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A PHYSICIST WRITES . . .

(June 2008)

I want to get to grips with a certain word which I know I havenít typed once in six years of writing these columns. Itís one of those terms that means something quite specific in physics, but has a rather more vague meaning in everyday language. Perhaps I have been subconsciously avoiding it for this reason ... no, I confess that Iíve deliberately been putting off using it. But now I shall bite the bullet!

First though, I must just return to something I wrote in March: ďTaking your eyes off the road to look at the speedometer can be risky sometimes, so you try to judge your speed from how fast the surroundings appear to be moving past.Ē A reader remarked that good drivers use several external sources of information to judge their speed, but the speedo itself shouldnít be dismissed (as I seemed to be doing), because surely it is the most immediately reliable indicator that we have of our speed. This is fair comment, but let me share some more thoughts with you.

Glancing down at the speedometer, and then back up, requires a greater readjustment of eye-focusing than looking around in front of you (outside the vehicle), and so it takes longer than you might think ó I would say a minimum of one second of attention taken away from the road. Have you tried instead to discern the rough position of the speedo needle while looking straight ahead? I donít find this difficult, and you might not either. Another thing: remember that your speedometer can legitimately read high (up to 10% more than your actual speed), and very probably does. But at least you can rely on it not to under-read.

Iíve been musing too on the different reasons why I might want to check the speedo. One is to watch my speed as I accelerate or slow down towards a speed limit. Another reason is to make sure I havenít drifted above the limit. A third is to reassure myself that the car hasnít got too much momentum for an approaching hazard, such as a bend or the end of a motorway exit slip-road...

There, Iíve done it! That was the word Iíve been avoiding: momentum. We use it to mean motion ó but not just speed, because you feel that a heavy object carries more momentum than a lighter one, hence it wonít slow down as easily. Is momentum, then, the same thing as kinetic energy (which Iíve discussed before)? No, itís quite different but just as significant, as I shall try to explain below. Anyway, for now letís just use the word in its vague sense of speed with some weight behind it.

Momentum is a valuable thing to possess. It can save you fuel. For example, if you can see that you will need to slow down or stop at an intersection or another hazard ahead, and you lift your foot earlier than you would normally have done, the momentum of the car will very likely still carry you all the way.

Or it can save you time. If you are facing a hazardous crossing of some sort, accelerating over it from a standstill will take you twice as long as arriving already up to speed (assuming you can do so, of course) and sailing over. And even if you are only moving slowly when you reach the point of departure, there will be a much smaller chance of your stalling at the moment you put your foot down, than if you are starting from rest.

In a stop-start queue, if youíve engineered enough space in front to let you keep some momentum, you can make a sideways adjustment to your line or even change lanes ó you canít do this if youíve halted!

And at a mini-roundabout, if three of you are all signalling right and eyeing each otherís vehicles nervously, keeping a small amount of momentum can give you priority even if you are the last to arrive. What I donít always find easy to remember is that the driver on the right probably wants me to keep moving and to cross in front, in order that he or she can go next (behind me and across the third vehicle). If instead everyone gave way to the right, it would all take much longer.

OK then, what does momentum mean to a physicist? It is simply the weight of an object (actually the proper word here is mass) multiplied by its speed: mv. An important property of momentum is that itís directional, which means that if two vehicles with equal amounts of it collide head-on ó sorry to dramatize ó their momentums will cancel and vanish, and both will stop.

If instead one vehicle had more momentum before the collision, because of being heavier and/or moving faster, it would win and push the other back. This is decided entirely by momentum, and not by their kinetic energy (Ĺmv2). But naturally they do lose KE as well: all the amount lost changes ultimately into heat and dissipates into the environment.

Momentum canít transform into something else like that, but it can be created, by the opposite of a collision. The classic example is when you are standing on a rowing boat and aiming to leap to the bank. What you donít realize is that you can only acquire momentum by giving the boat the same amount of it in the opposite direction, as you push. Its movement reduces the force you intended to apply, and the result is that your momentum and jumping speed are rather less than you expected ... splash! It was Isaac Newton who came up with the idea of Ďmomentumí to explain such things, three hundred years ago. Perhaps he had previously fallen off a punt into the River Cam.

A question at the back? Yes: when I leapt into my car and drove here, where did my momentum come from, if there was nothing zooming off in the other direction? Well, think about it. Didnít you push on the ground, first with your feet and then with your tyres? And isnít the Earth free to rotate? Anticipating your question, I did a calculation.

If you drive your two-tonne car letís say 500 miles in any particular direction, our whole planet (just like the boat) will roll a short distance the other way, relative to where it would otherwise have been of course. Effectively, it will have the same amount of extra backward momentum mv as your car possesses, until you stop driving. But donít let this go to your head ó the Ďshort distanceí we are talking about is roughly equal to the diameter of the nucleus of an atom!

Peter Soul

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