Lecture 2: Units/Coordinates/Definitions

Transcription

1 Lecture 2: Units/Coordinates/Definitions This Week s Announcements: Please get your iclickers this week if at all possible Class Webpage: visit regularly Week 1 Reading: Chapter 1 - Giancoli Week 1 Assignments: - MasteringPhysics: -Introduction to Mastering Physics

2 Basic Slide Format: - Very important text - Important text F = M a - Amplifying explanation - Amplifying explanation - Important equation. You must know (will be tested on) - put on your 3 x5 - start your 3 x5 now and build it as you go - Derivations / Examples. For your enjoyment - NOT REQUIRED but edifying for the more advanced/energetic students - Derivations / Example: - And: r H1 r H2 = r H1 r H2 cos(a) = 3d 3d cos(a) N F gr = ma net - derivations that you need to know - example / consequence of important equation - So: r H1 r H2 = r1 x r2 x + r1 y r2 y + r1 z r2 z = -d 2 + d 2 - d 2 = -d 2 3 d cos(a) = -d a = cos -1 (-1/3) = o - If derivation is apart of a example problem worked in class, know. - Answer needs to be known but not derivation

3 Today s Goal: - Establish the playing field and its corresponding scales and introduce the basics of motion in that coordinate system. KINEMATICS: - One needs to establish the nature of motion before we can begin to understand its causes. Uniform motion: Uniformly varying motion: Random motion:

4 Scaling the World: Units - Physics is not math - We are not just manipulating # s - So units need to be ascribed to the coordinates - put an absolute (typically arbitrary) scale on the universe Length (meters) time (seconds) Temperature (Kelvin) SI Units mass (kilograms) - We will be using SI (metric) units much of the time - BIG BENEFIT: Everything is multiples of 10 ALWAYS INCLUDE THE UNITS IN YOUR WORK!

5 Units Conversions - UNITS MUST BE CONSISTENT! - The trick to unit conversion: Multiply by 1 For example: converting ft to m: 1 ft ( ) m = m 1 ft 1 - Cancel units just like you would cancel numbers and variables For example: How many nanoseconds since the Big Bang? ( ) ( ) ( )( ) T 3600 s BB =13,700,000,000 yr d 24 hr 1 ns 1 d = 1 yr 1 hr s T BB =432,000,000,000,000,000,000,000,000 ns

6 Scientific Notation - When talking about big things like the universe or little things like the atom, writing # s like this is prohibitively time (tree) consuming. - Compress notation to the following standard form: 1.23 x Example: : between : exponent - number of places to shift left (+) or right (-) to get decimal value between For really big numbers the exponent often is all we care about ( order of magnitude ) T BB = 432,000,000,000,000,000,000,000,000.0 ns 26 places to the left (+) - Example: m H = kg 27 places to the right (-) = 4.32 x ns = 1.67 x kg

7 Scaling the World: Units - Certain multiples of the base unit have defined names - names are typically given it each power of three change Text Symbol Factor SciNot tera T giga G mega M kilo k hecto h deca da deci d centi c milli m micro µ nano n pico p

8 Clicker Question: 1) tory =? a) milli tory b) mega tory c) tera tory d) micro tory e) deca tory Text Symbol Factor SciNot tera T giga G mega M kilo k hecto h deca da deci d centi c milli m micro µ nano n pico p

9 Clicker Question: 1) tory =? a) milli tory b) mega tory c) tera tory d) micro tory e) deca tory Text Symbol Factor SciNot tera T giga G mega M kilo k hecto h deca da deci d centi c milli m micro µ nano n pico p wikicommons

10 Clicker Question: 2) How many heart beats are there in a typical human life expectancy? a) a few zepto beats b) a few nano beats c) a few kilo beats d) a few giga beats e) a few peta beats

11 Clicker Question: 2) How many heart beats are there in a typical human life expectancy? a) a few zepto beats b) a few nano beats c) a few kilo beats d) a few giga beats e) a few peta beats

12 Scientific Notation - ALGEBRA with scientific notation: - Addition/subtraction: - get exponents the same (non-standard scientific notation form) - add/subtract leading # s - Multiplication/division: - add/subtract exponents - multiply/divide leading # s - Powers/roots: 8.7 x x 10 2 = 8.7 x x 10 4 = x 10 4 = x 10 4 / 8.01 x 10 2 = (8.7/8.01) x 10 (4-2) = 1.1 x multiply exponents - raise leading # to power/root (9 x 10 2 ) 2 = 9 2 x 10 (22) = 81 x 10 4 = 8.1 x 10 5 (9 x 10 2 ) 1/2 = 9 1 / 2 x 10 (21/2) = 3 x 10 1

13 Significant Figures - Number of figures in a number that are meaningful : - Multiplication/division: - multiply/divide # s (you may keep more digits in the calculation process and use correct sig. figs. at the end) - Number of significant figures corresponds to the one with the fewest decimal places to the right of the decimal (round up if the first insignificant digit is 5, down if <5) - Often useful to convert to scientific notation first - Addition/subtraction: = x x10-3 = 6.0x Line up the decimal places, add/subtract - Number of significant figures corresponds to (no more) than the one with the fewest decimal places to the right of the decimal = Integers and mathematical constants/numbers are considered infinitely precise - 0 of coordinate system can be assumed infinitely precise (unless stated otherwise)

14 Space-time diagrams space (x) time - Graph shows the evolution of the position (1-D) in time (how things move in time) --- not (x vs. y) but x vs. time