AP multiple choice question: angular momentum change for a rebounding sphere

One of my favorite questions from the 2014 released AP Physics 1 practice exam involves angular momentum in a collision between a sphere and a pivoted rod.  Teachers can check out the question (I think) at this AP classroom link.  (If that doesn't work, search the AP classroom question bank for "A thin rod of length d".)

In this question, a sphere bounces off of a pivoted rod.  The rod rotates after collision, and the sphere rebounds with a given *linear* momentum.  The question asks for the change in the rod's angular momentum as a result of the collision.

Some folks have tried to understand the solution by combining linear and angular momentum.  But that's not correct!  It's never allowed to combine linear and angular momentum in the same equation - you've gotta either conserve one or the other.  Linear momentum never transfers to angular momentum (nor vice versa).

This particular AP question explicitly asks about angular momentum.  Therefore, even though the problem gives the linear momentum of the sphere as pf and pi before and after collision, we've got to use conservation of just angular momentum about the pivot.

Angular momentum of an extended object is Iw.  That's what we'd use for the rod, if we needed it.  For a point object, angular momentum is mvr, where r is the distance of closest approach.  In this problem, the variable d is the closest the ball ever can get to the pivot, so d is the distance of closest approach.

Now, the change in angular momentum of the rod is equal to the change in angular momentum of the ball - that's what angular momentum conservation means!  The ball's change in angular momentum is (mvid) - (-mvfd), because the ball rebounds - it changes direction, represented by the negative sign mathematically.  The negative signs cancel to make a positive sign.  Here the masses m and speeds vi and vf aren't given, but the linear momentum is: mvi *is* pi, and mvf *is* pf.  That's where we get pfd + pid as the answer!

2022 Conceptual Physics Summer Institute: July 16-17, Registration open!

Announcing the 2022 CPSI!  This year, I'm only offering a single session, the weekend of July 16-17.  We'll take up to 40 people, but when we're full, we're full! :-)  

Update 14 July - I've sent all registered participants a welcome letter, website, and zoom link.  If you're registered and DIDN'T get this email, please contact me right away!  And you can still sign up if you'd like.  A few spots remain.

Folks, I'm already teaching several AP summer institutes - see the left-hand sidebar for details.  But what if you are looking for physics professional development that is NOT aimed at college-level physics?  I mean, I meet so many of you each year who teach on-level, honors, college-prep, Regents... to all ages, to all varieties of student.  And in my personal mission to spread physics knowledge to as wide an audience as possible, these sub-college courses represent a critical first point of contact with our discipline.  I focus as much energy on my conceptual course as on my AP course each year.  So I'd like to focus some of my summer professional development expertise on those who teach these first-level courses.

We've done this for two years now.  See the comments at the end of this flyer for participant reviews.  They all say, this institute was an amazing, friendly, and productive experience.

I'm offering a two-day institute on July 16-17, 2022.  It will be online, broadcasting via Zoom from my lab.  Skip past the institute description for fees and registration instructions.  The single session will be limited to the first 40 who sign up.  The daily agenda is included here at the bottom of the page.

Jacobs Physics

Conceptual Physics Institute Description
July 16-17, 2022

All levels of high school physics can be taught conceptually – where verbal and experimental reasoning is prioritized over mathematical problem solving.  While mathematics are used extensively, they are used as a tool to create predictions about the workings of the natural world.  Whether you teach “general”, “on-level”, “honors”, “Regents”, or “college-prep” physics, a conceptual approach can be adapted to most any introductory physics topic – and to most any state or district standards. 

In our institute, we will discuss, practice, and share methods of teaching common physics content in a conceptual style.  I will be broadcasting from my laboratory via zoom.  Time will be devoted to experimental methods that are especially useful at the sub-college level; to course planning on a year-long and a unit basis; and to best-practices physics pedagogy, which differs substantially from pedagogy in other disciplines.

Participants will be given a full-year’s set of classroom-ready materials, including fact sheets, in-class and laboratory activities, assessments, and planning documents.  More importantly, through their interactions with the instructor and with their colleagues, participants will develop skills and ideas for adapting these materials to their specific classroom environment.  Those attending will also earn a certificate indicating their participation in 15 hours of physics professional development.

