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Let's think about
calculating torque.

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I have a force, F, being
applied to an object.

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And that object is
pivoted at a point,

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Q. I'll define R as the vector
from the pivot point, Q,

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to the point of the
application of the force.

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Torque is defined as the
cross product, R cross F,

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which we can also
write as R times F

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times the sine of theta.

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But what does that mean?

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I'll introduce two different
intuitive ways of understanding

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this mathematical expression.

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First, we can think about this
as the magnitude of F times

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the quantity, R sine theta.

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If we look at the
direction of the force,

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then it is easy to
see there R sine theta

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is just the part of R that is
perpendicular to the force.

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So here the torque is
equal to the magnitude

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of the force,
times the magnitude

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of this perpendicular
part of the vector R.

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This perpendicular portion
of the distance vector R

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is often referred to
as the moment arm.

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We can instead group
F with sine theta.

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So this means that we're
thinking of the cross-product

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as the distance R
multiplied by F sine theta.

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The component of
the force F, that's

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perpendicular to the
position vector R.

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Here I'm calculating
torque as the distance

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between the pivot point, and
where the force is applied,

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times the perpendicular
part of the force.

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Be very careful about
the sine theta term.

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In many cases the angle theta
that is given in the problem

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is not the angle that is
used in the expression.

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In this example, F
times the sine of theta,

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will actually give the parallel
component of the force.

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Therefore it is much
better to remember

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to take the perpendicular
component, rather than just

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memorizing sine of theta.