Re: Rotation of a body in free space.
- From: "hhc314@xxxxxxxxx" <hhc314@xxxxxxxxx>
- Date: Tue, 31 Jul 2007 16:05:16 -0700
On Jul 31, 5:28 pm, rsprawls <rspra...@xxxxxxxxx> wrote:
It's been a while since my last physics class. I have been doing some
research into rotation and torque, but it all assumes the axis of
rotation is fixed, that is it rotates freely, but it doesn't move
linearly in 3D space. I want to model the proper Newtonian movement
of a object that has a moment of inertia, but is not fixed in space.
As an example of what I'm trying to illustrate: An astronaut in orbit
taps one end of a free floating wrench. It's going to spin, sure.
But it won't spin in place. It'll spin away. What subjects do I need
to research to find at least a Newtonian level of modeling?
By Newtonian, I mean not requiring tensors. Vectors are fine (even
though I know vectors hadn't been invented when Newton was breathing).
I learned about and remember vectors. I never learned about tensors.
Likely your best bet to understand the motion of an unconstrained 3-
dimensional body in free space is to borrow or purchase a really goog
textbook on classical mechanics or theoretical mechanics. Look for a
chapter on "Motion of a rigid body in three dimensions" or similar
chapter title. Likely it will be one of the last chapters in the
textbook, for reasons that will become obvious when you study it.
Typically, problem such as you are addressing are traditionally not
encountered until the 3rd or 4th undergraduate year as a physics
major, and often deferred to graduate level studies. In simplicity, to
even address the problem you need to specify the locations of both the
center of mass and center of percussion of the wrench, its moment of
inertia, and where the impulse is applied. (I'm assuming that the
wrench is asymetric, like an adjustable Crecent Wrench, where the mass
is heavily concentrated in the head, with a more less linear
distribution of mass along the handle. The center of mass is easily
obtainable, while the center of percussion becomes a bit more
difficult. To obtain the moment of inertia will generally require you
to identify the axis of rotation, which in turn depends on where and
how the impuse is applied. The problem would be almost trivial if one
could assume that the axist of rotation were centered down the handle
of the wrench, and it simply spins along its long axis, but that would
not be a realistic assumption, but then you will next ask yourself if
the wrench would rotate around it's center of mass, or it's center of
percussion? (This is one of the favorite questions that appears on
final exams at this level of study, along with an example of the math
that led you to your conclusion.)
You have asked a very interesting question, who correct answer
involves quite a large number of physics considerations. As the
soluton of most advanced physics problems involves (as in the lyrics
of The Gambler), "Knowing what to throw away and knowing what to
keep", just about every alalytical solution requires the throwing away
of inconsequental factors (say possibly precession or nunation in this
case), these considerations are what makes the problem interesting.
Harry C.
.
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