Turn! Turn! Turn!

At the elementary school, we continued our theme of learning more
about how things move, in preparation for designing the playground at
the new school site.  Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built.  Today, we focused on spinning things.

We started with a spinnable chair.  A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair.  Then I
ask the volunteer to extend his/her arms as far as possible.  The
chair then spins much more slowly.  Arms in: the chair speeds up
again.  Arms out: slows down again.

I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating.  I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly.  A lot of them did refer to playground equipment,
though.  There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it.  But why does
pulling in your arms speed you up?

We had talked four weeks ago about how more massive things are more
difficult to accelerate.  And to decelerate.  In short, they have more
inertia.  Rotational motion has an added complication.  Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia.  So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung.  The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object.  Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass.  Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.

Next, I gave them a chance to apply this new principle.  I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends.  You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation!  Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate.  Surprisingly, the
connection was not instant.  (I wonder how often words are a dead
giveaway.  I used the word "rotation" here, but in class I just said,
"go like this."  I bet if I had said "rotate the rods" something would
have clicked.  But this something would not have been understanding of
physics!  Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances.  Next time, I should bring a scale to prove it!

Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends).  I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth.  We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle.  I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly.  That's
pretty cool, and that's what science is about. 

Next, we took a bicycle wheel and I passed it around.  Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction.  I asked in what real-life situations they
might have noticed the same thing.  "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant.  I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster.  When
you're not moving, the wheels can just fall over.  When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.

The same bicycle wheel can be used for a really neat demo.  Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel.  Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin.  Now flip the wheel over, and the chair
begins to spin the other way!  This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.

Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end.  They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why.  I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force.  If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round.  The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.

We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok!  I
didn't want to discourage creativity.  We also talked about space and
astronauts.  Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station.  Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way.  And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part.  One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second!  We know that because we can see a hot spot for a brief
period during each revolution.