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We're now entering
the part of 8.01

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which is the most difficult
for students and faculty alike.

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We are going to enter the domain
of angular momentum and torques.

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It is extremely nonintuitive.

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The good news, however, is that
we will stay with this concept

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for at least four
or five lectures.

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Today I will introduce both
torque and angular momentum.

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What is angular momentum?

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If an object has a mass m
and it has a velocity v,

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then clearly it has
a momentum p.

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That's very well defined
in your reference frame,

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the product of m and v.

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Angular momentum I can take
relative to any point I choose.

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I choose this point Q
arbitrarily.

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This now is the position vector,
which I call r of Q.

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Let this angle be theta.

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And angular momentum relative to
that point Q-- it's a vector--

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is the position vector relative
to that point Q cross p.

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So it is r of Q cross v,
and then times m.

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The magnitude of the angular
momentum, relative to point Q,

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is, of course, rmv,

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but then I have to take
the sine of the angle theta,

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so let's say it is
mv r sine theta

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and this I often call, shorthand
notation, r perpendicular.

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That r perpendicular is this
distance, relative to point C.

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What you just saw
may have confused you

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and for good reason,

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because I changed my index "Q"
to "C," and there is no C.

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The indexes should all be Q,
of course.

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So this r is the length
of this vector.

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It is the magnitude
of this vector.

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So this should have a "Q."

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And r of Q sine theta,
which I call r perpendicular,

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must have an index Q,
and that is this part here.

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This angle is 90 degrees

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and this here is r of Q
perpendicular.

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No Cs at all, only Qs--
I'm sorry for that.

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The direction of
the angular momentum is easy.

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You know how to do
a cross product.

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So in this case, r cross v

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would be perpendicular
to the blackboard

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and the magnitude is
also easy to calculate.

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Now comes the difficult problem
with angular momentum.

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If I chose any point
on this line, say point C,

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then the angular momentum
relative to point C is zero.

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Very obvious,
because the position vector, r,

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and the velocity vector, in this
case, are in the same direction.

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So theta is zero,
so the sine of theta is zero.

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So you immediately see
that angular momentum

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is not an intrinsic property
of a moving object,

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unlike momentum, whichis
an intrinsic property.

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If you sit there in 26.100,

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you see an object moving
with a certain velocity,

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it has a certain mass,
you know its momentum.

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What the angular momentum is

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depends on the point that you
choose, on your point of origin.

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If you had chosen this point D,

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then the angular momentum
would even be this way,

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because when you put here
the position vector in there

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you see r cross v is now coming
out of the blackboard.

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And this is why angular momentum
is such a difficult concept.

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But we will massage it in a way
that it will be very useful.

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Suppose I throw up an object
in 26.100

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and at time t equals zero,
the object is here

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and at time t,
the object is there.

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So this, then, is
the position vector at time t.

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The object starts off
with a certain velocity v

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and a little later, here,
say, the velocity is like so.

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And there is, of course,
a force on it, mg,

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which makes this curve.

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What is the angular momentum

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relative to point C
at time zero?

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The angular momentum
is clearly zero,

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because the point itself,
the mass itself, is at point C.

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So the position vector
has no length,

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so it's clear that it's zero.

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What is the angular momentum at
time t when the object is here?

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Well, that angular momentum
is clearly not zero,

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because you see here position
vector and you see the velocity,

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so clearly the angular momentum
was changing.

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Now you will say, "Of course
it was changing-- big deal."

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Because angular momentum has
a velocity vector in it.

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And here the velocity vector
is changing all the time,

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so, obviously, you would say the
angular momentum is changing.

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Well, yes, that is
not a bad argument,

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but I will now show you

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a case where the velocity
is changing all the time,

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but where angular momentum
is not changing.

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I choose the Earth going
around the Sun.

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Here's the Earth, with mass m.

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At point C here is the Sun.

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This is the position vector
r of C

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and the Earth has
a certain tangential velocity

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and the speed never changes,
but the velocity does change.

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So this is the position vector
at a later point in time.

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What now is the angular
momentum of the Earth

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going around the Sun,
relative to point C?

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I pick C now.

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Well, that angular momentum...

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If I take the magnitude
of the angular momentum,

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because the direction is
immediately obvious...

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If the object is going
around like this--

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this is the position vector--

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then the direction will be
pointing out of the blackboard.

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That's easy.

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So I'm only worried now
about the magnitude.

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So the magnitude is
the mass of the Earth

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times the magnitude
of the cross product

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between these two vectors.

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And notice
the angle is 90 degrees.

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So I can forget about the cross,
the sine of theta is one,

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and so I simply get mrv,
v now being the speed.

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This is the case
when the object is here,

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but when the object is here,
the situation has not changed.

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Again, r cross v, the magnitude,
is exactly the same,

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because the sine of the angle
hasn't changed.

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And so you see here a case

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whereby the velocity is
changing all the time

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but your angular momentum
relative to point C

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is not changing.

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Suppose I had chosen point Q.

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Is angular momentum changing
relative to point Q?

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You'd better believe it.

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There is a time that the object
will go through point Q.

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Well, then the angular momentum
is clearly zero

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because the position vector
is zero.

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If the object is here

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and you take the angular
momentum relative to point Q,

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for sure the angular momentum
is not zero.

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You have a position vector
and you have a velocity.

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So only relative to point C--
it's a very special case now--

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is angular momentum
not changing.

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So angular momentum is conserved
in this special case,

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but only about point C.

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And I want to address that in
a little bit more general way.

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I take the angular momentum
and I choose a point Q,

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and I know that the definition

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is position vector relative
to point Q cross p.

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I take the derivative,
time derivative dL/dt

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relative to that point Q.

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It's always important

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that you state
which point you have chosen

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relative to which you take
the angular momentum.

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That is going to be dr/dt...

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excuse me--

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cross p

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plus r of Q cross dp/dt.

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This is the way

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that you take the time
derivative of a cross product.

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We calculate the angular
momentum relative to point Q.

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So the index has to be Q
throughout the equation.

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The position vector,
relative to point Q.

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And in this equation, you see
the correct index Q here.

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You see the correct index Q
here, but I slipped up here

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and I put a "C" there.

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There is no "C" in this problem,
so this is also r of Q.

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Sorry for that.

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This, here, is the velocity of
the object, the velocity vector,

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which is always
in the same direction as p.

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So this is zero.

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dp/dt-- that is,
the force on the object--

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we've seen that before in 8.01.

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And so now we have that dL/dt,
relative to a point Q,

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equals the position vector r
from that point cross F.

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And this, now, is
what we call torque.

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And we write for that the symbol
tau... it is a vector.

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And I put in that Q again.

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And this is one of
the most important equations

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that will stay with us
for at least five lectures.

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What this is telling you

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is that if there is
a torque on an object,

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the angular momentum must be
changing in time.

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If there is no torque
on the object,

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angular momentum will be
conserved.

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And now you get some insight

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into this situation
that we just discussed.

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The force, the attractive force,

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gravitational force exerted on
the Earth is in this direction.

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The position vector is in this
direction, so r cross F is zero.

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There is no torque
relative to this point C,

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because the angle between
the two vectors is 180 degrees

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and so the sine
of the angle is zero.

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Therefore, no matter
where you are on the circle,

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always r cross F will be zero.

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There is no torque
relative to point C.

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But if you take point Q
or you take here some point A,

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clearly, there is going to be a
torque, a changing torque even,

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and so there you will have
a change of angular momentum.

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So there's something
very special about that point C

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and I will come back to that,
of course.

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Now I want to expand the idea
of angular momentum

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from one point object
that moves in space

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to an object like a sphere
or like a disk

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which is rotating
about its center of mass.

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And I will start with a disk.

