Unit 8 -- We're Going in Circles!

We had less than a day for this unit, what with invoices & post-tests & whatnot on the final day.  (& we didn't even get to momentum & impulse in Unit 9, so it worked out like it does sometimes in Laura's classroom.)  So I'm not going to talk about all the paperwork, that's a bit boring & at all germane to modeling -- I'm just going to talk about the circular motion craziness. :-)

& it did start out crazy -- Don has a flying pig!

So, what forces are acting on a flying pig?  & how to draw this?  (Let me tell you, this strained my artistic ability. :-) )  After we struggled a bit, Don admitted the wings were a red herring & had us consider a rubber stopper going in a circle on a string instead.  In both cases, the speed looked constant, but what about velocity?  What about acceleration?  What did the schema look like?  & then what does the force diagram look like?

Now, I know the centripetal force is towards the center, but drawing out the "shadow forces" of the string really showed why.  That's something I'll definitely do with Physical Science in the fall, because this is not anything that makes common sense.  If you feel pushed back (or down or whatever), the unbalanced force is in the opposite direction ... which is just weird.  If you are going in a circle, there has to be an unbalance force inward.

Don had a story for this unit that he swore was really his own.  While travelling cross country, his family stopped at a fair & he & his sister rode the Gravitron.  (You stand against a wall, the circular room starts spinning, & then the floor drops away.)  So while everyone is plastered to the wall, some guy across from Don unpeels himself from the wall, gets up, & starts walking around.  Yikes!  Now, this is totally a story I could steal. :-)

To show the "inward force", we all went out into the hall & somebody steered a bowling ball around in a circle with a meter stick.  To make the ball turn, you had to push it towards the middle.  Boom!  Unbalanced force pointing towards the middle!  So we added a new move to the velocity dance -- If one hand is pointing to the side, you're turning.  (The other physics group used rubber mallets -- They posted a straight-line race a while back.)  Somebody gave me a bowling ball years ago, but I eventually gave it to Goodwill.  Now I think I need to go get some retired balls from a bowling alley.

We did a few problems from worksheet #1 & drew out the force diagrams.  I wanted to make the top of the hill do something cool, but I was wrong.  (sigh)  The dots on the motion map were referred to as moments of circular motion.

Another good example of the Central Force Theory is spinning a cup of water on a tray.  The tray Don used was a little triangular piece of whiteboard while the tray I have is a lunchroom-type tray.  I can spin an orange around on mine -- it's got a textured surface & there's a little room to roll -- but Don couldn't spin a ball around on his.  Therefore, mine is better -- The kids were real impressed by the orange, & I was too, I honestly didn't think it would work.  (& this is when I realized that one of my group mates had been at that same workshop at MSTA last year.  How funny is that?)

But when you draw the force diagram for the spinning cup at the top of its arc, the only forces on it are pointing down.  How does it stay up?  Why doesn't it fall off?  Well, it is falling ... only it's falling exactly where the tray is moving to.  This kind of ties back into Don's demonstration of "throwing" rubber stoppers to a catcher -- The object is trying to move in a straight line, but the tray is moving around in a circle.  If you slow, sure, the cup goes flying, but otherwise the tray intercepts the falling cup perfectly ... & the water hardly wobbles.  (I actually like my demo better, with a clear plastic cup half-full of water instead of a red Solo cup filled with a bean bag.)

Then we talked about centrifugal vs centripetal, & it all depends on your frame of reference.  Don used the example of a kid holding a ball on the merry-go-round.  If you're standing outside the merry-go-round, when the kid lets go of the ball, you can see it move in a straight line.  However, if you're the kid, when you let the ball go, you see it move in a curved line, away from you.  People specifically mentioned the old "Frames of Reference" video, & I found it!  https://www.youtube.com/watch?v=aRDOqiqBUQY

Both Don & Laura say there's no good way to experimentally show this concept, or to show the relationship between the speed of the circular motion & the force & the string length.  The best they could come up with was having a bunch of rubber stoppers (of varying masses) on strings & let the kids twirl them around & mess with the string length.  They'll get the idea kinesthetically & you can build from there.

We had a reading, an overview of modeling instruction that's perfect for sending to administrators, but we never discussed it.  (& yes, I did send it along to my principal.)

& that's it.  That's as far as we got.  We made a lot of jokes about the end of the semester & cramming stuff in. :-)



Equipment List

Flying Pig or Cow, $10
https://www.giftofwings.com/store1/producti/index2.html

Graph-ruled Composition Book, $3
http://www.officedepot.com/a/products/320155/Office-Depot-Brand-Marble-Quad-Composition/

Bowling Ball (new but on sale), $43
http://www.bowlingball.com/

Rubber Mallet (16 oz), $6.50
http://www.amazon.com/General-2259323-Steelgrip-Rubber-Mallet/dp/B003MRPGDE/ref=pd_sim_469_4?ie=UTF8&refRID=1FD66S3HS35RZVA9KG8A