Prerequisites/Corequisites

A hard corequisite for this class is calculus, typically AP Calculus BC. We will require use of derivatives and integrals, and will also require you to be comfortable applying trigonometry, geometry, and algebra, including potentially some linear algebra. If your math skills are rusty or weak, you will want to be reviewing these or you risk falling behindWe will be applying derivatives and integrals early in the class, possibly a little in advance of when the fully mathematically rigorous details are covered in your calculus class. I will try to do this as gently as possible. You will probably find that taking physics together with calculus reinforces your learning of both; calculus was invented, in part, to make mechanics more sensible.

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Instructor and general schedule

The instructor is Dr Evangelista, Room G201, devangelista@frhsd.com

The course meets period 1 or period 3, with labs during period 4.

Dr Evangelista also teaches AP Physics C E&M afternoons on Monday, Wednesday, and Friday; and S&E Senior Projects on Tuesady and Thursday afternoons. He is available for extra help before school, during lunch and after school by appointment, period 2, and sometimes during period 4 when it is not a lab period.

Science and engineering

Engineering is possibly the easier field to wrap our heads around. Engineers build stuff, or more precisely, when people have some problem they need a solution for, engineers go and develop devices or processes or systems to solve the problem. They have been doing so since the first stone hand axes grasped by our hominid ancestors. Engineers built the pyramids and the Great Wall of China, the space shuttle, the P-51 Mustang, the rocket stove and the labubu. They obviously must use science, but they also use art and the human skills needed to understand what peoples’ needs are and how to balance competing design requirements. Physics, as a science of how stuff works, and mechanics, as a science of how things move, deform or deflect, inform engineers how the structures they make will work int he real world under real loads and use cases. For engineers, the application is king (or queen).

If that’s what engineers do, what do scientists do? Professor Tom Daniel at University of Washington would argue that scientists are there to answer questions. Specifically, Tom would say, “when sh#t happens, we need scientists to figure out answers”. They apply a method where questions are answered by posing testable hypotheses, eliminating what is not true, and provisionally accepting things that are not eliminated. In this way, science works to eliminate what is demonstrably false from our body of knowledge. It is around because it works; it leads to better, more “true” descriptions of the world we live in. Science may often have an application, but it need not; all it requires is that we have a question we are curious about and that we use the scientific method. The word science comes from scientia, Latin for knowledge or knowingsee USNA motto, Ex scientia tridens, “from knowledge, sea power”.

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The two together are a powerful pair. Science is a knowledge production engine that workscompared to explaining, say, a lunar eclipse as the bagging of a koi fish in a north pole spirit oasis, or the relationship of the earth to the sky as that of earth mother and sky father, and so on. Such stories have artistic value but not much explanatory power.

. Engineering uses science to solve problems. When science is coupled with engineering and the human drive to understand fellow humans problems and solve them, there is little the two cannot accomplish.

Physics in context of other sciences

How does physics fit in contextSee https://www.youtube.com/watch?v=YvtCLceNf30

of other sciences you have studied?

In biology your freshling year, you examined the diversity of life from molecules to ecosystems. The guiding question here was, “what is life?” We saw organization across many scales on many orders of magnitude, we saw diversity, we saw flows of energy, nutrients, and information across deep time, and hopefully it helped to contemplate how humans fit. Under all of that, evolution was the preeminent organizing principle to understand biology, written across 4 billion years of the history of life on earth. For students, this was a single big question with a single organizing principle (evolution) where you had to learn broadly across many concepts and domains the particulars of various patterns synthesized to understand the whole.

In chemistry, things were a little different. We started to take an approach, which we will continue in physics, where we try to understand the whole by peering at great detail into the parts. In chemistry we wanted to understand, “what is stuff?” Water, earth, fire, airMy brother and I discovered a new avatar, an airbender named Aang.

? Or are things made of atoms from a set of elements? For students, this was an introduction to a reductionist approach, and perhaps also a deeper introduction to applying math and testing ideas quantitatively.

What is the underlying question in physics? Some branches of physics take on “what is stuff” by delving deeper, breaking atoms to see what they are made of, and so on. Another deep underlying question, perhaps most relevant to our study of mechanics, is “where (and when) are we?” How can we describe where we are, and where other things are, and how all of it moves in response to forces, gravity, momentum, and energy; how do these change over time; and ultimately, what is the nature of space-time itself. Before we can delve in the deepest questions of relativity, however, it might be nice to start with the simplest descriptions of moving objects, thus we arrive at classical mechanics.

