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Let's consider a
wheel that's rolling.

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So our wheel is rolling
along a surface.

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The wheel has radius r.

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And I want to consider
the motion of a point P

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on the rim of the wheel.

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Now, I'll choose an
origin that's fixed.

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And in fact, here we're going to
talk about the reference frame

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A, which is fixed to the ground.

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And I would like to
consider-- my problem is

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to find both the position
of the point on the rim,

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the velocity of the
point on the rim,

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and the acceleration
of the point in the rim

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as a function of time.

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Now, the position vector is
given from my fixed origin

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to where the point
on the rim is.

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Now, this can be
quite complicated.

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But what we're going to do is
consider a second reference

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frame that is located at the
center of mass of the wheel.

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So our second frame,
we'll take reference frame

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and we'll call this
frame cm, is located,

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is moving with the center
of mass of the wheel.

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So in that reference
frame, we'll

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denote this point
by vector r cm,

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because we're in the
reference frame with respect

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to the center of mass, and
we're talking about the point P.

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Now, these vectors
are connected.

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And we'll call
this vector capital

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R. By our vector triangle,
capital R equals little rP--

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that's the position vector.

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And the fixed frame of the
ground is given by capital

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R plus r cm P.

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Now, as we've seen before
by differentiating,

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the velocity of the
particle is given

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by V plus V cm P. This one
is the velocity in frame

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fixed to the ground.

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This is the velocity
of the center of mass

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with respect to ground frame.

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And finally, V cm
P is the velocity

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in the center of mass frame.

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Now, in order to analyze
this law, what we'll now do

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is focus on what
the motion looks

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like if you're an observer
moving with the center of mass.

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And that's how we'll
begin our analysis.