"Introduction to General Physics
What is Physics?
A branch of natural science dealing with the behavior and composition of matter and its interactions at the most fundamental level.
• Classical Physics ：
Classical Mechanics, Thermodynamics, Electromagnetism (Electromagnetic Waves, Optics)
• Mordern Physics ：
Special Relativity, Quantum Mechanics, General Relativity…
The Basic Interactions
Interaction Strong Electromagnetic Weak Gravitational Relative Strength 1 10-2 10-6 10-38 Range 10-15 m Infinite 10-17 m Infinite
• Electroweak Interactions • Attemps to combine the strong and electroweak interactions
Concepts, Laws, Principles, Models and Theories
• Concept ( 觀念之狹義說法 ): an idea (such as a physical quantity) that is used to analyze natural phenomena. • Law: a statement or a certain mathematical relationship between physical quantities obtained by means of experimental or theoretical analysis. • Principle: a very general statement about how nature operates. • Model: a convenient analog or representation of a physical system. The phenomena occurring in the system are analyzed as if the system were designed according to the model. • Theory: a combination of concepts, principles, a model and initial assumptions to deduce specific consequences or laws.
物理量 (physical quantities)
• 物理量： 長度、面積、體積、時間、質量、位置、速度、加速 度、 動量、動能、位能、能量、功、功率、電荷、電流、 電場、磁場、電位勢、電容、電感、溫度、壓力… • 純量 (scalers) ： 由一 number) 表示；有大小 (magnitude) 、正負號、及單 位 • 向量 (vectors) ： 由一向量表示；有大小、方向 (direction) 、及單位。 • 單位 (units) ： 一般物理量皆必須賦予單位，否則無法完整表達其意義。
Systems of Units
• The International System of Units- the SI Units (SI, MKS or MKSA 制 ) m, kg, s and others (A, K, mol., cd) • The cgs Units – the centimeter-gram-second systems cm, g, s, … • The British Units ft, lb, s, … • Base Units ( 基本單位 ): m, kg, s, A, K, mol, cd (in SI) • Derived Units ( 衍生單位 ): N, J, W, Pa, Hz, C, V, Ω, F, T, Web, °C, lm, lx • 單位 轉換 ﹙標準 制 - 非標 準制 之間﹚ ： 50 mi/h = (50 mi/h ) (1.6 × 103 m/mi) ( 1h/3600s) = 22 m/s
質量單位
• 公斤 (kg, Kg, kilogram; 1 kg = about 2.2046 pounds ) : the mass of a platinum-iridium cylinder kept in the (BIPM) international Bureau of Weights and Measures in Sèvres, France.
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舊定義： 1 atm, 4°C, 一公升水之質量 ( 問題 : 純度、溫 度) • 原子質量 單位 , the unified atomic mass unit (u): = the mass of a carbon-12 atom/12 = 1.66053873 ×10-27 kg
原子鐘 (Atomic Clock)
•原子鐘的原理是利用原子共振 時的特定震盪頻率來作為時間 的基準，故非常準確 。 •世界第一台原子鐘 : 1949 年。 • 在 2000 年 , 美國 NIST ( 國 家標準及科技研究院 ) 研製出世界 最準的原子鐘 NIST-F1 ，每 2000 萬年誤差 ~ 1 秒 ( 精準 度 : 2 × 10-15) •中原大學物理系周志隆教授 網頁 (NIST- 原子鐘運作原理 ) http://wwwphys.cycu.edu.tw/~choucl/GPhysics/gen_phys/cesium.php
Cs-133 原子鐘運作原理 -1
Cs-133 原子鐘運作原理 -2
時間單位
秒 (the second, s) • Originally, it was defined as 1/86,400 of a mean solar day
(solar day: interval between the times at which the sun reaches the highest point on the sky on successive days.) • In 1967, the second was redefined in terms of certain radiation emitted by a beam of Cs-133 atoms (atomic clock): There are 9,192,631,770 vibrations of radiation in the radiation in one second.
