Technical English -I 3 rd week SYSTEMS OF UNITS

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Rosanna Brooks
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1 Technical English -I 3 rd week SYSTEMS OF UNITS

2D 3D Coordinate conversion (Transformation coordinates) From Cartesian to polar, or vice versa (below) From a local system to a global system (right) Polar to

2 2D 3D Coordinate conversion (Transformation coordinates) From Cartesian to polar, or vice versa (below) From a local system to a global system (right) Polar to Cartesian: Cartesian to Polar : x = r cosθ r + y = r sinθ 2 2 = x y θ = tan 1 ( y / x) Cartesian / polar / coordinate / conversion / transformation / local / global

3 Correlation analysis Correlation is a measure quantifying the relationship between two variables (an dependent and independent variable or between two independent variables). (R-correlation coefficient ranges between -1 and +1) (R <0 negative; R=0 no correlation; R >0 positive correlation) correlation / relationship / variable / correlation coefficient

4 Regression Analysis Regression analysis refers to assessing the relation between the outcome variable and input variable(s). Simply, it is to determine the most suitable form between one dependent variable and independent variables. Regression isa statistical measure used in engineering and other disciplines that try to determine the strength of the relationship between one dependent variable and a series of other independent variables. Regression models are useful for prediction of unknown values of a dependent variable base on available independent variables. Simple linear regression Multiple regression Curvilinear regression regression analysis / regression model / prediction

5 Simple Linear Regression y = f(x) = ax + b is a simple linear regression model where y is dependent variable, x independent variable and a, b regression coefficients. Year Discharge (m 3 /s) Rain (mm) ? ? ? 490 Regression line y = ax + b linear regression / prediction unknown available (observed) data

6 Multiple Linear Regression y = a 1 x 1 + a 2 x a n Polynomial (or curvilinear) regression y = + a 0 + a 1 x 1 + a 2 x 22 + a 3 x 33 + a 4 x a n x n n Here, y is dependent variable, x 1, x 2,., x n independent variables and a 1, a 2,., a n regression coefficients. regression model / multiple linear & polynomial regression / prediction

7 You have learned how we can define the position of a point in a Cartesian or Polar Coordinate systems. How you can define a point in a Cylindrical Polar Coordinate System? 2D 3D Cartesian P ( x, y, z ) Polar P ( λ, ϕ, r ) Cylindrical P(?,?,?)

8 MKS System CGS System SI System The MKS (Meter, Kilogram, Second) System The MKS system of units expresses any measurement of physical quantities using fundamental units of Length, Mass and Time, which are Meter, Kilogram and Second, respectively. Dimension Name (Unit Name) Length (Meter) Mass (Kilogram) Time (Second) The CGS (Centimeter, Gram, Second) System quantity / fundamental / unit / length / mass / time

9 The unit of measurement of the physical quantity of the variable should be invariable (This means that the magnitude of the particular of the unit of measurement should be remain same irrespective of the time and space). The unit of measurement should be easily reproducible. The units of measurement should be accepted universally in all the parts of the world and all the communities. quantity / invariable / magnitude / irrespective / reproducible / universally

10 Units Length Area Volume Mass Time Force Energy Power Pressure Angle A unit of measurement isa a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity. The units of all other physical quantities can be expressed as combinations of the base units. For example: The unit of Distance is meter (m). The unit of area is square meter (m 2 ) and volume is cubic meter (m 3 ). quantity / length / mass / time / force / energy / power / pressure / angle

11 The SI system of units extends the MKS system, by expressing any measurement of physical quantities using fundamental units of Meter, Kilogram, Second, Ampere, Kelvin, Candela, Mole. length / mass / time / force / energy / power / pressure / angle / luminous

12 The difference between MKS system and SI system arises from the difference in mainly selecting unit of force. The unit for force is Newton (denoted by N) in SI units while in MKS system, it is Kilogramme-weight (kg-wt) or simple called as Kilogramme(kg). System Basic units Force Mass Energy or Work Power Pressure or Stress MKS SI m,kg,s (kg=force) m,kg,s (kg=mass) kg kg.m/s 2 kg. s 2 /m kg.m kg N.m kg.m/s J/s kg/m 2 N/m 2 N=Newton J=Joule Joule W=WattWatt P a =Pascal quantity / length / mass / time / force / energy / power / pressure / angle

13 density / velocity / acceleration / momentum / impulse / action / stress

14 quantity / length / mass / time / force / energy / power / pressure / angle

15 quantity / length / mass / time / force / energy / power / pressure / angle

16 The most frequently used tera / giga / mega / kilo / hecto / deka / deci / centi / milli / micro / nano

17 inch / foot / yard / mile / ounce / pounds / acre / quart / gallon

18 1) What is Knot as a unit? 2) What is the difference between mile and nautical mile?

In recording measurements, it is necessary to understand 1. SIGNIFICANCE of numbers 2. importance of UNITS.

In recording measurements, it is necessary to understand 1. SIGNIFICANCE of numbers 2. importance of UNITS. CHEMISTRY IS LARGELY A QUANTITATIVE SCIENCE Theories and ideas are tested by measurement Measurements are usually quantitative have numbers Science is built on a foundation of mathematics. In recording