 

How much does it cost:  $200 for the weekend.  The schedule of events is listed below.

How do I register?
(1) Click the "donate" button below (or in the left column of the blog).  It will take you to paypal.
(2) Enter $200.00 as the donation amount, either through paypal or credit card
(3) Click "Add special instructions to seller" or "Add a note"
(4) In the note, please include your name, preferred contact email, and institution
(5) Fill in payment info and click "donate now"

That's all - I'll be back to you within a day or two confirming your registration, and sending you links to the classroom-ready materials.

Cancelation issues: If you register then can't attend, contact me via email.  As long as I can replace your spot, I'll send a full refund; if I can't replace your spot, I'll refund all but $25.

Schedule: Each session will include both whole-group presentation/discussion, and breakout groups for activities.  In between sessions and during breaks, Greg will be available for informal conversation. 

Saturday 16 July (all times eastern time)

10:00               Introductions

                        What does “conceptual” mean – defining levels of physics

Different levels of physics: developing your program

                        Different levels of physics: developing your resources

11:30               Eight styles of physics laboratory activities

            Including the two best-adapted for conceptual physics

My first day activity – reflection experiment

My first group laboratory experiment – refraction

1:00-1:30    break

1:30                 Sequencing your course

Starting the year right: the most important physics teaching skill

Justifying answers with facts

Simple ray diagrams for optics in conceptual physics

Justifying answers with equations

In-class laboratory exercises: circuits

                       

3:00                 The daily “quiz”

Tests and quizzes, targeted to different levels

                        Other sorts of assessment

                        Preparing for the trimester/semester exam

                        Adapting a conceptual course to external standards

                        In-class laboratory exercises: motion graphs

Afternoon – asynchronous

                        Read through the shared files

                        Read through the Jacobs Physics blog

                        Adapt to your district or state standards

                        Bring questions and ideas for the social or for Sunday

7:30                 Optional Zoom social: Dinner, dessert, drinks, and conversation.  BYOB, obviously. 

Sunday 17 July

10:00               Building and creating experiments with whatever you’ve got

                        Developing your own in-class lab exercises

                        Using or substituting inexpensive equipment

                        In-class laboratory exercises: direction of force and motion

11:30               Methods to speed your grading

                        In-class laboratory exercises: forces in 2-d

                        In-class laboratory exercises: motion in 2-d

                       

1:00-1:30    break

1:30                 The final third of the year – once skills are built

                        How I teach impulse/momentum

                        Energy bar charts at the conceptual level      

                        Laboratory exercises with harmonic motion

                       

3:00                 Sharing: Any Other Demos

Online simulations:

                                    The Physics Classroom

The Physics Aviary

                                    Vernier’s Pivot Interactives

                        Ending the year: the Physics Fight

Extended facts about orbits

In November when I *first* introduce Newton's Law of Gravitation and orbits, I keep things very simple.  I give the equation for gravitational force, define a gravitational field, and that's about it.  

We do a practice exercise where students must use circular motion facts to determine how the speed of a satellite in orbit depends on various parameters.  (We test predictions using an online simulation.)  You can see me do this exercise in AP classroom, on 3.8 Daily Video 1.

There's more to understanding orbits.  But students weren't ready for that "more" back in November.  Now they are.

In March as we begin our "tapering" review toward the May 12 exam, I want to revisit topics we've discussed previously, but in greater depth.  With regard to orbits, back in November we didn't know about energy or angular momentum!  Now we do.  So let's go back and discuss orbits again, this time with EVERYTHING we can think of.

Below are the NEW facts I'm bringing up, facts I ignored earlier in the course, alongside some commentary.

Two Types of mass:

Gravitational mass is measured using any relationship that involves a gravitational field or force.

Inertial mass is measured using any relationship that does NOT involve g, such as netF = ma or 

.

In all experiments ever performed, gravitational mass is equal to inertial mass.

