the language of physics Mathematics the language of physics Obj: Swbat use the rules of algebra to rearrange equations and solve for variables.

During the course of the year, we will learn approximately 70 equations that physicists use to describe the natural world. You have to be able to rearrange any of these equations to solve for any variable in them. Steps for isolating a variable: Locate the variable (duh) Using inverse operations, isolate the variable so that it is on one side of the equation and all other variables/numbers are on the other side. Look for any variables that are being added to or subtracted from our target variable and reverse the operation Look for any variables that are being multiplied or divided by our target variable and reverse them. If there are any exponents, use a radical to reverse them

Algebra : Example #1 Solve for a This is the key tool in finding the missing pieces to problems in physics! Solve for a

Algebra : Example #2 Ex #3: Solve for vi

Algebra : Example #3 Ex #2: Solve for r

Practice on your own

Obj: Swbat convert large and small numbers into scientific notation.

Scientific Notation Format: a x 10b eg: 491,000 = 4.91 x 105 Scientists need an easy way to talk about very large and very small numbers Mass of an electron = 9.1 x 10-31 kg Mass of the sun = 1.9 x 1030kg Format: a x 10b a is any number greater than or equal to 1 and less than 10 b is the exponent which represents the number of spaces we’ve move the decimal. eg: 491,000 = 4.91 x 105

Scientific Notation 0.000000367 = 3.67 x 10-7 Why do we not use the last 1 in the number? Practice with these examples 4,700 = ______________ .00000000321= ____________ 20,200 = _______________

Calculators : Order of Operations Biggest issue is proper order of operations Force correct order by using PARENTHESES Avoid parentheses by using EE notation

Calculators : EE Notation 3,000,000 Can be entered into the calculator as: 3 x 10 ^ 6 3E6 BETTER METHOD The calculator treats this as a SINGLE number – no PARENTHESES required!!!

Calculators : EE Notation Example What is the product of 2.0 x 102 and 4.0 x 10-4 ? Without EE notation: (2.0 x 10^2) x (4.0 x 10^-4) With EE notation: 2E2 x 4E-4 Answer: 0.08 or 8.0 x 10-2 or 8E-2

Scientific Notation : Review Use when writing very SMALL numbers Decimal moves right  DECREASE power of 10 Length of an Ant 0.004 meters 4.0 x 10-3 meters

Scientific Notation : Review Use when writing very LARGE Decimal moves left  INCREASE power of 10 Diameter of the Moon 3847800 meters 3.85 x 106 meters

Scientific Notation : Examples Express each in scientific notation Average speed of a snail 0.004 meters per second Length of a mitochondria 0.0000006 meters Mass of Eiffel Tower 9,070,000 kilograms Earth-Sun Average Distance 150,000,000,000 meters 1.5 x 1011 m 6.0 x 10-7 m 4.0 x 10-3 m/s 9.07 x 106 kg

Metric System Obj: swbat... identify fundamental units Convert between metric units by dividing and multiplying powers or ten

SI Units : Fundamental Units Based on International Standards Length meter (m) Time second (s) Mass kilogram (kg) Electric Current ampere (A)

SI Units : Derived Units Combinations of fundamental units Speed m/s Acceleration m/s/s Force kg·m/s2 Energy kg·m2/s2 1 s 2 s 3 s 4 s 5 s 10 m

Common & Useful Non-SI Units Units used in the U.S. or for convenience mile (mi) 1610 m inch (in) 0.0254 m minute (min) 60 s hour (hr) 3600 s

SI prefixes represent powers of 10 SI Prefixes : Overview SI prefixes represent powers of 10 Prefixes for Powers of 10 Prefix Symbol Notation tera T 1012 giga G 109 mega M 106 kilo k 103 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 1000 g = 1 x 103 g = 1 kg 0.000001 s = 1 x 10-6 s = 1 μs 0.054 m = 5.4 x 10-2 m = 5.4 cm 3.0 kJ = 3.0 x 103 J = 3000 J

Converting between metric prefixes SI Prefixes : Overview Prefix mega kilo “base” centi milli micro nano Symbol M k c m μ n value 106 103 100 10-2 10-3 10-6 10-9 Converting between metric prefixes In physics, we have to use certain units in our equations (meters for distance, kilograms for mass) but sometimes we won’t be given these units. In these cases, we have to convert from one prefix to another. eg: 150 grams into kilograms gram = 100 , kilogram = 103 0 -3 = -3  move 3 spaces to the left eg: 1.5 seconds into nanoseconds seconds = 100 , nanoseconds = 10-9 0 - -9 = 9  move 9 spaces to the right

Graphing obj: swbat... Set intervals for both axis, plot data points, determine the best fit line Identify the 4 basic types of graph shapes

Steps for creating a graph Collect your data (or it will be given to you.) Determine the range of the data. What are the highest and lowest values for each set? Make sure that all data points can fit on your graph, but you DO NOT need to use the entire graph. Label your axes. Plot your data. Draw a “line” of best fit.

Polynomial Relationship Graphs : Overview Inverse Relationship Polynomial Relationship Direct Relationship

Graphs : Examples Sketch a graph to show the relationship between… Fg and m in the equation: R and A in the equation: ac and v in the equation: Fg ac R m v A