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1-1 - 1-2 Physics and the Laws of Nature & Units of Length, Mass, and Time The study of physics deals with the fundamental laws of nature and many of their applications. These laws govern the behavior of all physical phenomena. We describe the behavior of physical systems using various quantities that we create for this purpose; however, there are three quantities — length, mass, and time — that we take as fundamental quantities and we use these three to create other quantities. We define a system of units for these quantities so that we can specify how much length, mass, or time we have. The system of units used in this book is the SI, which stands for Système International. In this system the unit of length is the meter (m), the unit of mass is the kilogram (kg), and the unit of time is the second (s). This system of units is still sometimes referred to by its former name, the mks system. SI units are based on the metric system. An important aspect of this system is its hierarchy of prefixes used for quantities of different magnitudes. Certain of these prefixes are used very frequently in physics, so you should become very familiar with them. Some of the more common ones are listed here:
Exercise 1-1 Metric Prefixes Write the following quantities using a convenient metric prefix. (a) 0.00025 m, (b) 25,000 m, (c) 250 m, (d) 250,000,000 m, (e) .0000025 m Solution (a) 0.25 mm (b) 25 km (c) 0.25 km (d) 250 Mm (e) 2.5 µm Practice Quiz
1-3 Dimensional Analysis In physics we derive the physical quantities of interest from the set of fundamental quantities of length, mass, and time. The dimension of a quantity tells us what type of quantity it is. When indicating the dimension of a quantity only, we use capital letters enclosed in brackets. Thus, the dimension of length is represented by [L], mass by [M], and time [T]. We use many equations in physics, and these these equations must be dimensionally consistent. It is extremely useful to perform a dimensional analysis on any equation about which you are unsure. If the equation is not dimensionally consistent, it cannot be a correct equation. The rules are simple:
Notice that only the dimension needs to be the same, not the units. It is perfectly valid to write 12 inches = 1 foot because both of them are lengths, [L] = [L], even though their units are different. However, it is not valid to write x inches = t seconds because they have different dimensions, [L] 
[T].
Example 1-2 Checking the Dimensions Given that the quantities x (m),
v (m/s), a (m/s2), and t (s) are measured in the units shown in parentheses, perform a dimensional analysis on the following equations. Picture the Problem There is no picture. Strategy Write each equation in terms of its dimensions and check if the equation obeys the preceding rules. Solution Part (a)
Insight Notice that in the dimensional analysis purely numerical factors are ignored because they are dimensionless. Since there are dimensionless quantities, dimensional consistency does not guarantee that the equation is physically correct, but it makes for a quick and easy first check. Practice Quiz
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