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Here we have a disk.

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The disk has mass M
and the disk has radius R,

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and at this point C is
the center of mass of this disk.

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It's rotating
with angular velocity omega

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and I want to know
what the angular momentum is

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of this rotating disk.

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The direction of the angular
momentum is going to be trivial.

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If it's rotating like this...

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If you take here a little
mass element, mass m of i,

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this is the position vector r
of i, relative to that point C,

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and here you have
the velocity, v of i.

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And you see immediately

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that r cross v
is coming out of the blackboard

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so that's easy.

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Angular momentum will be
in this direction,

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but what is the magnitude
of the disk as a whole?

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Well, let's first calculate
what the angular momentum is

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of this little mass element
about this point.

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So L of C
for mass element i equals...

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Oh, let's just
only worry about magnitude

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because already
we know the direction.

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So that is m of i

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and then the cross product
between r of i and v of i.

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But this angle is 90 degrees

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so I can forget
about the sine of theta.

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So I simply get r of i, v of i.

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r of i relative
to that point C times v of i--

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this is the magnitude.

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Now, I hate to see v of i
in a rotating disk

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because the velocity will depend

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on how far you are
away from the center.

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The velocity here is zero.

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However, they all
have omega in common.

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Every single element that you
choose has the same omega.

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So I'm always going to replace--
in a case like this--

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v by omega R.

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And so this then becomes
m of i, r of i of C.

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I get a square here
and I get omega.

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So I wrote down
v equals omega R,

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which, of course,
holds in general.

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It would have been better,
perhaps, if I had written down

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v of i equals
omega times r of i,

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because each element
little "i",

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which has
a position vector r of i,

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has a velocity which is given
by v of i equals omega r of i.

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But I condensed that, sort of,

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in one equation--
v equals omega R.

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But this is the connection
that will make it, perhaps,

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easier for you
to understand what follows.

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00:15:03 --> 00:15:09

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So that is the angular momentum
for this little mass element.

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But now I want to know

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what the entire angular momentum
is about that point C

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as an axis going
through the center of the mass,

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through the center of the disk
perpendicular to the blackboard.

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And now, of course,
I have to do the summation

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of all these elements i.

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I can bring the omega outside,
and I would have, then,

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the summation of m of i
r of i

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relative to that
point C squared.

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And you see immediately-- I
hope that you see immediately--

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that this is
the moment of inertia

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for a spin around the center
of mass for that point C.

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And so I can write for this,
I of C times omega.

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Now comes the question--
so this is the magnitude--

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00:15:56 --> 00:16:02
now comes the question,
is this angular momentum

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00:16:00 --> 00:16:06
different, for instance,
for this point A?

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And your first reaction
will be, "Yeah, of course,

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because it depends
on the point you choose."

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Well, the remarkable thing is
that if you have a rotation

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about the center of mass
which I have chosen here,

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then even if you calculate

269
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the angular momentum
relative to this point--

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or any other point,
even this point in space--

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you will always find
the same answer.

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But only in case

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that there is a rotation
about the center of mass,

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and we call that
the spin angular momentum.

275
00:16:35 --> 00:16:41
The spin angular momentum is an
intrinsic property of an object

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regardless of
which point you choose

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relative to which you calculate
the angular momentum.

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So in the case

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that an object is spinning
about its center of mass,

280
00:16:50 --> 00:16:56
you no longer have to specify

281
00:16:52 --> 00:16:58
the point that you have chosen,
your point of origin.

282
00:16:55 --> 00:17:01
You can really talk now
aboutthe angular momentum.

283
00:17:00 --> 00:17:06
The Earth is spinning
about its center of mass,

284
00:17:04 --> 00:17:10
so the Earth has an intrinsic
spin angular momentum.

285
00:17:08 --> 00:17:14
In addition, it has
an orbital angular momentum.

286
00:17:11 --> 00:17:17
If you want to talk

287
00:17:12 --> 00:17:18
about the orbital angular
momentum of the Earth, however,

288
00:17:15 --> 00:17:21
you'd better do it
relative to that point,

289
00:17:17 --> 00:17:23
otherwise it would be
changing in time.

290
00:17:18 --> 00:17:24
It's only uniquely defined
if you take this special point,

291
00:17:23 --> 00:17:29
because only about that point,

292
00:17:24 --> 00:17:30
which is the location
of the Sun,

293
00:17:26 --> 00:17:32
is the angular momentum--

294
00:17:28 --> 00:17:34
the orbital angular momentum
of the Earth-- not changing.

295
00:17:34 --> 00:17:40

296
00:17:37 --> 00:17:43
I'm going to do a daredevil
experiment with you

297
00:17:40 --> 00:17:46
and that is called
ice-skater's delight.

298
00:17:43 --> 00:17:49
You will see that
it is not a delight at all.

299
00:17:46 --> 00:17:52
But in any case, it is
definitely a fun experiment.

300
00:17:50 --> 00:17:56
I have here a turntable--
very little friction--

301
00:17:54 --> 00:18:00
and I'm going to rotate
the turntable about the center

302
00:18:00 --> 00:18:06
and I'm going to stand
on that turntable

303
00:18:04 --> 00:18:10
and I will hold in my hand
two weights, these two.

304
00:18:12 --> 00:18:18
They're each
about 1.8 kilograms.

305
00:18:16 --> 00:18:22
So these weights m,
1.8 kilograms...

306
00:18:21 --> 00:18:27
My entire mass--

307
00:18:23 --> 00:18:29
including the turntable
and my body, let's say--

308
00:18:25 --> 00:18:31
is about 75 kilograms.

309
00:18:30 --> 00:18:36
And I'm going to ask someone
to give me a little twist

310
00:18:34 --> 00:18:40
to rotate me
about this axis of symmetry.

311
00:18:39 --> 00:18:45
Rotate me, say,
if you look from below,

312
00:18:41 --> 00:18:47
let's say
I'm being rotated clockwise.

313
00:18:45 --> 00:18:51
So we have here a situation
of a rotation

314
00:18:47 --> 00:18:53
about the center of mass

315
00:18:49 --> 00:18:55
so we can talk about
the intrinsic angular momentum

316
00:18:52 --> 00:18:58
of this rotating system.

317
00:18:53 --> 00:18:59
And the angular momentum vector

318
00:18:56 --> 00:19:02
will obviously
be pointing upwards.

319
00:18:59 --> 00:19:05
That's clear.

320
00:19:00 --> 00:19:06
If you rotate clockwise
from below...

321
00:19:02 --> 00:19:08
Remember, here you were
rotating counterclockwise; 

322
00:19:05 --> 00:19:11
it was coming
out of the blackboard.

323
00:19:06 --> 00:19:12
Here you rotate clockwise,
it will be going up.

324
00:19:09 --> 00:19:15
So far, so good.

325
00:19:12 --> 00:19:18
There is a force on me
due to gravity-- mg, no concern.

326
00:19:19 --> 00:19:25
There is an equally
strong force, normal force up,

327
00:19:23 --> 00:19:29
and the two cancel
each other out.

328
00:19:25 --> 00:19:31
Once I have been given

329
00:19:26 --> 00:19:32
a certain rotation,
a certain angular velocity

330
00:19:28 --> 00:19:34
I'm going to pull my arms in
and pull my arms out

331
00:19:31 --> 00:19:37
and pull my arms in,
and when I do that,

332
00:19:35 --> 00:19:41
that does not cause
a net torque on the system.

333
00:19:38 --> 00:19:44
I can keep doing that
all the time

334
00:19:40 --> 00:19:46
and there is no net torque.

335
00:19:42 --> 00:19:48
And so angular momentum

336
00:19:44 --> 00:19:50
as we have specified
for a spinning object

337
00:19:47 --> 00:19:53
must be conserved,
cannot change.

