![]() For example, the length of a race, which is a physical quantity, can be expressed in units of meters (for sprinters) or kilometers (for distance runners). Measurements of physical quantities are expressed in terms of units, which are standardized values. For example, we define distance and time by specifying methods for measuring them, whereas we define average speed by stating that it is calculated as distance traveled divided by time of travel. We define a physical quantity either by specifying how it is measured or by stating how it is calculated from other measurements. And we shall find that (even in the potentially mundane discussion of meters, kilograms, and seconds) a profound simplicity of nature appears-most physical quantities can be expressed as combinations of only four fundamental physical quantities: length, mass, time, and electric current. To comprehend these vast ranges, we must also have accepted units in which to express them. Giving numerical values for physical quantities and equations for physical principles allows us to understand nature much more deeply than does qualitative description alone. From the incredibly short lifetime of a nucleus to the age of the Earth, from the tiny sizes of sub-nuclear particles to the vast distance to the edges of the known universe, from the force exerted by a jumping flea to the force between Earth and the Sun, there are enough factors of 10 to challenge the imagination of even the most experienced scientist. The range of objects and phenomena studied in physics is immense. Figure 1.15 The distance from Earth to the Moon may seem immense, but it is just a tiny fraction of the distances from Earth to other celestial bodies.
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