Understanding Dimensions of Translational Motion in MCAT Physics

As a pre-med student preparing to take your MCAT, you want to ensure you have a solid foundation in Translational motion for the physical sciences section, not just in terms of how to solve equations and apply formulas, but also a conceptual understanding of the information.

Depending on the type of physics course you took in college, you would have learned how to solve translational motion questions in 1, 2, or 3 dimensions. Yet for the MCAT you only have to worry about solving kinematics questions in 1 or two dimensions, or sometimes a combination of the two.

Understanding the nature of these dimensions will be the first step in mastering MCAT physics. The concept of ‘one dimension’ refers to motion occurring in a single direction. The direction can face any which way but will never veer off course.

Common single dimension problems in MCAT physics will refer to motion happening in the x-direction, or in the y-direction.

Just because the two are oriented 90 degrees from each other, doesn’t change they fact that they each represent a single direction.

In fact, you can even break from tradition in terms of what you call your ‘x’ or ‘y’ direction. The traditional graph you learned in school had you draw a line parallel to the horizontal as the x-direction, and other line perpendicular to the horizontal or parallel to the vertical as your y-direction.

And while this is still the case, you don’t have to stick with this if you don’t want to. You may choose to label your horizontal as ‘y’ and your vertical as ‘x’, as long as you are consistent with the associated math equations and appropriate units.

But let’s not forget our two-dimensional questions. If you have a line represented on a graph, somewhere between the x and y components, this is said to occur in 2 dimensions, because we’re not focusing on both the x-portion and y-portion of this line.

The Role of Physics in Society

If we could get into one of those wonderful Wellsian time machines, all shining oak and glass, with polished brass handles and instruments, and ride it back to some time in the latter half of the nineteenth century, we would encounter a very different world from the one of today. Especially for Americans, it is difficult to conceive of a world where the United States counted for relatively little on the world stage. The same applied even more to all the other countries of the Americas. Except for Canada and Cuba, the whole continent had won political independence from Europe during that century, but it was still perceived as an extension of European cultures, with limited input in world affairs.

The whole world was run, in effect, from a handful of Western European countries, led by Britain which, even without the United States, had an empire that covered about one quarter of the globe. Furthermore, it was by far the leading manufacturer of machinery, armaments and textiles in the world, with the Bank of England holding most of the gold used in world trade. France also had a very large empire and so did some very small European countries, like Holland, Belgium and Portugal. Germany and Italy were occupied for many years during this period with unifying their countries under one central authority and therefore missed out on most of the empire building activity, but Germany especially was rapidly catching up with Britain as a leading manufacturing nation by the end of that century.

Looking at the size of all these European countries on the map, one can only wonder how it came about that they were running most of the world at that time. What made their influence so overwhelming when, only a few centuries before, they had seemed on the verge of extinction from the black death? The answer to this question leads into the subject of this article.

What made the small Western European nations invincible at that time were the practical applications of natural laws, contained in Newton’s monumental synthesis, the Principia Mathematica, published in 1687. Only four years before that date, Western Europe had been very nearly overrun by the Ottoman Turks and was only saved by the opportune arrival of the king of Poland, Jan Sobieski, who rode his cavalry to the aid of the beleaguered Duke of Lorraine and his Christian coalition, fighting a desperate battle bfore the gates of Vienna. And a scant two hundred years later, the flood of inventions derived from applying the basic laws of physics enabled these same endangered little countries to rule the world.

Was that all there was to the story? If we had made our time machine land somewhere in England during this period, the latter half of the nineteenth century, we would have encountered some appalling and, to us today, totally unacceptable social conditions. But there would have been something else. English society at that time exuded an underlying confidence and certainty that we can only envy today. They were looking to science to solve all their problems by simply continuing along the same path they had been following for over a hundred years. And by science they meant the scientific way of looking at things, which meant not only building better steam engines, roads, railroads and ships, but also better social systems and laws, founded not on hereditary privilege but on usefulness to the community. They knew they still had plenty of work left but they felt they were on the right path and the coming twentieth century would bring very great benefits and solutions to problems.

Where did this “scientific way of looking at things” come from and why did it suddenly provide such an impetus to a few Western European nations? The answer lies not with Newton but beyond him, to Galileo. Galileo founded modern physics by providing the axiomatic postulates that defined this “scientific way” for the future. He first of all secularized science by removing God from the picture and installing nature and her laws in His place. Nature was all that was needed to explain the physical world in mathematical (scientific) terms. Then he concentrated the focus of his new physics on just matter and motion. What causes a change in motion is a physical force and these are the realities dealt with by Newton.

Galileo was a revolutionary innovator when it came to viewing the world. He looked at it analytically, without feeling any personal connection with the objects he was analyzing. This change from the medieval, participatory, experience of the world enabled Galileo and later thinkers like Newton to express natural phenomena and natural laws in mathematical, logical terms. The previously impenetrable laws of nature were explained in simple, rational ways that ordinary people could understand. They could see that, if you confined God and the upper world to a realm of belief only, the only reality you had to deal with in nature consisted of the physical objects that, in Lord Kelvin’s phrase, were “quantifiable” and “measurable”.

By the end of the nineteenth century, the whole of nature was becoming a well-lighted room, with every new advance in science adding to the brightness of the illumination. It was fully expected that physics would finish its theoretical work very soon. As the same Lord Kelin said in the 1880s: “There is nothing new to be discovered in physics now; all that remains is more and more precise measurement”.

Here, then, is the origin of that confidence and certainty which was such a feature of Victorian society, which could be seen in any portrait of the plump and prosperous persons of the new moneyed classes of the time. There was complete harmony between the way people experienced the world as the only solid reality and the way science explained this world in laws that were predictable and logical, with causes leading to their calculable effects as certainly as billiard balls colliding on a table.

