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We recently introduced a
vector quantity called torque--

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a sort of rotational
analog to force.

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And we saw that an applied
torque changes the angular

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motion of a rotating
body in just the same way

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that an applied force
changes the linear motion

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of a translating body.

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This week, we're
going to introduce

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the concept of angular
momentum, which

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relates to torque and rotational
motion in the same way

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that ordinary momentum
relates to force

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and translation of motion.

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Like torque, angular
momentum is defined

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in terms of a cross product
or a vector product.

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Specifically, the angular
momentum vector L for a point

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mass is equal to the
cross product R cross P ,

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where R is the position
vector measured from a chosen

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reference point and P is the
ordinary momentum vector.

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We will also encounter a
third conservation principle,

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this time for angular momentum.

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An applied torque causes the
angle the moment of to change.

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However, if there are no
external torques on a system,

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then the angular
momentum of the system

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is conserved or
remains constant.

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This is a powerful tool
for solving many problems.

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One subtlety is that
angular momentum like torque

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is defined relative
to a specified point.

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So for a given system,
the angular momentum

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with respect to one
point might be conserved,

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while the angular momentum with
respect to a different point

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might be changing.

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Often in analyzing
the system, we

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must be careful about our
choice of reference point

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for torques and angular
momentum in order

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to take full advantage of
the conservation principle.

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Angular momentum
is a particularly

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subtle and non-intuitive
concept in comparison

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to momentum and energy.

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And the resulting motion
is often surprising.

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It is worthy of
particularly careful study.