WEBVTT

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Up until now, we have
been studying the motion

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of point-like objects.

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In this module, we
are going to consider

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the motion of extended
objects, specifically

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objects that are rigid bodies.

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By rigid, we mean
that the distance

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between any two points on the
object always stays the same.

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In other words, the
shape of a rigid body

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does not change or deform.

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There is a useful relation
known as Chasles' theorem that

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states that the
general arbitrarily

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complicated displacement
of a rigid body

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can be broken up into
two parts-- first,

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the translational motion
of its center of mass,

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and second, the pure
rotation of the object

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about its center of mass.

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We already know how
to analyze the center

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of mass translational
motion through our study

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of point-like objects.

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This week, we will consider
the rotational motion

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of rigid bodies, once
again distinguishing

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between kinematics, a geometric
description of the motion,

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and dynamics, the
underlying cause of changes

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in the rotational motion.

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On a microscopic level, we can
think of an extended rigid body

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as made up of a
very large number

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of small point-like pieces
all attached together.

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For rotation about a fixed axis
through the center of mass,

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each little piece
will move in a circle

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about the rotational axis.

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The radius of the
circle will vary

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depending upon
where in the object,

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that particular piece sits.

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However, because all
of these small pieces

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are moving collectively as
part of a single rigid body,

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they will all have the same
angular velocity and angular

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acceleration at
any given instant.

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This gives us a way to specify
the kinematics or geometrical

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description of
rotational motion using

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the vector quantities of
angular velocity and angular

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acceleration.

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We will also consider the
dynamics of rotational motion.

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We will see that an
applied external force

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is able to change the rotational
motion of a rigid body,

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depending upon exactly where on
the body the force is applied.

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This leads directly to
the concept of torque,

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a vector quantity
that represents

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a sort of rotational force.

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Finally, we will see that
we can link the kinematics

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and dynamics of
rotational motion

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through a rotational equation
of motion, analogous to the role

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that Newton's second law plays
for translational motion.

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This relation states that
the angular acceleration

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is proportional to
the applied torque

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and also depends upon how
the mass of the object

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is distributed.