Chapter 1 Measurement

Despite the mathematical beauty of some of its most complex and abstract theories, physics is above all an experimental science.

1-1 Physical quantities, standards and units What will be measured? What will be measured? Physical quantities: mass, length, time, force… What’s the standard for a measurement? What’s the standard for a measurement? Maintaining and developing standards is an active branch of science. Units Units There are seven kinds of base units in SI system.

1-2 The international system of units CGPM( 国际度量衡大会 ) selected as base units the seven quantities displayed in Table 1-1. This is the basis of the International System of Units, abbreviated SI.

Table 1-1 SI Base units QuantityNameSymbol TimeSeconds LengthMeterm MassKilogramKg Amount of substance MoleMol TemperatureKelvinK Electric current AmpereA Luminous intensity Candelacd

The use of non-SI units is particularly popular with astronomers, many of whom are in love with the angstrom. Am I a nine giga-angstrom (10 9 ) waist or a ten?

1-3 The standard of time We can use any phenomenon that repeats itself as a measure of time. In 1967, the 13th CGPM adopted a new definition: One second was defined to be 1/86400 of one day. The second is the duration of 9,192,631,770 vibrations of a (specified) radiation emitted by a (specified) isotope of the cesium atom.

1-4 The standard of length The first international standard of length was a bar of a platinum-iridium alloy called the standard meter. The first international standard of length was a bar of a platinum-iridium alloy called the standard meter. In 1983, the 17th CGPM redefined the meter as the length of the path traveled by light in vacuum during a time interval 1/299,792,458 of a second. In 1983, the 17th CGPM redefined the meter as the length of the path traveled by light in vacuum during a time interval 1/299,792,458 of a second. In 1960, the 11th CGPM defined the meter as the length of 1,650, wave length of a special radiation of Kr 86. In 1960, the 11th CGPM defined the meter as the length of 1,650, wave length of a special radiation of Kr 86.

1-5 The standard of mass The SI standard of mass is a and assigned as a mass of 1 kilogram (prototype). The SI standard of mass is a platinum-iridium cylinder and assigned as a mass of 1 kilogram (prototype). are sent to standardizing laboratories in other countries. Secondary standards are sent to standardizing laboratories in other countries. Atomic mass unit Atomic mass unit

1-6 Precision and significant figures ( 有效数字 ) The number of significant figures tells us the precision of the measuring result. The number of significant figures tells us the precision of the measuring result. There are a few simple rules to follow in deciding how many significant figures to keep: There are a few simple rules to follow in deciding how many significant figures to keep: Rule 1. x=3.0m and x=0.0030km imply that we know the value of x to be two significant figures. Rule 1. x=3.0m and x=0.0030km imply that we know the value of x to be two significant figures. Be careful about ambiguous notations: x=300m

Rule 2. When multiplying or dividing, the number of significant figures in the product or quotient should be no greater than the number of significant figures in the least precise of the factors. Thus Rule 2. When multiplying or dividing, the number of significant figures in the product or quotient should be no greater than the number of significant figures in the least precise of the factors. Thus Be careful of this:

Rule 3. In adding or subtracting, the least significant digit ( 最小的有效数字 )of the sum or difference occupies the same relative position as the least significant digit of the quantities being added or subtracted. In this case the number of significant figures is not important; it is the position that matters. Rule 3. In adding or subtracting, the least significant digit ( 最小的有效数字 )of the sum or difference occupies the same relative position as the least significant digit of the quantities being added or subtracted. In this case the number of significant figures is not important; it is the position that matters. Example: Example: 103.9kg+2.10kg+0.319kg= kg=106.3kg 103.9kg+2.10kg+0.319kg= kg=106.3kg

Example: 1.A student is calculating the surface area of a single sheet of paper. He measures the length to be L= 27.9cm; He measures the width to be W=21.6 cm. The student should record the area of the paper as (in cm 2 ): A) B) C)602 D)603 Correct answer is D).

2. A student is calculating the thickness of a single sheet of paper. She measures the thickness of a stack of 80 sheets with vernier calipers, and finds the thickness to be L= 1.27 cm. Which of the following answers has the correct number of significant digits? (in mm): A) B) C) 0.16 D) 0.2 Correct answer is B).