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We'd like to consider
torques on a body.

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Let's draw an arbitrary body,
and let's consider a point s,

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that we're about to
calculate the torque.

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Now, we know that
forces on the body

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can be both internal
and external.

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And we'd like to show that
all internal torques will

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cancel in pairs.

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The way we'll do that is,
suppose we pick an object.

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We'll label it with mass
mi, and another object,

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we'll label that with mass mj.

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These are small mass
elements in the body.

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And we'd like to know something
about the internal forces.

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Now, let's make the assumption--
and this is the key property--

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that the force due to
this interaction between j

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and the i-th particle
pointing that way-- and here's

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the Newton's third law pair--
that these forces lie--

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are directed along the line
connecting the two bodies.

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With this assumption,
we'll now show

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that the torque due to these
two internal forces, [INAUDIBLE]

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Newton's third law
pairs will cancel.

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So let's calculate that out.

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So we draw our vector from
rsi, and our other vector rsj.

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And now we're in position
to add these two torques.

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So we have the torque
on s due to this pair is

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equal to the sum of
rsi cross fji plus

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rs-- that's an r-- make
sure we get that right.

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We have rsj cross fij.

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Now, the third law pair says
fji is equal to minus fiji.

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And so, if we substitute-- let's
put the minus sign over here--

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we get rsi minus rsj cross fji.

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Now, let's look at this
vector in particular.

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We can draw it again over
here, just to see it.

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Here s.

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Here is rsi.

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Here is the vector
rs, that's rsj.

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And we want to now consider
the vector rsi minus rsj.

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Notice that this
vector is directed

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along the lines connecting the
i-th and the j-th particle.

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And we've made an
assumption that fji is also

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along that line.

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So these two vectors,
in this particular case,

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are either parallel
or anti-parallel.

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And hence, the torque due
to the sum of these internal

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forces cancel in pairs.

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And this means we
only need to address

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the torque due to
external forces that

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are acting on individual
elements in a body.