Kind: captions
Language: en
I want to thank the sponsor of this
episode last pass which remembers your
passwords so you don't have to more
about them at the end of the show what
you are looking at is known as the Jana
Becca effect or the tennis racket
theorem or the intermediate axis theorem
but we'll get to that now you may have
seen clips like this one before but in
this video I will provide the best
intuitive explanation of how this effect
works or at least that's my goal
now it involves arguably the best
mathematician alive Soviet era secrets
and the end of the world so in 1985
cosmonaut Vladimir Jana Bekoff was
tasked with saving the Soviet space
station Salyut 7 which had completely
shut down the mission was so dramatic
that the Russians made a movie out of it
in 2017 and after rescuing the space
station Jana back off unpacked supplies
sent up from Earth which were locked
down with a wingnut
and as the wingnut spun off the bolt he
noticed something strange the wingnut
maintained its orientation for a short
time and then it flipped 180 degrees and
as he kept watching it flipped back a
few seconds later and it continued
flipping back and forth at regular
intervals
this motion wasn't caused by forces or
torque supplied to the wingnut there
were none and yet it kept flipping it
was a strange and counterintuitive
phenomenon one that the Russians kept
secret for 10 years why the secrecy well
that is what we're gonna find out
6 years later in 1991 a paper was
published in the Journal of dynamics and
differential equations called the
twisting tennis racket and although it
was related it of course makes no
mention of the secret Jana Beck of
effect the paper says if you hold a
tennis racket facing you and then flip
it in the air like this
it not only rotates the way you intend
it to it also makes a half turn around
an axis that passes through its handle
so the side that was originally facing
you will be facing away when you catch
it now to understand this we need to go
through some basics like there are three
ways
spent a tennis racket about its three
principal axes the first is about an
axis that runs through the handle like
this the second is the way we were
spinning it before with an axis that
runs parallel to the head of the racket
and the third is about an axis that runs
perpendicular to the head of the racket
now it's easier to spin the racket
around some of these axes than others
that is you get more angular velocity
for a given amount of torque it's
easiest to spend the racket around this
first axis it gets going really fast and
that is because the mass is distributed
closer to this axis than to any of the
others we say it's moment of inertia is
the smallest when spinning in this
orientation spinning about the third
axis has the greatest moment of inertia
and so the racket gets spinning pretty
slowly and that's because this mass is
distributed as far from this axis as
possible so this is the maximum moment
of inertia axis now what you'll notice
with spins about these axes is that
they're stable there's no rotation
happening about any of the other axes
when you try to rotate around the first
or third axis but rotating about the
second axis the intermediate axis where
the moment of inertia is in between the
other two
well that is where you get this half
twist and there's virtually nothing you
can do to stop it and it's not just
tennis rackets of course I've done this
before with cell phones and with a disc
with a hole in it I took this disc on an
ice rink and in a zero g plane I have
been obsessed with the intermediate axis
theorem and what you need to make the
intermediate access effect work is an
object that has three different moments
of inertia about its three principal
axes and well that's not every object
this object for example a spinning ring
has only two different moments of
inertia for rotation like that and then
rotations like this spinning things is
not a specialty Wow feel like it should
be rotations like that that's that's the
one I was looking for anything with
spherical symmetry has only one
of inertia so these objects will not
demonstrate the tennis racket theorem
for that you need what's called an
asymmetric top something with three
different moments of inertia in its
three different principal axes now the
tennis racket paper claims the twisting
phenomenon seems to be new it is not
mentioned in general texts on classical
mechanics amongst other sources that
they've checked but it is actually it's
even in the textbook they cited Landau
and Lifshitz
in fact an understanding of the
intermediate axis theorem goes back at
least another a hundred and fifty years
to a book called the new theory of
rotating bodies by Louis so so this is
old physics but in space the phenomenon
looks like something new in microgravity
the effects are just so much more
striking than a half twist of a tennis
racket and it random intervals on social
media these videos crop up to frenzied
questions of is this real and what's
going on how does this work well a
number of simulations and animations
have been made but if you really want to
understand what's happening
most people resort to the math including
me in the past
well the mathematics is kind of
complicated and boy is there a lot of
math there's this story of a student who
asked famous physicist Richard Feynman
if there was any intuitive way of
understanding the intermediate axis
theorem and as the story goes he thought
about it carefully and deeply for ten or
fifteen seconds and then said no well
the goal of this video is to prove
Fineman wrong to provide an intuitive
explanation of the intermediate axis
theorem but the explanation is not mine
it actually comes from one of the
greatest living mathematicians Terry Tao
he has won the Fields Medal amongst a
host of other awards and for this video
I actually asked him for an interview
but he declined because he's busy
solving centuries-old math problems so
you know fair enough but that's okay
because we have the explanation he
posted to math overflow in 20
and it goes like this imagine we have a
thin rigid massless disc centered in our
coordinate system now add some heavy
point masses to opposite edges of the
disks on the x-axis even though their
point masses I'll put some large cubes
around them to remind us of their
significant mass then add some light
point masses on opposite edges of the
disc on the y-axis now this disc has