338
00:19:50 --> 00:19:56
L equals I omega.

339
00:19:54 --> 00:20:00
But as I pull my arms in, my
moment of inertia will go down.

340
00:19:59 --> 00:20:05
And if my moment of inertia
goes down,

341
00:20:01 --> 00:20:07
then if this product
has to remain constant,

342
00:20:03 --> 00:20:09
my angular velocity must go up.

343
00:20:06 --> 00:20:12
And vice versa, so when I pull
my arms in, I will go faster

344
00:20:09 --> 00:20:15
and when I do this,
I will go slower.

345
00:20:12 --> 00:20:18
And I want to be a little bit
quantitative with you.

346
00:20:16 --> 00:20:22
I simplify my own body
by a geometric object

347
00:20:22 --> 00:20:28
for which I can calculate
the moment of inertia

348
00:20:25 --> 00:20:31
which is a cylinder.

349
00:20:27 --> 00:20:33
I may not look like a cylinder,

350
00:20:28 --> 00:20:34
but close enough
for all practical purposes.

351
00:20:32 --> 00:20:38
And this cylinder has a radius
of about 20 centimeters--

352
00:20:37 --> 00:20:43
not too bad,
it sort of fits me--

353
00:20:40 --> 00:20:46
and I'm going to rotate
this cylinder around this axis

354
00:20:44 --> 00:20:50
and I can calculate now
what the moment of inertia is.

355
00:20:47 --> 00:20:53
The cylinder has
a mass of 75 kilograms,

356
00:20:49 --> 00:20:55
has a radius of 20 centimeters,
and so the moment of inertia--

357
00:20:54 --> 00:21:00
in the situation that,
for instance

358
00:20:57 --> 00:21:03
I have these two objects
next to my body here

359
00:20:59 --> 00:21:05
or I have them like here, so
this is my shorthand notation--

360
00:21:02 --> 00:21:08
equals simple
one-half M R squared.

361
00:21:06 --> 00:21:12
Remember, that was
the moment of inertia--

362
00:21:09 --> 00:21:15
we discussed that last time--
of a rotating disk

363
00:21:13 --> 00:21:19
which rotates
about the line of symmetry.

364
00:21:18 --> 00:21:24
And so, if I put in the
numbers here, the 75 kilograms,

365
00:21:23 --> 00:21:29
and I take a radius
of 20 centimeters, then I found

366
00:21:26 --> 00:21:32
that this is about 1.5
in our mks units.

367
00:21:31 --> 00:21:37
But now I'm going to put
my arms like this

368
00:21:36 --> 00:21:42
and now the moment of inertia
will go up.

369
00:21:39 --> 00:21:45
And I'll make a very crude
calculation how much it goes up.

370
00:21:43 --> 00:21:49
My arm length is
about 90 centimeters.

371
00:21:46 --> 00:21:52
The weights here
are 1.8 kilogram.

372
00:21:50 --> 00:21:56
So I just assume
that my arms have no weight

373
00:21:54 --> 00:22:00
for simplicity, that all the
weight is in these two objects.

374
00:21:57 --> 00:22:03
It's a simplification, but you
will see it's a dramatic change

375
00:22:00 --> 00:22:06
and that's
all I want you to see.

376
00:22:02 --> 00:22:08
So now the moment of inertia,
when my arms are like this.

377
00:22:06 --> 00:22:12
Of course, there's my body,
which is the 1.5.

378
00:22:11 --> 00:22:17
That is still there

379
00:22:12 --> 00:22:18
but now there is
an additional component:

380
00:22:15 --> 00:22:21
one from this mass,
which is M R squared,

381
00:22:19 --> 00:22:25
and one from this mass,
which is M R squared,

382
00:22:21 --> 00:22:27
where this is now that radius r.

383
00:22:25 --> 00:22:31
And so I get twice that mass

384
00:22:29 --> 00:22:35
and then I have to take R
squared, which is 0.9 squared,

385
00:22:34 --> 00:22:40
and I have to take the 1.8,

386
00:22:37 --> 00:22:43
because that's the moment
of inertia

387
00:22:39 --> 00:22:45
of this object about this point.

388
00:22:41 --> 00:22:47
It is M R squared, I assume
that my arm has no mass.

389
00:22:45 --> 00:22:51
And when you add this up,
you'll find 4.5 in mks units,

390
00:22:52 --> 00:22:58
kilograms meters squared.

391
00:22:56 --> 00:23:02
And now you see, if I go
from this situation to this,

392
00:22:59 --> 00:23:05
my moment of inertia goes down
by a factor of three

393
00:23:02 --> 00:23:08
and if my moment of inertia goes
down by a factor of three,

394
00:23:04 --> 00:23:10
my angular velocity must go up
by a factor of three.

395
00:23:07 --> 00:23:13
And vice versa.

396
00:23:11 --> 00:23:17
I want to do this experiment

397
00:23:12 --> 00:23:18
but this experiment
is not without danger.

398
00:23:16 --> 00:23:22
The problem with this experiment

399
00:23:18 --> 00:23:24
is that the moment
that you pull your arms in

400
00:23:20 --> 00:23:26
you get immediately
extremely dizzy

401
00:23:23 --> 00:23:29
and you can lose your balance

402
00:23:25 --> 00:23:31
and you can fall
flat out on the floor.

403
00:23:26 --> 00:23:32
And I have just talked
this morning

404
00:23:28 --> 00:23:34
with some student here
who did that in high school

405
00:23:30 --> 00:23:36
and he told me

406
00:23:32 --> 00:23:38
that, indeed, one of
the teachers went flat down

407
00:23:34 --> 00:23:40
and I'll try not
to do that today.

408
00:23:37 --> 00:23:43
So I need really assistance
from someone whom I can trust.

409
00:23:41 --> 00:23:47
Do you think I can trust you?

410
00:23:43 --> 00:23:49
Not you.

411
00:23:44 --> 00:23:50
(class laughs )

412
00:23:46 --> 00:23:52
LEWIN:
That's an honest answer.

413
00:23:47 --> 00:23:53
You're a strong man--
can I trust you?

414
00:23:52 --> 00:23:58
The first thing I want you to do
is to help me get on here,

415
00:23:57 --> 00:24:03
because even getting on here
is not easy.

416
00:23:58 --> 00:24:04
If I just step on here,
I will probably fall.

417
00:24:03 --> 00:24:09
Okay, so stand there,
put your arm around my neck.

418
00:24:05 --> 00:24:11
Support me strongly, yeah, okay.

419
00:24:12 --> 00:24:18
All right, there we go.

420
00:24:14 --> 00:24:20
Now, stay with me for a while,
okay, just stay there.

421
00:24:20 --> 00:24:26
All right, now you give me
a reasonable angular velocity,

422
00:24:26 --> 00:24:32
whatever you think
is reasonable.

423
00:24:27 --> 00:24:33
I'll tell you if it's
completely unreasonable.

424
00:24:29 --> 00:24:35
(class laughs )

425
00:24:31 --> 00:24:37
LEWIN:
Give me a push, that's fine.

426
00:24:34 --> 00:24:40
Wow... is it fine?

427
00:24:35 --> 00:24:41
Now, you walk a little bit away.

428
00:24:37 --> 00:24:43
If I fall, try to catch me.

429
00:24:38 --> 00:24:44
(class laughs )

430
00:24:41 --> 00:24:47

431
00:24:43 --> 00:24:49
LEWIN:
Okay, my arms go in now.

432
00:24:47 --> 00:24:53
My arms go out.

433
00:24:51 --> 00:24:57
My arms go in.

434
00:24:54 --> 00:25:00
My arms go out.

