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Re: [Phys-l] Good Questions



On 10/07/2006 06:26 PM, Cliff Parker wrote:
Questions I can ask my
high school physics class that will cause them to apply things they have
learned over the years in an effort to figure out the way things are or how
they work.

1) Suppose we rotate something by 90 degrees in the yaw direction, and then
rotate it by 90 degrees in the roll direction. The combination of these
two rotations is just some overall rotation. Describe the overall rotation
in terms of a single rotation around a single axis. Specify the orientation
of the axis and the angle of rotation.

It is possible to calculate the answers to all such problems, but this is
beyond the scope of the course. Instead I expect HS students to figure
out the answer by rotating a model and figuring out how to describe the
results.

2) Suppose we rotate something by 90 degrees in the yaw direction, then
90 degrees in the roll direction, then -90 degrees in the yaw direction,
then -90 degrees in the roll direction. Describe the overall result.

Hint: It is a nontrivial rotation; the second pair of rotations do
not undo the first pair.

Hint: Do question (1) first.

======

One point is to make the students qualitatively aware that in 3D, rotations
are nonlinear and noncommutative.

Being able to calculate compound rotations is useful in many applications,
including robotics, autopilots, flight simulators, et cetera.

One drawback of these questions is that some students will immediately
wonder how to handle more-general combinations of rotations. The question
is easy to ask, but the answer is beyond the scope of the course. In
marketing this is called "overhanging the market" i.e. drumming up demand
for a product you can't (yet) deliver.

======================================================

For a quantitative treatment (not suitable for HS, especially in October),
see:
http://av8n.com/physics/rotations.htm