Early on, I'm excited for students to simply understand that 100 kg is not a force, and that a 100 kg object on the moon has a mass of 100 kg.  There's no way I'm gonna try to explain the very subtle difference between gravitational and inertial mass!  Now, though, it's okay to add this subtlety on.

Gravitational potential energy

Near the surface of a planet, the potential energy of a planet-object system is mgh, with h = 0 at the lowest point of the motion.

Away from the surface, the potential energy of a planet-object system is treated differently:

·         PE is larger the farther from the planet’s center.

·         PE has a negative value (except when the object is way far away from the planet, in which case PE is zero).

·         The equation for potential energy is

Don’t use this equation unless you must derive an expression.  The negative sign is confusing.

That last italic piece is important.  Most AP1 orbits questions are not going to use this actual equation!  The first bullet is the big deal... planets getting farther away from one another increase their potential energy.  That means the potential energy gets closer to zero, gets less negative... but that subtlety is beyond many of my students.  Not to worry!  These facts will allow for a correct and clear answer to virtually any gravitational PE problem.

Orbits

In a circular orbit of a satellite around a planet, consider the planet-satellite system:

·         Kinetic energy is constant (same speed)

·         Gravitational potential energy is constant (same orbital radius)

·         Angular momentum mvr is constant (no external torques)

·         Total mechanical energy is constant (no external work, and no internal energy)

 

To find the speed of a circular orbit, set gravitational force

 equal to ma, with

In an elliptical orbit of a satellite around a planet, consider the planet-satellite system:

      ·         Kinetic energy is NOT constant (speed changes)

      ·         Gravitational potential energy is NOT constant (orbital radius changes)

      ·         Angular momentum mvr is constant (no external torques)

   ·         Total mechanical energy is constant (no external work, and no internal energy) 

Now that the class is well familiar with the concepts of energy and angular momentum, I want to be explicit about conservation in orbits.  This set of facts is also a good reminder/reinforcement of the statements elsewhere in my fact sheets about the conditions under which mechanical energy and angular momentum are conserved!

Woodberry Forest Conceptual Physics Tournament - May 22 2022. Come be a juror! (We will pay...)

In my school's conceptual physics program, we give cumulative written exams after the first and second trimesters.  In lieu of a final exam*, we are once again running the Woodberry Forest Conceptual Physics Tournament!  This is a competition for 9th graders, to be held at 1:00 on Sunday May 22 2022.  We've done this before, in 2017 through 2019.  Now we are back.

*No, to be clear to all, we're not giving an A to the winner and an F to the person in last place.  That's silly.  We're just having a fun, competitive tournament, to determine a winner.  Jurors engage in discussion and conversation with participants about their problems.  Jurors then award scores and write comments for the participants; jurors aren't assigning grades!

How does this tournament work?

On May 2, I will reveal a slate of three problems to the 68 participants.  These problems will be in the style of AP Physics 1 "paragraph response" questions.  Except, rather than just answer in a paragraph, the students will spend the month of May setting up experiments to provide evidence for their answers.  By tournament time, each student will be expected to be prepared to discuss the solution to two of the three problems, with both theoretical and experimental support.

At the tournament, each student will participate in two "physics fights."  Think of these physics fights like a miniature version of a graduate thesis defense.  Students will have a strict limit of two minutes to present their solution to a group of two or three jurors, who then will engage each student in conversation about the problem for five minutes.  The students are evaluated by the jurors not only on the quality of their solution, but also on their ability to discuss the solution, to confidently hold a conversation with the jury.

Importantly, jurors are explicitly instructed on their primary role - to find out how much the students DO know, not to expose what they don't know.  

How do the students prepare?

Starting on May 2, all conceptual physics classes the rest of the year will be devoted to tournament preparation.  They'll set up experiments in class, they'll be assigned to write up their solution as homework, they'll practice presenting.  

Most importantly, our AP physics classes will spend their final weeks of the school year serving as mentors to the conceptual students.  I will assign each AP student to lead groups of two or three 9th graders.  The AP students will dive into the problems with the conceptual class, helping to create and analyze experiments, helping the freshmen to understand the details of their presentations, and serving as mock-jurors in practice sessions.  This mentoring serves as the final project in lieu of the exam in the AP classes.

