Link to "AP Live" video playlist from Spring 2020

Folks, from March through May, I presented live, 45-minute shows preparing students for the weird 2020 AP Physics 1 exam.  Although the exam-specific information is relevant ONLY to the 2020 exam - the 2021 exams will be in standard format and include all topics - the content and general exam preparation advice is still useful and entertaining.

I keep fielding questions about whether those shows are still available.  They are!  They're sorta buried on the College Board youtube page, because they don't want this year's students to think that the 2020 exam information applies to future years.  But the videos are still available, because teachers and students do want to access them.  

My Physics C - mechanics independent study students have found these particularly useful, because even though they focus on Physics 1, the concepts in Physics 1 are required prerequisites for understanding the more mathematical Physics C- mechanics problems.  

Here is the link to the playlist!

Josh Beck - who is an awesome physics teacher and AP reader - presented about half of the shows, and I did the other half.  My pet hippopotamus Edna and her friends only show up in my episodes.  Enjoy!

Mail Time: Linearizing a parabolic distance vs. time graph

An APSI participant writes:

I had a question regarding linearization.  We just did the free fall lab and a student graphed their data to get the parabolic curve of d vs t.  When asked what they would do to linearize, they stated to convert d to v and graph v vs. t.  

When they determined v, they did d/t for each point.  Then plotted that value for Vavg vs time.  Is this an acceptable way of linearizing?  

My first instinct is no, because the slope of the v-t graph, while still the acceleration, does not produce the value as it would if you did d vs t^2.  

The slope of their v-t graph was 5.15 m/s/s.  If they would have plotted d vs t^2, they would have a slope of 5.45 m/s/s with an acceleration of 10.9 m/s/s for g.

This is a common approach by early-in-the-year AP Physics students.  They did not do this right... 

By dividing just d/t for each point, they took the average velocity from the beginning - that's not how a velocity-time graph is made, and that quantity is rather meaningless in the experiment you describe.  Basically never divide the values of two data points!  :-)

What WOULD be a reasonable alternative approach to this experiment would be to make a legit velocity-time graph: by taking the slope of a tangent line to each point on the d vs. t curve.  Then plot those *instantaneous* speeds as a function of time.  That's a true velocity-time graph, for which the slope is acceleration.

Of course, that sounds way, way more complicated than just using lab linearization approaches of writing the relevant equation, then plotting data as it appears in the equation, d and t^2.  

Hope that helps!

Notation for Newton's Second Law: F, Fnet, Sigma-F. And Julius Sumner Miller.

Alex writes in:

I was listening to Julius Sumner Miller lecture on YouTube while doing some work last night and noticed that he said F=ma. 

So my question is using the term net force something that teachers just use? Was it something that wasn’t used then but is common vocabulary now?

Glad you reminded me about Julius Sumner Miller (which is still what my brain wants to call my colleague Julius Reynolds, because until him I'd never actually known a Julius other than Orange Julius).  I should watch some of those videos with my AP class when we're online in December!  Make sure you watch the one where he puts random stuff in liquid nitrogen, and forgets some things in the carafe.  JSM is a big, big influence on my teaching style, and I'll bet you can tell.  He didn't have a pet hippopotamus named Edna, though, more's the pity.

That's an interesting history question, Alex... there are people who research the history of physics education.  I wonder... I copied Gardner Friedlander, one of my go-to folks for AP Physics history, in case he has something to add.  (He did - see below!)

Before we start - I am not discussing whether your personal version of Newton's Second Law is the best one.  Of course it is, and all others are inferior.  I will not publish any comments that talk about why one notation is best.  I'm discussing the various notations, their history, their pros and cons.  If you use sigma-F but I don't, that doesn't mean you're better than me or vice-versa.  Really. We all have our reasons for our notation.

I do seem to remember that when I grew up - and I watched JSM in high school physics class all the time, on VHS - the phrase in common use was just "F=ma."  I looked back at the earliest AP solution set I can find, and it says sigma-F = ma.  (There was no equation sheet back then, before the days of graphing calculators.)  The 1983 New York Regents exam says "a=F/m."  I'd love some evidence that my recollection of "F=ma" being the common statement is correct... certainly I think that was the non-physics-class zeitgeist meme that people would say.

When I started teaching in 1996, I always used the notation "Fnet," emphasizing that only the NET force could be set equal to ma.  See, I discovered quickly the common issue that students would pluck a force value from the problem statement, pluck a mass, and smash them together into F=ma to get an acceleration.  I didn't like the sigma-F notation because students tended to add force numbers without reference to direction when they saw that.*

*or they would cluelessly wonder "what's that big ol' squiggly E, I dunno, it's got an F next to it, I guess."

In the AP physics 1 revolution, the curriculum design committee (led by some top rate physics educators) decided to rewrite as a=sigma-F/m, because this emphasizes that acceleration is usually the quantity that is the result of the various forces.  I had some discussions with a big group about whether and why that made sense or didn't make sense, and how that change should be explained.  On the equation sheet now, it reads a=sigma-F/m = Fnet/m.  I don't know, but I suspect, that this dual notation is to accommodate the two dueling camps of physics teachers: those who prefer students to write using vector notation "Fn + (-mg) = ma" because down is the negative direction, getting a negative acceleration if the acceleration is downward; and those who prefer students to not use negative signs but just magnitudes of forces, writing either "Fn-mg=ma" or "mg-Fn=ma" starting with the direction of acceleration.  The former is sigma-F=ma, the latter is Fnet=ma.

