Now that we've seen how coordinates are related
between two inertial frames, I want
to consider a slightly more advanced example
for a moment, which is supposed that capital V, the vector
velocity of frame S prime relative to inertial frame S,
is not a constant.
So in this case, suppose that frame S prime has
an acceleration, capital A, relative to S.
We now say that as prime is a non-inertial frame, because it
is accelerated relative to frame S. Now
we saw that in inertial frames, one always
measures the same acceleration for the same object,
even though you'll measure different velocities
in different positions in general.
That's not going to true in a non-inertial frame.
In a non-inertial frame, the acceleration, A prime,
is equal to the acceleration of frame S minus capital
A, the acceleration of frame S prime relative to S. Remember,
capital A is 0 for S prime being an inertial frame,
when capital V is a constant.
But if capital V is not a constant,
then capital A is not 0.
So you will measure different accelerations
in these different frames.
Now what that tells us is that Newton's laws are going
to look a little different.
And let's see how that works.
So now, the force measured in frame S prime-- I'll
call that F prime-- we expect that from Newton's second law
to be the mass times the acceleration A prime.
But that is the mass times the acceleration measured
in frame S minus m capital A, the acceleration of frame S
prime relative to frame S.
Now I can rewrite this as two terms.
One I'll call F physical, which represents the physical forces
acting on the object.
And the second term, I'm going to call
F fictitious for reasons that we'll see in a moment.
So what this means is the following
is that an observer in frame S prime in order
to explain the motion of the object using Newton's laws
will have to invoke not just the physical forces interacting
on the object, which might be due to gravity
or rope pulling or an engine pushing
or a hand acting on something, but will also
have to both an apparent force, which I'll call F fictitious,
that acts on everything.
And in this case, F fictitious is equal to minus m capital A.
But that force will not be associated, will not
be identifiable with any actual, real physical interaction.
It's an artifact of the choice of coordinate system.
It's an artifact of the non-inertial coordinate system
that frame S prime is in.
For that reason, we call it a fictitious force.
And it's to be distinguished from real, physical forces
of the type that we've been talking about up until now.
So you may have seen earlier that
for the motion of an object in a circle around some center point
implies the presence of an inward acceleration
toward the center of the circle.
So as a consequence of that, a rotating reference frame,
for example, a reference frame that
rotates with the Earth's rotation,
is accelerated relative to an inertial frame.
This results in a fictitious force
that has two terms, a centrifugal term and a Coriolis
term.
You may have come across this Coriolis force
and centrifugal force before.
These are examples of fictitious forces
because they arise from the choice of coordinate system.
They're an artificial force.
They don't correspond to actual, physical interactions,
but are an artifact of the rotating, non-inertial
coordinate system.
Now, in this course we will confine ourselves
to inertial reference frames.
And therefore, we'll only be considering
real, physical forces and interactions.
However, there are advanced applications
where the use of a non-inertial frame has certain advantages.
And you may encounter those as you
go to more advanced courses.