Another possible approach to videotaping a conical pendulum.
1) Ask students to film several circular trajectories between r
of 2 cm and 20 cm, for example. Let them discover that the
trial-and-error approach is not easy; one has to be "lucky"
to get a nearly circular path. Why is it so?
2) Most often launchings results in elliptical, rather then
circular, trajectories. This observation can lead to an
assignment. Plot the measured velocities (of nearly circular
orbits) versus the measured radii. Is this an essentially linear
dependence? Yes it is. Ask them to justify it theoretically.
I am assuming they know that a=v^2/r and that the restoring
force acing on the bob is essentially proportional to r.
3) Nearly every physics textbook has a planetary data table.
Ask them to use this table and to plot the v=f(r) relation
for our planets. Is this also a linear curve? No, in this case
v=2*Pi*r/T become smaller when r is increasing. In fact
the v^2 is essentially proportional to 1/r. Why do planets
behave differently from the conical pendulum bob?
4) Depending on teaching philosophy an instructor can refer
to the law of Universal Gravitation or, PREFERABLY,
guide students to the "discovery" that the centripetal restoring
forces acting on planets must be proportional to 1/r^2; it can
not possibly be proportional to r, as for a bob. I am nearly
certain that Jane Jackson would use the second approach.
In an Astronomy class guide students to the discovery of
Kepler's third law. I hope some new teachers will find
these pedagogical suggestions useful.
5) In most schools it would not be practical to give each
group of students a camcorder and ask for the extraction
of numerical data from the frame-by-frame analysis of
trajectories. A more realistic approach would to assign
this as a project for one group and to discuss the data in
class, or even in several classes.
Ludwik Kowalski