OK, "quiz" isn't really the right word, because I don't know the right answer. But here's something weird that I noticed a while ago, and since I needed an excuse to fool around with video a bit, I thought I'd shoot some pictures of it:

Here's the deal: My cell phone is gently curved on one side. If I put the phone on a table with that side down, it will spin reasonably freely, with very little effort. If I try to spin it fast, though, it very quickly develops a pronounced wobble that damps out the spin very quickly. You can see it in the YouTube video above.

So, the question is: Why does that happen?

(I noticed this while we were interviewing students for a position in the student residential life system that I'm involved with. I think I was starting to annoy the students who were on the interview committee, because I spent the next two hours spinning my phone at different speeds, in different directions, on different surfaces...)

An additional piece of information that might be useful: the effect is much more pronounced on the lab bench where I shot this video than on the lecture-room table where I first noticed it. When I first saw it, the phone would complete a few revolutions before wobbling, and a couple more while wobbling.

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I imagine the thing has a rocking resonant frequency of sorts, that's at a higher frequency than gets induced at slow rotation. With the antenna, it's clearly imbalanced along the vertical (longest) axis. When you spin it faster, it eventually matches the rocking resonance frequency, and takes over the momentum of the phone.

I don't know...but I have seen something similar. IIRC you could purchase (from a magic/trick store) a stone with a curved back. It was also asymetric w.r.t. its long axis. If it was spun up in one direction it would exhibit the behaviour shown by your phone. In the other direction the spin would just gradually get slower.

Have you tried spinning your phone anti-clockwise? If it spins properly perhaps you should investigate the asymmetry introduced by the antenna.

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Martin

#2's comment was what I was going to post, essentially. If you wiki "rattleback," you can see some toys that can accomplish the same type of thing. They will spin freely one way, but if you spin them the other way it couples to a rocking motion along one of the short axes which then starts them spinning the easy way. I bet something similar is going on here; the exterior of the cellphone is probably fairly symmetric but it certainly doesn't have a uniform density or anything like that.

Looks like you have an overdamped rattleback. Perhaps it will reverse its spin completely if you place it on a surface with even less friction.

yeah, i agree, it is a rattleback.

rattlebacks motion is similiar to two pendulums coupled with a weak spring. start one pendulum swinging and it's motion will decrease in amplitude as the others amplitude increases.

in the case of the rattleback, the two motions are rotation and rocking. if you start it spinning in the proper direction, then it will change over to rocking motion. conversely, if you start it rocking, it will change over to spinning motion.

i have one on my desk.

I have the same, or nearly the same, model phone.

There seems to be a slight directionality, as the rattle is more pronounced in the counterclockwise direction. It's hard to tell, since I can't get a good spin on with my hand without introducing a bit of a wobble - and more wobble in one direction than the other.

I agree that it's related to a rattleback, but all the online rattleback discussions I can find focus on the asymmetry of the thing. Your phone is behaving symmetrically (or nearly so, according to 01Jack@6).

If you taped weights to the upper left and lower right corners, you might get the classical rattleback one-way spin.

My guess about the coupling mechanism is that when the thing spins fast, it lies at a different angle. (Centrifugal force levelling it out.) But that changes the contact point on the curved face. So now it wants to spin around a different axis. Maybe you could design a curve that would smoothly converge on a new stable state, but your phone does the opposite -- the process wants to diverge. So the axis shifts more and force increases, until the thing skids and blows some energy on friction.

Jearl Walker's old Amateur Scientist column in Scientific American discussed rattlebacks. Wikipedia gave two references, and I can still remember reading the 1985 column. You will want to track this down for two very good reasons:

(1) Excellent discussion.

(2) Jearl Walker got his Ph.D. at the U. of Maryland.

* Walker Ph.D., Jearl. "The Amateur Scientist: The mysterious 'rattleback': A stone that spins in one direction and then reverses." Scientific American, 241:172-84. Scientific American Inc. New York. 1979.

* Walker Ph.D., Jearl. "The Amateur Scientist: Rattlebacks and tippe tops; Roundabout: The physics of rotation in the everyday world." Scientific American, 33-8, 66. Scientific American Inc. New York. 1985.

It happens for the same reason that you have to have your tires balanced on your car.

if i recall correctly, the asymmetric shape shape means that the moments of inertia about the principle axes are such that the inertia tensor is not diagnolized. there are cross terms that couple motion about the spinning and rocking axes as long as the spinning is in the right direction.

so for the phone, i bet the uneven weight distribution and shape leads to a similar inertia tensor that mixes various roatational modes.

