Fundamentals of Mechanics/Units and Vectors/SI Units

Introduction Conversion Factors A physical quantity is a quantitative description of a physical phenomenon. For a precise description, one has to measure the physical quantity and represent this measurement by a number. Such a measurement is made by comparing the quantity with a standard; this standard is called a unit. For example, mass is a physical quantity that refers to the quantity of matter contained in an object. The kilogram is one of the units used to measure mass and, until 2019, was defined as the mass of a specific platinum–iridium alloy cylinder, kept at the International Bureau of Weights and Measures. (In 2019, the kilogram was redefined to be in terms of precisely measured and defined fundamental constants, an in-depth discussion of which is beyond the scope of this book.) Therefore, when we say that a block’s mass is 300 kg, we mean that it is 300 times the reference definition. All units chosen should obey certain properties such as being accurate, accessible, and should remain stable under varied environmental conditions or time. (The 2019 redefinition of the kilogram addressed this last point specifically, as the reference prototype did change in mass very slightly over its 130 year history.) table 1.1Table 1.1 The SI system's seven fundamental base units Quantity Unit Name Unit Symbol length meter m mass kilogram kg time second s temperature kelvin K electric current ampere A luminous intensity candela cd amount of substance mole mol In 1960, the International System of Units was established. Its abbreviation, SI, is derived from its French name Système international d'unités. As shown in Table 1.1, the SI system consists of seven fundamental base units, each representing a quantity assumed to be naturally independent. The system also includes two supplementary units: the radian, which is a unit of the plane angle, and the steradian, which is a unit of the solid angle. All other quantities in physics are derived from these base quantities. For example, mechanical quantities such as force, velocity, volume, and energy can be derived from the fundamental quantities length, mass, and time. Furthermore, powers of ten are used to represent the larger and smaller values for a certain physical quantity as listed in Table 1.2. The most recent definitions of the SI units of time, length, and mass, each depend on defining a particular fundamental constant to be an exact value. Those definitions are as follows: table 1.2Table 1.2 Prefixes for powers of ten Factor Prefix Symbol Factor Prefix Symbol 10−30 quecto- q 1030 quetta- Q 10−27 ronto- r 1027 ronna- R 10−24 yocto- y 1024 yotta- Y 10−21 zepto- z 1021 zetta- Z 10−18 atto- a 1018 exa- E 10−15 femto- f 1015 peta- P 10−12 pico- p 1012 tera- T 10−9 nano- n 109 giga- G 10−6 micro- µ 106 mega- M 10−3 milli- m 103 kilo- k 10−2 centi- c 102 hecto- h 10−1 deci- d 101 deka- da The second is defined to be the amount of time elapsed during precisely 9 192 631 770 hyperfine transitions of a cesium-133 atom in its ground state, at rest, and at a temperature of 0 K. The meter is defined to be the distance that light travels in a vacuum during one 299 792 458th of a second. This is done by fixing the value of the speed of light in a vacuum to be precisely 299& 792 458&m/s (along with the definition of the second above). The kilogram is defined by fixing the value of a third fundamental constant, the Planck constant, to be precisely 6.626 070 15 × 10−19 J·s, the dimensions of which are equivalent to kg m2/s (along with the definitions of the second and the meter above). The details of how these units are defined and how their corresponding fundamental constants are measured are well beyond the scope of this text. However, the important thing to note here is that these definitions are precisely defined, accurate, and should remain stable for the foreseeable future.