1. Dimensions of Physics

2. The essence of physics is to measure the observable world and describe the principles that underlie everything in creation. This usually involves mathematical formulas.

3. The Metric System first established in France and followed voluntarily in other countries renamed in 1960 as the SI (Système International d’Unités) seven fundamental units

4. Dimension can refer to the number of spatial coordinates required to describe an object can refer to a kind of measurable physical quantity

5. Dimension the universe consists of three fundamental dimensions: space time matter

6. Length the meter is the metric unit of length definition of a meter: the distance light travels in a vacuum in exactly 1/299,792,458 second.

7. Time defined as a nonphysical continuum that orders the sequence of events and phenomena SI unit is the second

8. Mass a measure of the tendency of matter to resist a change in motion mass has gravitational attraction

9. The Seven Fundamental SI Units length time mass thermodynamic temperature meter second kilogram kelvin

10. The Seven Fundamental SI Units amount of substance electric current luminous intensity mole ampere candela

11. SI Derived Units involve combinations of SI units examples include: area and volume force (N = kg m/s²) work (J = N m)

12. Conversion Factors any factor equal to 1 that consists of a ratio of two units You can find many conversion factors in Appendix C of your textbook.

13. Unit Analysis First, write the value that you already know. 18m

14. Unit Analysis Next, multiply by the conversion factor, which should be written as a fraction. Note that the old unit goes in the denominator. 18× 100 cm 1 m m

15. Unit Analysis Then cancel your units. Remember that this method is called unit analysis. 18× 100 cm 1 m m

16. Unit Analysis Finally, calculate the answer by multiplying and dividing. =1800 cm18× 100 cm 1 m m

17. Unit Analysis Bridge

18. Convert 13400 m to km. 13400 m × 1 km 1000 m = 13.4 km Sample Problem #1

19. How many seconds are in a week? 1 wk × 7 d 1 wk =604,800 s × 24 h 1 d × 60 min 1 h × 60 s 1 min Sample Problem #2

20. Convert 35 km to mi, if 1.6 km ≈ 1 mi. 35 km × 1 mi 1.6 km ≈ 21.9 mi Sample Problem #3

21. Principles of Measurement

22. Instruments tools used to measure critical to modern scientific research man-made

23. comparing the object being measured to the graduated scale of an instrument Accuracy

24. dependent upon: quality of original design and construction how well it is maintained reflects the skill of its operator Accuracy

25. the simple difference of the observed and accepted values may be positive or negative Error

26. absolute error—the absolute value of the difference Error

27. Percent Error observed – accepted accepted × 100%

28. a qualitative evaluation of how exactly a measurement can be made describes the exactness of a number or measured data Precision

29. some quantities can be known exactly definitions countable quantities Precision

30. irrational numbers can be specified to any degree of exactness desired potentially unlimited precision Precision

31. When you use a mechanical metric instrument (one with scale subdivisions based on tenths), measurements should be estimated to the nearest 1/10 of the smallest decimal increment.

32. The last digit that has any significance in a measurement is estimated.

33. Truth in Measurements and Calculations

34. Remember: The last (right- most) significant digit is the estimated digit when recording measured data. Significant Digits

35. Rule 1: SD’s apply only to measured data. Significant Digits

36. Rule 2: All nonzero digits in measured data are significant. Significant Digits

37. Rule 3: All zeros between nonzero digits in measured data are significant. Significant Digits

38. Rule 4: For measured data containing a decimal point: Significant Digits All zeros to the right of the last nonzero digit (trailing zeros) are significant

39. Rule 4: For measured data containing a decimal point: Significant Digits All zeros to the left of the first nonzero digit (leading zeros) are not significant

40. Rule 5: For measured data lacking a decimal point: Significant Digits No trailing zeros are significant

41. Scientific notation shows only significant digits in the decimal part of the expression. Significant Digits

42. A decimal point following the last zero indicates that the zero in the ones place is significant. Significant Digits

43. ...and be careful when using your calculator!

44. Rule 1: All units must be the same before you can add or subtract. Adding and Subtracting

45. Rule 2: The precision cannot be greater than that of the least precise data given. Adding and Subtracting

46. Rule 1: A product or quotient of measured data cannot have more SDs than the measurement with the fewest SDs. Multiplying and Dividing

47. Rule 2: The product or quotient of measured data and a pure number should not have more or less precision than the original measurement. Multiplying and Dividing

48. Rule 1: If the operations are all of the same kind, complete them before rounding to the correct significant digits. Compound Calculations

49. Rule 2: If the solution to a problem requires a combination of both addition/subtraction and multiplication/division... Compound Calculations

50. (1) For intermediate calculations, underline the estimated digit in the result and retain at least one extra digit beyond the estimated digit. Drop any remaining digits. Compound Calculations

51. (2) Round the final calculation to the correct significant digits according to the applicable math rules, taking into account the underlined estimated digits in the intermediate answers. Compound Calculations

52. What about angles and trigonometry?

53. The SI uses radians. A radian is the plane angle that subtends a circular arc equal in length to the radius of the circle. Angles in the SI

54. 2π radians = 360° Angles in the SI Angles measured with a protractor should be reported to the nearest 0.1 degree.

55. Degrees to Radians: Conversions Multiply the number of degrees by π/180.

56. Radians to Degrees: Conversions Multiply the number of radians by 180/π.

57. Report angles resulting from trigonometric calculations to the lowest precision of any angles given in the problem. Angles in the SI

58. Assume that trigonometric ratios for angles given are pure numbers; SD restrictions do not apply. Angles in the SI

59. Problem Solving

60. Read the exercise carefully! What information is given? What information is sought? Make a basic sketch

61. Problem Solving Determine the method of solution Substitute and solve Check your answer for reasonableness

62. Reasonable Answers Does it have the expected order of magnitude? Make a mental estimate Be sure to simplify units Express results to the correct number of SDs