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Spinning needles

by hkyriazi
Tags: needles, spinning
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hkyriazi
#1
Jan13-07, 05:28 PM
P: 96
In a gravity-less world without friction, starting with a stationary needle, would one be able to make it spin by first flicking it, to cause it to twirl (so that its axis of rotation is perpendicular to its long axis), and then tap its ends repeatedly in some way so as to cause the twirling motion to transform into spinning (i.e., so that the axis of rotation is lined up with the needle's axis)?

(I posted a long and somewhat involved variant of this question on the "homework/introductory physics" section over a week ago -- though it's not a homework problem -- without getting any response. It was titled "A simple rotational problem." I thought that posing it in this simpler way, I might at least get a comment or two.)

One possibility would seem to be to have the twirling needle be scooped up by the wide end of an accelerating funnel, so that, in effect, the needle would be "going down the drain," making a series of reorienting, frictionless contacts with the sides of the funnel. Let's say the funnel approaches the needle so that its axis of symmetry is almost (but not quite) lined up with the needle's angular momentum axis (off only a bit, so that the needle doesn't get lodged in the funnel).

The question is, when the needle comes out of the funnel (whose bottom is just barely wider than the needle), so that its own axis has been forced to rotate almost 90 degrees, so as to basically line up with its original angular momentum axis, will it be spinning?

I say yes, and that it'd be spinning much faster than it twirled, owing to the much smaller moment of inertia in this orientation. But, I have an expert who disagrees with me (Professor Eugene Butikov, of the Univ. of St. Petersburg, Russia), who says the needle would have zero spin about its long axis, and would immediately go back to twirling, but at an angle determined by the last contact it makes as it leaves the funnel.
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hkyriazi
#2
Jan16-07, 09:05 PM
P: 96
In another version of the same problem, I posited that one merely tap the ends of the horizontally twirling needle, such that when it's floating right in front of one's face, one lightly taps the left tip downward, and the right tip upward, so that one imparts a relatively small torque that points right at you, and at right angles to the needle's initial angular momentum.

The question is, what is the motion of the needle after those light taps?

If one considers oneself to be rotating in the same frame as the object, so that the object appears stationary, ones taps would obviously cause the needle to twirl counterclockwise with its center of mass stationary. The top side of the needle would flip over and back once with each vertical rotation. The inertial frame's horizontal twirling has the top side always up, and so when one combines these two motions -- a strong horizontal twirling and weak vertical twirling -- the main motion must still be an approximately horizontal rotation, but now where the top of the needle rotates to the bottom and back up periodically, which means the needle must be spinning about its axis, which means it must also be precessing somewhat.

Does this seem like a reasonable qualitative analysis to anyone besides me?


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