@rob #10: If the inertia tensor is not diagonal, then you have not found the principal axes of the system. The inertia tensor is real and symmetric, so it is always diagonalizable and the eigenvalues are always real. The eigenvectors determine the directions of the principal axes.

Even if you think you are spinning it around a principal axis, you can see this effect. Try tossing in the air a spinning box whose height, width, and depth are all different, and see what happens when you spin about each principal axis. The short axis and the long axis work well, because small deviations of the rotation vector from these axes tend to stay small. If you try to spin it about the intermediate axis, it tends to tumble, because the system is unstable: small deviations in the rotation vector from the intermediate axis do not stay small. (Future lecture idea: this was a demonstration in my upper level mechanics course.)

@Eric #11: Exactly.

Everyone else, try this with a remote control. It's fun.

The rotation of a rigid body. Sofya Kovalevskayaâs 1887 papers on the rotation of a rigid body about a fixed point represent an attempt to penetrate an unexplored region of mathematical physics using the resources of analytic function theory. The problem she was attempting to solve is a system of six ordinary differential equations.

Her approach was a combination of two approaches â- power-series and closed-form...

The way in which the two approaches were combined is interesting in itself. She first asked whether the

equations could have meromorphic solutions, that is, solutions expressible as power series in time (including

possibly a finite number of negative powers of time). That portion of the problem is the power-series approach.

Two such cases were already known and had been studied in detail by Euler and Lagrange. Having determined the third and only new case in which such solutions exist, she set out to find the solution in closed form, thereby making use of the very latest results of mathematical research in the form of theta functions of two variables.

More data: try surfaces with different friction, and try putting a weight on top of the phone (above the point of contact with the surface).

Interesting question.

My first thought was of the motion of a tri-axial rigid body, where motion about the axis with the intermediate moment of inertia is unstable. Examples: a chalkboard eraser or a book, or my cell phone. Rotation about the axis with the smallest (or largest) moment of inertia is well behaved, but the third is highly unstable. Usually the unstable axis is the end-to-end flip, as it is for my cell phone (which has no external antenna) and one remote control that was handy. Sadly, my phone is too flat to spin like yours will, but the seemingly symmetrical remote control will rattle like your phone if spun fast enough.

Your phone does not act like a rattleback (the ones made by breaking the symmetry about the long axis by adding masses to it), where the motion goes from spinning to end-to-end rocking. Like my remote, it seems to want to rock side-to-side (around the axis with the lowest moment of inertia) rather than end-to-end. This makes me suspect it is acting like a football, where you can start it spinning lying on its side and (if you spin it fast enough) get it to pop up and spin on its point. Small perturbations in the original motion are enough to transfer energy to rotation about the axis with the smallest moment of inertia with enough left to raise the center of mass.

What happens if you spin the phone in the air rather than on a table?

Have you ever done that trick with a football?

So, this has been answered, but I thought I might try to put it in slightly different words, hopefully clearer.

Basically, it's because of asymmetries in the cell phone (as others noted). The specific asymmetry is that when you compose the moment of inertia tensor for the cell phone, it doesn't have a diagonal axis corresponding to spinning on the table as you are trying to do.

Because the spin axis is not aligned with one of the diagonal axes of the moment of inertia tensor, when you start spinning it on the table in that manner, the spin precesses around the other axes. This is what it tries to do when it rocks: it is trying to spin around an axis parallel to the table, but it is unable, so it ends up rocking back and forth.

Incidentally, my cell phone does the exact same thing. Each time I spin it, however, it takes a different number of rotations to enter the rocking motion (sometimes, when I spin it very fast, it takes a rather large number of rotations to enter the rocking motion, other times it happens almost instantly). Presumably each time I start it spinning I begin it at a different point in the transition between rocking and spinning. When I spin it more slowly, the rocking motion seems less pronounced, so it may be happening all the time, and just not be apparent. Or it may just be that it doesn't go around enough times to start the spinning motion.

My guess about the coupling mechanism is that when the thing spins fast. Rotation about the axis with the smallest (or largest) moment of inertia is well behaved, but the third is highly unstable.

@Eric Lund:

yeah, i vaguely remember that now. i guess i will need to crack open my old CM texts! thanks!