Then came the twentieth century and physics breached the atomic barrier. The solid reality of physical objects (which Newton dealt with) disintegrated in the subatomic world of particles. It became obvious that these particles were not just very small bits of the same matter that people were familiar with. As time went on and quantum mechanics kept gaining ground, the very reality of the existence of such particles as separate entities became doubful. One of the greatest physicists of the twentieth century, Werner Heisenberg, put it this way:

“In the experiments about atomic events we have to do with things and facts, the phenomena that are just as real as any phenomena in daily life. But the atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than of things or facts”.

But any object in nature that Newton dealt with is simply composed of a very large number of these “atoms or elementary particles”. If these are not real and the objects themselves are real, where does reality begin? Is reality merely a function of the number of atoms you can put together? We can begin to see why we no longer enjoy that feeling of certainty and confidence in having the right answers which our Victorian ancestors laid claim to.

We still, or at least most of us do, feel the world as Galileo did. We still feel that the physical objects of nature are the only solid reality, and this includes gases, which may not be visible but which we know consist of just those same “atoms and elementary particles” whose reality can, apparently, no longer be taken for granted. Our science today no longer reflects the way we feel about the world. The old harmony is gone. However, most of us still have faith in science’s ability to explain the world to us. In Newton’s time, science was readily understood by educated people. His laws could be taught to schoolchildren. Even if he could not really explain what gravity actually was, Newton proved mathematically that its operation could be explained successfully by saying that it worked in direct proportion to the masses of the bodies involved and in inverse proportion to the square of the distance between them. Today, the mathematics of physics has become so difficult that only a small group of specialists can understand it. Ordinary people, even if they are reasonably well acquainted with science, can no longer contribute to the debate in terms of the mathematical work involved.

However, physics has now reached the point where in both theory and practice in, for instance quantum mechanics, the consequences and implications of the work done are philosophical as well as mathematical. This may have the effect of bringing this very remote and difficult science once more into an area of more public debate. The mathematics would, of course, remain off-limits to ordinary mortals, but the conceptual structure that Galileo bequeathed to later thinkers, especially with regard to reality, might need revision and others besides theoretical physicists might usefully be brought into the picture. Galileo, like most educated people of his time, was well versed in the Platonic concepts of reality. To Plato, the knowledge to be gained from the physical world was fleeting and unreliable, being merely the subjective result of our sense perceptions. Real, true knowledge, which did not depend on human senses and was therefore objective, was to him a property only of the upper, divine world. However, when Galileo came to stating his axiomatic postulates regarding future scientific methods, he felt that matter and motion – and only matter and motion – were suitable for science because they did not depend on any human presence or any human senses. He felt that these two “qualities” were independently (and therefore objectively) real. His thinking in this regard affected the course of the entire future of physics, though in time, not just matter and motion but all physical phenomena came to be regarded as independently (and therefore objectively) real, as we have seen.

However, physics, in its own, normal development in the last hundred years, has come to realize that all physical phenomena, perceived through the senses, must be subjective in nature. Even matter and motion involve the sense of sight and Galileo erred in thinking that these two qualities of the physical world could somehow be considered objective, or independent of man’s senses. But if everything we perceive in nature has, by definition, to be subjective, then no physical phenomena can have an independent identity or history of their own, which would cause very serious rethinking about the early periods of this earth, before the appearance of man. For these reasons, it seems reasonable to suppose that our concepts of reality in modern physics are the ones that most need new thinking, so that a revised framework of concepts might be worked out, within which the physics of the future can operate.

Choosing a Spindle and the Physics of Handspinning – How Spindle Weight is Important

When choosing a drop spindle, it helps to know a little about the physics of drop spindles, and how that affects the kind of yarn you can make with a spindle. In this article, we’ll discuss spindle weight, and why it is an important factor in choosing a drop spindle.

It is quite obvious that a light spindle is better for light yarns. If a spindle is too heavy for the yarn you’re spinning, the weight of the spindle pulls the fibres apart, snapping the yarn and dropping the spindle (the old joke is that they’re called drop spindles for a reason!) before you can get enough twist to hold the fibres together. But spindle weight also affects another factor – inertia.

In simple terms, we can think of inertia as a measure of how much an object tends to keep doing what it’s doing, whether that’s staying still, or moving. Objects with higher inertia are more difficult to get moving or to speed up, but once they’ve been set going, it takes more effort to slow them down or stop them, as well. Inertia is directly proportional to mass (if you want the equation, it’s I=mr¬≤ where I is the moment of inertia, m is mass and r is radius from the centre of rotation) so simply put, a spindle with more mass has more inertia than a lighter one of the same whorl diameter.

Lower inertia means that light spindles can spin fast – because they are easier to set moving, a spinner can get a fast spin with little effort. Fine yarns and short or fine fibres need to be spun quickly – friction holds the fibres together, and the fewer fibres that are in contact with each other, the less friction there is holding them together. To make a yarn strong enough to use, or even to support the weight of the spindle, means we have to increase the friction by putting in a lot more twist – and that means spinning fast on a drop spindle, or using a supported spindle. On the other hand, lighter spindles are difficult to keep spinning long enough to put any significant amount of twist in heavy yarns.

Spindles are slowed down by three forces – friction from air particles, loss of kinetic energy to sideways movement if the spindle wobbles, and, more significantly, the force exerted by the yarn you’ve just spun trying to unwind itself. The thicker the yarn, the more fibres you are trying to wrap around each other, and the stronger that untwisting force will be; so to spin thicker yarns we need a spindle that can overcome that force. That is, a spindle with higher inertia. Because it takes more effort to slow or stop it, it will be able to spin for longer even with thick yarns.