We need jurors.

The key, I think, to any class project is external assessment.  I and the other conceptual physics teachers will play the role of coach and advocate, always encouraging and helping the students to deepen their understanding of the problems and to improve their presentations.  Our relationship will be purely supportive, enthusiastic, positive.  

We can't then turn around and grill these same students as examiners!  That'd be like our football team's coaching staff refereeing the state finals.  Even -- especially -- if their officiating were fair, the coach-student relationship, both in before and after the game, would be irrevocably compromised.

So we need jurors.  We can pay.

Would you like to come to Woodberry on May 22 to be a juror?  We'd ask you to arrive at lunch time, like 11:30.  We would have a meeting of all jurors in our beautiful dining hall over lunch.  

Then we'd ask you to be a juror for a couple of hours' worth of physics fights.  You'll be partnered with several other examiners over the course of the afternoon, getting to know a diverse set of fun folks from all over.  When all students have presented their two physics fights (to two separate juries), we'll gather the jurors for conversation, coffee, snacks, and their paycheck.

In any case, our goal is to be done by 3:30, or possibly 4:00 if there are logistical issues.  No later -- our students will be attending the final seated meal with their advisors that night followed by study hall, so we can't run late.

We will pay you $100 plus lunch (and even dinner, if you'd like to stick around) for your time.  (If you're coming from more than a few hours away, we can put you up on campus on Saturday or Sunday night.) I think you'd find that the camaraderie among the jurors and the engagement with the students will make the trip worthwhile.

Who's eligible as an juror?

Anyone who has passed a college-level physics class.  This includes alumni of your advanced physics class, even if they're still juniors or seniors in high school - we've had several teachers bring a van of students, and they've had an awesome time.  We've had local college or graduate students on juries, we've had parents, alumni, colleagues who teach other subjects, grandparents, friends... Anyone willing to engage in conversation about physics at the high school level, as long as you can recognize good and bad physics, we'd love to have you.  We are looking for a diverse juror pool, which especially includes diversity in age - truly, we want folks in their teens as well as folks in their 70s, and everywhere in between. When I run the USIYPT, I find the mixture of undergraduate / graduate / professor / high school teacher / industrial physicist / retired physicist on the juror panel allows some amazing relationships to develop.  I'd love to create a similar vibe here.

How can I sign up?

Send me an email, or contact me via Twitter, or call me -- my contact information is on the Woodberry Forest School faculty page.  I'll send you more information, including the three problems, and our current draft of the scoring rubric.

We would like to get 54 jurors - the first 54 who sign up.  I can't wait to see some blog readers - I'll even introduce you and your students to my pet hippopotamus, Edna.  :-)

Fluids is Coming - what equipment do I need?

Reader Ryan writes in:

I saw the potential changes to the CED [which are happening in 2025!] in AP Physics 1 with Fluids being added as a unit. What supplies would you recommend for this unit?

Good news is, you've got a couple of years.  The only substantive change in the works for P1 is to add a fluids unit to the other seven existing units.  And, this change will take effect for the 2025 exam.  

Fluids is nice because, well, the primary thing you need is a fluid - and water is plentiful.  :-)  I'm gonna have to think and decide what is worth money and what's not.  I mean, Bernoulli can be demonstrated with a hose, or with a tennis ball can.  You probably already have identifiable metal cylinders in your chemistry department that you can use to discuss Archimedes principle. Problem 2 on the 2010 AP Physics B exam is one I wrote based on an experiment I do - but with water, not oil.  I mean, it's easy enough to do this experiment with alcohol or vegetable oil, but it's much messier to clean up.

I'm sure I'll post other ideas eventually [like this one], but nothing strikes me as a must-have like smartcarts or photogates or carts-with-tracks.  I'd hold off buying stuff, and then when you see something that would make your life easier, buy it then!  If you have a limited budget, don't spend anything at all on fluids, just add more smartcarts or similar.