Triple Twirl

Select an object having approximately uniform density throughout and in the shape of a rectangular solid with no two sides equal. Almost any hardcover book will do nicely.

Let the three axes between the centers of opposite pairs of faces be labeled X, Y, Z: the X-axis is the longest, the Z-axis is the shortest, and the Y-axis is intermediate.

Pick up the object in both hands along one of the axes and toss it gently into the air, twirling it about the axis. About the X-axis it will rise, fall, and twirl stably, and about the Z-axis likewise. About the Y-axis it never will, no matter how carefully you toss it. Try it if you don’t believe me. It’s quite mind-boggling to experience.

Now, come back here and explain, please.


  1. I did it easily, so I'm guessing I cheated in some way. About the x axis it flipped the book top over bottom, about the y it flipped side over side, about the z it twirled around 360 degrees. Did I apply illegal vector forces?

  2. Anonymous11:38 AM

    They should all be 360 rotations!

  3. twirled in a circle along the xy axis, i mean, like when you twirl pizza dough.

  4. This comment has been removed by the author.

  5. err..not on the xy axis, but twirling ON the xy PLANE, about the z axis.

  6. I meant it in the way john described it in his just previous comment. I didn't understand what anonymous was getting at.

  7. Wabulon, I didn't get it, though. I was able to twirl the book around all axes. Did I apply illegal vector forces? Can you be more specific how I may throw the book?

  8. Say we're going to use the X-axis. Lay the book on the table with the X-axis parallel to the edge of the table nearest you. Lay your hands upon the book at either end. Slip your second or third fingers under the book. Lift, holding the book between your first few fingers and thumb. Toss, lifting your fingers and depressing your thumbs as you do so, giving the book a spin.

  9. Susan Underhill8:54 AM

    What I find is that it wobbles in the Y axis but flips smoothly in the X and Z axes.

  10. Thank you, susan--at least one person agrees with God and me.

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