435
00:24:55 --> 00:25:01
Okay, now
I'm completely dizzy now.

436
00:24:57 --> 00:25:03
This is no joke,
so stop me, yeah?

437
00:25:00 --> 00:25:06
Just hold it.

438
00:25:01 --> 00:25:07
(class laughs )

439
00:25:04 --> 00:25:10
LEWIN:
No, just hold me, hold me.

440
00:25:08 --> 00:25:14
Okay, get my hand.

441
00:25:10 --> 00:25:16
Okay... okay,
you passed the course.

442
00:25:14 --> 00:25:20
(class laughs )

443
00:25:15 --> 00:25:21
(class applauds )

444
00:25:20 --> 00:25:26

445
00:25:22 --> 00:25:28
Whew! Sacrifice
for the sake of science.

446
00:25:26 --> 00:25:32
(groans theatrically )

447
00:25:28 --> 00:25:34
All right, I've done worse.

448
00:25:30 --> 00:25:36

449
00:25:33 --> 00:25:39
If we have a collection
of many points--

450
00:25:38 --> 00:25:44
like we earlier discussed
with momentum--

451
00:25:42 --> 00:25:48
points that interact
with each other...

452
00:25:44 --> 00:25:50
They could be stars
who gravitationally interact.

453
00:25:49 --> 00:25:55
They could be objects which
are connected with springs.

454
00:25:52 --> 00:25:58
They have internal interactions
which go on all the time.

455
00:25:55 --> 00:26:01
They bounce off each other,
they collide,

456
00:25:57 --> 00:26:03
they break up in pieces,
internal friction, anything.

457
00:26:02 --> 00:26:08
Then if I take two
of these objects,

458
00:26:05 --> 00:26:11
if this one, for instance,
is attracted towards this one,

459
00:26:09 --> 00:26:15
then action equals
minus reaction

460
00:26:12 --> 00:26:18
and these two forces are
identical in magnitude.

461
00:26:16 --> 00:26:22
So if I take any point Q here,
no matter where you choose it,

462
00:26:19 --> 00:26:25
that willnever put a torque
on that system

463
00:26:23 --> 00:26:29
because the two forces cancel
each other out.

464
00:26:26 --> 00:26:32
And so now we get the final
conservation of angular momentum

465
00:26:32 --> 00:26:38
in all its glory

466
00:26:33 --> 00:26:39
if only we add, here,
one little word-- "external."

467
00:26:41 --> 00:26:47
The angular momentum
of asystem...

468
00:26:43 --> 00:26:49
This was angular momentum
of just one object;

469
00:26:46 --> 00:26:52
this is the angular momentum
of a system of many particles.

470
00:26:48 --> 00:26:54
They could be connected
with springs.

471
00:26:51 --> 00:26:57
There could be chemical
explosions going on.

472
00:26:53 --> 00:26:59
They could plow into each other.

473
00:26:55 --> 00:27:01
They could break each other up.

474
00:26:56 --> 00:27:02
The angular momentum
will not change

475
00:26:59 --> 00:27:05
if there is no net
external torque on that system,

476
00:27:02 --> 00:27:08
because all
the internal torques cancel out

477
00:27:05 --> 00:27:11
because action equals
minus reaction.

478
00:27:07 --> 00:27:13

479
00:27:11 --> 00:27:17
So if we now compare
conservation of angular momentum

480
00:27:14 --> 00:27:20
with conservation of momentum,

481
00:27:16 --> 00:27:22
then in the case of
the conservation of momentum,

482
00:27:19 --> 00:27:25
remember, when we have
a system of objects,

483
00:27:21 --> 00:27:27
in the absence of an external
force on the system as a whole,

484
00:27:26 --> 00:27:32
the net external force,
momentum was conserved.

485
00:27:30 --> 00:27:36
Now we have...
with a system of particles

486
00:27:32 --> 00:27:38
in the absence
of a net external torque,

487
00:27:36 --> 00:27:42
angular momentum is conserved.

488
00:27:38 --> 00:27:44

489
00:27:41 --> 00:27:47
In the case
of the ice-skater's delight,

490
00:27:45 --> 00:27:51
when you pull your arms in,

491
00:27:47 --> 00:27:53
the moment of inertia goes down
and so your frequency goes up.

492
00:27:52 --> 00:27:58
When a star shrinks,
its radius goes down,

493
00:27:56 --> 00:28:02
its moment of inertia goes down,

494
00:28:00 --> 00:28:06
and therefore its angular
velocity must go up.

495
00:28:04 --> 00:28:10
Moment of inertia goes
with R squared.

496
00:28:08 --> 00:28:14
What determines the size
of a star?

497
00:28:13 --> 00:28:19
If this is a star,

498
00:28:16 --> 00:28:22
then inside this star is
a furnace, nuclear furnace.

499
00:28:19 --> 00:28:25
Nuclear fusion is going on.

500
00:28:22 --> 00:28:28
That produces heat and pressure,
which wants to expand the star.

501
00:28:29 --> 00:28:35
On the other hand,
there is gravity,

502
00:28:31 --> 00:28:37
which says,
"Sorry, you can't do that.

503
00:28:34 --> 00:28:40
I want to hold you together."

504
00:28:37 --> 00:28:43
In fact, gravity would like
to collapse the star.

505
00:28:40 --> 00:28:46
And nature finds a balance
between the gravity

506
00:28:44 --> 00:28:50
and this pressure due
to the nuclear furnace.

507
00:28:48 --> 00:28:54
Now, there comes a time

508
00:28:49 --> 00:28:55
that the nuclear furnace
has been completely consumed.

509
00:28:53 --> 00:28:59
For our Sun, that takes an
additional five billion years.

510
00:28:56 --> 00:29:02
The Sun has already been
burning nuclear fuel

511
00:28:59 --> 00:29:05
for five billion years.

512
00:29:00 --> 00:29:06
It has another
five billion to go.

513
00:29:04 --> 00:29:10
And once the nuclear fuel
has been consumed,

514
00:29:07 --> 00:29:13
there are three end-products of
the dead star that is left over.

515
00:29:14 --> 00:29:20
And these three end-products
are the following:

516
00:29:18 --> 00:29:24
Number one is called
a white dwarf.

517
00:29:24 --> 00:29:30
It has a radius approximately
the same as the Earth,

518
00:29:27 --> 00:29:33
some 10,000 kilometers,

519
00:29:30 --> 00:29:36
and the mass of a white dwarf...

520
00:29:32 --> 00:29:38
There's a whole range of them,
but a typical number, say,

521
00:29:35 --> 00:29:41
is half the mass of the Sun.

522
00:29:37 --> 00:29:43
So that's
one possible end-product.

523
00:29:40 --> 00:29:46
This will be the fate
of our Sun, by the way.

524
00:29:42 --> 00:29:48
The density of
such an object is quite high--

525
00:29:45 --> 00:29:51
some ten to the rho--

526
00:29:47 --> 00:29:53
will be roughly ten to the 6th
grams per cubic centimeter.

527
00:29:52 --> 00:29:58
Another possibility is that
you end up with a neutron star.

528
00:29:59 --> 00:30:05
A neutron star has a radius
of about ten kilometers,

529
00:30:05 --> 00:30:11
and it has a mass of roughly
1.5 times the mass of the Sun,

530
00:30:11 --> 00:30:17
and its density

531
00:30:12 --> 00:30:18
is about ten to the 14 grams
per cubic centimeter,

532
00:30:15 --> 00:30:21
which is even higher
than the density of nuclei.

533
00:30:20 --> 00:30:26
And then there is a possibility,
which is even more bizarre,

534
00:30:24 --> 00:30:30
that you end up
with a black hole.