長度單位
公尺 (m, meter) ：
• 18 世紀： 1 m = 地球赤道至北極距離 ×10-7 • 20 世紀 1960 前 : 1 m = the distance between two fine scratches on a Pt-Ir bar stored under controlled conditions in Sèvres, France. • 1960: as 1650763.73 λ of the orange light emitted by Kr-86 • In 1983 the meter was redefined as 1 meter = the distance traveled by light in a vacuum in 1/299,792,458 seconds ☆ The speed of light in vacuum = 299,792,458 m/s ☆ Other units of length: cm, mm, µm, nm,…, Å
Power of Ten Notation & Significant Figures
• For practical purposes, very large or very small numbers should be expressed in terms of power of ten notation. 原子很小 ( 直徑 ~1-5 ×10-10 m), 原子核很小 (~10-14 m) 星球質量很大 , 星球之間距離很遠 , … 光波波長 , 頻率… 測量數字精確程度為有限，宜適當表示之；尤其在計算 時：
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• In products and divisions, the number of significanat figures in the final result should equal that of the factor with the least number of significanat figures. 例 : 36.479×2.6/14.85 ≅ 6.387 (your answer?) → 6.4 • In addisions and subtractions, only the least number of decimal places should be retained. 例 : 17.524+2.4 – 3.56 = 16.364 (your answer?) → 16.4
Some Physical Constants
Physical Quantity
Atomic mass unit (u) Avogadro constant (NA) Speed of light in vacuum (c) Permeability constant (µ0) Permittivity constant (ε0) Elementary charge (e) Electron mass (me) Proton mass (mp) Gravitational constant (G) molar gas constant (R) Boltzmann constant (kB) Planck constant (h)
Value (Uncertainty)
1.660 538 86 (28) × 10-27 6.022 1415 (10) × 1023 299 792 458 (exact) 12.566 370 614 ×10-7 (exact) 8.854 187 817 ×10-12 (exact) 1.602 176 53 (14) × 10-19 9.109 3826 (16) × 10-31 1.672 621 71 (29) ×10-27 6.6742 (10)×10-11 8.314 472 (15) 1.380 6505 (24) ×10-23 6.626 0693 (11)×10-34
Unit
kg 1/mol m/ s N/A2 F/ m C kg kg m3 /kg·s2 J /mol· K J /K J ·s
Order of magnitudes ( 數量級 )
• Earth Mean radius ≅ 6.37 × 106 m Mass ≅ 5.98 × 1024 kg Mean distance to sun ≅ 1.49 × 1011 m • Moon Mean radius ≅ 1.74 × 106 m Mass ≅ 7.36 × 1022 kg Mean distance to earth ≅ 3.84 × 108 m • Sun Mean radius ≅ 6.96 × 108 m Mass ≅ 1.99 × 1030 kg • An order of magnitude estimate: 193.7 ×39.64 / 8.71 ~ 2 × 102 × 4 × 101 / 9 ~ 103 1 年多少秒： 365 d/y × 24 h/d × 3600 s/h ~ 3 × 107 s/y
Dimensional Analysis ( 因次分析 )
• Each derivede units in mechanics can be reduced to factors of the base units: mass, length, and time. [mass] = M, [length] = L, [time] = T • The notation [ x ] refers to the dimensions of x. [ velocity ] = [distance/time]= LT-1 [ acceleration ] = [velocity/time]= LT-2 [force]= [mass × acc.]= MLT-2 • Dimesional analysis can be used to check the function form of relations, since when y = f(x), [ y ] = [f(x) ]. If the dimensions on two sides of the equation are different, then, this relation must be wrong.
Reference Frames ( 參考框架 - 座標系 ) and Coordinate Systems ( 座標系統 )
• 直角座標 (the Cartesian coordinates) • 極座標系 (plane polar coordinates) y (x, y) y r
x= r cosθ y= r sinθ r= x2 + y2
x
θ
tanθ = y/x
O
x
Vectors, Components, Unit Vectors
y
2 2 A = Ax + Ay = A . A is a unit vector, if A = 1.
(Ax, Ay)
Ax= A cosθ Ay= A sinθ tanθ = Ay/ Ax
x
Ay O
A
θ
Ax
A = Ax x + Ay y, where x and y are unit vectors ˆ ˆ ˆ ˆ in the x − and y − directions, respectively.
Homework
• Excercises: 3, 4, 5, 11,12,13,15,17, 23,24,25, 34, 35, 36, 37, 48, 49, 50 • Problems: 2, 3, 4
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