{"items": [{"author": "Paul", "source_link": "https://www.facebook.com/jefftk/posts/256231654398998?comment_id=256239471064883", "anchor": "fb-256239471064883", "service": "fb", "text": "You've got a long skinny flywheel there.", "timestamp": "1314720791"}, {"author": "Paul", "source_link": "https://www.facebook.com/jefftk/posts/256231654398998?comment_id=256253357730161", "anchor": "fb-256253357730161", "service": "fb", "text": "So, is it acting like a gyroscope or not? Hmmm...", "timestamp": "1314722928"}, {"author": "Chris", "source_link": "https://plus.google.com/117346402173047680184", "anchor": "gp-1314723052819", "service": "gp", "text": "So, by a push, I'm going to assume you mean an impulse, and not a force.\n
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\nSupposedly, the composition of two rotations is always a single rotation around a different axis, but that's referring to a change in position, not a change in position per time.\n
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\nMy mathematical intuition is that you add the angular velocity of the two rotations. You currently have an angular velocity pointing straight right. The angular velocity of the push you're giving is into the screen. That would suggest that the combined angular velocity would be into the screen angled to the right and thus the rod would not stay in the plane of the screen as my physical intuition says it would. However, gyroscopes don't follow my physical intuition either, so I'm tempted to not trust it.\n
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\nI would really like to try this at some point and find out which intuition is correct. Think we could set it up somehow? Maybe suspend the rod in a contraption that allows 3 dimensional rotations and then apply the correct forces? Not sure how we would go about that though. The other possibility would be to model the rod as a mesh of points with very strong springs between them and see how they operate. That way we wouldn't have to model rotation, we would get it as part of the result.\n
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\nWikipedia didn't reveal the answer to me directly, but the comment about infinitesimal rotations being commutative hints that my mathematical intuition might be right.\n
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\nLinks:\n
\nhttp://en.wikipedia.org/wiki/Angular_velocity\n
\nhttp://wiki.answers.com/Q/What_is_the_plural_of_axis", "timestamp": 1314723052}, {"author": "Chris", "source_link": "https://plus.google.com/117346402173047680184", "anchor": "gp-1314723443635", "service": "gp", "text": "Actually, the gyroscope might be the perfect model. If we model it as a force instead of an impulse, I believe that the downward force will also cause a sideways movement so that it's no longer confined to the plane of the screen. Maybe tonight I'll write up a simulation using my magnet modeling software.", "timestamp": 1314723443}, {"author": "Hassan", "source_link": "https://plus.google.com/109686970531250960199", "anchor": "gp-1314723629808", "service": "gp", "text": "I checked my hunch with an engineering buddy, and he agrees that it should start tumbling around both axes. There are equations you could use to determine the spin around each axis (which I think would let you map its actual path) but that would have been a lot more work. There is software to simulate this sort of thing, but I don't know about free versions/alternatives.", "timestamp": 1314723629}, {"author": "Jeff Kaufman", "source_link": "https://plus.google.com/103013777355236494008", "anchor": "gp-1314724830818", "service": "gp", "text": "@Hassan\n Does it end up spinning around one new axis, or doing something weirder?", "timestamp": 1314724830}, {"author": "Eric", "source_link": "https://plus.google.com/105086402673996622245", "anchor": "gp-1314725278700", "service": "gp", "text": "Well, according to the physics curriculum I know, you would just add the angular momenta - so it should escape the plane of the screen and start tumbling about a new axis. And some experience with experiments of this sort means I agree. I confess I've never seen a really clean demonstration, though - but yes, this is the weak form of the gyroscopic effect. ", "timestamp": 1314725278}, {"author": "Jeff Kaufman", "source_link": "https://plus.google.com/103013777355236494008", "anchor": "gp-1314727153097", "service": "gp", "text": "@Eric\n is \"tumbling about a new axis\" different from \"rotating about a new axis\"?", "timestamp": 1314727153}, {"author": "Hassan", "source_link": "https://plus.google.com/109686970531250960199", "anchor": "gp-1314728527224", "service": "gp", "text": "Well, at any given time you would be able to express the motion as a rotation around a single point (not necessarily one inside the rigid body). Without more work (and perhaps more information than we have?) I don't know whether that would always be the same point - that is, whether the cylinder would resolve on a stable rotation with a constant axis, or if the 'tumble' would mean that the center of rotation was also changing.", "timestamp": 1314728527}, {"author": "Chris", "source_link": "https://plus.google.com/117346402173047680184", "anchor": "gp-1314729033308", "service": "gp", "text": "Without some force acting on the object, the center of rotation can't move.", "timestamp": 1314729033}, {"author": "Eric", "source_link": "https://plus.google.com/105086402673996622245", "anchor": "gp-1314732263879", "service": "gp", "text": "Chris has it right - the axis can't move except under an external force. (Conservation of angular momentum.) Gyroscopes resist a change of axis simply because their angular momentum is already high, so any momentary impulse does little - and ends up applied almost symmetrically as the object rotates out from under.\n
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\nIn short - I'm pretty sure it ends up with a single sort of rotation.", "timestamp": 1314732263}]}