Whodathunk this many people had experience flipping hammers?
I wasn’t expecting nearly this much attention to this thread. Thank you all for your answers. I will endeavor to explain the answer to my 11 yr old who was scratching his head along with me on this one.
I posted:
To which zut replied:
So I tested it. I have 3 symmetrical hammers. The rubber mallet rotated only once out of 12 tries. The deadblow hammer did not rotate in 12 tries. The two-pound copper hammer was harder to handle than the others, and I dropped it 11 out of 12 tries. I caught it once, by the head. The two-pounder taught me nothing, except about my clumsiness.
Please note that I did not grip the hammers like a handshake. To keep my palm from imparting any spin, I held my thumb over the end of the handle. I held my forefinger underneath, a few inches forward.
In my past experiments with a claw hammer and the same method, the hammer rotated every time. This reinforces Mangetout’s statement about the face being heavier than the claw.
I am not a physicist, though I have a rudimentary understanding of some of the principles. I can’t begin to explain my practical results. You physicists can have a crack at it, if you like, but don’t tell me it’s impossible.
The effect in question is “Rotational Stability” and the people who said it’s the intermediate axis that’s unstable are correct. You can see the effect with any rectangular object that is homogenous in mass distribution and sides of three different lengths, e.g. remote control, small piece of wood, a book, etc. And I know people are talking about hammers and spatulas, but the effect is the same, since they all have three mutually perpendicular axes of rotation. If you carefully toss the object such as to cause rotation about only one axis, you’ll see that the object will seem to execute a “flip” in mid-air about one of the axes.
Which part? Elaborate.
Your statement that “the effect doesn’t happen with a symmetrical hammer” is incorrect. Telling you that is not the same thing as telling you it’s impossible to throw a hammer just squarely enough to minimize the perturbation. I’ve done that myself, although not very reliably, with a claw hammer.
The part about “this is a very good example to help understand the dynamics of the whole thing” coupled with the part about “the hammer head is conspicuously heavier than the claws.” The fact that the head is asymmetric is true, but it doesn’t, by itself, explain the rotational instability. If you thought it did, then your statement is incorrect. If, on the other hand, you meant “the imbalance as it leaves your hand likely leads to a perturbation of the unstable system, causing the twist,” then your statement is true, but misleading, because it could be read to mean the asymmetry is necessary. As a demonstration of that, I refer you to AskNott’s post.
Flipping remote controls has been a lifelong hobby of mine. After years of practice, I can pretty reliably flip remotes, books, and other similarly shaped items without having the unstable axis flip. It is a great way to win a few bucks at a party by challenging others 
The unstable axis has a very small critical point for forgiveness, after which it becomes exponentially unstable. I suspect it is something like a 3-axis saddle-shaped hyperbolic surface, but I’ve usually had too many drinks to explore the math by the time I start pondering it that deeply.
Expert level is to try for n+1 rotations without an axis flip. 2 flips is incredibly difficult, I’m maybe 1:10 doing this if I have my flipping chi flowing, otherwise it’s near impossible. I’ve done 3 once or twice, and it was the cause for great rejoicing and drinking.
A good example, but a slight nitpick: If you toss the book so that it rotates about the other two principal axes, it remains stable (those axes are the one that runs through from front to back cover, and the one that runs vertically parallel to the spine). As another reference (for those interested):
from * Structure and Interpretation of Classical Mechanics* by Gerald Jay Sussman, Jack Wisdom, and Meinhard Edwin Mayer.
I should have phrased it, “If you carefully toss the object such as to cause rotation about each of the three axes at a time, you’ll see that the object will seem to execute a ‘flip’ in mid-air about one of the axes. About the other two, it won’t.”
I did actually think the latter - the conspicuous asymmetry of the hammer head makes perturbation inevitable - and it makes it happen in a predictable fashion. If you flick a hammer with a symmetric head, the effect is haphazard - it doesn’t manifest the same way - or at all - in every instance.