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When a batter swings at a ball, the result is often disappointing for the batter. Striking the ball is better than missing it completely, but a miss-hit is not much better. Both are very common. Only rarely does a batter strike the ball cleanly, or head-on. By a head-on strike we mean one where the bat strikes the ball squarely in the middle of the ball, in the meaty part of the bat, and at right angles to the path of the ball. Such a strike will be satisfying in the sense that the ball will then come off the bat at the maximum possible speed. However, it might head straight back to the pitcher. Usually, this is not what the batter wants. Perhaps he wants to hit the ball slightly late or slightly early so that the ball heads off in the general direction of first or third base. Alternatively, he might prefer to strike the ball below its center to project the ball up into the air or to impart additional spin to the ball. [ABSTRACT FROM AUTHOR]

The superior performance of non-wood bats is due to the fact that they are hollow rather than solid. The wall of a hollow bat vibrates like a drum when it strikes the ball, emitting a characteristic high pitched ping sound. The wall vibrates not while the bat and ball are in contact, but after the ball leaves the bat. The enhanced performance of a hollow bat is not due directly to the vibration of the wall of the bat. Rather, the enhanced performance is due to the fact that the wall bends slightly and then springs back as the ball leaves the bat. It is the springiness of the wall that gives rise to the improved performance of the bat. If the wall could somehow do its job more efficiently, it wouldn΄t ping at all. The wall would then give all its stored elastic energy back to the ball, shooting the ball out at high speed, and there would be no energy left in the wall for it to vibrate. [ABSTRACT FROM AUTHOR]

One of the things that physicists like to do is to study collisions. Indeed, modern physics had its origins in the 1600s with attempts by Sir Isaac Newton and others to understand collisions between various objects such as hard or soft balls. These days, most collision experiments in physics are concerned with tiny subatomic particles colliding at extraordinary high speeds. That is where the frontiers of physics are being pushed forward, but there are still a lot of small discoveries being made about collisions between ordinary objects such as bats and balls. In fact, a large part of this book is based on theoretical and experimental work done during the last 10 years to understand bats and balls. [ABSTRACT FROM AUTHOR]

Most people can walk or run successfully, without tripping or stumbling, even without any special coaching. Similarly, most people can swing a bat without needing anyone to show them how. The problem is, everyone has trouble connecting with the ball. In fact, some people claim that hitting a baseball is the single most difficult task of all sporting tasks. [ABSTRACT FROM AUTHOR]

Twelve simple projects are described in this chapter that you can undertake at home or elsewhere. The projects deal with the flight of balls through the air and the properties of bats and balls. The object of each project is to get you thinking about the physics of baseball and softball. The best way to do that is to undertake a few experiments yourself. You can play or watch baseball or softball for your whole life without ever thinking about the physics behind it. But if you do start thinking about it, then you will probably be surprised that there is much more physics in the game than you ever thought possible. Depending on your background and interests, a baseball or softball game can be viewed as a whole series of physics experiments, an exercise in psychology or biomechanics, or just simply a fun sport to play and watch. To others, it is more important than any of those things. It is matter of life and death. [ABSTRACT FROM AUTHOR]

Almost all major sporting activities are played with a ball. The rules of the game always include rules about the type of ball that is allowed, starting with the size and weight of the ball. The ball must also have a certain stiffness. A ball might have the correct size and weight but if it is made as a hollow ball of steel it will be too stiff and if it is made from light foam rubber with a heavy center it will be too soft. Similarly, a ball needs to bounce properly. A solid rubber ball would be too bouncy for most sports, and a solid ball of plasticene would not bounce at all. The correct size, weight, stiffness and bounce for each ball used in each sport has evolved over many years of trial and error. That evolution settled down 30 or 40 years ago to something that everyone was more or less happy with. [ABSTRACT FROM AUTHOR]

In recent years, batmanufacturers have been experimenting with flexible bat handles in an attempt to increase bat performance. Some manufacturers claim that better performance is obtained with flexible handles, while other manufacturers claim that stiff handles are better. For example, in 2007, Easton advertised a bat using its flexible handle ConneXion technology, while Louisville Slugger were simultaneously advertising their stiff handle technology. Easton claimed that: ˵Acting like a hinge, the ConneXion provides the most efficient energy transfer from handle to barrel, resulting in maximum bat head whip for a quicker bat and more power through the hitting zone.″ Louisville Slugger claimed that: ˵The last thing you want at the moment of contact is for your bat handle to flex. When the handle flexes, the barrel can΄t. That reduces your trampoline effect. A stiff handle produces more barrel flex, resulting in a maximum trampoline effect and, ultimately, greater performance.″ [ABSTRACT FROM AUTHOR]

An interesting aspect of a bat and ball collision, from both a practical and a physics point of view, is that the batter can exert a huge force on the ball without feeling any particular discomfort at the handle end of the bat. The force on the ball is much larger than the force exerted by the batter on the bat. The batter swings the bat by exerting a force of around 50 lb on the handle. The bat then magnifies that force by a factor of about 100–5,000 lb or so when it collides with the ball, enough to squash the ball in half. Only a small fraction of that huge force gets back to the handle to trouble the batter. If the ball is struck at the sweet spot of the bat, then the batter feels almost no effect at all. It seems almost as if Newton΄s third law does not apply to baseball or softball bats. Newton΄s third law says that for every action there is an equal and opposite reaction. If there is a force of 5,000 lb on the ball then there will definitely be a force of 5,000 lb acting back on the bat. How come the batter is blissfully unaware of that fact? [ABSTRACT FROM AUTHOR]

