I get out my electric motor and attach a ruler (propellor) through its
center and rotate it while letting the class see it with a variable
strobe light shining on it. Then I start asking some questions: What
is the mathematical relationship that causes it to appear not to be
rotating? Is this the only relationship? What is actually happening if
it appears to move slowly backwards? What is going on if I cause it to
appear as if there are two rulers at right angles? Three rulers? Four
rulers? Where have you seen this in your "every day" life? etc etc...
I think that this kind of "demo" shows them some equipment that they
might be using early in the year and starts them thinking about the
questions that need to be asked and shows them a nice relationship
between Mathematics and Physics. You could take a few minutes up to 10
or 15 at least if you wanted to. I have the feeling that many would
have answered several of the questions by just saying "Oh, that's the
strobe effect" and I want them to see that that kind of answer is not
sufficient or this year.
I also set up a simple pendulum and photogate and show them how I
measure the period. I then ask their opinion of the dependence of
period on length and mass. We then do some quick, informal trials to
test their hypotheses just recording times on the board. Again they see
some equipment and start thinking Physics in just a few minutes.