Physics 16 is an introduction to mechanics at the level of Newton's laws of motion. We will present Newton's laws within the first three weeks of the course and apply them to standard phenomena of introductory mechanics: pulleys, ropes, springs, levers, friction and inclined planes. We will develop concepts and techniques to solve more challenging mechanics problems; chief among these techniques are the conservation laws of energy, momentum, and angular momentum. We will learn when these quantities are conserved and how to use conservation laws to simplify mechanics problems.
Many of the concepts introduced in Physics 16 will be important in other contexts; an understanding of energy, power, force, work and momentum is critical to every subsequent physics course, to chemistry, geology, and astronomy, and to small-scale (molecular) and large-scale biology (ecology).
Newton's laws are most easily understood using calculus, and we will frequently refer to concepts, such as derivatives and integrals, from calculus. An understanding of calculus is important, and a solid grasp of trigonometry is critical. However, this is not a math class: we will distinguish between physics (writing down a self-consistent set of equations that uniquely define the important properties of a system) and math (solving those equations); the former is important, while the latter is a chore. We will discuss the difference between a mathematical solution and the physically allowed portions of that solution.
The methods we develop could, in principle, be used to solve very complex problems, but the math becomes prohibitively tedious and time-consuming. Most problems we encounter will involve, at worst, piecewise constant acceleration. At the end of the course we will encounter situations requiring non-constant accelerations: periodic motion of a mass and of a wave. Time permitting, we will see how Kepler's laws of planetary motion – the culmination of centuries of inquiry – are nothing more than a special case of Newton's laws with a particular force field.
The lecture portion of the course will focus primarily on problem solving. Exams will be effectively small, timed problem sets. The lab portion will apply the concepts from lecture to real situations, where dropped factors of two will become blindingly obvious. We will discuss measurement error and develop formal techniques for error propagation.