Mail Time: Is Pluto's Angular Momentum About the Sun Conserved?

Dear Greg, 

I have been reviewing with my students and want to pose this question to them but am having a bit of difficulty with the solution:

The dwarf planet Pluto goes around the sun in an elliptical orbit.  Consider Pluto only.  Is its angular momentum about the sun conserved?  Justify your answer.  

I know that in an elliptical orbit the distance between the sun and Pluto would change and therefore angular momentum would not be conserved.  However what is throwing me off is considering Pluto only.  Does this mean you do not take into consideration the elliptical path?

Angular momentum is conserved when the system experiences no net torque.  Pluto alone is the system.  What forces act on Pluto?  Just the (gravitational) force of the sun.  Does that force provide a torque about the sun?  No - the force of the sun on Pluto is always directed toward the sun, so there is no lever arm for that force about the sun.  (Another way to say it: the line of the force of the sun on Pluto goes through the axis of rotation, which is the sun itself.)  So angular momentum is conserved.

How does that square with the elliptical orbit?  Angular momentum for the point-object Pluto is mvr, and that can’t change.  So when the distance from the sun r is small, the speed v is large, and vice versa.  That is in fact the case for all planets.  The earth moves faster around the sun in (northern hemisphere) winter, when we’re about 3% closer to the sun, than in summer when we’re a wee bit farther away.

GCJ

Oh My Gawd, It's a Test!

How does your class react when you announce an upcoming test?

Ideally, they say nothing.  They register the reminder with the same demeanor with which the New England Patriots took the field for their seventh Super Bowl this century: calm confidence mixed with a tinge of nervous anticipation.

Too often, though, your announcement incites a game of misery poker, each student in turn offering a complaint, a sarcastic comment, or an increasingly dramatic vision of how the upcoming test will ruin his life.  How do we as physics teachers encourage an appropriate culture around testing?

It starts with the very first comment about the very first test.  If you let small passive-aggressive comments go unchallenged early, they'll eventually turn into big actual-aggressive comments that can't be mitigated.

I deal firmly, kindly, and somewhat publicly with the student who fans the flames of drahma.  "Oh my goodness, I studied for hours and I know I'm gonna fail.  Here goes nothing."

In front of all, I'll put the same phrase in the context of sports: "Johnny, you're a baseball player... you just said to your team and coach, 'I'm next up to bat.  Just know that I suffered through these horrible practices all week, I'm still terrible, and I'm gonna strike out right now before I let a grounder go through my legs next inning.'  What would your coach say?  Oh, that's right, she'd bench you.  She'd replace you with someone who wasn't explicitly and aggressively saying he'd let the team down."

On a team, such chicken little talk gets the social shunning it deserves.  Why do we let it pass in academics?  Nip it in the bud.  The silent majority of students will appreciate the more positive atmosphere you create by shutting down the drahmatists.

If a student continues to kvetch, or even if he gives me negative body language, I'll take him aside and appeal to his* ego.  "So, Johnny, you're one of the better students in the class.  How do you think your words make Joey feel?  He's going to think, jeez, if JOHNNY thinks he's gonna fail, what chance to I have?  The class needs positive leadership from you, Johnny, and leadership begins with poise and confidence."

* I teach at a boys' school.  I imagine that my approach would work similarly in a co-ed environment, but I have no direct evidence.

But students have legitimate questions about the upcoming test.  Of course.  I can't shut those questions down... I must communicate the form, content, and performance expectations of the test.

Nevertheless, I don't need to answer silly or irrelevant questions; I don't need to answer questions twice; and I don't need to answer passive-aggressive questions that are really whiny complaints.

What's going to be on the test?  Answer it once per year: everything we've discussed.  [Smile.]  I'm not doing my job as a teacher if I give you permission to forget everything I've taught you.

Make the format consistent and transparent.  Hand out the cover sheet ahead of time, indicating the number of each type of question and time limits.  If the students don't expect surprises; and better, if the gossip amongst generations of students never includes stories of surprise or gotcha questions; then you can more reasonably demand that your students stop with the fear-mongering.

Will there be a curve?  Again, answer out loud once per year: the cover sheet includes the point values for each section, along with the number of points necessary for each grade.  If you pass a sheet like this out for every test, there's no reason for anyone to ask about it in class.

What if I fail?  Are there retakes?  Can I do extra credit?  Can I lawyer up after the test to convince you to give me an A?  Can we go back to that fourth down play when New England didn't cover Nick Foles and the Eagles scored the winning touchdown?  What do you think, should we give the Patriots another try?  I mean, they've worked their tails off all season, they tried so hard, can't we have some mercy on them?  

I have a connection with most of my class through sports.  Feel free to use other avenues of public life.  "Can we go back to early November 2016?  Remember when Ms. Clinton didn't campaign in Wisconsin, Michigan, or Florida?  Perhaps the Republican party would allow a re-vote, or some extra credit for Clinton in the electoral college... after all, she tried so hard..."  

Whatever works for you and your class.  Just shut down the complaining.  It will be appreciated by most, and worth it come exam time.

Carry on

Welcome back, class.  I know the first day of school after break is sorta useless, and I know it's hard to remember things we talked about two weeks ago, so...

...so you just lost a day of teaching.

Look, it's not like I'm blind or stupid.  I notice the days that are more difficult to maintain student focus.  Typical culprits include days immediately before or after a scheduled vacation or a major non-academic event like the state championship football game or the prom.  I know my seniors will engage far better in the fall than the spring, while freshmen are the opposite.

Fact is, these difficult days are still school days.  I've still got a job to do; the AP exam or the class final doesn't get pushed back because of last night's Duke vs. North Carolina game.  These days will never be as effective as an ideal day.

But that doesn't mean simply punt on them.  Have a plan.  Do something as active and engaging as you can manage.  These aren't the days for long discussion or lecture sessions, not for testing, not for difficult creative lab work.  These are good days, however, for straightforward, active lab work.  For one of those The Physics Classroom interactives.  For starting a new topic with an eye-catching demo showing a discrepant event.

No matter what your plan, though, your demeanor is the most critical component to the quality of your class on a difficult school day.  

Why do students consider that, for example, they shouldn't have to think too hard in class the day after the Super Bowl?  Because all the adults around them say so.  (Not, in the vast majority of cases, because the students were out drinking and climbing greased lampposts until 5:00 am the night before.  Philadelphia-area schools possibly excepted.)

If you start class with a pre-made excuse to not pay attention, well, why are you surprised or disappointed when the students don't pay attention? 

Keep calm and carry on.  "Did you see that game last night, Mr. Lipshutz?!?"  "Yes, it was fantastic!  I'd love to talk through the Eagles' gutsy playcalling at the lunch tables - amazing.  For now, though, here's our three minute bell quiz which will remind us of last week's topics... you may begin."