Gardner Friedlander says: He quoted several sources from the last 50 years that use all three versions of what should be set equal to ma: F, Fnet, sigma-F.  

His thought - which I agree with, now - is that the difference is probably not so much a historical trend, but rather the intended audience.  Julius Sumner Miller and Paul Hewitt were aiming at a general, non-mathematical audience trying to understand physical concepts, so used just F.  Mathematically based courses preparing students for continuation in the physical sciences used sigma-F.  And those aiming for an in-between audience, like AP Physics B, AP Physics 1, high school honors courses - they tended to go for the in-between notation of Fnet.

And in a final twist... I've started changing my notation to "netF = ma".  I've noticed for years that Fnet is confused with Fn for normal force; and that it's a misconception that "Fnet" is a separate force like the friction force or a tension that should be on a free body diagram.  By using the language of unbalanced and balanced forces (as the Physics Classroom does), the net force is just the unbalanced force; so netF emphasizes something different from Fnet.

Are Kepler's Laws Covered in AP Physics 1?

Kepler's laws are never a starting point for an AP Physics 1 question.  

That said... situations involving gravitation and planetary orbits are part of Physics 1.  AP Physics 1 does include circular orbits, from which one could in principle do the work that derives Kepler's T^2-r^3 law.  AP Physics 1 does include angular momentum conservation, from which one can understand the same consequences as Kepler's equal areas/equal times law.  There's no need to understand elliptical orbits, just circular orbits.  

Physics C includes some questions where the best approach is to cite one of Kepler's laws and logic from there.  Physics 1 does not - the approach to every planet problem starts with Newton's law of gravitation or conservation of angular momentum.

The physics behind a football spiral

I was forwarded this article (wsj subscription required) in which author Jason Gay issues a warning: SPORTSWRITER DOING PHYSICS!  Well, I've done a lot of sportswriting and I've done a lot of physics.  I give Gay enormous credit, because his physics explanation was crystal clear to me.

Gay explains a recent paper in the American Journal of Physics, in which the authors show that gravity by itself is not sufficient to cause a football to spiral in the direction of its motion throughout its flight - conservation of angular momentum suggests that the initial angular momentum can't change without an external torque (which gravity does not supply).  The football's path should bend in a parabola... but the point of the ball should always point in the same direction.  Then air resistance should cause the ball to rotate end-over-end, "like a duck".  Presumably he means a duck in flight who suddenly experiences cardiac arrest, but I won't quibble with sportswriters' analogies.

This paper's authors - Richard Price, William Moss, and TJ Gay - show that contrary to previous models, torque provided by air resistance continually changes direction.  This changes the direction of the angular momentum such that the spiral always points tangent to the football's path.  Cool.  That makes sense.

Now, I'm an experimentalist... my next step would be to hire Patrick Mahomes (the reigning Super Bowl MVP, quarterback for the Kansas City Chiefs) to attempt to throw a spiral in NASA's enormous vacuum building.*  If the paper is right, then even Patrick Mahomes should not be able to throw a proper spiral.  Rather, though the football should spiral, the nose of the ball should continue to point in whatever sorta-upward direction it was spinning when the ball was released.  Without air, there'd be no threat of a dead-duck motion, but the spiral shouldn't gracefully arc throughout the flight as in the NFL Films films.

* Or perhaps on the moon.

Anyone want to write this grant?

Mail Time: I love the AP Physics 1 Workbook. Why isn't there a physics 2 or physics c workbook?

If you teach AP Physics 1, I hope you've discovered the Workbook.  It's great.  But, the question was asked, why only for Physics 1?  Why not provide the same sort of scaffolded, sequential, task-modeling exercises for all physics courses?

There's not a Physics 2 or C workbook simply because of the necessary person-hours - and high-end expert person-hours at that - required to produce the book!  Amy Johnson, who's as expert as you'll meet, spent a truly ridiculous amount of time spearheading that project (and writing much of it herself).  

Then, AP Physics 1 was prioritized because that's the largest and hardest course, the one where it's rather commonplace for a school to tell a biology teacher "oh, you are certified in science, you can teach AP Physics 1, good luck."  I've met so many of these unfortunate folks.  They often become outstanding physics teachers!  But in those first couple of years, they need an anchor.  

The workbook can be that anchor.  While it's in no way good practice, it is nevertheless possible for an overwhelmed and inexperienced teacher to do nothing but assign the workbook, page by page... and their students would have a fighting chance of success in the course.  Then the teacher can build on that foundation in future years.  

And finally, P1 is the most misunderstood AP course.  "1 - Algebra-Based" conveys a sense of simplicity to nonexperts, such that administrators and parents and amateur college counselors routinely push weak students into this course, expecting an easy STEM AP credit - yet P1 is, statistically, the most difficult AP course of all.  Teachers don't always know better, either: so many assign Giancoli calculational problems, teach nothing beyond plug-n-chug, then are surprised and sour-grapes-y when few students pass the exam.  

The workbook is there to demonstrate the kinds of verbal responses that will be necessary on the exam; and to guide students (and teachers) toward building the necessary communication skills.  For strong students, AP C can be picked up from textbooks and Khan Academy-style videos.  Physics 1 isn't so easily mastered, even by top-rate students.

Hope that helps explain... Really, the physics folks involved with the College Board are trying to help everyone.  They ain't perfect, and they can't please everyone, but they're trying!  :-)