535
00:30:27 --> 00:30:33
I will not talk
about black holes today

536
00:30:29 --> 00:30:35
but I will get back
to that later in 8.01.

537
00:30:33 --> 00:30:39
And a black hole,
for all practical purposes,

538
00:30:36 --> 00:30:42
has no size at all.

539
00:30:38 --> 00:30:44
The mass of the black hole
must be larger than we think--

540
00:30:42 --> 00:30:48
three solar masses-- and so
the density is infinitely high.

541
00:30:49 --> 00:30:55
Whether you end up
to be a white dwarf,

542
00:30:51 --> 00:30:57
a neutron star or a black hole

543
00:30:53 --> 00:30:59
depends on the mass
of the progenitor--

544
00:30:57 --> 00:31:03
of the star that collapsed

545
00:30:58 --> 00:31:04
when the fuel, when
the nuclear fuel was gone.

546
00:31:02 --> 00:31:08
And in order to form
a neutron star,

547
00:31:03 --> 00:31:09
you would have
to start off with a star

548
00:31:05 --> 00:31:11
of probably at least ten solar
masses, maybe even more.

549
00:31:09 --> 00:31:15
So our Sun will not become
a neutron star,

550
00:31:11 --> 00:31:17
but our Sun will ultimately
become a white dwarf.

551
00:31:15 --> 00:31:21
Now, it would be
a reasonable question to ask,

552
00:31:18 --> 00:31:24
Why do you end up only with
these three possibilities?

553
00:31:20 --> 00:31:26
Why is there nothing in between?

554
00:31:22 --> 00:31:28
Look, there is a huge difference

555
00:31:24 --> 00:31:30
from 10,000 kilometers
to ten kilometers.

556
00:31:26 --> 00:31:32
Is there nothing in between?

557
00:31:28 --> 00:31:34
And the answer to that
lies in quantum mechanics,

558
00:31:30 --> 00:31:36
which is not part of this course
but you will see that in 8.05.

559
00:31:34 --> 00:31:40
Why are there only these two?

560
00:31:35 --> 00:31:41
And then if you get
into general relativity,

561
00:31:38 --> 00:31:44
then you will understand

562
00:31:39 --> 00:31:45
why there is, then, this third,
very bizarre possibility.

563
00:31:44 --> 00:31:50
When a star collapses,
two things happen.

564
00:31:48 --> 00:31:54
First of all,

565
00:31:50 --> 00:31:56
there is a huge amount of
gravitational potential energy

566
00:31:52 --> 00:31:58
that is released
in the form of kinetic energy.

567
00:31:57 --> 00:32:03
The stuff falls in-- we call
it gravitational collapse.

568
00:32:00 --> 00:32:06
And that gravitational
potential energy

569
00:32:01 --> 00:32:07
converts to kinetic energy

570
00:32:03 --> 00:32:09
and that ultimately converts
to heat and to radiation.

571
00:32:07 --> 00:32:13
If I take an object here,
a piece of chalk,

572
00:32:10 --> 00:32:16
and I drop that, that you can
call gravitational collapse.

573
00:32:15 --> 00:32:21
Gravitational potential energy
is converted to kinetic energy

574
00:32:18 --> 00:32:24
and, ultimately,
it goes to heat.

575
00:32:22 --> 00:32:28
Here we're talking about a star
which is imploding, collapsing,

576
00:32:27 --> 00:32:33
and the amounts of
gravitational potential energy

577
00:32:30 --> 00:32:36
that become available
are enormous.

578
00:32:34 --> 00:32:40
In addition to this
huge amount of energy release,

579
00:32:37 --> 00:32:43
the star must spin up, because
its moment of inertia goes down

580
00:32:43 --> 00:32:49
and therefore
the angular velocity must go up.

581
00:32:49 --> 00:32:55
I want to do a little bit
of quantitative work on this.

582
00:32:53 --> 00:32:59
And I want to take
an object like our Sun

583
00:32:57 --> 00:33:03
and I would like
to collapse that object

584
00:33:00 --> 00:33:06
from its present radius--

585
00:33:02 --> 00:33:08
of the Sun, which is
about 700,000 kilometers--

586
00:33:06 --> 00:33:12
I want to collapse that
to a neutron star

587
00:33:08 --> 00:33:14
with a radius of ten kilometers,

588
00:33:10 --> 00:33:16
even though I know
and I told you

589
00:33:12 --> 00:33:18
that the Sun will
not become a neutron star.

590
00:33:17 --> 00:33:23
It's just to get
some feeling for the numbers.

591
00:33:20 --> 00:33:26
So we take an object
like the Sun,

592
00:33:23 --> 00:33:29
which has a radius
of about 700,000 kilometers,

593
00:33:30 --> 00:33:36
and we're going to collapse
that to a neutron star

594
00:33:32 --> 00:33:38
which has a radius
of about ten kilometers.

595
00:33:39 --> 00:33:45
The mass of the Sun is two
times ten to the 30 kilograms,

596
00:33:47 --> 00:33:53
and for those of you
who are good at math,

597
00:33:49 --> 00:33:55
they can calculate--

598
00:33:51 --> 00:33:57
when you collapse this object
without losing any mass,

599
00:33:54 --> 00:34:00
you keep all the mass, but you
shrink it to ten kilometers--

600
00:33:57 --> 00:34:03
how much gravitational
potential energy is released?

601
00:34:00 --> 00:34:06
And that is a staggering number,
and I call that delta u.

602
00:34:05 --> 00:34:11
It is a loss of gravitational
potential energy

603
00:34:08 --> 00:34:14
which is about ten
to the 46 joules.

604
00:34:12 --> 00:34:18
And this number is
truly mind-boggling.

605
00:34:17 --> 00:34:23
This is converted
to kinetic energy

606
00:34:20 --> 00:34:26
and then it is converted to heat
and all forms of radiation.

607
00:34:27 --> 00:34:33
To give you a feeling for how
absurdly large this number is,

608
00:34:32 --> 00:34:38
if you take the Sun

609
00:34:34 --> 00:34:40
and you take all the energy
that the Sun produces

610
00:34:37 --> 00:34:43
in its ten billion years
that it will live,

611
00:34:42 --> 00:34:48
the total energy output of
the Sun is a hundred times less

612
00:34:45 --> 00:34:51
than this number, and this comes
out in a matter of seconds.

613
00:34:49 --> 00:34:55
So it is a mind-boggling idea
that the Sun is producing

614
00:34:54 --> 00:35:00
in ten billion years,
the lifetime of the Sun...

615
00:34:57 --> 00:35:03
It is producing less energy
than what happens

616
00:35:01 --> 00:35:07
during a stellar collapse
to a neutron star.

617
00:35:05 --> 00:35:11
Hundred times less.

618
00:35:07 --> 00:35:13
So, when this in-fall occurs

619
00:35:09 --> 00:35:15
and this huge amount of energy
is released,

620
00:35:12 --> 00:35:18
the outer layer bounces off
the inner core and is expelled

621
00:35:17 --> 00:35:23
and that's what we call
a supernova explosion.

622
00:35:19 --> 00:35:25
The outer layers are thrown off

623
00:35:22 --> 00:35:28
with speeds typically some
10,000 kilometers per second.

624
00:35:26 --> 00:35:32
Our Sun will not become
a neutron star,

625
00:35:28 --> 00:35:34
but it will become
a white dwarf.

626
00:35:32 --> 00:35:38
We talked about
the Crab Nebula last time,

627
00:35:35 --> 00:35:41
and the Crab Nebula is a remnant

628
00:35:36 --> 00:35:42
of a supernova explosion which
occurred-- believe it or not--

629
00:35:39 --> 00:35:45
on the Fourth of July
in the year 1054.

630
00:35:43 --> 00:35:49
Talking about fireworks.

