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00:00:03,520 --> 00:00:05,500
So now what we'd
like to do is try

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00:00:05,500 --> 00:00:08,600
to understand how to apply the
law of addition of velocities.

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00:00:08,600 --> 00:00:10,510
So we can express the
velocity of the point

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00:00:10,510 --> 00:00:13,690
on the rim in the reference
frame fixed to the ground.

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00:00:13,690 --> 00:00:15,400
Now, the important
thing to realize

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00:00:15,400 --> 00:00:19,300
is v is the velocity
of the center of mass

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00:00:19,300 --> 00:00:21,190
of the wheel with
respect to the ground,

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00:00:21,190 --> 00:00:25,780
and every single point on the
wheel has that same velocity v.

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00:00:25,780 --> 00:00:28,720
So let's draw a
picture of our wheel.

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00:00:28,720 --> 00:00:33,080
Here we're in the
ground reference frame.

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00:00:33,080 --> 00:00:41,090
And let's first draw
four points on the wheel

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00:00:41,090 --> 00:00:45,140
and draw this velocity v. Every
single one of these points

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00:00:45,140 --> 00:00:54,475
has the same velocity
v, v, v, and v.

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00:00:54,475 --> 00:00:59,280
Now, let's add to
that the velocity

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00:00:59,280 --> 00:01:02,050
of a point on the rim as
seen in the reference frame

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00:01:02,050 --> 00:01:04,239
moving with the center of mass.

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00:01:04,239 --> 00:01:07,480
We just saw that every
single point on the wheel

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00:01:07,480 --> 00:01:10,120
is undergoing circular motion
in that reference frame.

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00:01:10,120 --> 00:01:13,539
So now let's draw
those velocities.

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00:01:13,539 --> 00:01:15,490
I'll just draw it right below--

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00:01:15,490 --> 00:01:21,730
vcmp, down here vcmp.

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00:01:21,730 --> 00:01:26,320
Notice here it's in the
opposite direction, vcmp,

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00:01:26,320 --> 00:01:30,680
and up here it's pointing up.

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00:01:30,680 --> 00:01:34,750
So when we add these two
vectors together, what we get

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00:01:34,750 --> 00:01:37,750
is a longer vector
in this direction.

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00:01:37,750 --> 00:01:40,570
It would be the sum
of these two pieces.

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00:01:40,570 --> 00:01:42,640
So it would point like that.

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00:01:42,640 --> 00:01:44,229
That's vp.

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00:01:44,229 --> 00:01:48,729
Over here it's the
vector decomposition.

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00:01:48,729 --> 00:01:49,830
So it's in that direction.

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00:01:49,830 --> 00:01:53,460
Here it's a shorter vector vp.

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00:01:53,460 --> 00:01:57,970
And over here it's
the vector sum vp.

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00:01:57,970 --> 00:02:00,010
So now what we've
been able to do

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00:02:00,010 --> 00:02:02,600
is describe the
velocity of the point p

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00:02:02,600 --> 00:02:05,530
as a combination,
the vector addition,

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00:02:05,530 --> 00:02:08,680
of how the center of mass
of the wheel is moving

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00:02:08,680 --> 00:02:12,190
and the circular motion as seen
in a reference frame moving

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00:02:12,190 --> 00:02:14,080
with the center of mass.

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00:02:14,080 --> 00:02:17,440
Now what we want to explore
is special conditions,

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00:02:17,440 --> 00:02:21,790
which we'll refer to as rolling
without slipping, slipping,

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00:02:21,790 --> 00:02:23,372
or sliding.