1. Measurements and Mathematics in Physics

2. Fundamental Units: provide the basis for every other unit of measure 1.Length: meter (m) 2.Mass: kilogram (kg) 3.Time: second (s) 4.Electrical current: Ampere (A) 5.Angles: degrees (check your calculator mode) 6.Temperature: Kelvin (K) 7.Amount of substance: mole (mol)

3. Derived Units: units formed from the fundamental units 1.Area:m 2 2.Volume: m 3 3.Density: kg/m 3 4.Frequency: Hertz (Hz) = s -1 5.Force: Newton (N) = kg m/s 2 6.Energy: Joule (J) = N m = kg m 2 /s 2

4. Prefixes

5. Conversion Factors (factor label method) 1 kilogram = ______grams Rearranged: OR 1 millimeter = ____________ meters Rearranged: OR How do you know which set up is correct? - the unit that you start with goes on the bottom, the unit that you need to solve for is on the top

6. Practice.0063 m = ____________ mm 390,000 g = ____________ kg 0.0018 ks = ____________ s 22.4 g = ____________ Mg 377 mm =____________ cm 42,000 cm =____________ km 250cm =____________ m 432 pm = ____________ mm

7. What is the length of the following?

8. Significant Figures Definition: all the known values from a measurement including a last estimated digit Reason for sig figs: all measurement tools present a some uncertainty to their measurement

9. Determining the # of Sig Figs in a measurement 1.Is the decimal present or absent? 2.Begin at the appropriate ocean side of the measurement 3.Move to the first non- zero digit 4.Count all digits moving across

10. Recall the measured value from earlier: How many significant digits are there in our measured value?

11. Indicate the number of significant figures in the following measurements: 0.00734 cm 3 _____ 510 mL_____ 510. mL_____

12. Addition and subtraction with Sig Figs The answer has only as many decimal places as the measurement having the least number of decimal places. Procedure: 1. line up all measurements by decimal points 2. perform the calculation on your calculator 3. draw a line down next to the first, last significant digit from the values being calculated 4. round your answer off the answer to the digit to the left of the line

13. Example: A 0.50 kg block is placed on the back of a 1.7325 kg cart. What is the mass of the cart – block system? 1.7325 + 0.50____

14. Multiplication and Division Rule: The solution to a multiplication or division problem can only have as many significant figures as the starting measurement with the least number of significant figures. Procedure: 1. perform the calculation on your calculator 2. count the number of significant figures in the starting measurements 3. round your answer off the answer to the least number of significant figures

15. Example: A student found the mass of an object to be 50.11 grams and the volume of the object to be 22.0 mL. What is the density of the object?

16. Example: Gold has a density of 19.320 g/mL. If a piece of gold has a volume of 14.8 mL, what is the mass of the object

17. Example: What is the mass of 75.2 mL of mercury? (density of mercury is 13.546 g/cm 3 )

18. Trigonometry Review Determine the length of sides a and b. 25 m 35° a b

19. Graphing Review 1.Title = dependent variable vs independent variable a.x – axis = independent variable b.y – axis = dependent variable

20. Graphing Review 2.Slope a.Formula: m =  y = y 2 – y 1  x = x 2 – x 1 b.Significance: dependent on units of the variables Ex) What is the physical significance of a mass vs volume graph?

21. Graphing Review 3.Area under the graph a.Calculate: base x height OR - if a triangle A = ½ base x height b.Significance determined by units Ex) What would be the significance of the area under a graph on a velocity (m/s) vs time (s) graph for a particular time interval?

22. Graph Relationships 1.Direct General formula: y = mx + b

23. Graph Relationships 2.Parabolic General Formula: y = x 2

24. Graph Relationships 3.Inverse General Formula: y = 1/x

25. Graph Relationships 4.Square Root General Formula: y = √x