631
00:35:46 --> 00:35:52
The supernova explosion was
noticed by Chinese astronomers.

632
00:35:52 --> 00:35:58
They called this a guest star.

633
00:35:55 --> 00:36:01
Chinese astronomers were
very prestigious.

634
00:35:59 --> 00:36:05
The reason for that was

635
00:36:01 --> 00:36:07
that these Chinese astronomers
advised the emperor.

636
00:36:04 --> 00:36:10
They looked at the sky
and they derived from the sky

637
00:36:09 --> 00:36:15
information that was key
for the emperor.

638
00:36:11 --> 00:36:17
They knew how to interpret
the occurrence

639
00:36:14 --> 00:36:20
of comets or, for instance,
shooting stars,

640
00:36:17 --> 00:36:23
or a particular
line-up of planets

641
00:36:20 --> 00:36:26
and certainly the appearance
of a guest star.

642
00:36:22 --> 00:36:28
And they would know
that, for instance,

643
00:36:24 --> 00:36:30
a comet in a certain part
of the sky might mean

644
00:36:26 --> 00:36:32
that there would be hunger
or there would be diseases,

645
00:36:29 --> 00:36:35
there would be famine,

646
00:36:30 --> 00:36:36
or it would be a good time
for a battle

647
00:36:32 --> 00:36:38
or it would be a bad time
for a battle.

648
00:36:33 --> 00:36:39
And that's
what these people were doing.

649
00:36:36 --> 00:36:42
They were advising the emperor

650
00:36:38 --> 00:36:44
and therefore they were keeping
a very close eye on the sky.

651
00:36:41 --> 00:36:47
No pun implied.

652
00:36:45 --> 00:36:51
This star was visible for weeks
during the day when it exploded,

653
00:36:51 --> 00:36:57
and it was the brightest star
in the sky for years to come.

654
00:36:57 --> 00:37:03
It is a complete puzzle
why there isn't a single report

655
00:37:01 --> 00:37:07
by any European astronomer

656
00:37:04 --> 00:37:10
on the occurrence
of the supernova of 1054.

657
00:37:07 --> 00:37:13
It is very puzzling.

658
00:37:09 --> 00:37:15
Now, you can argue that in
the Netherlands and in England

659
00:37:11 --> 00:37:17
there are always clouds,
it's always raining,

660
00:37:13 --> 00:37:19
so you can't see the sky--
okay, I grant you that.

661
00:37:15 --> 00:37:21
But then we have Italy, and we
have Spain and we have France.

662
00:37:19 --> 00:37:25
And it is very strange.

663
00:37:20 --> 00:37:26
It must have been
a cultural thing.

664
00:37:22 --> 00:37:28
Somehow in the 11th century,

665
00:37:25 --> 00:37:31
somehow, Europe was
not interested

666
00:37:27 --> 00:37:33
in looking at the sky.

667
00:37:29 --> 00:37:35
This is something
they could not have missed,

668
00:37:31 --> 00:37:37
but they didn't write it down.

669
00:37:35 --> 00:37:41
I now want to pursue
the spin-up of this star

670
00:37:38 --> 00:37:44
when it collapses from 700
kilometers to ten kilometers.

671
00:37:44 --> 00:37:50
If we round the numbers
off a little bit,

672
00:37:47 --> 00:37:53
then the reduction in radius
is about 100,000.

673
00:37:51 --> 00:37:57
It's really only 70 -->  but
let's just make that 100 --> 
0:37:56 --> 00:38:02
ten to the 5th.

674
00:37:58 --> 00:38:04
That means R square goes down
by a factor of ten billion.

675
00:38:03 --> 00:38:09
And if R square goes down
by a factor of ten billion,

676
00:38:07 --> 00:38:13
then the moment of inertia goes
down by a factor of ten billion,

677
00:38:11 --> 00:38:17
and so omega must go up
by a factor of ten billion.

678
00:38:14 --> 00:38:20
If you started off with a star

679
00:38:16 --> 00:38:22
that rotated about its own axis
in a hundred days,

680
00:38:19 --> 00:38:25
it ends up rotating around
in one millisecond

681
00:38:23 --> 00:38:29
when it has become
a neutron star.

682
00:38:27 --> 00:38:33
A neutron star, ten kilometers.

683
00:38:30 --> 00:38:36
It has about the same mass
as the Sun, a little more.

684
00:38:33 --> 00:38:39
And it spins around
in one millisecond.

685
00:38:36 --> 00:38:42
At the equator
of the neutron star,

686
00:38:38 --> 00:38:44
you reach about 20%
of the speed of light.

687
00:38:44 --> 00:38:50
We know of hundreds
of neutron stars in the sky.

688
00:38:47 --> 00:38:53
Two of them have, in fact,

689
00:38:49 --> 00:38:55
rotational periods
of 1.5 milliseconds--

690
00:38:52 --> 00:38:58
many of them much slower--

691
00:38:54 --> 00:39:00
and we discussed last time
why that is.

692
00:38:56 --> 00:39:02
Because remember, in the case
of the Crab Pulsar,

693
00:39:00 --> 00:39:06
the pulsars slow down.

694
00:39:01 --> 00:39:07
Nature is tapping on the
rotational kinetic energy

695
00:39:04 --> 00:39:10
of these pulsars

696
00:39:06 --> 00:39:12
and is converting it
into other forms of energy--

697
00:39:09 --> 00:39:15
in the case of the Crab Pulsar,

698
00:39:11 --> 00:39:17
radio emission,
optical emission, gamma rays,

699
00:39:14 --> 00:39:20
X rays and even jets.

700
00:39:17 --> 00:39:23
The Crab Pulsar was slowing down
every day 36.4 nanoseconds,

701
00:39:23 --> 00:39:29
which led to
a staggering power output.

702
00:39:26 --> 00:39:32
I still remember the number.

703
00:39:28 --> 00:39:34
I think
six times ten to the 31 watts.

704
00:39:30 --> 00:39:36
In 75 years, the pulsar
slows down by one millisecond,

705
00:39:35 --> 00:39:41
so the 33 milliseconds

706
00:39:37 --> 00:39:43
would become 34 milliseconds
in 75 years.

707
00:39:43 --> 00:39:49
If the star has an original...

708
00:39:46 --> 00:39:52
There's no star,
that was a disk, right?

709
00:39:48 --> 00:39:54
If the star has
an original magnetic field

710
00:39:50 --> 00:39:56
which most stars do--

711
00:39:52 --> 00:39:58
oh, I lost my star,
but that's okay--

712
00:39:54 --> 00:40:00
then in the collapse

713
00:39:56 --> 00:40:02
the magnetic fields
will become stronger.

714
00:39:58 --> 00:40:04
And this is something
you will learn about in 8.02,

715
00:40:01 --> 00:40:07
why it becomes stronger.

716
00:40:02 --> 00:40:08
So most of these neutron stars
have strong magnetic fields

717
00:40:05 --> 00:40:11
and most rotate very fast.

718
00:40:09 --> 00:40:15
And for reasons
that we don't quite understand,

719
00:40:12 --> 00:40:18
many of them blink at us.

720
00:40:15 --> 00:40:21
They blink at us
in radio emission.

721
00:40:19 --> 00:40:25
We believe that there are
two beams of radio emission

722
00:40:22 --> 00:40:28
like a lighthouse

723
00:40:24 --> 00:40:30
going out from the two magnetic
poles of the neutron star,

724
00:40:26 --> 00:40:32
and as the neutron star rotates
and you are on Earth,

725
00:40:29 --> 00:40:35
if it sweeps over you

726
00:40:31 --> 00:40:37
you see radio emission,
radio emission, you see nothing.

