Basic math skills you should already have Physics 102 Goderya Why Measurements? A basic scientific activity Measure is to gain information. Measurements allow us to compare Example: A body temperature (98.6 F) Standards Standard Unit Comparing two objects with a third called the standard unit. Who defines the standards? 1
Three Basic Measurements Common Measurement Length Weight Time Some are combination of these Speed = distance/time Way back in History Length Cubit: Elbow to tip of the middle finger ~ 18 inches Ell: The distance between the nose and the outstretched arm ~ 27 inches Palm: ~ Height ~ 4 inches Foot: ( uncia or a pace) ~ 12 inches 5280 feet equals 1 mile Today Length Modern Standard: System International (SI) Length is measured in meters You should know this 1 m = 100 cm 1 cm = 10 mm 1 m = 1000 mm 1 inch = 2.5 cm Algebraic notation for length are d, S, D and L or l 2
Way back in History Weight Heaviness of objects Bags of wheat or rice Today Mass Property of matter In SI units mass is measured in kilograms (kg) and grams (g) You should know this 1 Kg = 1000 gm Algebraic notation for mass is m, M What is the difference between weight and mass? Time- How to make the Perfect Clock? In the past Motion of Moon and Earth, Seasons, hour glass etc Today - Atomic Clocks You should know this 1 year = 365 days 1 Day = 24 hours 1 hour = 60 minutes 1 minutes = 60 seconds 1 century = 100 years Algebraic Notation for time is t, or T 3
System of Units These are most common. Foot, Pound, Seconds (FPS) Centimeter, Grams, Seconds (CGS) Meters, Kilograms, Seconds (MKS) or SI The world uses MKS, while US still uses FPS, Why? We will use the SI system Learn How to Convert Unit Conversion From one system to the other Within one system bigger unit to a smaller measure, multiply with an appropriate conversion factor. Smaller to bigger unit than divide. See the text for conversion tables Try this simple ones examples You should be able to do such simples ones on your fingertips Convert 1000 centimeters to meters Convert 1 mm to meters Convert 10 meters to millimeters Convert 492.5 grams to kilograms 4
Powers of Ten and Scientific Numbers 10 (+ / -) exponent Nearest Star to the Sun is 43,000,000,000,000 km is the same as writing 4.3 x 10 13 km Visible light is 0.0000005 m is the same as writing 5 x 10-7 m Name Number Power Prefix Trillion 1,000,000,000,000 10 12 tera Billion 1,000,000,000 10 9 giga Million 1,000,000 10 6 mega Thousand 1,000 10 3 kilo Hundred 100 10 2 hecto Ten 10 10 deca One 1 1 unit One-tenth 0.1 10-1 deci One-hudreth 0.01 10-2 centi One-thousandth 0.001 10-3 milli One-millionth 0.000001 10-6 micro One-billionth 0.000000001 10-9 nano One-trillionth 0.000000000001 10-12 pico Working with scientific Numbers 10 3 + 10 3 = 1000 + 1000 = 2000 10 3-10 2 = 1000-100 = 900 10 3 x 10 5 = 10 3+5 = 10 8 10 3 x 10-5 = 10 3-5 = 10-2 10 3 / 10 5 = 10 3-5 = 10-2 10 3 / 10-5 = 10 3-(-5) = 10 3+5 = 10 8 5
See text for details How to work with Significant Digits Numbers in 2 significant ifi tdigitsit 3.1414 = 3.1 2.4 x 2.5 = 6.0 3.7/2.5 = 1.5 3.5/2.25 = 1.6 Proportionality Directly proportional Inversely proportional X Y X 1/Y Constants Proportionality Constant: X Y -> X = C Y Other Constants: X = C (2 Y π) 6
Equations Mathematical sentence Generalize information 5 apples + 10 apples = 15 apples Do you remember how to solve? Equations in one variable x + 10 =5, What is x? If not this is a good time to review or learn Do you know how to solve equations in two variables? x + y = 10 and x y = 5, what is x and y if not, this is a good time to review it from your high school math book. Do you know how to rearrange terms in an equation? If F= GMm/R 2, what R in terms of F, M, m and G if not review your algebra text 7
Do you remember the basic rules for manipulating algebraic quantities? If F 1= a/b and F 2= c/b, what is F 1/F 2? If not, review examples from your algebra textbook. Do you remember the Pythagorean theorem? If not, review it form your high school math book and do some examples Do you know what a radian is? Basic things you should know 1 revolution = 2π radians = 360 1 = 60 1 = 60 How many degrees is 1 radian? 8
Do you remember the basic Right Triangle trigonometry? tan θ, cosine θ, sine θ, and their inverse If not, review it from you high school math book. What is the sum of all angles in any triangle? Graphs What are they? What can it tell you? How to plot them? Linear Graph y = M x + c M = slope c = Intercept stance in m Dis 15 A Linear Graph Intercept Y values M = 10 m / 5 s = 2 m/s c = 1 m 5 10 m 5 s 2 7 Time in Seconds X values 9
Non-Linear Graph A Non-Linear Graph Maximum Y values Y Intercept X Intercept X values You Decide If all of the above is a piece of cake You are good to go for this class! If all of this sounds familiar but don t remember, a review can fix You should not have much problem If you know a few things and you do not know other things You will have to work hard to catch up otherwise you will not make it thru this class If you don t know all or most of these You will not make it thru this class. You should drop it. You will be required to take a skill test in the second week, during the lab period. 10