WEBVTT
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So now what we'd
like to do is try
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to understand how to apply the
law of addition of velocities.
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So we can express the
velocity of the point
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on the rim in the reference
frame fixed to the ground.
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Now, the important
thing to realize
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is v is the velocity
of the center of mass
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of the wheel with
respect to the ground,
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and every single point on the
wheel has that same velocity v.
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So let's draw a
picture of our wheel.
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Here we're in the
ground reference frame.
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And let's first draw
four points on the wheel
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and draw this velocity v. Every
single one of these points
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has the same velocity
v, v, v, and v.
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Now, let's add to
that the velocity
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of a point on the rim as
seen in the reference frame
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moving with the center of mass.
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We just saw that every
single point on the wheel
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is undergoing circular motion
in that reference frame.
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So now let's draw
those velocities.
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I'll just draw it right below--
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vcmp, down here vcmp.
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Notice here it's in the
opposite direction, vcmp,
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and up here it's pointing up.
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So when we add these two
vectors together, what we get
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is a longer vector
in this direction.
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It would be the sum
of these two pieces.
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So it would point like that.
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That's vp.
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Over here it's the
vector decomposition.
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So it's in that direction.
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Here it's a shorter vector vp.
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And over here it's
the vector sum vp.
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So now what we've
been able to do
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is describe the
velocity of the point p
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as a combination,
the vector addition,
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of how the center of mass
of the wheel is moving
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and the circular motion as seen
in a reference frame moving
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with the center of mass.
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Now what we want to explore
is special conditions,
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which we'll refer to as rolling
without slipping, slipping,
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or sliding.