Chapter I
Physics and Measurement
Measurement and precision:
Measurements are stated in the form of numbers. The number of significant figures is the number of digits, which are known to be accurate.
When reporting a result, the number of significant digits in your answer should be equal to the smallest number of significant digits of the numbers used in calculation. In other words, if your calculation involves multiplying three numbers, the answer should be stated in terms of the least significant digits of the three numbers multiplied.
Units of measurement:
The three basic units of measurement are length, time, and mass. The two most common systems of measurement are the metric system and the English system. The metric system is advantageous because the numbers are based on a system of tens or powers of tens.
In 1960, an international committee formulated a system of standards and designations for several fundamental quantities, which was known as the SI system of units. Length, mass, and time were measured by the meter, kilogram, and second respectively.
Length
·In 1799 the universal standard length of a meter was defined as being one ten- millionth of the distance from the equator to the North Pole (magnetic or geographic?).
·As late as 1960, the meter was the distance between two lines inscribed on a bar of platinum-iridium alloy, which was resistant to shape change from heat.
·In 1983, the definition of a meter changed to the distance light travels in vacuum during a time interval of 1/299,792,458 sec.
Mass
The SI unit of mass, the kilogram (approx 2.2 lbs) is defined as the mass of a particular cylinder of platinum-iridium alloy, which is kept under controlled atmospheric conditions at the International Bureau of Weights and Measures, in France.
1.2 Dimensional AnalysisThe term Dimensional Analysis may be a bit foreign, but usage of such a thing is very commonplace. Who has never heard of velocity (m/s), area (m2), volume (m3), or acceleration (m/s2)? For all of these things are coined as being examples of Dimensional Analysis. Dimensional Analysis makes use of the idea that dimensions may be treated as algebraic quantities.
Scientists, especially ones in physics like to divide things into simple divisions like mineral, animal, or vegetable. In the case of physics, all quantities can be expressed as length (L), time (T), or mass (M). For instance, instead of saying area is length times width, we can say it is L squared (L2). Or we could say that velocity is not change in distance over change in time but it is L/T. In this way, any measurement can be expressed as L, T, or M.
For example, the relationship of two or more dimensions (e.g., meters and seconds to get m/s) allows us to find an algebraically correct expression in which to use Dimensional Analysis. Some of the examples of Dimensional Analysis is listed below:
Example of Dimensional Analysis
The definition of area
is length times width
,
units: [L2]
SI units: m2
(1.1)
The definition of
volume is length times width times height.
, units:
[L3] SI Units: m3
(1.2)
The definition of speed
is distance divided by time. 
units: [L/T] SI units: m/s
(1.3)
The definition of velocity
is displacement divided by time. 
units:
[L/T] SI units: m/s
(1.4)
The definition of acceleration is the change in velocity divided by the change in time.
units: [L/T2]
SI units: m/s2
(1.5)
The definition of density
is mass divided by volume. 
units: [M/L3]
SI units: kg/m3 (1.6)
