WEBVTT
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Here, we will talk
about in the calculation
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of angular momentum.
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People often forget
that angular momentum
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can be calculated
for any object,
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even for an object
that's traveling
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in a straight line and
not rotating at all.
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For example, here
I have an object
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with mass m moving at a
speed v along a street line.
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Another important
thing to keep in mind
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is that angular momentum does
not have a definite value.
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It depends on the choice of
origin, which is arbitrary,
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although some choices
are easier to calculate
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or more useful than others.
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Here, I will choose this
completely random point
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to be my origin.
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Notice that it can be
any point in space.
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Angular momentum is
a lot like torque.
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They both involve a cross
product of a distance vector
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with another vector.
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For angular momentum, it's
the distance vector r,
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the vector from the
origin to the object,
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cross p, the momentum
of the object, or mv.
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Once again, we can
write the magnitude
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of this cross-product as
r times mv times the size
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of the theta between the two.
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But it's often more
helpful to think
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about this as r times
sine theta times mv.
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In other words, the r sine
theta is the component
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of the position vector that's
perpendicular to the direction
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of the momentum.
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Let's practice with
a few other examples.
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If I have a ball moving up and
I have my origin at the side,
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then this is the
perpendicular distance.
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So the angular momentum is
r perpendicular times mv.
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A reference point that's
the same horizontal distance
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away from the object will see
the same angular momentum.
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Notice that in this case,
the angular momentum is not
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changing as the ball moves,
because the perpendicular
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distance is not
changing with time.
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In this case, if the ball
is moving at an angle,
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we again, have to
take the perpendicular
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component of the position vector
to find the angular momentum.
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This second reference point is
now a different distance away.
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So the angular
momentum is larger.
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Now, let's talk about the
sign of angular momentum.
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You can calculate the
sine of a cross product
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with the right hand rule.
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Make sure your vectors
are tail to tail when
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you compare the directions.
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So in this case, we have that
r cross v points into the page.
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In the case of circular
motion, r and v
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are always perpendicular.
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So we can just multiply
the magnitudes together.
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And the sine tells us which way
we're going around the circle.
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If we consider out of
the page to be positive
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and the angular
momentum is positive,
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then the object is
circulating counter-clockwise.
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If the angular
momentum is negative,
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the object is
circulating clockwise.