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Now that we've seen how
coordinates are related

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between two inertial
frames, I want

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to consider a slightly
more advanced example

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for a moment, which is supposed
that capital V, the vector

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velocity of frame S prime
relative to inertial frame S,

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is not a constant.

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So in this case, suppose
that frame S prime has

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an acceleration, capital
A, relative to S.

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We now say that as prime is a
non-inertial frame, because it

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is accelerated relative
to frame S. Now

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we saw that in inertial
frames, one always

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measures the same acceleration
for the same object,

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even though you'll measure
different velocities

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in different
positions in general.

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That's not going to true
in a non-inertial frame.

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In a non-inertial frame,
the acceleration, A prime,

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is equal to the acceleration
of frame S minus capital

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A, the acceleration of frame S
prime relative to S. Remember,

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capital A is 0 for S prime
being an inertial frame,

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when capital V is a constant.

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But if capital V
is not a constant,

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then capital A is not 0.

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So you will measure
different accelerations

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in these different frames.

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Now what that tells us is
that Newton's laws are going

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to look a little different.

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And let's see how that works.

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So now, the force measured
in frame S prime-- I'll

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call that F prime-- we expect
that from Newton's second law

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to be the mass times the
acceleration A prime.

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But that is the mass times
the acceleration measured

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in frame S minus m capital A,
the acceleration of frame S

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prime relative to frame S.

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Now I can rewrite
this as two terms.

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One I'll call F physical, which
represents the physical forces

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acting on the object.

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And the second term,
I'm going to call

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F fictitious for reasons
that we'll see in a moment.

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So what this means
is the following

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is that an observer in
frame S prime in order

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to explain the motion of the
object using Newton's laws

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will have to invoke not just
the physical forces interacting

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on the object, which
might be due to gravity

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or rope pulling or
an engine pushing

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or a hand acting on
something, but will also

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have to both an apparent force,
which I'll call F fictitious,

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that acts on everything.

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And in this case, F fictitious
is equal to minus m capital A.

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But that force will not
be associated, will not

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be identifiable with any actual,
real physical interaction.

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It's an artifact of the
choice of coordinate system.

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It's an artifact of the
non-inertial coordinate system

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that frame S prime is in.

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For that reason, we call
it a fictitious force.

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And it's to be distinguished
from real, physical forces

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of the type that we've been
talking about up until now.

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So you may have
seen earlier that

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for the motion of an object in a
circle around some center point

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implies the presence of
an inward acceleration

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toward the center of the circle.

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So as a consequence of that,
a rotating reference frame,

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for example, a
reference frame that

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rotates with the
Earth's rotation,

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is accelerated relative
to an inertial frame.

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This results in a
fictitious force

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that has two terms, a
centrifugal term and a Coriolis

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term.

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You may have come across
this Coriolis force

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and centrifugal force before.

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These are examples
of fictitious forces

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because they arise from the
choice of coordinate system.

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They're an artificial force.

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They don't correspond to
actual, physical interactions,

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but are an artifact of
the rotating, non-inertial

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coordinate system.

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Now, in this course we
will confine ourselves

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to inertial reference frames.

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And therefore, we'll
only be considering

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real, physical forces
and interactions.

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However, there are
advanced applications

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where the use of a non-inertial
frame has certain advantages.

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And you may encounter
those as you

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go to more advanced courses.