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When we discuss the
rolling of the wheel,

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we chose a reference
frame fixed to the ground.

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So that was what we called frame
A. And in that reference frame,

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the motion of the point P on
the rim was quite complicated.

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Now what we'd like to look at
it in the reference frame moving

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with the center of mass.

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And we call that frame cm.

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Now the picture
there is much easier

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because the object is--
in that reference frame,

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the center of mass
is not moving.

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And the point P on
the rim, the object

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is just undergoing
circular motion.

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So in that frame, the
velocity of that point P

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in the center of mass frame
is just tangent to the circle.

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And as the object moves
around, at a later time,

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the velocity is
always tangential.

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And in this reference frame,
it's just pure circular motion.

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And we know that the speed
in that reference frame

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is given by the radius of the
wheel times the rate d phi

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to dt.

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And here let's define the
variable theta this way.

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And so, in this frame
what's happening

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is pure circular motion.

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Now we know our law of
addition of velocity

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tells us that the velocity
in the frame fixed

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to the ground of that point
is equal to the velocity

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of the center of mass
plus the velocity

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of the object, the
point on the run

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in the center of mass frame.

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Now what we want
to do now is draw

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a picture which illustrates this
law of addition of velocities.