Tennis Serve Physics

On a kick serve, the racket meets the ball at high speed, with the ball literally sliding down on the racket strings for several inches before it leaves the racket. The strings themselves stretch for as much as an inch at the impact.

This is why there’s a ‘sleight-of-hand magic’ to the kick serve. The racket continues its path ‘beneath’ the ball, which at first has near-zero velocity; in slow motion, you can see that the racket head ‘moves ahead’ of the ball just immediately after impact. The server may get the feeling that he has caught the ball and is then ‘pulling the ball down’ as he continues with the serve’s follow through. (In fact, he has hit up on the ball, but with the racket on a circular path, which is why the follow-through is to the side, rather than forward.) The ball initially travels up and then arcs down because of gravity and spin.

All this happens because the body is sideways (not facing the net), and bent at the waist so that the swing path is left to right in relation to the body but ‘up and over’ in relation to an imaginary vertical line ending on the ground. The ‘up and over’ motion also reflects the ‘shoulder over shoulder’ rotation that creates the power for the serve.


From Popular Mechanics


Pancho Gonzalez’s serve on YouTube



Keynes, Macroeconomics, and Traffic

Orlando Roncesvalles (oroncesval4@gmail.com)

Back in 1936, a smart aleck named Keynes (John Maynard, or just Maynard) cooked up something he called The General Theory of Employment, Interest, and Money. He thought of unemployment as something to be solved, possibly in the same way that Albert (surname Einstein) thought “relativity” was the mystery to get fixated on. The parallels stop pretty much there despite the historical fact that failed mathematicians sought to infuse physics into economics, a project that took a long time to be discredited (not until 2008 anyway, when the Great Financial Crisis finally put paid to the misconception that physics and economics can mix, the latter having the muddle-like consistency of dirty motor oil and the former the empirical clarity of replicable experiments).

The genius of Keynes was in his insistence that the short run mattered more than the long run (when we would of course all have died). In that short run, slack in an economy (or unemployment) could be dealt with by public works. This idea was nothing new — even the Roman emperors knew that public spectacles kept people employed (even entertained). Keynes came up with the idea that in the short run, aggregate supply (or output, later standardized into GDP or gross domestic product) would have to adjust to what he called aggregate demand, whose components included consumption, investment, and government expenditure. Textbooks would later call this equality between aggregate demand and supply as “goods equilibrium.”

But Keynes then married the idea of goods equilibrium with something we might today call “asset equilibrium”— a situation wherein people are content to hold the quantity or amount of money in their pockets.

Asset equilibrium meant that peoples’ “liquidity preference” was satisfied through the movements of the interest rate as the price of credit and the opportunity cost of holding money. Money demand was driven by GDP and the interest rate, while money supply was a policy variable in the hands of the central bank. The equality of money demand with supply would be at the market-determined interest rate. Recognizing such an equilibrium was a way of bringing in the workings of the money and banking system into a fuller explanation of the gyrations of the business cycle. After all, the money markets determined interest rates, and these rates in turn drove business investment, which of course is a component of aggregate demand in the goods market.

The essence of Keynesian thinking was and remains the workhorse of macroeconomics (that specialty within economics that concerns itself with the short run determination of GDP and interest rates).

After Maynard, everyone then had a field day. The business-cycle savants focused on the confidence-based elements of aggregate demand (consumption and investment); the politicians latched on because government spending was their domain and Keynesian economics provided cover for influence and corruption; and the bankers were very much in on the act of determining interest rates. Macroeconomics caught on as the thing to know before one can say anything about the national or global economy.

It turns out that the apparatus of macroeconomics can be tweaked to help us understand the relationship between GDP and traffic.

Recently, a noted legislator reiterated the idea that prosperity (a growing GDP) was behind our traffic woes. I interpret what the legislator said to mean that without the heaven of a business boom, we wouldn’t have the hell of traffic. We should sit back and no more challenge him and his ilk to take public transportation because of course he already knew the answer: We are prosperous, so that we should just grin and bear it!

A critical but opposite view has nonetheless come forward. It is the idea that traffic is a brake on prosperity. The more severe the traffic, the less the GDP.

So, which is it? Is it a positive correlation between GDP and traffic? Or a negative one?

Keynes would likely scoff at the seeming contradiction. The negative correlation is the working of goods equilibrium if we realize that the severity of traffic negatively impacts aggregate demand. Bad traffic keeps consumers from traveling to malls, and smart businesses would likewise invest less if traffic drags down sales projections. Bad traffic kills GDP.

The positive correlation is something else. As GDP grows, the more we want to acquire transportation assets, such as cars and motorcycles. But in the short run, there is only so much roadway for all, and traffic problems arise.

The two disparate relationships – goods equilibrium and “traffic equilibrium” – are synthesized in the macroeconomics apparatus. Smart students will see that the thought experiment is the same as that of the infamous IS-LM apparatus of macroeconomics, where IS represents goods equilibrium and LM represents assets equilibrium; we now simply replace assets equilibrium with traffic equilibrium. Traffic equilibrium, by itself, reflects the positive influence of GDP on the severity of traffic problems, though it also suggests that the less the traffic, the more that people will demand transportation assets (this is the analog to the idea that the lower the interest rate, the more we would prefer liquidity or hold money).

What does all this mean? Can we now have a “clean” sorting out of the two disparate influences – the one of GDP on traffic and the other of traffic on GDP?

The answer is this. As an economy grows so of course does GDP. If the traffic infrastructure is left “as is,” traffic problems worsen, and governmental neglect is the culprit. This is because the traffic infrastructure (like monetary policy) is in the hands of the economic authorities. The infrastructure is in fact a public good. Still, the hapless citizens aren’t exactly helpless. They can move closer to where they work or work closer to where they live. They can drive less and consume less, and coincidentally lessen their carbon footprint. As a modern Marie Antoinette might say, let the travelers have their air-conditioned “me time.” Except that the peasants don’t eat cake or have their James (the proper name for chauffeurs of Rolls or Benz automobiles). Apparently there is no free lunch, and traffic is here to stay. Embrace it.

But if we were to solve the supply side of the transport asset equation, we reduce the severity of traffic, and the GDP boom continues or strengthens.

How to improve the traffic infrastructure is then the key. It is the magic but elusive password. Our legislators are perhaps simply not up to the challenge. Boot them, but don’t use the Denver boot. It won’t work because they’re too self-important. They’ve so far set things up so that they don’t suffer the inconvenience of public transport. Instead, they tell the ordinary citizen that it’s his fault because he enjoys a prosperous economy. Nuts.