Explaining the world

A large number of ants behaving as a liquid, and as a solid.

The job of a physicist is to find simple rules that predict the things that happen in the world around us. From the size of avalanches and forest fires, to the shape of red blood cells, to the flow of traffic in cities, all of these things can be explained by simple rules and principles that govern the dynamics of nature. Once we can explain the world around us, we can attempt to change it by turning these principles around and using them to design things like electric cars, or rockets, or hydroelectric dams. In this gentle introduction to mechanics, you'll be exposed to some interesting phenomena in the world around us, and asked to explain how or why they happen. Although these are elementary examples, they encapsulate the essential experience of doing real physics research. Here are some tips to get started.

• Try to make your question as crisp as you can in your head, and strip it down as much as you can without throwing away essential details.
• If your question overwhelms you, try to simplify it.
• Use your intuition and understanding of other processes to reason about the one at hand.
• Use extreme cases to help rule out incorrect solutions.

When you spin a cup of tea, the leaf particulate at the bottom tends to come together at the center of the cup. Why is that?

The spinning of the liquid in the cup sets up a circular motion. In order to maintain circular motion, there must be a force pushing the liquid toward the center of the cup (think of how when you go around a turn in the car, either the seat belt of the wall of the car strongly pushes you toward the center of the turn). This is accomplished by a gradient of pressure that increases from the center of the cup toward the outer rim. Particles at the bottom of the cup are slowed by the friction of dragging along the surface, and thus the force they feel from the pressure gradient exceeds what's needed to keep them on a circular path. This causes the pressure gradient to push them toward the center of the cup until they reach the middle (where they feel no pressure), where they stop.

I would hint reformulating the question: why is the setting [in which the leaf particles are near the center and the liquid particles are farther from the axis of the spinning] at a lower energy level than the opposite setting, where the leaf and liquid particles swap place? The leaf's being at the bottom means/is because the density of the leaf > the density of the liquid. The total energy stored in the spinning of the (leaf+liquid) whole system is lower if the higher density particles are closer to the axis and the lower density particles are farther from the axis. That is why what was at the bottom, moves closer to the center=axis when spun. And similarly, what floats on the surface (e.g. foam, cream), moves towards the rim. Does it depend on whether the particles are accelerating, spinning with a constant speed, or slowing down?

The pressure gradient is fixed, does not depend on whether the leaf or the liquid is at the rim. Every particle suffers the centrifugal force, the only question is who is more averse. It is a relative question, you cannot give an absolute explanation, which holds for every particle, no matter whether leaf or liquid. It would not distinguish them. You need to refer to some aspect in which the parties are different. Could we make it clear that it is the friction coefficient (between the leaf or liquid particles and the bottom of the cup) that determines which particles are at the center/rim? Is density also a factor? Is friction or density the stronger factor? On the surface there is another friction (between the particles and the air). Where will the leaf particles be if the spinning happens when they are sinking, halfway between the surface and the bottom?

One of the best features of physics is the universality of the principles. Mechanisms identified in the dynamics of quantum fields can very well be applied to problems in materials science. Nonetheless, we can broadly classify the kinds of things we'll study in mechanics.

• Particles: Point particles are an essential fiction in mechanics. With good justification, they allow us to represent objects by a point at its center of mass. Though an obvious simplification, particles greatly simplify our mathematical reasoning and end up being a pretty faithful representation. Great progress has been made by characterizing the behavior of particles which can then be applied to extended bodies. Explore the range of particle motions in Newton's laws, rocket physics, and the Lagrangian formulation of mechanics.
• Fields: While particles are familiar to everyday experience, fields are what govern the interaction of particles and provide for the interesting dynamics in the world around us. A simple example is the gravitational field which arises from the intrinsic mass of a given object. When you jump into the air, what brings you back to the ground is the gravitational field of Earth. Remarkable, the same field also governs the motion of the planets. Start to find out more about fields and how they shape the motion of matter in Gravitation, magnetic field lines , deriving Kepler's laws, and charge, and electric fields .
• Conservation laws: Physics would be very hard if all there were was particles and fields. Mathematical analysis often becomes intractable in physics, and it can even be the case that choosing the wrong way to look at a problem will make the difference between it being easy, or impossible. Happily, there are deep principles buttressing the structure of physics which state that certain things must always be conserved. It is often the case that we can shortcut very tedious calculation by appealing to these conservation principles. Get started with conservation of energy, and conservation of momentum.