Additional relevant thoughts for physics

“All models are wrong, some are useful.”Attributed to British statistician George P Box, see https://en.wikipedia.org/wiki/All_models_are_wrong

We will try to proceed from simple to more complicated, looking for models that are complex enough to explain phenomena we are interested in but no more complicated than thatSee also https://en.wikipedia.org/wiki/Occam%27s_razor

. Einstein suggested everything should be made as simple as possible, but no simplerEinstein, A. 1934. On the Method of Theoretical Physics. University of Chicago Press. Excerpt at https://www.informationphilosopher.com/solutions/scientists/einstein/Method_of_Theoretical_Physics.pdf

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If we hit a problem we do not know how to solve, we will also take a divide and conquer approach. We will try to decompose a hard problem into smaller, more solveable subproblems.

Mechanics for translational systems

The first part of our studies will deal with translational systems, ones that are moving along a straight line in one dimension, or perhaps ones that are moving in two or three dimensions. The objects we will deal with will be simplified to be point masses and we will deal with measuring and mathematically modeling their position, velocity, acceleration, momentum, and kinetic and potential energy in various situations. If you have ever wondered the movement of a roller coaster or freefall ride, a ping pong ball, the jump of a talitrid amphipod in a tidepool, or what would happen if you threw a newly hatched baby bird, they are described easily by such models. The models are built using calculus, and it is here where we will first apply the ideas of derivatives and integrals.

Mechanics for rotational systems

After we have covered translational systems, we will extend our ideas to rotational systems where the mass is distributed in space rather than at a single point, and where spinning is important, as in a gyroscope, a rifle bullet, a drum major’s baton, or a planet. We will find that in these systems too, there are notions of angular position, angular velocity, angular acceleration, angular momentum, and energy. Combining these with what we learn for translational systems will allow use to apply physics to describe a wider range of motions, situations, and devices.

Simple harmonic motion

Systems that oscillate trade energy back and forth between potential and kinetic energy. The vibrations that result are important in a wide range of phenomena and devices, we will examine two easy cases of simple harmonic motion (simple pendulum and mass-spring oscillator) and look at our first solutions of the differential equations of motion describing these systems. We will also extend these notions to a non-ideal physical pendulum, and think about how what we learn might apply to other systems. If you were to continue in physics or an engineering major, these concepts become important in waves and vibrations, in parts of electrical circuits, in the propagation of waves through waveguides, channels, antennas, and media, and so on.

1. Kinematics

The first unit will be kinematics, the mathematical study of motion. We will use vectors to model the position, velocity, and acceleration of objects moving in 1-, 2-, or 3-dimensions. We will also look at circular motion. We will introduce the ideas of the derivative and integral relationships between kinematic variables.

2. Forces

Next we will examine force; force applied to a mass results in accelerationYou might have heard of Newton’s second law of motion, \(\sum{\vec{F}}=m\vec{a}\).

. This unit will cover Newton’s laws of motion. The canonical forms of various types of force will be introduced, such as friction, spring forces, drag forces, gravity and weight, buoyancy, etc. The ideas introduced here are fundamental to fields such as statics in mechanical and civil engineering.

3. Energy

We will introduce energy and work; expressions for kinetic and potential energy in simple mechanical systems; and the conservation of energy. In combination with kinematics and Newton’s laws, energy conservation and energy methods in general provide another tool to develop equations describing physical systems that is often much quicker and easier to use depending on the situation.

4. Momentum

Momentum, the product of mass and velocity, is another quantity that is conserved in the absence of external forces. In some systems, notably collisions, momentum provides an easier way to analyze the interactions that happen. Momentum and impulse are useful in explaining a wide range of everyday phenomena; the ideas are also central to understanding certain propulsion systems such as jets, rockets, propellers and rotors, etc.

5. Rotational motion

The ideas we developed about position, velocity, and acceleration will be applied to rotating systems such as gyros, wheels, batons, or any spinning object where the mass is not all concentrated at a single point, but is instead a rigid body. Along with mass we will need to consider the moment of inertia (a measure of how centrally distributed the mass is), and we will need to extend the concept of force to include torque or moment.

6. Angular momentum and energy in rotational systems

Along with angular position, angular velocity, and angular acceleration, we will find the angular momentum and energy associated with rotating systems and use these to solve more complicated problems, up to and including the orbits of planets and satellites.

7. Simple harmonic motion

We will introduce vibration and simple harmonic motion by examining two systems, a simple pendulum and a mass-spring oscillator, looking at the interchange between potential and kinetic energy and solving simple second order differential equations of motion. This is the final topic covered on the AP test.