If rear flows = forward flows then there is no CM motion. The equal
rear/forward flows in the CM frame are superimposed upon the forward CM
flow when viewed from the Lab frame, giving an unbalanced forward flow.
The launcher must exert a net forward force on the particle system ( and
thus accelerate the CM forward), else it could only spin "in place".
Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net http://www.velocity.net/~trebor
----- Original Message -----
From: "William Beaty" <billb@ESKIMO.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Tuesday, July 23, 2002 12:50 PM
Subject: Re: smoke-ring paradox
| On Tue, 23 Jul 2002, Bob Sciamanda wrote:
|
| > Yes, all the streamlines are circular in the CM frame. But in the lab
| > frame the CM has a forward momentum.
|
| In the lab frame, if forward flow must equal rearward flow in order to
| satisfy continuity, isn't the net momentum zero? Changing the frame
would
| change the observed momentum of the entire "atmosphere", it wouldn't
| affect the momentum of the moving pattern.
|
|
| > Compare with a forward travelling, spinning frisbee (or football).
|
| The density of those objects is far greater than the density of air.
| Compare a stone wich moves through vacuum. Better to imagine a blob of
| gelatine moving through a water tank, or a blob of aerogel moving
through
| air, and then ignore the tiny extra mass of the molecules in the gel
| network.
|
|
| In fact, this trick question haunted me for ages before I solved it by
| observing a very crude animation I made. It originally arose during
| fights about (gasp!) Newton vs. Bernoulli regarding airfoil lifting
force.
| If all streamlines are closed loops, how can an airfoil deflect a net
| amount of air downwards? Yes, circulation can exist, however the net
| downward transport of air must be zero. The "Bernoulli" camp concludes
| that no air moves downwards on average, therefore an airfoil flys
because
| of pressure difference alone, not because of F=MA of
downards-accelerated
| air. Sounds like an air-tight argument, yet it contains an unnoticed
| "leak."
|
| :)
|
|
| (((((((((((((((((( ( ( ( ( (O) ) ) ) ) )))))))))))))))))))
| William J. Beaty SCIENCE HOBBYIST website
| billb@eskimo.com http://amasci.com
| EE/programmer/sci-exhibits amateur science, hobby projects, sci fair
| Seattle, WA 206-789-0775 unusual phenomena, tesla coils, weird sci
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