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Conservation of angular momentum vs. linear momentum 
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#1
Jan312, 07:08 PM

P: 757

From a little bit of thinking, this is what I concluded:
A system initially at rest can change its angular position without any outside torques (the final state will also be at rest). A system initially at rest cannot change its displacement without an outside force. In other words, cons. of linear momentum also implies that a system cannot move its CM without outside forces, however, cons. of angular momentum does not prohibit a body from changing its angular orientation without outside torques, due to the fact that rotational inertia can be changed internally. Is this correct, or can anyone offer counterexamples? 


#2
Jan412, 02:33 AM

P: 644

If you put coinciding angular marks on the wheels, and let them rotate in opposite directions, they may stop in a configuration where the marks again coincide, but at a different angular position since each wheel were of different mass, but this is due to the periodic topology of the set of angular position configurations. So if your linear space has a periodic topoogy, a composite object can also change the position of its centreofmass without breaking the law of conservation of linear momentum. 


#3
Jan412, 05:56 AM

Mentor
P: 15,202

TR Kane and MP Scher, A dynamical explanation of the falling cat phenomenon, Int'l J. Solids and Structures (1969) R Montgomery, Gauge theory of the falling cat, Fields Inst. Commun., 1 (1993), 193218. Edit For a nontechnical summary of these two papers, see M Abrahams, Cat physics – and we are not making this up, The Guardian, 17 October 2011, http://www.guardian.co.uk/education/...chcatphysics 


#4
Jan412, 11:46 AM

P: 757

Conservation of angular momentum vs. linear momentum
I was inspired by the cat when thinking this up, however this is not a threat about cat physics. Turns out, the angular displacement feat is possible because rotational inertia can be changed arbitrarily from within the system (without the need for outside torques). However, there is no linear analog to this, that is, mass cannot be changed within an isolated system therefore a net linear displacement is impossible without an outside force if it is initially at rest. Is this correct?



#5
Jan412, 11:55 AM

Mentor
P: 15,202

http://dspace.mit.edu/bitstream/hand...pdf?sequence=2 


#6
Jan412, 12:17 PM

P: 3,097

Here's a article + video of how to do the swimming in case you are stranded in space and need to get back to your ship :)
http://www.science20.com/hammock_phy...gh_empty_space 


#7
Jan412, 12:42 PM

Sci Advisor
Thanks
PF Gold
P: 12,266

I think this is bordering on 'reactionless propulsion' idea, which is one of those heretical ideas. Poor Prof. Eric Laithwaite was pilloried for investigating this in his later years, despite not being just 'nutty' about it.



#8
Jan412, 08:08 PM

P: 757

I meant to ask this question in the classical, newtonian sense, not GR or QM or anything like that.



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