three different moments of inertia about
its three principal axes rotating around
the x-axis has the smallest moment of
inertia since only the light masses are
moving rotating about the z axis has the
greatest moment of inertia since all
four masses are going around and
rotating about the y axis has the
intermediate moment of inertia rotating
like this the only forces in the discs
are centripetal forces which accelerate
the big masses towards the center this
keeps them turning in uniform circular
motion now what if we change reference
frames so now we're rotating with the
disc well then we see centrifugal forces
appear normally I don't like talking
about centrifugal forces because well if
you analyze things in inertial frames of
reference you never have to deal with
them but if you're in a rotating frame
of reference then centrifugal forces do
appear in the analysis pushing any
masses away from the rotation axis and
those forces are proportional to their
distance from the axis in this case the
y axis so here there is no centrifugal
force on the small masses because
they're located right on the y axis so
the only centrifugal force acts on the
big masses outwards and that's balanced
by the centripetal forces pushing
inwards now this is all fine and good
but what if the disc is bumped so that
it's no longer rotating perfectly about
the y axis
well now the small masses will
experience some centrifugal force
proportional to their distance from the
y axis tension forces within the disc
ensure that these small masses remain
orthogonal to the big masses and since
the big masses are still spinning in
roughly the same positions as they were
before with lots of inertia they
constrain the small masses to lie more
or less in the Y Zed plane
the little centrifugal forces on these
small masses start accelerating them and
those forces get bigger as the masses
move further and further from the y axis
and they keep accelerating until they
flip onto opposite sides now for the
first half of this flip the centrifugal
forces are accelerating the small masses
but in the second half the centrifugal
forces slow the masses down reversing
all the previous acceleration so that
they basically come to rest when they
reach the opposite side the pattern then
repeats indefinitely with the disc
flipping back and forth at regular
intervals and there you have it an
intuitive explanation for the
intermediate axis theorem or tennis
record they're more janovec effect or
whatever you want to call it so if this
is well established classical physics
why did the Soviets make it classified
for ten years well possibly because of
what Janna Bekoff did after observing
the strange behavior of the wingnut he
attached a ball of modeling clay or
plasticine to it and tried spinning that
and sure enough he found that just like
the wingnut this ball flipped over
periodically and the implication was
that maybe since the earth is a spinning
ball in space it too could flip over I
mean we know the Earth's magnetic poles
have reversed in the past so could this
be related in 2012 with the Mayan
prophecies of the end of the world
speculation about the Janna Bekoff
effect proved irresistible for some
conspiracy theorists and people in the
media Plus on May 13th 2012 the official
site of the russian federal space agency
Roscosmos posted an article in honor of
Janna Becca's 70th birthday and in it
they said the spinning nut of Janna
Bekoff caused astonishment and
simultaneous danger to a certain part of
the scientific world a hypothesis was
proposed that our planet in the course
of its orbital motion can execute the
same overturn so how do we assess the
validity of this hypothesis I mean is
the earth actually going to flip over
well we can get some
from simple experiments performed by
astronaut Don Pettit aboard the space
station he shows that a book will spin
stable about its first or third axis
just as we'd expect and a solid cylinder
will also spin stable II around its
first or third axis but a liquid filled
cylinder spinning about the first axis
that's the one with the smallest moment
of inertia it's unstable and it'll end
up rotating about its axis with the
largest moment of inertia why is this
for an isolated object spinning in space
you'd probably think both its angular
momentum and its kinetic energy would be
constant but that's only half true
angular momentum stays constant
but kinetic energy can be converted into
other forms of energy like heat so in
this case as the liquid sloshing around
inside the energy can be dissipated and
spinning about the axis with the
smallest moment of inertia also means
spinning with the greatest kinetic
energy and as this kinetic energy is
dissipated the cylinder has no other
option but to spin about the axis that
achieves the minimum kinetic energy and
that is the one with the largest moment
of inertia so when it's rotating
end-over-end for a given amount of
angular momentum then rotating with the
maximum moment of inertia is the lowest
energy State so that is the state that
all bodies will tend towards if they
have any way of dissipating their energy
the u.s. learned this the hard way with
their first satellite the Explorer one
it was designed to spin about its long
axis and be spin stabilized but within
hours of achieving orbit it was rotating
end over end but what happened I mean it
seems like a rigid cylinder well the
problem was these flexible antennas they
allowed the satellite to dissipate
energy as they swung back and forth
gradually reducing the kinetic energy of
the satellite until it had to rotate by
the axis that maximized its moment of
inertia now the earth is just like this
it has ways of dissipating energy
internally so over time it has come to
spin about the axis with maximum moment
of inertia and most astronomical objects
do the
same Mars for example has a mass
concentration or major positive gravity
anomaly called the Tharsis rise and it
is located not coincidentally at the
equator because that puts it as far as
possible from the axis of rotation and
ensures that Mars is rotating with the
maximum moment of inertia most asteroids
far from rotating about random axis
they spin almost all of them around the
axis with the maximum moment of inertia
so the earth won't flip it's spinning
about the axis with the maximum moment
of inertia and that is stable hey this
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