727
00:40:33 --> 00:40:39
You see radio emission,
you see radio emission.

728
00:40:36 --> 00:40:42
So many pulsars whose beam
doesn't sweep over the Earth

729
00:40:39 --> 00:40:45
we would never be able to see,
of course.

730
00:40:42 --> 00:40:48
And in the case
of the pulsar in the Crab

731
00:40:44 --> 00:40:50
it is even more special,

732
00:40:45 --> 00:40:51
because that pulsar
also blinks at us

733
00:40:48 --> 00:40:54
in the optical, in the X rays
and in the gamma rays.

734
00:40:53 --> 00:40:59
And so now I would like
to show you some slides

735
00:41:01 --> 00:41:07
and discuss in a little bit more
detail the supernova explosions

736
00:41:08 --> 00:41:14
and the fabulous light output
and the spin-up,

737
00:41:16 --> 00:41:22
so I have to make it quite
dark... make it completely dark.

738
00:41:26 --> 00:41:32
There we go.

739
00:41:30 --> 00:41:36
And so the first slide is
simply an artist's conception--

740
00:41:37 --> 00:41:43
don't take this too seriously--

741
00:41:40 --> 00:41:46
of these beams
of radio emission.

742
00:41:43 --> 00:41:49
This is, then,
the rotating neutron star,

743
00:41:46 --> 00:41:52
and if the axis of rotation
doesn't coincide

744
00:41:49 --> 00:41:55
with the magnetic dipole axis,

745
00:41:52 --> 00:41:58
and if you have
these radio beams--

746
00:41:53 --> 00:41:59
which we do not understand
how they are formed--

747
00:41:56 --> 00:42:02
there you can see,
when they rotate

748
00:41:58 --> 00:42:04
how they can sweep over you.

749
00:41:59 --> 00:42:05
Now you may say, "Well,
that's a little bit artificial,

750
00:42:02 --> 00:42:08
"because why would
the axis of rotation

751
00:42:05 --> 00:42:11
be different from
the magnetic dipole axis?"

752
00:42:08 --> 00:42:14
Well, that is not an exception
at all in astronomy.

753
00:42:11 --> 00:42:17
The Earth itself has
a magnetic dipole axis

754
00:42:14 --> 00:42:20
which doesnot coincide
with the axis of rotation.

755
00:42:18 --> 00:42:24
In fact, almost all the planets
in our planetary system
 

756
00:42:21 --> 00:42:27
have a magnetic dipole axis

757
00:42:23 --> 00:42:29
which makes a large angle
with the axis of rotation,

758
00:42:26 --> 00:42:32
so that's the rule in astronomy,
rather than the exception,

759
00:42:29 --> 00:42:35
even though it may not be easy
to understand that.

760
00:42:32 --> 00:42:38
And these blue lines, then,
represent magnetic field lines.

761
00:42:37 --> 00:42:43
You will see more of them than
you like when you take 8.02.

762
00:42:41 --> 00:42:47

763
00:42:44 --> 00:42:50
And here is Jocelyn Bell.

764
00:42:47 --> 00:42:53
Jocelyn Bell was
a graduate student

765
00:42:49 --> 00:42:55
under Anthony Hewish
in Cambridge, England,

766
00:42:52 --> 00:42:58
and she discovered pulsars.

767
00:42:57 --> 00:43:03
She found in the radio data--

768
00:43:00 --> 00:43:06
which were obtained
using a new telescope

769
00:43:03 --> 00:43:09
that Anthony Hewish had built--

770
00:43:06 --> 00:43:12
she found in there
periodic signals--

771
00:43:10 --> 00:43:16
pulses,
if you want to call them--

772
00:43:12 --> 00:43:18
you see some of them
here at the bottom,

773
00:43:15 --> 00:43:21
and they were 1.3 seconds apart.

774
00:43:18 --> 00:43:24
And she reported that
to Anthony, and Anthony said,

775
00:43:21 --> 00:43:27
"Well, they've got to be
nonsense, of course.

776
00:43:23 --> 00:43:29
"I mean, there's
not an object in the sky

777
00:43:25 --> 00:43:31
"that is going to give us pulses

778
00:43:27 --> 00:43:33
with a separation
of 1.3 seconds."

779
00:43:29 --> 00:43:35
So they just assumed that
it was caused by an elevator,

780
00:43:32 --> 00:43:38
by maybe milking cow machines
or things of that nature,

781
00:43:36 --> 00:43:42
motorcycles... and so they
did every conceivable thing

782
00:43:39 --> 00:43:45
to check whether, indeed,
this was a man-made phenomenon.

783
00:43:44 --> 00:43:50
But they could not
find anything,

784
00:43:47 --> 00:43:53
and it was Jocelyn, through
her incredible brilliance,

785
00:43:51 --> 00:43:57
who was able to convince Anthony

786
00:43:54 --> 00:44:00
that indeed this is
an object that is in the sky

787
00:43:58 --> 00:44:04
and that the radiation
doesn't come from the Earth.

788
00:44:02 --> 00:44:08
And when they realized that,
they realized that this would be

789
00:44:05 --> 00:44:11
the discovery of not
only the century

790
00:44:08 --> 00:44:14
but of all of mankind,
because they said,

791
00:44:10 --> 00:44:16
"Well, who could possibly
send radio beams at us

792
00:44:14 --> 00:44:20
"and modulate them
with a period of 1.3 seconds?

793
00:44:17 --> 00:44:23
Only intelligent life
can do that."

794
00:44:20 --> 00:44:26
And so they called this first
object "Little Green Man."

795
00:44:23 --> 00:44:29
But just before they published--

796
00:44:25 --> 00:44:31
they discovered it
in 1967, by the way--

797
00:44:27 --> 00:44:33
they found a second pulsar

798
00:44:29 --> 00:44:35
which had a slightly
different frequency

799
00:44:31 --> 00:44:37
than the 1.3 second period,
and so then they realized

800
00:44:34 --> 00:44:40
~that it was probably
not intelligent life

801
00:44:37 --> 00:44:43
but that it was
an astronomical object.

802
00:44:39 --> 00:44:45
So they gave that second object
the name "Little Green Man II,"

803
00:44:42 --> 00:44:48
but they abandoned
that idea very quickly.

804
00:44:46 --> 00:44:52
Now comes the sad part
of the story.
 

805
00:44:48 --> 00:44:54
In 1974, Anthony Hewish
was awarded the Nobel Prize

806
00:44:51 --> 00:44:57
for this discovery.

807
00:44:53 --> 00:44:59
And Jocelyn,
who more than deserved it,

808
00:44:55 --> 00:45:01
whoreally was the discoverer,

809
00:44:57 --> 00:45:03
who was the person who proved
that this was astronomical,

810
00:45:01 --> 00:45:07
did not share
in the Nobel Prize.

811
00:45:04 --> 00:45:10
It is upsetting, it is sad.

812
00:45:07 --> 00:45:13
I have discussed it
with Jocelyn several times--

813
00:45:09 --> 00:45:15
I know her quite well--

814
00:45:11 --> 00:45:17
and she takes it actually very
lightly, too lightly, I think.

815
00:45:15 --> 00:45:21
Still, people
feel unhappy about it

816
00:45:18 --> 00:45:24
and still, after so many years--

817
00:45:19 --> 00:45:25
the Nobel Prize
was awarded in 1974--

818
00:45:22 --> 00:45:28
every time that I think about
this magnificent discovery

819
00:45:26 --> 00:45:32
and I think about Jocelyn,

820
00:45:28 --> 00:45:34
I think about
this gross injustice.

821
00:45:33 --> 00:45:39
Here we see the Crab Nebula
again, we've seen it before.

