Consider a piece of broomstick or dowel-rod, maybe a foot or
18" long. There are various ways of imparting angular motion
to it:
a) You could make it flip end-over-end in a pure yawing motion.
b) You could make it spin on its axis in a pure rolling motion.
c) Or you could do some combination of yaw and roll, resulting
in some sort of wobbling motion.
These three modes are depicted in http://www.av8n.com/physics/img48/gyros.png
where for each mode I have attached to the broomstick a small
disk indicating the plane of rotation. Equivalently you can
imagine an /axis/ of rotation perpendicular to the disk.
Obviously if you _constrain_ the plane (or axis) of rotation, you
can achieve any mode of rotation you like. So that's not very
interesting. Instead we consider unconstrained motion.
-- In practice you can toss a broomstick. This can be very
educational, if you know what to look for. Paint the broomstick
to make the spin easier to perceive. Any high-contrast pattern
will do. A barber-pole pattern is particularly amusing, and is
easy to achieve by means of masking tape.
-- In theory you can imagine a cylindrically-symmetric spaceship
moving freely in outer space. (This is the original motivation
for of my thinking about the subject.)
Question 1: For each of the three modes depicted in the figure,
how easy or how hard is it to set up unconstrained rotation, so
that the plane of rotation bears approximately the indicated
relationship to the stick?
Question 2: For each of the three modes, to what extent is the
motion _gyroscopically stable_?
The point here is to think about the fundamental physics that gives
rise to gyroscopic stability.
-- This isn't about nutation. We are talking about a freely
moving object, so there can't be any nutation.
-- Similarly we know the angular momentum vector is constant i.e.
fixed in space.
-- An important question is, in what way is the angular momentum vector
/attached/ to the object? For instance, is angular momentum stuck in
the object the same way magnetic flux lines are stuck in a metal by
eddy-current effects?
You can ask the same questions about a disk: It can flip end-over-end
like a tiddly-wink, or it can spin symmetrically, or it can do something
in between. This is perhaps a little harder to visualize in a hands-on
demonstration, but OTOH it is a little closer to the usual gyroscope
rotor geometry.
Question 3: Let's switch to considering /cubes/. Choose all that apply,
and explain why or why not:
3a) Is a cube gyroscopically stable when spinning about any of the
conventional cube axes?
3b) Is a cube gyroscopically stable when spinning about any of the cube
diagonals?
3c) Is a cube gyroscopically stable when spinning about any arbitrary
axis that passes through the center?
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FWIW my childhood understanding of these topics was wildly wrong. I
/thought/ I knew the score, from experience playing with toy gyroscopes
and from reading gee-whiz explanations of "gyroscopic stability" in
science books. Phooey. When I got to college, early in first term
they had a demo that looked like this: http://www.av8n.com/physics/img48/gyro-disk.png
The axle (diagrammed in red) was skew to the heavy wheel's axis of symmetry.
The cradle (diagrammed in blue) rested on the table, and you could /try/
to hold it still with your hand while the wheel was turning. Wow, did
that thing ever wobble. The angular momentum was not collinear with
the angular velocity, that's for sure.
This device works OK as a lecture demo in front of the room, and works
even better as hands-on demo. It suffices to give each student a few
seconds of hands-on time.
I searched for a few minutes but did not find a PIRA description of
this device. Does anybody know if it has been written up anywhere?
If not, somebody should do so.