1. Dimensions of Physics

2. This usually involves mathematical formulas.
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. Measurements - Quantitative
Unit of measurement – the unit being measured
Pure number – the number of units determined by the act of measuring
Measurement – the product of the pure number and the unit of measurement

13. Your Turn to Decide
4 feet
extra large
Hot
100 ºF
Sunny 96

14. 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.

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

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

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

18. Unit Analysis
Finally, calculate the answer by multiplying and dividing.
100 cm 1 18 m × =
1800 cm m

19. Unit Analysis Bridge

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

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

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

23. Dimensional Analysis Converts from one unit to another
Conversion Factor – a fraction (ratio) comparing two units
Examples:
12 inches = 1 foot
3 feet = 1 yard
100 cm = 1 m
60 s = 1 min
Conversion factors can be inverted!!

24. Grid Method for Conversions
Given Information
Conversion
Requested Information
(Understood 1)
Factor

25. Grid Method for Conversions
Convert 8.4 miles to feet.
8.4 miles
5280 feet
44,352 feet
(Understood 1)
1 mile

26. Grid Method for Conversions
Convert 8.4 miles to feet.
8.4 miles
5280 feet
44,352 feet
(Understood 1)
1 mile

27. Dimensional Analysis 14 x 1018 s
How many days is equal to 14 x 1018 s?
14 x 1018 s
1 min
1 hour
1 day
60 s
60 min
24 hours

28. Types of measurement Quantitative- use numbers to describe
Easy to verify
Easy to agree upon, no personal bias
The measuring instrument limits how good the measurement is
Qualitative- use description without numbers

29. How good are the measurements?
Scientists use two words to describe how good the measurements are
Accuracy- how close the measurement is to the actual value
Precision- how well can the measurement be repeated

30. Differences
Accuracy can be true of an individual measurement or the average of several
Precision requires several measurements before anything can be said about it
Example

31. Let’s use a golf analogy.

32. Accurate? No
Precise?
Yes

33. Accurate?
Yes
Precise?
Yes

34. Precise? No
Accurate?
Maybe?

35. Accurate?
Yes
Precise?
We cant say!

36. Principles of Measurement

37. In terms of measurement
Three students measure the room to be m, 10.3 m and 10.4 m across.
Were they precise?
Were they accurate?

38. The Metric System
An easy way to measure

39. Converting k h D d c m
how far you have to move on this chart, tells you how far, and which direction to move the decimal place.
The box is the base unit, meters, Liters, grams, etc.

40. Conversions k h D d c m
Change 5.6 km to millimeters

41. Significant figures (sig figs)
How many numbers mean anything
When we measure something, we can (and do) always estimate between the smallest marks. 2 1 3 4 5

42. Significant figures (sig figs)
The better marks the better we can estimate.
Scientist always understand that the last number measured is actually an estimate 1 2 3 4 5

43. Sig Figs All nonzero numbers are significant!
So….what do we do with zeros??
We follow the rules!

44. Significant Digit Rules
Only applied to measured data.
Counting numbers are infinitely significant!
All nonzero digits are significant!
All zeros between nonzero digits are significant!
In a decimal number all zeros to the right of the last nonzero digit are significant!

45. Significant Digit Rules
In a decimal number all zeros to the left of the first nonzero digit are NOT significant!
In a number WITHOUT a decimal all trailing zeros (zeros to the right of the last nonzero digit) are NOT significant!

46. Remember….
Scientific Notation only shows significant digits in the decimal part of the expression.
A decimal point following a zero at the end of the number indicates that the zero is significant.

47. Problems 50 has only 1 significant figure
if it should have two, how can I write it?
A decimal following a zero at the end.
50.
A line over the significant zero 50
Scientific notation
5.0 x 101
now the zero counts

48. Sig figs. How many sig figs in the following measurements? 458 g

49. Sig Figs.
405.0 g
4050 g
0.450 g g g
Next we learn the rules for calculations

50. Adding and Subtracting with Sig Figs
The last sig fig in a measurement is an estimate.
Your answer when you add or subtract can not be better than your worst estimate.
You must round the answer to the least precise place of the measurement in the problem

51. For example
27.93
6.4 +
First line up the decimal places
27.93
6.4 +
27.93
6.4
Then do the adding
Find the estimated numbers in the problem
34.33
This answer must be rounded to the tenths place

52. Rounding rules
look at the number to the right of the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
round to four sig figs
to three sig figs
to two sig figs
to one sig fig

53. Practice
6.0 x x 103
6.0 x x 10-3

54. Multiplication and Division
Rule is simpler: Same number of sig figs in the answer as the one with the least number of sig figs in the question
3.6 x 653
2350.8
3.6 has 2 s.f. 653 has 3 s.f.
answer can only have 2 s.f.
2400

55. Practice
5.345 • 3.9
4.5 ÷ 6.245
4.50 • 6.245
• 0.043
3.876 ÷ 1983
16047 ÷ 700
2400 • 123
4.5 x 102 • 1.45 x 103

56. Truth in Measurements and Calculations

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

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

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

60. Compound Calculations
(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.

61. Compound Calculations
(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.

62. What about angles and trigonometry?

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

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

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

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

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

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

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

70. 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.

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

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

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

74. Percent Error
observed – accepted
accepted
× 100%

75. Problem Solving

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

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

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