Abstract
Clarity in physics requires precise definitions of terms, such as work and energy , that have fuzzy meanings in everyday usage. Some of the common terms and concepts (e.g. force , velocity , acceleration , momentum ) are thus introduced and defined, as an introduction to the material of later chapters, where they will be extensively utilized. Since the book is devoted to readers with only a basic background of mathematics, some of the necessary mathematical tools and concepts are also briefly explained.
[Ignorance] of the principle of conservation of energy … does not prevent inventors without background from continually putting forward perpetual motion machines… Also, such persons undoubtedly have their exact counterparts in the fields of art, finance, education, and all other departments of human activity… persons who are unwilling to take the time and to make the effort required to find what the known facts are before they become the champions of unsupported opinions—people who take sides first and look up facts afterward when the tendency to distort the facts to conform to the opinions has become well-nigh irresistible.
Robert Millikan
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Notes
- 1.
Modern calculus is considered to have been developed independently in the 17th century by Isaac Newton and Gottfried Leibniz.
- 2.
In most cases the laws of physics are expressed by means of differential equations, which means that the derivatives of the relevant functions are calculated keeping all variables fixed except the one of interest in the specific term.
- 3.
Approximately G = 6.673 × 10−11 N(m/kg)2.
- 4.
The possible variability of fundamental physical constants is discussed in Chap. 13.
- 5.
Occam’s razor is an epistemological principle, devised by William of Ockham (c. 1287–1347), which states that, among competing hypotheses that predict equally well, one should always select the one with the fewest assumptions. Other, more complicated solutions may ultimately provide better predictions, but, in the absence of differences in predictive ability, the fewer assumptions, the better.
- 6.
To be more precise, the derivative is the limit of the ratio Δf / Δt, when Δt tends to zero.
- 7.
If the function f depends not only on time (as in the example in the text) but also on other variables, such as the coordinates of the position where the function is evaluated, the derivative may be calculated as a partial derivative proceeding as illustrated in the text, but keeping all variables fixed with the exception of one of them. E.g., given a function f(x, y, z) of x, y and z, the partial derivative with respect to y is written \( w = \partial f/\partial y \).
- 8.
The other being Einstein’s E = mc 2 (see Chap. 7).
- 9.
E.g. D. Halliday, R. Resnick, J. Walker: Fundamentals of Physics, or Young, Freedman and Lewis Ford: University Physics with Modern Physics, or Douglas C. Giancoli: Physics for Scientists and Engineers with Modern Physics, as well as many others.
- 10.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular axes.
- 11.
F = m a = m d v/dt = (if m is constant) d(m v)/dt = d p/dt.
- 12.
Incidentally Lavoisier was guillotined during the French revolution, but not because of his sayings. Among his accusers there was an amateur chemist, Jean Paul Marat, whom Lavoisier had previously rejected as an associate to the Academy of Sciences.
- 13.
As the vectors are in opposite directions, the angle between them is 180°, which has a cosine of −1.
- 14.
Approximately g = 9.81 ms−2.
- 15.
From Animal Farm by George Orwell (1947) “All animals are equal, but some animals are more equal than others.”.
- 16.
By Sadi Carnot (1824) and Rudolf Clausius (1850), independently. It can be easily proved that the two formulations are equivalent.
- 17.
We discuss measurement errors and their sources in Chap. 3.
References
I. Newton, Philosophiæ Naturalis Principia Mathematica (“Mathematical Principles of Natural Philosophy”) (1687)
G. Galilei, Dialogue Concerning the Two Chief World Systems (1631)
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Barrett, R., Delsanto, P.P., Tartaglia, A. (2016). Dramatis Personae (The Actors). In: Physics: The Ultimate Adventure. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-31691-8_2
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