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So we're now beginning to
make our complete study

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of rigid body motions
about fixed axis.

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Let's consider something
like a bicycle wheel.

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Here's the center of
mass of the wheel.

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And our bicycle wheel--
the center of mass

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has some velocity.

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And here's ground.

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And the reference frame
is the ground frame.

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Now if the bicycle
wheel is rolling,

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then there will be some type of
rotational motion of the wheel.

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So you can imagine a point
on the rim is rotating.

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And so what we have here
is a angular velocity

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of this bicycle,
which we'll write

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like this, our vector omega.

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And we'll use our
right hand rule

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to establish that
direction for omega.

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And now in this
reference frame, we

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have translational motion
of the center of mass.

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And we have rotational motion
around the center of mass.

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If we go to the center
of mass reference frame--

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so if you want just a
little cartoon to show that,

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here's your observer.

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And your observer
is moving with VCM.

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And so in that frame, the
center of mass is at rest,

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and the only thing
we have is rotation

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about the center of mass.

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And so in this
picture, our motivation

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will be that the total external
force causes the center of mass

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to accelerate.

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And that's how we can figure
out the center of mass motion.

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And in this picture,
we no longer

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have to consider
translational motion.

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And what we'll study
and learn to analyze

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is just pure rotation
about the center of mass--

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so torque will produce
angular acceleration.

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We can talk about
the rotational energy

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about the center of mass.

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And so we'll begin our
analysis of rotational motion

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of translation and rotation
by focusing our interest

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in the center of mass
frame-- so we've just

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isolated the rotational motion.