Newton's Laws

What underlying ideas or theories seem best able to organize the topic into some coherent whole? What are the most powerful, clear, and relevant theories, ideologies, metaphysical schemes, or meta-narratives?

The most powerful underlying idea or theory in this topic:
Newton's Laws represent one of the clearest examples of what the philosopher Thomas Kuhn calls a "paradigm shift." By reducing all of dynamics to three simple laws based around the principle of force, Newton overturned a number of basic assumptions about the workings of the cosmos. Some of these assumptions, most notably Aristotle's law of inertia, linger unconsciously with us still. We can appreciate the significance of Newton's Laws by grasping just how revolutionary and counter-intuitive they are.

An alternative:
Newton's three laws all focus on the idea of force. With this one concept, which applies identically in all its diverse applications, Newton replaced a far more heterogeneous conception of dynamics. This achievement does not only make scientific reasoning simpler. When we see a single, unifying principle at work in phenomena that we had hitherto thought of as totally unrelated, our overall understanding of the cosmos changes. A cosmos governed by force is very different from the convoluted cosmos imagined by medieval scholars.

Another alternative:

Newton has been credited with bringing about a "mathematization of nature." His three laws--the second law in particular--make it possible for us to express our observations of natural phenomena in mathematical terms. Thanks to Newton, we can perceive a world of numbers and formulae running parallel to the world we observe of sights and sounds. Newton's laws provide the key to the door between these two worlds, allowing us to enrich our understanding of the perceptible world with the world of mathematics that lie behind it.

Content that exposes the scheme or theory most vividly:
The idea of a paradigm shift may not be familiar to students, and while a close reading of Kuhn is hardly necessary for this unit, it might help students to introduce them to the idea of a paradigm shift. We might begin by brainstorming examples of times that we've changed our minds about something. We might investigate what prompted us to change our minds, whether it was difficult or easy to change our minds, and what underlying beliefs, convictions, or assumptions remained unchanged through this process of changing our minds. By highlighting this last question, we can draw out the distinction between a paradigm shift and a simple matter of changing one's mind about something by reference to the depth of the beliefs that are changed. What would be necessary to shift our core beliefs? How would we adjust to this change? What resistances might we have to overcome in order to embrace it fully?

Lay out the content that will present a strong meta-narrative of the topic:
The importance of Newton's Laws becomes all the more apparent when we consider them in the context of their historical achievement. We can better appreciate the importance of Newton's Laws if we understand the medieval conception of dynamics that Newton replaced. In this context, Newton emerges as a revolutionary figure who changed the world through the clarity of his perception, rather than simply as a starting point for the study of physics.

Newton was the first to show, with his theory of gravitation, that the dynamical laws that govern the movement of the heavens are identical to the dynamical laws that govern the sublunary sphere. In so doing, he was the first to show that all observable phenomena can be classed under a single set of laws. We might want to consider how our understanding of the cosmos would be different if we believed that there was more than one set of scientific principles at work. By asserting that there are certain regularities that apply to everything in the cosmos, the laws of physics replace God at the primary engine of change. It's worth recalling the Newton was himself a devout Christian, and that he adamantly denied that his laws of motion refute the existence of God. However, Newton's Laws did transform God from a willful miracle worker to a "divine watchmaker" who set all things to work according to a set of regularities that He ordained.

Newton's laws of motion also overturned the Aristotelian conception of inertia, according to which the natural state of bodies is rest. According to Aristotle, objects in motion will tend toward rest unless there is a constant force acting upon them. It might be worth impressing upon students that most of us tend to assume that this is how force works even now. It might be worth challenging them to accept that, whatever they've learnt from physics class, their natural inclination is probably still in favor of Aristotle. If we can appreciate just how odd it sounds to assert that objects will move with a constant velocity in the absence of a net force acting on them, we can appreciate how remarkable it is that Newton made this discovery, and without the aid of NASA videos of astronauts living in zero gravity environments. Once we appreciate the paradigm shift involved in moving from an Aristotelian to a Newtonian conception of inertia, we can consider how such a shift changes our conception of the cosmos. A cosmos where everything tends toward rest is very different from a cosmos where steady velocity is the norm, and things only come to rest through the application of a net force.

