1. Doing Physics 1.Realms of Physics 2.Measurements & Units 3.Working with Numbers 4.Strategies for Learning Physics

1.1. Realms of Physics Realms: Atoms & Moelcules Thunderstorms & Rainbows Stars, Galaxies, Universe. Technological Applications: Microelectronics Medical Imaging Cars, Airplanes, Space Flight Goal: Unified description of everything physical.

DVD Player: Which realms of physics are involved ? Spinning disc: Mechanics Motion of cars, planets, … Stability of bridges, skyscrapers, … Sound waves: Oscillatory / Wave Motion Ocean waves, Tsunami, Earth quakes, Sonic Boom, … DVD-Write: Thermodynamics Refrigerators, Heat engines, Energy transfer, … Circuitry: Electromagnetism Computers, Microwaves, TV, … DVD-Read: Optics Microscopes, Telescopes, Spectrometers, Optic fibres, … Laser: Quantum Physics / Relativity Periodic table, nuclear fission / fusion, Black holes, …

1.2. Measurements & Units SI / MKS units (Systeme International d’Unites) Length: Meter (m) 1 / 10,000,000 of equator-north-pole distance. 1889: standard meter bar. 1960: wavelength of light. 1983: 1 / 299,792,458 of distance traveled by light in 1s in vacuum. Mass: Kilogram (Kg) Standard mass (Pt-Ir) in Sevres, France. Time: Second (s) 1 / (24  60  60) of period of Earth rotation (day). 1956: 1 / 31,556, of year : 9,192,631,770 periods of radiation from cesium-133.

Other base units: Current: Ampere (A) Temperature: Kelvin (K) Substance: Mole (mol) Luminosity: Candela (cd) Supplementary units: Angle: Radian (rad) Solid angle: Steradian (sr)

Derived units: Newton = N = Kg  m / s 2 = Kg  m  s  2 Other units: English units (ft, lb, s). CGS units (cm, g, s). Changing Units: See Appendix C Size of bacteria ~ m. 10  m. Distance to 左營 ~ 31,000 m. 31 km.

Units Matter: A Bad Day on Mars 1999: Mars Climate Orbiter ($125m) entered Mars atmosphere by mistake & was destroyed. Root cause: Both English & SI units were used without conversion.

1.4. Working with Numbers Radius of proton: 1 / 1,000,000,000,000,000 m Size of Galaxy: 1,000,000,000,000,000,000,000 m Reach of telescope: 100,000,000,000,000,000,000,000,000 m Scientifc notation: 1  10  15 m 1  m 1  m 4,185 =  = 1.2  10  4

Tactics 1.1. Using Scientific Notation Addition / Subtraction: Change all terms to the same exponent first. Multiplication / Division: Digits:  /  Exponents: + /  Powers / Roots: Digits: power / root Exponents:  power /  root

Example 1.2. Scientific Notation: Tsunami Warnings Tsunami: entire ocean (top to bottom) participates. Speed = Acceleration due to gravity h = depth of water= 3.0 km

Significant Figures Significant figures (digits) of an integer: all digits between the leftmost & rightmost non-zero digits. Trailing zeros are ambiguous. of a real number: all digits except leading zeros. Examples: Numbers with 5 sig. dig. : , , , Caution: An integer sometimes denotes infinite accuracy (  sig. dig. ). e.g., 2 in the formulae C = 2  R & A =  R 2. Note: may be taken as having 10 sig. dig.

Accuracy & Significant Figures means  2.94 is between 1.6 & 1.8 Accuracy worsens after each calculation. Result has accuracy of the least accurate member.  /  : Number of significant digits = that of the least accurate member. + /  : result is rounded off to the rightmost common digit. Bridge = km ( accuracy = km ) Ramp = 65.4 m = km ( acc = km ) Overall length = km km = km Overall acc = km, error =  km  Overall length = km  = ( # sig. dig. = 6 ) R E = 6.37  10 6 m ( # sig. dig. = 3 ) 2  R E =  10 6 m Overall # sig. digits = 3  2  R E = 40.0  10 6 m i.e.or

Error Analysis Let s Q be the uncertainty in quantity Q.     For

Example 1.3. Uranium fuel rod in nuclear reactor Before insertion, rod length = m After insertion, rod length = m Q: What is the increase in length? A: m  m = m = 8 mm Accuracy = 1 mm Error =  m =  1 mm  Increase in length is 8 mm ( 1 sig. dig. ) Any intermediate results must have at least 1 extra sig. dig. to avoid rounding errors. Caclulator: apply round-off & truncation only at the end.

Estimation Example 1.4. Counting Brain Cells Q: Estimate the mass of your brain & the number of cells it contains. A: Head is ~15 cm wide. Discounting bones: ~10 cm wide. Assuming cube shape, vol ~ ( 10 cm ) 3 = 1000 cm 3. Mostly water  density = 1 g / cm 3.  Brain mass ~ 1000 g = 1 Kg. Brain cell size ~ red blood cell size ~ 10  5 m ( Table 1.1 )  Cell vol ~ (10  5 m) 3 = 10  15 m 3 Number of cells in brain: Actual data: Average adult brain mass ~ 1.3 Kg, N ~

1.4. Strategies for Learning Physics Challenge: Must be equally adept in both concepts & mathematics. Simplicity: A few basic principles govern everything. Problem Solving: An IDEA Strategy Interpret : Intrepret & understand problem. Identify applicable concepts & principles. Identify players involved. Develop: Draw diagram & label objects. Determine relevant formulas & values. Evaluate: Evaluate / execute the formulas. Assess: Assess correctnes of result (use common sense, consider special cases, etc.)