Base Units in SI Help (page 3)
Introduction to Base Units in SI
In all systems of measurement, the base units are those from which all the others can be derived. Base units represent some of the most elementary properties or phenomena we observe in nature.
The fundamental unit of distance, length, linear dimension, or displacement (all different terms meaning essentially the same thing) is the meter, symbolized by the lowercase nonitalicized English letter m. Originally, the meter was designated as the distance between two scratches on a platinum bar put on display in Paris, France. The original idea was that there ought to be 10 million (10 7 ) meters along a great circle between the north pole and the equator of Earth, as it would be measured if the route passed through Paris (Fig. 6-1). Mountains, bodies of water, and other barriers were ignored; the Earth was imagined to be a perfectly round, smooth ball. The circumference of the Earth is about 40 million (4.0 × 10 7 ) m, give or take a little depending on which great circle around the globe you choose.
Fig. 6-1 . There are about 10 million meters between the Earth’s north pole and the equator.
Nowadays, the meter is defined more precisely as the distance a beam of light travels through a perfect vacuum in 3.33564095 billionths of a second, that is, 3.33564095 × 10 −9 second. This is approximately the length of an adult’s full stride when walking at a brisk pace.
The base SI unit of mass is the kilogram, symbolized by the lowercase non-italicized pair of English letters kg. Originally, the kilogram was defined as the mass of 0.001 cubic meter (or 1 liter) of pure liquid water (Fig. 6-2).
This is still an excellent definition, but these days scientists have come up with something more absolute. A kilogram is the mass of a sample of platinum-iridium alloy that is kept under lock and key at the International Bureau of Weights and Measures.
It is important to realize that mass is not the same thing as weight . A mass of 1 kg maintains this same mass no matter where it is located. That standard platinum-iridium ingot would mass 1 kg on the Moon, on Mars, or in intergalactic space. Weight, in contrast, is a force exerted by gravitation or acceleration on a given mass. On the surface of the Earth, a 1-kg mass happens to weigh about 2.2 pounds. In interplanetary space, the same mass weighs 0 pounds; it is weightless .
The SI unit of time is the second, symbolized by the lowercase nonitalicized English letter s (or sometimes abbreviated as sec). It was defined originally as 1/60 of a minute, which is 1/60 of an hour, which in turn is 1/24 of a mean solar day . A second was thus thought of as 1/86,400 of a mean solar day, and this is still an excellent definition (Fig. 6-3). However, formally, these days, 1 s is defined as the amount of time taken for a certain cesium atom to oscillate through 9.192631770 × 10 9 complete cycles.
One second also happens to be the time it takes for a ray of light to travel 2.99792458 × 10 8 m through space. This is about three-quarters of the way to the Moon. You may have heard of the Moon being a little more than one light-second away from Earth. If you are old enough to remember the conversations Earth-based personnel carried on with Apollo astronauts as the astronauts walked around on the Moon, you will recall the delay between comments or questions from earthlings and the replies from the moonwalkers. The astronauts were not hesitating; it took more than 2 seconds for radio signals to make a round trip between Earth and the Moon. In a certain manner of thinking, time is a manifestation or expression of linear dimension, and vice versa. Both of these aspects of nature are intimately related by the speed of light, which Albert Einstein hypothesized is an absolute.
The SI unit of temperature is the kelvin, symbolized K (uppercase and nonitalicized). It is a measure of how much heat exists relative to absolute zero, which represents the absence of all heat and which is therefore the coldest possible temperature. A temperature of 0 K represents absolute zero. Formally, the kelvin is defined as a temperature increment (an increase or decrease) of 0.003661 part of the thermodynamic temperature of the triple point of pure water. Pure water at sea level freezes (or melts) at + 273.15 K and boils (or condenses) at + 373.15 K.
What, you might ask, is the meaning of triple point? In the case of water, it’s almost exactly the same as the freezing point. For water, it is the temperature and pressure at which it can exist as vapor, liquid, and ice in equilibrium. For practical purposes, you can think of it as freezing.
The ampere, symbolized by the uppercase nonitalicized English letter A (or abbreviated as amp), is the unit of electric current. A flow of approximately 6.241506 × 10 18 electrons per second past a given fixed point in an electrical conductor produces an electrical current of 1 A.
Various units smaller than the ampere are often employed to measure or define current. A milliampere (mA) is one-thousandth of an ampere, or a flow of 6.241506 × 10 15 electrons per second past a given fixed point. A microampere (μA) is one-millionth or 10 −6 of an ampere, or a flow of 6.241506 × 10 12 electrons per second. A nanoampere (nA) is 10 −9 of an ampere; it is the smallest unit of electric current you are likely to hear about or use. It represents a flow of 6.241506 × 10 9 electrons per second past a given fixed point.
The formal definition of the ampere is highly theoretical: 1A is the amount of constant charge-carrier flow through two straight, parallel, infinitely thin, perfectly conducting media placed 1 m apart in a vacuum that results in a force between the conductors of 2 × 10 −7 newton per linear meter. There are two problems with this definition. First, we haven’t defined the term newton yet; second, this definition asks you to imagine some theoretically ideal objects that cannot exist in the real world. Nevertheless, there you have it: the physicist venturing into the mathematician’s back yard again. It has been said that mathematicians and physicists can’t live with each other and they can’t live without each other.
The candela, symbolized by the lowercase nonitalicized pair of English letters cd, is the unit of luminous intensity. It is equivalent to 1/683 of a watt of radiant energy emitted at a frequency of 5.4 × 10 14 hertz (cycles per second) in a solid angle of one steradian. (The steradian will be defined shortly.) This is a sentence full of arcane terms! However, there is a simpler, albeit crude, definition: 1 cd is roughly the amount of light emitted by an ordinary candle.
Another definition, more precise than the candle reference, does not rely on the use of derived units, a practice to which purists legitimately can object. According to this definition, 1 cd represents the radiation from a surface area of 1.667 × 10 −6 square meter of a perfectly radiating object called a blackbody at the solidification temperature of pure platinum.
The mole, symbolized or abbreviated by the lowercase nonitalicized English letters mol, is the standard unit of material quantity. It is also known as Avogadro’s number and is a huge number, approximately 6.022169 × 10 23 . This is the number of atoms in precisely 0.012 kg of carbon-12, the most common isotope of elemental carbon with six protons and six neutrons in the nucleus.
The mole arises naturally in the physical world, especially in chemistry. It is one of those strange numbers for which nature seems to have reserved a special place. Otherwise, scientists surely would have chosen a round number such as 1,000, or maybe even 12 (one dozen).
A Note About Symbology
Up to this point we’ve been rigorous about mentioning that symbols and abbreviations consist of lowercase or uppercase nonitalicized letters or strings of letters. This is important because if this distinction is not made, especially relating to the use of italics, the symbols or abbreviations for physical units can be confused with the constants, variables, or coefficients that appear in equations. When a letter is italicized, it almost always represents a constant, a variable, or a coefficient. When it is nonitalicized, it often represents a physical unit. A good example is s, which represents second, versus s , which is often used to represent linear dimension or displacement.
From now on we won’t belabor this issue every time a unit symbol or abbreviation comes up. But don’t forget it. Like the business about significant figures, this seemingly trivial thing can matter a lot!
Practice problems of these concepts can be found at: Units And Constants Practice Test
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