I commonly use the term "centrifugal force" when talking with
students. Almost everybody knows what I mean ... be every so
often I get pushback from somebody who says:
"There's no such thing as centrifugal force.
I know because my high-school physics teacher told me so."
Therefore: For the benefit of the students, and as a favor
to teachers in later courses: Please say something like this:
Centrifugal force exists in the rotating reference frame
and not otherwise.
If you want to say that rotating frames are outside the scope
of the course, that's OK. I'm 100% fine with that. In contrast,
it is not OK to say that such things do not exist.
The recommend approach will /reduce/ your workload. It is
quicker and easier to say two things that the students
believe
1) Centrifugal force exists in the rotating reference frame
and not otherwise.
2) Rotating frames are beyond the scope of the course.
This is quicker and easier -- not to mention more correct --
than saying centrifugal force does not exist. That is
easy to say the first time, but they're not going to
believe you. They have too much first-hand experience
with centrifugal forces, e.g. during tight turns in a
car. If you want them to disbelieve this, or to pretend
to disbelieve this, you'll have to come back to it many
times. Besides, what's the point of browbeating them
into believing something they /shouldn't/ believe?
============
There are a lot of situations where using a rotating
reference is seriously useful. I'm not saying you have
to teach it if you don't want to ... really I'm not ...
but you ought to leave the door open for students to
learn about it later.
I would also point out that this is just a special case
of the more general idea of accelerated reference frame.
You cannot come anywhere near a modern (post-1907)
understanding of gravitation without using accelerated
reference frames.
Beware that it is easy to find grievously wrong discussions
of rotating-frame physics. The usual hand-wavy approach
gets the wrong answer for the centrifugal field, wrong by
a factor of 2.
This illustrates the general rule that intuition plus math
will take you a lot farther than intuition alone. The
math tells you there are two terms, each of which has a
nice intuitive interpretation ... but everybody who tries
to do without the math finds one of the contributions and
gives up before finding the other.