By Leonard Susskind, George Hrabovsky
ISBN-10: 046502811X
ISBN-13: 9780465028115
A world-class physicist and a citizen scientist mix forces to coach Physics 101—the DIY way
The Theoretical Minimum is a ebook for an individual who has ever regretted no longer taking physics in college——or who easily desires to know the way to imagine like a physicist. during this unconventional advent, physicist Leonard Susskind and hacker-scientist George Hrabovsky provide a primary path in physics and linked math for the ardent novice. in contrast to most well-liked physics books—which provide readers a style of what physicists comprehend yet shrink back from equations or math—Susskind and Hrabovsky really train the talents you want to do physics, starting with classical mechanics, your self. in keeping with Susskind’s greatly well known Stanford University-based (and YouTube-featured) continuing-education path, the authors conceal the minimum—the theoretical minimal of the title—that readers have to grasp to check extra complicated topics.
An substitute to the traditional go-to-college approach, The Theoretical Minimum offers a device equipment for newbie scientists to benefit physics at their very own speed.
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Extra resources for The Theoretical Minimum: What You Need to Know to Start Doing Physics (Theoretical Minimum, Book 1)
Sample text
But the two coordinates are 90° out of phase; when x is maximum y is zero, and vice versa. The most general (counterclockwise) uniform circular motion about the origin has the mathematical form R cos Ω t R sin Ω t. x t yt Here the parameter Ω is called the angular frequency. It is defined as the number of radians that the angle advances in unit time. It also has to do with how long it takes to go one full revolution, the period of motion—the same as we found in Exercise 6: T 2Π Ω Now it is easy to calculate the components of velocity and acceleration by differentiation: vx vy ax ay R Ω sin Ω t R Ω cos Ω t R Ω2 cos Ω t R Ω2 sin Ω t (3) This shows an interesting property of circular motion that Newton used in analyzing the motion of the moon: The acceleration of a circular orbit is parallel to the position vector, but it is oppositely directed.
For this purpose, we can ignore the z axis and think of the motion in the x, y plane. To describe it we must have two functions, x t and y t . To be specific we will choose the particle to move in the counterclockwise direction. Let the radius of the orbit be R. It is helpful to visualize the motion by projecting it onto the two axes. As the particle revolves around the origin, x oscillates between x R and x R. The same is true of the y coordinate. But the two coordinates are 90° out of phase; when x is maximum y is zero, and vice versa.
We can graph these functions to see how they vary (see Figures 8 through 10). Spaces, Trigonometry, and Vectors 21 We can graph these functions to see how they vary (see Figures 8 through 10). sin Θ 1 Π 2 Π 3Π 2 Θ 2Π 1 Figure 8: Graph of the sine function. cos Θ 1 Π 2 Π 3Π 2 Θ 2Π 1 Figure 9: Graph of the cosine function. tan Θ Π 2 Π 3Π 2 Θ 2Π Figure 10: Graph of the tangent function. There are a couple of useful things to know about the trigonometric functions. The first is that we can draw a triangle within a circle, with the center of the circle located at the origin of a Cartesian coordinate system, as in Figure 11.
The Theoretical Minimum: What You Need to Know to Start Doing Physics (Theoretical Minimum, Book 1) by Leonard Susskind, George Hrabovsky
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