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Ch1 Introduction. 1.1 Standards of length, mass time SI Units Length (m) the distance traveled by light in vacuum during a time interval of 1/299792458 second Km =1000m cm = 0.01 m 1 m = 39.37 in. = 3.281 ft 1 km = 0.621 mi Mass (Kg) the mass of a specific platinum iridium alloy cylinder kept at the International Bureau of Weight and Measures at Sèvres, France 1 Kg g= 2.20462 lbs(pound is a unit of force.) Time(sec) 9 192 631 700 times the period of oscillation of radiation from the cesium atom. Speed = L/T exception Temperature.(K,T) Charge(C, Q) Guessing an equation by using dimensional analysis Acceleration equation [a] = L/T2 [v] = L/T [x] = L a= v t x=? E = mc2 this famous equation can be guessed from dimensional analysis. [E] = M L2/T2 =[m c2] Do not forget units when you write answers. 2300 2 or 4 Two main rules In multiplying/dividing two or more quantities, the number of significant figures in the final product is the same as the number of significant figures in the quantity which has the lowest significant figures. When numbers are added/subtracted, the number of decimal places in the result should equal the smallest number of decimal places. examples 1.23 x 4.5 = 5.535 but the number of sig. figure should be 2, since 4.5 has the lowest sig. figure, 2 so the final answer should be 1.23 x 4.5 = 5.5 1.3 Dimensional analysis 1.4 Uncertainty in Measurement and Significant 1.23 + 4 = 5.23 Dimension: the physical nature of a quantity Figures but the smallest number of decimal places is 1, L: length significant figure is a reliably known digit. so the final answer is M:mass 1.23 + 4 = 5 certain uncertain 8.65 T or t:time However, Dimensions of most physical quantities can be 1.23 + 4.00 written as the combinations of Length, Mass in this case, the smallest number of decimal and time. places is 0.01, so the final answer is 1.23 + 4.00 = 5.23 Dimensions can be treated as algebraic 8.6 uncertain certain quantities. [] is often used to denote the Scientific notation. dimension of a quantity How many significant figures each number has? It is not clear how many significant figures 4000 123 3 has. In this case, scientific notation is useful. Volume = L3 1.23 3 A x 10n where 1<A<10 Area = L2 0.00011 (leading zeroes are not sig.) Ch1 Distance between two points 11.5 Conversion of units d ( x2 x1 ) 2 ( y2 y1 ) 2 Conversion factors can be used to convert units from one to another. In the conversion of units, Polar coordinate system (r,θ) the units are treated as algebraic quantities. examples Final unit beginning unit Final unit beginning unit 10 MPH to m/s 10 miles / h x 1609 m /1 miles =16090 m/h x 1 h/ 60 min x 1 min /60 s =4.5 m/s r Define positive sides when you use it. r θ Find x in terms of r and θ. θ This is useful when we study rotation. 1.8 Trigonometry SOH-CAH-TOA sinθ = opposite/ hypotenuse cosθ= adjacent/ hypotenuse 1.6Estimation and order of magnitude tanθ= opposite/adjacent calculations Order of magnitude calculation can be useful Pythagorean theorem when you need a rough estimation of a quantity r2 = x2 + y2 Inverse function 45 ~ 10 θ = sin-1x 75 ~ 100 You can calculate the inverse functions by using 123567 ~ 105 calculator, but you need to careful about the unit. The result can be in radian or degree, 1.7 Coordinate system depending on the settings Cartesian coordinate system (x,y) y Examples Example 1.10 in the text book. x x