822
00:45:36 --> 00:45:42
The red filaments that you see
here are the result of matter

823
00:45:41 --> 00:45:47
that was blown off
when the implosion occurred

824
00:45:44 --> 00:45:50
and when the outer layers
bounced off the inner core.

825
00:45:47 --> 00:45:53
And originally they had a speed

826
00:45:49 --> 00:45:55
of about 10,000 kilometers
per second

827
00:45:51 --> 00:45:57
and by now-- it is
about 1,000 years later--

828
00:45:54 --> 00:46:00
these speeds have
been reduced somewhat.

829
00:45:57 --> 00:46:03
But here at the center
you see the pulsar,

830
00:46:01 --> 00:46:07
and last time I showed
you convincing evidence

831
00:46:03 --> 00:46:09
that this is the pulsar,
because it's blinking at us.

832
00:46:06 --> 00:46:12
It has a diameter
of about seven light-years.

833
00:46:10 --> 00:46:16
It is a distance from us
of about 5,000 light-years.

834
00:46:14 --> 00:46:20
In terms of angular size
in the sky,

835
00:46:16 --> 00:46:22
it's about five arc minutes
in size,

836
00:46:18 --> 00:46:24
which is about one-sixth of the
angular diameter of the Moon.

837
00:46:23 --> 00:46:29

838
00:46:30 --> 00:46:36
This is a drawing, a cave
drawing, made by Navajo Indians,

839
00:46:34 --> 00:46:40
and some people have
speculated to what extent

840
00:46:37 --> 00:46:43
the Navajo Indians may have seen
the supernova in 1054.

841
00:46:40 --> 00:46:46
It's unclear,
but it is a possibility.

842
00:46:42 --> 00:46:48
The Moon certainly gets
very close to the supernova,

843
00:46:45 --> 00:46:51
but it also gets very close to
Venus, and so this is something

844
00:46:48 --> 00:46:54
that is not well established,
but it is a possibility.

845
00:46:51 --> 00:46:57
Here you see a galaxy
in which a supernova occurred,

846
00:46:58 --> 00:47:04
and when the supernova occurs
at its brightest,

847
00:47:01 --> 00:47:07
it can be brighter than
all hundred billion stars

848
00:47:05 --> 00:47:11
in the galaxy.

849
00:47:06 --> 00:47:12
That's how much energy
is released in optical light.

850
00:47:09 --> 00:47:15
You see that it is at least
as bright as the entire galaxy.

851
00:47:13 --> 00:47:19
From this picture to this
picture is about one year.

852
00:47:16 --> 00:47:22
This occurred in 1972
and over the period of one year,

853
00:47:20 --> 00:47:26
you can still see this star
quite clearly,

854
00:47:24 --> 00:47:30
but it has diminished
in strength quite a bit.

855
00:47:30 --> 00:47:36
And then a great thing happened
in February 1987,

856
00:47:36 --> 00:47:42
on the 23rd of February.

857
00:47:38 --> 00:47:44
The supernova went off
in the Large Magellanic Cloud,

858
00:47:40 --> 00:47:46
which is a satellite galaxy
to our own galaxy.

859
00:47:43 --> 00:47:49
It's a distance of
about 150,000 light-years,

860
00:47:47 --> 00:47:53
and there was an astronomer who
was observing in South America.

861
00:47:51 --> 00:47:57
His name is Ian Shelton,

862
00:47:55 --> 00:48:01
and he left the dome
to look at the stars

863
00:47:58 --> 00:48:04
and he decided
to take a pee outside.

864
00:48:01 --> 00:48:07
And as he was taking a pee--
these were his own words--

865
00:48:04 --> 00:48:10
he looked at the Large
Magellanic Clouds and he said,

866
00:48:07 --> 00:48:13
"Hey, that is funny! That star
is not supposed to be there."

867
00:48:10 --> 00:48:16
And he was the discoverer
of what is now known as 1987A,

868
00:48:16 --> 00:48:22
an enormous supernova going off
so close to where we live.

869
00:48:24 --> 00:48:30
And the next slide shows you

870
00:48:26 --> 00:48:32
the same portion
of the Large Magellanic Clouds

871
00:48:28 --> 00:48:34
and you can clearly see that
there is a very bright star.

872
00:48:31 --> 00:48:37
He could see this
with his naked eye.

873
00:48:33 --> 00:48:39

874
00:48:39 --> 00:48:45
This is a picture made
by the Hubble Space Telescope

875
00:48:44 --> 00:48:50
of supernova 1987A.

876
00:48:48 --> 00:48:54
The inner ring that you see

877
00:48:51 --> 00:48:57
is the result of matter
that was thrown off by the star

878
00:48:58 --> 00:49:04
before it went
into supernova explosion

879
00:49:01 --> 00:49:07
some 25,000 years earlier.

880
00:49:04 --> 00:49:10
It expelled gas in its equator.

881
00:49:07 --> 00:49:13
This is really a circle,
although it looks

882
00:49:10 --> 00:49:16
like an ellipse because
of the projection effect.

883
00:49:13 --> 00:49:19
And this ring of matter
moved out

884
00:49:15 --> 00:49:21
with a speed of about
eight kilometers per second

885
00:49:19 --> 00:49:25
and it has a radius
of about eight light-months.

886
00:49:24 --> 00:49:30
And so eight months after
the supernova explosion,

887
00:49:28 --> 00:49:34
the ultraviolet light and
the X rays from the supernova

888
00:49:31 --> 00:49:37
caught up with this ring
of matter and they excited it

889
00:49:35 --> 00:49:41
and it became visible.

890
00:49:36 --> 00:49:42
Before the supernova explosion,
this ring was not visible.

891
00:49:43 --> 00:49:49
We are expecting in a few years
that the matter itself

892
00:49:46 --> 00:49:52
that was thrown off
with a much more modest speed

893
00:49:48 --> 00:49:54
of about 10,000 kilometers
per second...

894
00:49:51 --> 00:49:57
that that matter will also plow
into this ring

895
00:49:54 --> 00:50:00
and then we expect
some real fireworks again.

896
00:49:58 --> 00:50:04
There is no explanation
that people agree upon

897
00:50:02 --> 00:50:08
for these two
called "hourglass" rings.

898
00:50:06 --> 00:50:12
They are quite mysterious and
there are papers written on it

899
00:50:09 --> 00:50:15
and people disagree
on their origin.

900
00:50:14 --> 00:50:20
Supernovae explosions
in our galaxy

901
00:50:17 --> 00:50:23
and in the Large Magellanic
Clouds are quite rare.

902
00:50:24 --> 00:50:30
We expect no more than
about one in a hundred years.

903
00:50:29 --> 00:50:35
The previous one that could be
seen with the naked eye

904
00:50:32 --> 00:50:38
was in the year 1604.

905
00:50:34 --> 00:50:40
It's called Kepler supernova.

906
00:50:36 --> 00:50:42
And 1987A was really the first

907
00:50:39 --> 00:50:45
that could be studied
with modern equipment--

908
00:50:41 --> 00:50:47
radio observatories,
X-ray observatories

909
00:50:44 --> 00:50:50
in orbit around the Earth.

910
00:50:49 --> 00:50:55
With some luck, you may see
a supernova explosion

911
00:50:51 --> 00:50:57
naked eye in your life.

912
00:50:53 --> 00:50:59
The chance is no better than ten
percent, so maybe it will help

913
00:50:57 --> 00:51:03
if occasionally
you take a pee outside

914
00:51:00 --> 00:51:06
and you become as famous
as Ian Shelton did,

915
00:51:03 --> 00:51:09
who is now a very famous man.

916
00:51:05 --> 00:51:11
See you Monday.

917
00:51:07 --> 00:51:13

918
00:51:15 --> 00:51:21.000