List the major tools necessary for the analysis and explain their pertinence:
Newton's Laws are deceptively simple. An elementary school student could perform the mathematical calculations required by the Second Law, and the first and third are really just easily grasped procedural principles. Consequently, it is rather surprising how easy it is to come up with problems, which involve nothing more than these three rules, and yet which stump all but the brightest students.

The reason is twofold. First, it is a tribute to the brilliant simplicity of Newton's Laws that they can be used to solve complicated pulley problems and the like without reference to any further principles. Newton's Laws themselves may be simple, but they are sufficiently powerful to tackle some very tricky problems unaided. Second, students often slip up, in particular with regard to the first and third laws, because they haven't fully grasped the Newtonian paradigm. For example, it can be tricky to get our minds around the idea that we are able to move forward when we walk because the earth pushes us forward while we push it back. Just as we cannot move about in a dinghy without jostling the dinghy, so we cannot move about on the earth without jostling the earth. If we don't notice that, it's just because the earth is much bigger than a dinghy. Coming to terms with the fundamental ideas, like that the earth is not fixed beneath our feet, require a tremendous shift in our thinking. We may assume that Newton and his laws are old hat, but even four hundred years later they can be awfully difficult to come to terms with. By reinforcing the counterintuitive genius of Newton's Laws as we familiarize students with them, we can induce a sense of wonder and a preparedness to rethink assumptions, which will be essential if we are to learn to apply Newton's Laws with confidence.

List the main problems raised by the general idea or theory that cannot be solved with the tools at hand, and indicate what further tools might help:

There are a number of directions we can take in exploring the limitations in the paradigm of Newton's Laws. Since a unit on Newton's Laws is typically followed by a unit on work, energy, and power, we might want to explore how these further concepts will be necessary in order to solve certain problems dealing with potential and kinetic energy, not to mention the more general problem of explaining where force comes from.

We can also point out that Newton's Laws only explain force in the most general sense. We need further principles, such as Hooke's Law or Coulomb's Law or Newton's on Law of Gravitation, to explain how various forces manifest themselves. When introducing these further laws, it might be worth showing how they work in tandem with Newton's Second Law. The solution to many problems require two separate equations for force, so we can solve them by using Newton's Second Law in conjunction with a more particular law.

While students being introduced to Newton's Laws will probably not yet be ready to move on to modern physics, it might be worth giving relativity and quantum physics a mention as a further example of a paradigm shift. While Newton overturned old ways of thinking, his own paradigm was itself overturned in the early twentieth century. Hard as it might be to come to terms with the worldview embodied in Newton's Laws, we can assure students that it will be even more mystifying trying to come to terms with the worldview of modern physics.

Coming to appreciate the power of paradigms, as well as the significance in paradigm shifts can impact the lives of adolescents on a number of levels. There is an obvious parallel between the idea of a paradigm shift and the changes adolescents experience in the transition from childhood to adulthood. By developing a conceptual apparatus that makes sense of paradigms and paradigm shifts, students might vicariously develop a conceptual apparatus that gives them a stronger sense of control and agency on the dramatic changes in their own lives.

By this time, students have presumably gathered a sense of what a paradigm shift is, and why this concept applies so emphatically to Newton's Laws. Though we have shown that these laws overturn Aristotle's law of inertia and the assumed distinction between the heavens and the sublunary sphere, it might be worth reflecting on just how different a Newtonian worldview is. It might be a fun challenge to brainstorm different ways in which the world would be different if we still held a pre-Newtonian conception of dynamics. What sorts of phenomena in the modern world would pose a serious challenge to a pre-Newtonian paradigm?

Newton's Laws are not heavy on mathematics, and while it is important to make sure students can apply the Second Law correctly, the bulk of the content is primarily conceptual. To return to the example cited above, it's not so important that students can calculate precisely the acceleration with which they push the earth backwards with every step they take forwards (though this could be a fun exercise), but rather that they get their minds around the idea that they are indeed pushing the earth backwards, and that this is their means of locomotion. To this end, it is worth investing some time into developing some conceptually challenging problems. As much as pulley problems can reinforce the basic principles of Newton's Laws, they do not convey the shift in thinking required by Newton's Laws to the same extent as a problem dealing with how we push the earth backward when we walk, or with what would happen if we tried pushing a box forward while standing on a frictionless surface. We might even want to challenge students to develop their own examples of problems that exemplify the sort of counter-intuitive thinking required by Newton's Laws.