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Let's consider the motion
of a single particle

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moving with a velocity v in a
ground reference frame, say.

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Recall that we defined the
momentum of this object as mv.

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And we know that
Newton's second law

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can be written in terms of
the change of momentum dp/dt.

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And when we integrated
Newton's second law,

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for impulse causes
the integral of ADP

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from some time t prime
equals 0 to some time t.

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So we're integrating t prime.

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And here, we're
taking your momentum

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from some initial momentum
to some momentum at time t.

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We have that the impulse
causes the momentum

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of this single
particle to change.

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And in particular, this
is what we call impulse.

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And if the impulse is 0--

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so as an example, if the
impulse fdt prime equals 0,

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that tells us that the
momentum of our particle

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has not changed.

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Now, let's consider our same
thing for angular momentum.

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The only difference is that
we choose some point s.

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And we'll write the vector
rs to where the object is.

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And our angular momentum
we defined about the point

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s was the vector from s.

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And we can indicate
maybe to the mass m.

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So it's a vector from s to where
the object is located cross

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the momentum of the object.

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And this is how we define
the angular momentum.

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And recall that
our basic concept

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is that the torque about
s causes the angular

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momentum about s to change
for this single particle.

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Now, torque is if there's a
force acting on the particle.

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So for instance, if the force
were acting at some angle.

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Not only does the force change
cause the momentum to change,

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but we know that if
there's a torque about s,

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it will cause the angular
momentum of the particle

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to change too.

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Now, let's talk about
the angular impulse,

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which is integrating
the torque from

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say some time t prime
equals 0 to some time t.

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And that's the integral of
the angular momentum about s.

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And now we're integrating
this from some initial angular

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momentum to some final
angular momentum.

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And just as before, we have
that the angular impulse

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will result in a change
of angular momentum.

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And in particular, if
our angular impulse is 0,

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that implies that the angular
momentum of this particle

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is constant.

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And so you can
see the analogies.

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The important fact to realize
is that in the reference frame,

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momentum does not
depend on any point,

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but our angular
momentum does depend

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on the choice of the point s.

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And in particular, in terms of
the impulse, the torque about s

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is also a quantity
that depends on s.

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And so that's the
analogy between momentum

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of a single particle and angular
momentum of a single particle.