they'll ask.*

*Yes, I'm aware that students must be able to calculate for more than two objects, in which case the equation I wrote is technically incomplete.  Students will figure out how to add a third or fourth object just fine once they have experience calculating for two objects.  In first year physics, complicated but precise mathematical notation obscures rather than elucidates meaning.  Sort of like any statement that includes the word "technically."

The AP Physics 1 exam famously has minimal use for numerical answers.  Only one of the ten revised "science practices", with which each AP Physics 1 exam question must align, includes calculating numerical quantities.  So while "here are two objects and their positions, calculate the location of their center of mass" is a legitimate question, expect this end-of-textbook-chapter-style problem to be rare.  But what else is there?  Think of the same kinds of questions that are asked about kinematics or energy:

* How would the center of mass position change if the left-hand object's mass were doubled?  If both masses were doubled?  If a third object were placed somewhere?

* Graph the position of the center of mass as a function of the mass of one object; graph the position of the center of mass as a function of time with this known external force acting on the system.

* Describe an experiment which will determine the center of mass position for this set of objects on a thin plank.  Now here's some data from that experiment; plot the data and use the slope of a best-fit line to determine the center of mass position.

All these questions start with the center of mass formula, but use the formula to make predictions, graphs, experimental conclusions.  And that's AP Physics 1 in a nutshell.