6 Sep 2005 I received an email from someone who was involved with a play entitled "Momentum", asking for whatever information on the subject I could provide (including references to scholarly journals or perhaps websites that might be of assistance). I found the idea pretty cool: I'm fascinated by artistic works that touch on physics. My reply is below. In retrospect, I think that I probably said too much: information overload isn't as much of a problem in the written word as it is in a lecture, but it's still worth watching out for. I did try to address that here by labeling a few particularly important bits (as I explain in my reply). ---------------------------------------------------------------------- Hmm. If you're like most people, I'm guessing that you don't have a lot of experience with physics. (Well, not in the formal sense, anyway! Most people are expert physicists on an intuitive level, with such remarkable skill that they can lift objects, understand reflections in a mirror, and even catch a flying ball!) So I'll try to keep my comments on a very basic level, and I apologize in advance if I start spouting jargon or go too fast. If you _do_ have a bit of a physics background, my apologies for the simple explanation that follows. I'll label some particularly important paragraphs with "***". For the record, you won't need any "scholarly journals" here unless you want to get very cutting edge indeed (or unless you want to go back many decades or centuries to the original writings that discussed the concept). The vast majority of what we know about momentum can be found in textbooks: it is one of the most basic concepts in physics. Also, keep in mind that while momentum is a fundamental part of physics, the word has many (related) meanings in colloquial English, too. I'd guess that a play named _Momentum_ will draw on a wide range of those. *** So, what is momentum? The first and most basic statement of the concept of momentum comes from Newton's First Law of Motion: "An object in motion will remain in motion unless acted on by an outside force." (That's sometimes called the "Law of Inertia"; "inertia" and "momentum" are closely related concepts.) In physics, an object's "momentum" can be thought of as the "amount of motion" that it has: the greater its momentum, the harder it is to stop it or to turn it in another direction. *** What makes an object harder to stop? Well, the faster it's moving, the more you have to slow it down, so momentum must depend on speed. (In fact, it turns out that the direction is important, too; physicists call speed in a specified direction "velocity".) And the heaver it is, the harder you have to push to slow it down, so momentum must depend on "mass" (which is a physicist's technical term for what we normally think of as weight). ***The formal mathematical definition of momentum (in classical physics) is the product of those two quantities: momentum = mass * velocity To give a few examples, a flying gnat is fast but its mass is very low, so it doesn't have much momentum. That means that it's easy for a gnat to turn around and buzz in another direction (which you've probably seen firsthand). On the other hand, a slowly rolling car still has a lot of momentum because it's so very heavy: it would be hard to push one to a stop even at very low speeds. As yet another example, a bullet is pretty lightweight, but when it is fired from a gun its enormous speed gives it very high momentum (and if a person tragically gets in its way, the effort of absorbing all that momentum will break their flesh and bones). *** Now, as I mentioned earlier, "velocity" implies not just speed but direction. So since momentum is proportional to velocity, momentum always has a direction, too. That's a very fundamental fact about momentum! Changing an object's direction can be just as hard as stopping it completely. *** Another remarkable fact about momentum is that the _total_ amount of momentum in a system will never change. Physicists call this rule "Conservation of Momentum", and they say that "momentum is conserved". For example, if you're playing pool and you hit the cue ball into the eight ball, when the cue ball slows down the eight ball will start moving to make up the difference. If your shot is perfectly straight, the cue ball may stop moving entirely while the eight ball rolls away with the same velocity that the cue ball used to have. (It would _have_ to be the same velocity: because the balls have the same mass, conservation of momentum must imply equal velocity before and after.) If your shot is a little off center, the cue ball and the eight ball will both bounce away at different angles. But you'll find that their "sideways speeds" are exactly equal, because the total "sideways" momentum before they hit was zero. (Remember, momentum has direction! If there was no momentum to the left or right before the balls hit, there can't be any total momentum left or right afterward, either.) What if one mass is bigger than the other? Well, imagine a bowling ball: when you roll the heavy ball down the lane, it has a lot of momentum. When it hits a one of the light pins, the ball slows down a little bit but the pin goes flying! That's because the ball is so much heavier than the pin: because the total momentum has to be conserved, a small decrease in the ball's speed leads to a big increase in the pin's speed. "MASS * velocity = mass * VELOCITY". That's also why you don't want to get hit by a car! You're so much lighter, the car will throw you across the road and hardly slow down at all. Conservation of momentum is always true, although sometimes it can be hard to see. For example, if you skid to a stop in a car you might think that its momentum has vanished, but what's actually happened is that the friction between the tires and the road has transfered the car's momentum to the Earth itself (which is so big that we don't even notice the change). Forces like friction and air resistance can make it _look_ like momentum is going away in many situations, when really it's just being transfered somewhere that we can't easily see it. *** Another interesting fact is that light carries momentum, even though light has no mass. It's not _much_ momentum, of course, but it's certainly there! You might have seen a science demonstration of this at some point, where a little black and white pinwheel is placed in a vacuum jar. When bright light shines on the pinwheel, it starts to spin. (This only works if the details are set up correctly, of course.) For light, the usual "mass * velocity" equation doesn't apply, since light has no mass and all light has the same velocity. Instead, the momentum carried by light depends on its intensity or brightness (which sort of corresponds to mass: it's the "amount" of light) and its _color_! It turns out that blue light has a lot more momentum than red light (other colors are mostly in between; it corresponds precisely to the colors of the rainbow). And special kinds of "light" like X-rays are in a sense even more blue than we can see: they carry a _lot_ of momentum (at least as compared to other light), which is why too much exposure to X-rays can be dangerous: when they hit your body tissues, all that momentum can make the molecules in your cells break, leading to burns or even cancer. That's why we get sunburns from ultraviolet light, too: it's more blue than blue, though not as bad as X-rays. *** That's the basics of momentum in classical physics. When you get to the 20th century, things get a bit more interesting. In quantum mechanics we learn that it is impossible to perfectly measure an object's position and its momentum at the same time. This is called the "Heisenberg Uncertainty Principle". For example, if you measure its position very carefully, you won't be able to tell how fast it's going. This is often explained by trying to imagine how you would look at the object: usually, you'd shine light on it, but as I just said, light carries momentum! If the light bounces off of the object and into your eye, that will change the momentum of the object (just like the cue ball changed the momentum of the eight ball). That's just a rough example, but the position/momentum difficulties hold true in general. Einstein's theory of special relativity has things to say about momentum, too. For instance, it turns out that "mass * velocity" is only _approximately_ true. If the velocity is very high, close to the speed of light, then the momentum grows much faster than this: momentum = gamma * mass * velocity, where gamma = 1 / (square root of[ 1 - (velocity/speed of light)^2 ]) That's a messy formula, I know, and you probably don't need to understand it. The point is, momentum is more subtle than Newton and the other classical physicists thought it was. In fact, Einstein showed that momentum was closely related to "energy" (that is, roughly, an object's stored capacity to do work), and that energy can actually be thought of as "momentum in the direction of time". (And the connection is an important one: "Conservation of Energy" is another very important law of physics, just as important as "Conservation of Momentum".) Whew! That may be enough to get you started, anyway. If you want more details, practically any introductory physics textbook will discuss momentum at great length. Even if you aren't mathematically inclined, I'm sure that most good "Physics for Poets" type books will discuss momentum in some detail (and probably more clearly than I've managed here). Let me know if you have more questions! Steuard Jensen