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We will now introduce a
new kinematic quantity
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called angular momentum.
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Angular momentum
will be very useful
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when we describe the
rotation and objects.
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In particular, how will
it be related to torque.
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Now, what is angular momentum?
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Suppose we have an
object of mass m.
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And it's moving
in this direction.
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And it has momentum p.
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Remember, p equals mv.
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Angular momentum is always
defined about some point.
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So suppose we choose a
point s, and I wanted
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to find the angular
momentum about
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s due to this motion
of the object.
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And the way it's defined is I'll
draw a vector from the point
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s to where the object is.
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And our definition of angular
momentum about s is equal--
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this is three lines
for our definition--
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it's the vector cross
product of the vector rs.
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We have the vector p.
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Now, how do we define the
direction of this vector?
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Well, the way we do
that for any vector
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product is we take
the two vectors
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and we put them tail to tail.
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So let's start off
by drawing the vector
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rs in that direction.
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And now when you
take a cross product,
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we draw an arrow from the
first vector to the second one.
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Remember, cross in vector
products are the same thing.
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And now we want to
use our right hand
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rule to get the direction
of the angular momentum.
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So we curl our fingers.
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And notice in this
case, it's pointing
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into the plane of the figure.
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And so the direction of the
angular momentum about s
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is given into the plane of
the figure in our light board.
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Now, we'll learn how to
calculate this cross product
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in detail.
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But suppose we have
our vectors which
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are in a slightly
different arrangement
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as seen in this figure here.
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Well, what we see is with the
vector p and the vector rs,
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we still use our right
hand rule to calculate
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the direction of Ls.
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Notice, whenever you have
a vector cross product,
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that the vector Ls is
perpendicular to both
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the vectors rs and is
perpendicular to the vector p.
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And you can see in
both of these examples
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that the angular momentum is
perpendicular to the plane
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formed by the vectors rs and p.