Rapier, in order for physicists to make things easier when describing rotational motion, a convention was developed known as the right hand rule. Wiki gives a pretty good description, but basically if you point your fingers in the positive x direction and curl them towards the positive y direction, your thumb will be pointed in the positive z direction. If a box is spinning counterclockwise on a table, with the table being on the xy plane (with positive x pointing along the bottom to the right, and positive y pointing along the left away from us), the box will be defined as having an angular momentum vector in the positive Z direction.
To expand on your thought experiment, if we allow the box to levitate for the purposes of this discussion and thwack its underside closest to us, that will impart angular momentum in the Y direction (because it’s spinning about the y axis). Now, we can describe its spin by simply adding the Z and Y components together; assuming it’s spining at the same speed along both axes, it will be a 45 degree line of length root 2* between the Y and Z axes.
Similarly, if we thwack its left side upwards, the new vector will be at 45 degrees to each of the axis and will have length root 3*.
*These numbers are found via Pythagoras, and would have different angles and magnitudes if the forces applied weren’t equal.
It’s not easy to explain why it happens, but the basic result is that for the three principal axes, the axis of rotation is only stable for the first and third–that is, the axes with the greatest or least moments of inertia.
It’s still true that at any given moment, the object is only rotating along a single axis (which might not be lined up along a principal axis). However, that axis can move around due to the aforementioned instability.
In the case of the video you linked to, the rotation axis alternately points in one direction, and then exactly opposite that direction. In between, the axis traces a path between those two points.
If you want to do an experiment, grab a smallish hardback book (this is easier than the racket). Hold it closed with some rubber bands.
Now, try tossing it in the air along each of the main axes. You’ll find that it spins stably on the axis that points up (if you hold the book with the cover facing you) or the axis that points through the book (i.e., through the pages).
But if you try to toss it so it spins on the medium axis–that is, the one that’s horizontal when holding the book normally–there’s an extra rotation. It will pretty much always spin an extra half-turn or so in the air. It’s difficult to say why this happens–but it does.
It is not true that rotation is always about a single axis. It can be approximated that way on some time scales, but if the “axis” is changing with time, then it’s not actually an axis of rotation.
Um, not exactly. In the slow-mo third section you can see that the axis of rotation is unchanged, it’s the handle’s orientation with respect to that axis that flips. That is, except during the flips you clearly see the handle rotating counter-clockwise while pointing in approximately the same direction.
Upshot: An object might have only one primary axis of rotation, but that doesn’t mean it can’t be constantly shifting it’s orientation with respect to that axis. Dealing with heavy tumbling objects in zero-g is going to be a bitch.
Yes, that’s what I meant (perhaps I could have been clearer). There’s no significant transfer of angular momentum to the environment (only after many such flips does it slow down due to air drag), so the “global” axis of rotation can’t change significantly. But the axis with respect to the handle can change due to the tennis racket instability.
Although the effect is smaller, the least-inertia axis is also unstable. The Explorer I satellite was intended to rotate along its long axis, but it didn’t stay that way for long. Internal energy dissipation meant it would seek out the axis with the least kinetic energy, which is the one with the highest inertia.
It’s just semantics I guess, but I wouldn’t say that. At an instant in time, there is a definite single axis of rotation. It’s not so different from saying that velocity vectors exist, even though particles can move on curved paths.