Wednesday, July 29, 2015

Classical Mechanics: an Experiment You Can Try at Home

Classical mechanics is the branch of physics that deals with bodies in motion: velocity, momentum, forces, acceleration. And it can be pretty boring. Let's face it --  none of us went into physics because we fell in love with blocks sliding down inclined planes, with or without friction. We went into physics to learn about black holes, quantum mechanics, or the fate of the universe. But classical mechanics is the basis of all of the rest of physics, so it's what everyone studies first. And, unfortunately, for many people it ends up being their only formal contact with physics.

But even in classical mechanics there are interesting byways and surprising results that most people are unaware of.  Here's a cute experiment you can easily do at home that illustrates one of these unexpected results.

To do this experiment, you need a rectangular block of some kind.  It can be a piece of wood, a brick, or anything with a similar shape.  The important thing is that the three dimensions of the block all have to be of different lengths -- you can't use a cube!  If nothing is readily available, just get a book and tape the pages shut.

Your rectangular block has three different "axes" corresponding to the three different dimensions of the block.  Pick out the shortest of these, and toss the block into the air, spinning it around this axis. (If you are using a brick, I suggest you do this outside, away from children and pets). The block should spin very stably in the air before it falls to the ground. Now pick out the longest axis, and do the same thing -- spin it around this axis as you toss it into the air.  You should see the same thing -- the block will spin around this axis until it falls down.  Now there's only one other possibility -- spinning it around the middle-sized axis (maybe we should call this the Goldilocks experiment).  But if you do this, you'll get a surprise. Instead of spinning stably, the block will twist all around in the air. So the bottom line is that a block can spin in the air around its longest axis or its shortest axis, but not its middle one!

What causes this?  The mathematics is too complicated even for a first-year college physics course -- it involves things called inertia tensors and other mathematical monstrosities. But the short answer is actually pretty simple. When the block is spinning around its long or short axis, any slight change in the direction of the spin produces a force in the opposite direction, which pushes the block back to its original direction of spin. So the block happily keeps spinning in the same direction -- this is what's known as a "stable equilibrium." But when the block is spinning around its middle axis, a change in the direction of spin causes a force in the same direction as this change, so that the spin gets more and more out of alignment.  The block just topples randomly instead of spinning smoothly. This is an "unstable equilibrium." These ideas of stable and unstable equilibrium are extraordinarily important -- they're found throughout all of physics. And you can demonstrate them with a simple block of wood.

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