One of the problems faced by a batter is that the ball approaches the batter at high speed, up to 90mph. Batters are somewhat sluggish in responding to this situation. It takes a certain time before they react, and when they do their arms and legs are too heavy to respond instantly. It doesn΄t help that the bat itself is quite sluggish, except of course when actual contact with the ball is made and then a heavy bat is an asset rather than a liability. [ABSTRACT FROM AUTHOR]

The bending of a bat at impact raises a number of interesting physics questions. Since the ball bounces after the bending wave travels about one foot along the bat, how much of the bat is actually involved in the collision? If the tip of the bat bends before the handle starts to bend, will the bend cause the bat to rotate or does it cause the bat to vibrate? And how does the bat ˵know″ that it musn΄t vibrate when the ball is struck at the sweet spot, especially considering that the bat doesn΄t even know where it was struck until the bending wave gets to each end of the bat and reflects back to the impact point. [ABSTRACT FROM AUTHOR]

Of all the technical issues that concern bat and ball sports, the one that is of most interest to most players concerns bat performance. Players would like to hit the balls far as possible, using the most powerful bat that they can afford and that they are allowed to use. They would also like the bat to be as light as possible so that it is easy to swing and connect with the ball. Therein lies a dilemma. Heavy bats are more powerful, but they are harder to swing. Light bats are easy to swing but they lack the punch of a heavy bat. [ABSTRACT FROM AUTHOR]

Most of the physics in this book can be understood in terms of basic high school mechanics and slightly beyond. This chapter is provided for those who might need some extra guidance or a kick-start. The author has taught a course in sports mechanics for physical education teachers for many years. Many of the students arrive at University without ever having studied physics and only a small amount of mathematics. Some arrive after being in the work force for a few years and have forgotten everything they knew from high school. [ABSTRACT FROM AUTHOR]

The sight of a baseball or softball flying through the air evokes different responses in different people. If the ball is headed toward the batter then the batter will be frantically trying to figure out what the ball is doing and where it is going. If the ball is headed toward one of the bases then the player running to that base will be wondering whether he will make it in time. If the ball is headed toward the fence then some of the spectators will be cheering and some will be moaning. These are the sorts of emotional reactions that make the game what it is. It is the combined effect of the importance and the uncertainty of the outcome that keeps players on their toes and spectators on the edge of their seats. [ABSTRACT FROM AUTHOR]

It is obvious to anyone observing a bouncing basketball that the ball squashes when it bounces, and that it expands back to its original shape when it bounces up off the floor. The same thing happens when any ball bounces, although it usually happens too fast to be seen by eye. A basketball spends about 20 ms (0.02 s) in contact with the floor which is just enough time to catch a glimpse of the ball squashing. For most other balls, the time spent in contact with the floor is so short that the action can only be captured with the aid of a fast camera. For a baseball or a softball, the contact time is only about 1ms. [ABSTRACT FROM AUTHOR]

Pitching mechanics can mean different things to different people. To coaches and players, pitching mechanics refers to biomechanics, to the actions of all the different body segments involved, the correct sequence of those actions, the alignment of the fingers along the ball, injury prevention, and so on. In this chapter, we examine the mechanics of pitching from a physics point of view. That is, we treat pitching as a mechanics problem. There are three main questions that we ask. The first question is: how does a pitchermanage to release the ball at just the right moment to project it at the angle he or she wants to pitch it? The second question is: why can a baseball be thrown faster than a brick? And the third question is: How can a pitcher transfer as much energy as possible from his or her arm to the ball? The second question might seem a little strange at first sight, but the answer is not as simple as youmight expect [ABSTRACT FROM AUTHOR]

The basic task of the pitcher is to throw the ball so that it passes over the home plate at a height between the batter΄s knees and shoulders. In baseball, the strike zone extends from the knees to a point midway between the shoulders and the top of the pants. In fast pitch softball the strike zone is essentially the same, although the upper part of the zone is defined as the bottom of the sternum. In slow pitch softball, the zone extends to the shoulders. [ABSTRACT FROM AUTHOR]

A good place to start our discussion of the physics of baseball and softball will be to examine the basic equipment used, namely bats and balls. We will have a lot more to say about bats and balls in other chapters, but first it will be useful to look at the basic properties of bats and balls, mention briefly some of the history of the subject, and then consider how bats are designed to appreciate the main differences between solid wood, and hollow aluminum or composite bats [ABSTRACT FROM AUTHOR]

It is four decades since Phelps (1967) and Friedman (1968) unveiled the natural rate of unemployment hypothesis, and the concept of an equilibrium rate of unemployment is central to the prevailing theories of labour market behaviour and the relationship between unemployment and inflation. Moreover, the natural rate and associated unemployment gaps are seen as important reference points, typically as part of a broad range of indicators, by policy makers who need to assess short-term inflation developments and/or consider appropriate decompositions of fiscal balances into their structural and cyclical components. Yet, as surveys and symposia have illustrated (Bean 1994, Cross 1995, Journal of Economic Perspectives 1997), there remains much uncertainty both about which factors do and do not determine equilibrium rates of unemployment, and about the corresponding numerical values. [ABSTRACT FROM AUTHOR]