I want to add one more "misconception item" to our list.
Let me mention that I do not like when people refer to it as
my list. There are over 40 items there and I have very little
to do with most of them, except cutting and pasting. What
follows is the draft for a new item. I will wait for comments
before appending it (?) to our list.
Ludwik Kowalski
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x) It is not true that a conical pendulum can be viewed as
a superposition of two "mutually perpendicular" simple
pendula oscillating with the same frequency and same
maximum spherical angle TET. Why not?
First because the concept of perpendicularity does not
apply to curved lines. Only very short segments of
two circles, in mutually perpendicular planes, can be
"approximately perpendicular" (in the third plane). This
approximation, by the way, can be used to derive the period
of a simple pendulum without calculus (that is without
treating F=m*a as a differential equation).
And second, because it is not possible to have "the same
THETA and the same frequency" at large angles. The
conical pendulum and the simple pendulum do have nearly
identical periods at small angles (assuming L and g are
identical) but at large angles the dependence of T on angle
is different in each case. It turns out that for a simple
pendulum T decreases with THETA while for a conical
pendulum T increases with THETA.
One may be surprised by such experimental facts because
in both cases the restoring force is F=m*g*sin(TET). The
so-called "simple" pendulum can be viewed as "more
complicated" than a conical pendulum where the magnitude
of F remains constant. In a simple pendulum the bob moves
back and forth but in the conical pendulum it never moves back.
In that respect the PHI coordinate (azimuthal angle) is more
like the x coordinate of a particle moving along a straight line.
It can be replaced by arc=PHI*r, provided PHI is in radians.
The concept of amplitude does not apply to a conical
pendulum. But the concept of period does.