Gyroscopes
When we spin a top, initially it wobbles. But on most occasions it straightens up after some time and the spins steadily till it loses its speed and finally falls. Why does it become steady after the initial wobbling?
Labels: funphysics
posted by Rajesh Lal at
7:46 AM
15 Comments:
Initially it wobbles due to the kinetic force cause by us to make it move however gyroscopic forces take effect and make it stable.
I guess that friction at the point of contact with the ground (or "tower") will cause the wobble to decay. If that's wrong, I expect that quantense's services will be required, as the analysis will probably not be straightforward.
and there is a centrifugal force, which will lead sufficiently small deviation of rotation from precisely horizontal to rise it up. For me the dissipation force of friction has independent role in our top-problem as with egg-problem. Dissipative friction slows the rotation, but centrifugal force does it more stable from energical point of view.
It's the end. The beginning is:
Compare it with such situation. Consider a hard-boiled egg on the table. Put it horizontally and rotate very rapidly. After a while you'll notice it rise up. Why? Because vertical state has less energy (rotation kinetic energy and potential gr. energy, which we may not take into account for sufficiently rapid rotation), and centrifugal force will force it to rize.
Centrifugal force will cause the heavier portions to go outward, which determines what axis it will eventually stabilize at.
The top is designed, that when it's spining totally upright, that it's RG (Radius of Gyration) is practically zero. Since the RG is 0, there is no wobble.
The initial woble is due to the fact that it is nearly imposible to make it start spinning on the correct axis where the RG is 0. If it's not perfectlly virtcal, then the RG is greater than zero, and has a wobble. Once the centrifugal force stands it up, the RG drops to 0 and it stablizes.
It's the same with bowling balls, they are technically gyroscopes themselves. Each ball make has a specific RG. (Depeding on how it's drilled, that RG is slightly modified, but that's a different story). The gist is, when you release the ball, the ball is usually on an axis with higher RG. This causes a wobble in the ball, then helps reduce the friction with the lane allowing it to get further down the lane before it begins to hook. Once the centrifugal force of the ball chanes it's axis, then the RG drops, allowing the ball more friction on the lane.. ie.. stronger hook on the end.
Man I miss bowling..
Hi quantense. Thanks for the stuff about the spinning egg, I'd completely forgotten about that phenomenom. I'll see if I can try to understand it - it seems counter-intuitive.
(Unfortunately) it's not obviously directly connected with the posted problem. Guess what, I've found an link, you can play with a computer generated gyrsoscope there. It shows the wobble as a cycloid like motion, which damps down to a more sinusoidal shape: http://faculty.ifmo.ru/butikov/Applets/Gyroscope.html it does have a friction control, but it doesn't say where the friction is acting.
I was only considering the friction at the point of contact, not in the bearings. I'm thinking about gyroscopes rather than spinning tops.
I wonder how many eggs Ragknot has been cooking! The egg must be hard-boiled.
EB have you been consulting your brother again? :) I liked your analysis of the bowling ball - I hadn't even thought about it before, especialy the trick for reducing friction. For what it's worth, the radius of gyration squared is proportional to the moment of inertia, so it can't go to 0, but it will minimize.
I'm not convinced, in general, about the top rising. I only know why gyroscopes precess. Although I haven't got one to play with, my memory is that they're more like a gyroscope and that they have a angle of lean and that they precess.
Interesting "spin"-offs coming in for this problem.
Now that I think about it, your right. The top won't stand up completly, it's tip will make circles around a focal point.
But, as far as the RG and axis, it's as I described. Initially, the top is spinning on an unstable axis with a high RG, but the centrifugal force casues it to change it's spining axis where the RG is greatly reduced (stableized).
Yes, it will still precess slightly. The radius of it's precession around the focal points is based on how far off the inistal axis was from the stable axis.
Theoretically, if you release it absolutely virtical on it's stable axis, it will spin on a single point. (and if the RG is absolutely zero, it'll stay balanced on it's point after it stops spinning, but manufacturing can't really produce a top with absolutly 0 RG.)
PS. My brother is on vacation visiting the the folks this week.
Hi EB. I've never knowingly seen a textbook about gyroscopes or tops that considers the centrifugal force. Thank you for introducing me to the idea; I've now got to think about it. I realise that quantense had used that term also, I just didn't stop to actually think about it.
So, are you the physicist in the family?
this is staightfofward...
cenntrifugal force over comes mistake in spinning.
Hi Chris. Thanks for the link. This won't be counterintuitive if notice that it doesn't violate any law. If there's arbitrary no nutation, i.e. gyroscope is very stable (when it has high angualar velocity), it doesn't fall because it's weight is in equlibrium with the force of table reaction. Nutation arises in any realistic cases because despite forces are in equlibrium, there's gravitational force momentum, which causes the fall. So it falls a bit, but this leads to decrese of gravity force mimnetum, and centrifugal force (which is due to precession rotation) rises it again, because precession angular velocity is the same, but kinetic energy of rotation will be less if gyroscope rises. This is a nutation.
I belive friction in that applet is in disc self rotation axis, it just slows the rotation.
The difference between that case and egg (or top) is that in that case there's a fixed point of gyroscope. In our problems there's not. But centrifugal force also tends to make less energy state.
In textbooks there's no nutation, as usuall, because it'a quite diffucult to solve equation with it. It's supposed that rotation is very rapid and gyroscope just precesses.
Hi quantense. Thanks for the extra explanations and the reminder about nutation. I can see the the egg and the gyroscope/top are quite different situations because of the point of contact. The egg has a continuous range of radii of gyrations. The gyroscope would seem to be much easier to analyse. I agree that the friction in the linked applet is almost certainly the bearing friction and not the friction at the point of suspension. It seems my initial guess wasn't completely mad!
I've just noticed I'd wrote "arbitrary nutation". It's a misprint of course. No arbitrariness.
nah.. i'm no physicist. I'm a wanderer, the black sheep so to speak.. heck.. my folks didn't even give me a name. They just called me "Euclid's Brother."
I dabble here and there and know just enough of various topics to get me in trouble in almost any venue.
because it gains its balance, (but only for a short period of time)
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