Meeting times, textbook, homework, exam, grading policies
Written solutions, study groups, and plagarism.
Plan for what we'll cover this semester, and what will be learned.
Review mechanics from Physics 2170 or equivalent. For instance, in Halliday, Resnick, and Walker, look over Chapters 1 to 12.
In Taylor, read sections 1.1 and 1.2 for today, and 1.3 to 1.5 for Friday.
We will be studying classical mechanics in the Newtonian form this semester. Next semester's course (PHY6200, soon to be renumbered to PHY5210) will delve into the Langrangian form of mechanics and a bit of special relativity and Hamiltonian mechanics.
Classical mechanics is one of the oldest branches of physics, yet still an active area of research today. Even when not directly the focus of research, an understanding of classical mechanics is essential to the design of many devices. For instance, atomic force microscopes rely on changes to the vibration of a macroscopic tip, governed by classical mechanics, to sense the atomic level forces in a sample, governed by quantum mechanics.
Time, space (distance), and mass (weight) are quantities that we know from experience. We can sense the passage of time, we can observe distance, and we feel weight. Everyone has some understanding of these quantities before they begin the study of Physics.
Experience tells us that the motion of an object doesn't depend on our choice of how we measure the motion -- choice of starting point of measurement, unit of measurement, starting point in time, ... Nor does it depend on the direction of axes, when the motion occurs in more than one dimension. But we do know that displacement, velocity, and acceleration have both magnitude and direction. Mathematical objects with these same characteristics are vectors, making it an obvious choice to write the rules of mechanics in terms of vectors.
Vectors exist independently of a coordinate system, but for solving problems we normally need to express vectors in a particular coordinate system. In three dimensional space, a vector in a particular coordinate system is described by three numbers, the components of the system. For standard Cartesian coordinates, there are a number of equivalent notations for the three components of a vector: x-hat, y-hat, and z-hat; i, j, and k; e1, e2, e3; and (x,y,z). We will use these notations, depending on convenience. In the future we will also see notations for coordinate systems other than Cartesian, namely polar/cylindrical, and spherical coordinates.
Here we review the rules of vector algebra. Now we have two types of objects, vectors and scalars (plain numbers).
Vectors can be added and subtracted by adding or subtracting corresponding components. It is not allowed to add a vector and a scalar. Vectors can be multiplied by a scalar. In Cartesian coordinates, this is done by multplying each component by the scalar.
"Multiplying" two vectors can be done in either of two ways, one that yields a scalar and one that yields another vector. The scalar (or dot) product of two vectors yields a scalar, and is obtained by multiplying corresponding components and summing:
| | | i | j | k | | | |
| t = det | | | rx | ry | rz | | |
| | | sx | sy | sz | | |