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UNIT 1: Math and Measurement

UNIT 1: Math and Measurement. Physics 2013-2014. Physics. What is Physics? Physics is the study of the physical world Use a small number of basic concepts, equations, and assumptions to describe the physical world VIDEO: http://www.youtube.com/watch?v=AEIn3T6nDAo. Areas of Physics.

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UNIT 1: Math and Measurement

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  1. UNIT 1: Math and Measurement Physics 2013-2014

  2. Physics • What is Physics? • Physics is the study of the physical world • Use a small number of basic concepts, equations, and assumptions to describe the physical world VIDEO: http://www.youtube.com/watch?v=AEIn3T6nDAo

  3. Areas of Physics

  4. The Scientific Method http://www.youtube.com/watch?v=_7sSuhQ1_24

  5. SI Base Units

  6. SI Units – Conversion Factors

  7. Accuracy and Precision

  8. Significant Figures • Significant figures indicate Precision • Significant figures are digits in a measurement known with certainty plus the first digit that is uncertain • There are specific rules for determining whether zeros are significant figures

  9. Rules for Zeros – Significant Figures

  10. Calculations and Significant Figures • Addition and Subtraction • The answer is expressed with the same precision as the least precise number • Multiplication and Division • The answer has the same number of significant figures as the measurement with the least number of significant figures

  11. Tables, Graphs, and Equations • We can use mathematics to describe measured or predicted relationships between physical quantities • Graphs and Tables can be particularly helpful to show relationships or portray data in manner to easily display results • In some cases we may be able to fit Linear equation to a given set of data using linear regression analysis

  12. Linear Regression Analysis • Regression lines can be used as a way of visually depicting the relationship between the independent (x) and dependent (y) variables in the graph. A straight line depicts a linear trend in the data (i.e., the equation describing the line is of first order. For example, y = 3x + 4. There are no squared or cubed variables in this equation). A curved line represents a trend described by a higher order equation (e.g., y = 2x2 + 5x - 8). It is important that you are able to defend your use of either a straight or curved regression line. That is, the theory underlying your lab should indicate whether the relationship of the independent and dependent variables should be linear or non-linear. • In addition to visually depicting the trend in the data with a regression line, you can also calculate the equation of the regression line. This equation can either be seen in a dialogue box and/or shown on your graph. How well this equation describes the data (the 'fit'), is expressed as a correlation coefficient, R2 (R-squared). The closer R2 is to 1.00, the better the fit. This too can be calculated and displayed in the graph..

  13. Linear Regression Analysis

  14. Linear Regression Analysis

  15. Linear Regression Analysis

  16. Linear Regression Analysis Example: Equation of the line fitting y=mx + b How good is the fit? coefficient of determination, indicates how well data points fit a line or curve

  17. Standard Deviation • Calculate the mean or average of each data set. To do this, add up all the numbers in a data set and divide by the total number of pieces of data. • Subtract the deviance of each piece of data by subtracting the mean from each number. Note that the variance for each piece of data may be a positive or negative number. • Square each of the deviations. • Add up all of the squared deviations. • Divide this number by one less than the number of items in the data set. For example, if you had 4 numbers, divide by 3. • Calculate the square root of the resulting value.

  18. Standard Deviation

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