1. Physics chapter 11 Models, Measurements, and Vectors

2. Physics chapter 12 Physics is…. The study of nature. the study of the natures of matter and energy. The study of the relationship between matter and energy.

3. Physics chapter 13 Physics is based on Experiments Observations

4. Physics chapter 14 The language of physics The laws of physics can almost always be expressed using mathematical relationships. So, mathematics is the language of physics.

5. Physics chapter 15 Why study physics? A fundamental science Technology Scientific insight into everyday world

6. Physics chapter 16 Theories Principles Laws

7. Physics chapter 17 Idealized models Model  Simplified version of a complicated physical system We neglect minor effects on the system to concentrate on the major effects.

8. Physics chapter 18 Units We use the metric or SI system Base units  Meter – m – length  Kilogram – kg – mass  Second – s – time All answers must have units, or they are meaningless

9. Physics chapter 19 Prefixes Added to units to indicate mulitples of 10 or 1/10 Kilo – 1000 or 10 3 – kilometer – km Nano – 10 -9 – nanosecond – ns Milli – 10 -3 – milligram – mg Micro – 10 -6 – microsecond –  s Page 6 for more

10. Physics chapter 110 Unit analysis Also called dimensional analysis. Units must work out. Units are treated just like algebraic symbols in equations

11. Physics chapter 111 Example 1

12. Physics chapter 112 Alternative method (Example 2)

13. Physics chapter 113 Unit Conversions Use ratios Carry your units through to make sure they cancel

14. Physics chapter 114 Example 3 Convert 6 ft 1 in to m.

15. Physics chapter 115 Uncertainty More accurate measurements have less uncertainty. We can express uncertainty in two ways:  75.6  3.78 cm  75.6 cm  5%

16. Physics chapter 116 Significant figures We usually don’t write numbers with uncertainties. Instead, we use significant figures.

17. Physics chapter 117 Significant Figures All the digits known in a measurement, plus one that is somewhat uncertain. All nonzero digits are significant Zeros are governed by four rules 1. Zeros between nonzero digits are significant  203 has 3 sig figs  5.0279 has 5 sig figs

18. Physics chapter 118 Significant Figures 2. Zeros in front of all nonzero digits are not significant  0.0035 has 2 sig figs  0.0008 has 1 sig fig 3. Zeros at the end of a number and after the decimal point are significant.  75.000 has 5 sig figs  0.000800 has 3 sig figs

19. Physics chapter 119 Significant Figures 4. Zeros at the end of a number but before the decimal point may or may not be significant. If a zero is just a placeholder, it is not significant. If it has been measured, it is significant. To show all zeros are significant, use a decimal point. To show some are, use scientific notation (later)  2000 has 1 sig fig  2000. has 4 sig figs

20. Physics chapter 120 Examples 4 2.5  2 sig figs 2.50  3 sig figs 250  2 sig figs 250.  3 sig figs 250.0  4 sig figs 0.0025  2 sig figs 0.00250  3 sig figs 0.002501  4 sig figs

21. Physics chapter 121 Multiplication and Division The result should have the same number of significant figures as the least number of significant figures in any factor.

22. Physics chapter 122 Example 5 Since 1.2 only has 2 sig figs, our answer can only have 2 sig figs. We would record our answer as 1.6

23. Physics chapter 123 Example 6 Since 8 only has 1 sig fig, the answer should only have 1 sig fig. Record the answer as 3

24. Physics chapter 124 Addition and Subtraction The result has no significant figures beyond the last decimal place where all of the original numbers had significant figures.

25. Physics chapter 125 Example 7 Since 1.040 only has 3 sig figs after the decimal, the answer can only have 3 sig figs after the decimal. Record the answer as 1.253

26. Physics chapter 126 Example 8 Since 900 has its last sig fig in the hundreds column, then the result’s last sig fig must be in the hundreds column. Record the answer as 300

27. Physics chapter 127 Conversion factors Conversion factors are considered exact, and do not affect significant digits. There are exactly 100 cm in 1 m, so don’t use the 100 to figure out how many significant digits your answer should have.

28. Physics chapter 128 Scientific Notation Useful when writing very small or very large numbers Also useful for indicating the number of significant figures 696,000,000 m = 6.96 x 10 8 m 4,000,000 km = 4 x 10 6 km or 4.00 x 10 6 km

29. Physics chapter 129 Precision vs. Accuracy Bathroom scale with 5 pound increments might be very accurate, but is not very precise. Doctor’s office scale with 1/10 pound increments is very precise, but might not be very accurate. A good measurement is both accurate and precise.

30. Physics chapter 130 Estimates and orders of magnitude Read section 1.6, including the example.

31. Physics chapter 131 Vectors Have magnitude and direction Typed in bold with an arrow over them Handwritten with an arrow over them

32. Physics chapter 132 Vectors Two vectors with the same direction are parallel. Two vectors with the opposite direction are antiparallel. Two vectors with the same direction and magnitude are equal.

33. Physics chapter 133 Vector magnitude The magnitude of a vector is a scalar (a number) and is always positive. Write it as the vector name without the arrow or like this:

34. Physics chapter 134 Vector addition - geometrically Place the tail of the second vector at the tip of the first vector. The vector sum, or the resultant, is the vector connecting the starting point and the ending point.

35. Physics chapter 135 Example 9 Miss Becker drives 4 mi north and then 11 mi west. How far and in what direction is she from her starting point?

36. Physics chapter 136 Vector subtraction Just flip around vector B and then add.

37. Physics chapter 137 Vector components Any vector can be separated into component vectors that are parallel to the Cartesian (x and y) axes. The vector sum of these components is equal to the original vector

38. Physics chapter 138 Finding vector components We can find vector components using trigonometry. These equations work when  is measured CCW from the positive x- axis.

39. Physics chapter 139 Example 10

40. Physics chapter 140 Vector addition – using components Each component of the resultant vector is equal to the sum of the corresponding components of the vectors being added

41. Physics chapter 141 Finding vector magnitude and direction If given a vector in terms of its components, we can find its magnitude and direction using trig

42. Physics chapter 142 Finding vector direction

43. Physics chapter 143 Example 11 Find the resultant vector in terms of  A) components  B) magnitude and direction

44. Physics chapter 144 Example part A)

45. Physics chapter 145 Example part B)

46. Physics chapter 146 Example part B) Is this right?

47. Physics chapter 147 Tan -1 can be tricky Angles that differ by 180° have the same tangent. Your calculator doesn’t know which one you want.