# A Physics Lesson

## On the Spinning of Clubs

(by Boppo (Bruce Tiemann))

First, about the physics, and such. There are two schools of how you spin clubs, depending on whether your looking to be flashy or good. (OK, that's an oversimplification...) For the flashy style you decide how high you want to throw the clubs, and then you decide how many spins you want to put on, usually some high number. Having picked a height, you can put two, three, or any number of spins on each club just by putting lots of effort into your wrists. Whoever heard "doubles and triples go to the same height as singles" heard from a pure flashy juggler. Done with three clubs, low triples look sharp and impressive to non-jugglers; it's almost hard to see the clubs they're spinning so fast.

The other style, which I use, is to NOT put any spin on the clubs deliberately using the wrist, only from the natural motion of the arm that also throws the club up. I call this "natural spin." Trust me that even if your wrist is in a cast, if you throw a club up it will spin: Your forearm rotates around your elbow as you move your arm up for the throw, and that rotation is imparted to the club even without putting spin on using your wrists. Thus, flats are more difficult than merely not putting spin on, because actually you need to cancel the natural spin, and that's an unnatural throw.

Now, how do the heights vary with the different spins? For natural spins, if you throw it higher, it will both spin faster (because your elbow rotated faster to throw it higher), AND it will stay in the air longer (because you threw it higher) so altogether, it makes more spins before coming down. Physics dictates that natural doubles are exactly twice as high as natural singles and triples are three times as high. How high that actually is depends on how long your forearms, are: longer arms mean higher throws for a given number of spins. (Actually, it's how far the distance from the club's center of gravity to the pivot point is, so when you think a club "has a loftier spin" it has a c.g. farther out.)

Perhaps even more surprisingly, how high, in feet, that a natural throw goes is independent of gravity; a five-foot high natural double here goes five feet up on the moon, or on Jupiter, if it's the same juggler throwing them. Of course it takes a lot longer to go up five feet on the moon, so everything is slower, but it's not any bigger.

I prefer natural spins for two reasons. First, for a given number of spins, the natural throw will always take longer to return than a spun throw, so it will be a slower pattern. Second, if you are making spin errors, overspun or underspun, you don't need to think of two things, height and spin, but rather only one since the height and the number of spins are related. That is, you merely need to think "hmm, the club was overspun, I need to throw it LOWER" - and the spin takes care of itself.

The reason I said earlier about the flashy vs. good is, well, look at all the people who do five or more clubs, and see how high their patterns are! As they say, when in Rome... If YOU want to do numbers, do as the numbers jugglers do! Very few do five doubles as high as three singles... Four is no different in this regard.

I can do five clubs with single spins. The best way I can describe it is: Imagine you're juggling five large, dead fish, and you don't want them to break in half when you throw them. Actually the pattern is very simple, but the simplicity has a certain subtlety to it. It's so subtle that it took me about three years to see how easy it was! ;) However, I find it easier than three clubs flats.

## Why the Hammer Rotates

(by Marc Hertlein)

### The experiment

This effect belongs in the category of weird effects that you never knew existed. It's best tried with a hard cover book, held shut with a rubber band (or any other block-shaped throwable object).

There are three main axes that you can flip the book around:

1. The long axis through the center of the book (parallel to the spine).
2. The short axis through the center, parallel to writing on the front.
3. The spin-like-a-record axis perpendicular to the covers.
Any other axes are a kind of combination of the above and make things more complicated (the book will wobble and do other weird stuff).

Now try flipping/spinning the book around each of these axes separately. Do it. Now!

Notice something?

Axes (1) and (3) work, but axis (2) won't stay, and the book wobbles!

### The reason

Turns out (here comes the physics), if you would calculate the moment of inertia around each of the three axes (kind of the measure of how hard one has to twist to get the thing turning around the axis), you would find that the moment around axis (1) is the smallest, (2) is in the middle, and the moment around axis (3) is largest.

If one would look at the equations for rotations of a solid object (one would only do that if one was a grad student in physics or mechanical engineering) and solve them (even harder than comprehending them) one would discover that the rotation around axis 2) is unstable. Kind of like a rod pendulum upside down. Or a balanced club.

If the thing gets just a little away from the balanced position, it starts to take off faster and faster, exponentially. On the other hand, if the pendulum hangs down, any displacement from the exact center point just makes it swing back to the center (sinusoidally) and it is stable. Same thing for rotation axes 2 and 3 (or 1), respectively.

So this exactly is why it's so hard to flip the book around axis 2 without also having it flip sideways. Only if you throw perfectly around the axis will the book not start to wobble. Depending on the dimensions of the book this can be very hard. Same holds for the hammer. Or for any object with 3 different moments of inertia around its axes.

The weighting of the object has nothing to do with all this, except it determines where these 3 axes are located and intersect. This one point of intersection around which the object always rotates is called the center of gravity, by the way.

### Other juggling objects

And now you know why juggling things work the way they do. Try juggling sickles. "Ring" throws will be stable, "pancake" throws will wobble. Clubs have moments 1 and 2 the same, so this wobbling doesn't happen. Same with rings. Clubs have moment 3 *smaller* than 1 and 2, i.e. flats are not quite as easy as spins (need faster rotation for same stability). Rings have moment 3 *larger*, so it's slightly easier to throw them around that axis. And balls have all three moments the same, so no one cares. Does anyone care anyway?

I think I heard that Boppo classifies jugglable objects into 3 categories: balls, clubs and rings. Any other object is basically the same as those, for (his) juggling purposes. Hm. Based on the above, care to guess how he (probably intuitively) got to classifying things like that?

Actually, he forgot the category of "book", which he probably groups with the clubs, seeing that sickles belong into that. I propose to call these objects ARPTJ's (a real pain to juggle)...

A Physics Lesson / Juggling Information Service / help@juggling.org