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So far in the course, we've
been studying the motion

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of collections of particles.

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We would know like to
consider rigid bodies.

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Now, rigid bodies can
be translated in space

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as I move it like this.

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Or we can rotate this rigid
body about some point.

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I can rotate it
about the end point.

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I can rotate it
about a point which

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we call the center of mass.

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So I can rotate it about
the center of mass.

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I can take the
rigid body and I can

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rotate it about
the center of mass,

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and also translate it in space.

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So there's many types
of motions that we

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can do with rigid bodies.

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Sometimes the motions
are quite complicated.

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If I spin it like that, it is
a very more complicated motion.

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You can see that it's
rotating about this axis.

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So what we'd like
to do now is analyze

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how to think about the
motion of rigid bodies.

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And what we'd like to do
is idealize our rigid body.

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So even though we
looked at a rod here,

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let's just draw some extended
idealized rigid body.

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And let's identify two
points in that rigid body--

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the j-th point and
the k-th point.

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And we'll think
of our rigid body

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as a bunch of point-like
particles mj and mk.

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And the important thing
that defines a rigid body

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is the condition that
the distance-- and we'll

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draw a vector from the k-th
particle to the j-th particle.

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So we'll draw that as rjk.

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And actually, I'd like to
write it from the k-th particle

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to the j-th particle rjk.

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And our condition is that the
magnitude of this vector, which

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I'll denote as rjk is constant
for all points j and k.

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Now, what does that mean?

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That means the distance
between any two

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points in the rigid body
stays fixed no matter

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how the rigid body is
moving and no matter what

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two points I choose.

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The distance between
any two points is fixed.

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So we'll rewrite this as the
distance between any two points

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is fixed.

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So that doesn't change.

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And that's what we call
the rigid body condition.