1. Unit I Units and Measurement
Objectives - Express lengths, mass, time in SI units. - Convert distances between different units. - Describe time intervals in hours, minutes, and seconds. - Convert time in mixed units to time in seconds. - Describe the mass of objects in grams and kilograms.

2. It All Starts with a Ruler!!!

3. I. Two Systems of Units
Metric system and International System of Units
meter
kilogram
second
Kelvin
2. English system
inches, feet, yards, and miles.
pound
Fahrenheit

4. 3. SI units meter (m): unit of length kilogram (kg): unit of mass
second (s): unit of time

5.  meter, (SI unit symbol: m), is the fundamental unit of length in the International System of Units (SI).
Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole (at sea level).
Since 1983, it has been defined as "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second."
National Prototype Metre Bar ( alloy of ninety percentplatinum and ten percent iridium) in  International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France.

6.  kilogramme ( kg), is the base unit of mass in the International System of Units (SI)
Is defined as being equal to the mass of the International Prototype of the Kilogram (platinum–iridium alloy) in International Bureau of Weights and Measures in Sèvres, France

7. Second (sec or s)
The second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

8. UNITS (Systéme Internationale)

9. 4. Examples
The units for length, mass, and time (as well as a few others), are regarded as base SI units.
These units are used in combination to define additional units for other important physical quantities such as force and energy.

10. II THE CONVERSION OF UNITS A) relation between different units
1 ft = m
1 mi = km
1 liter = 10-3 m3

11. Example 1.1
Grandma traveled 27 minutes at 44 m/s.
How many miles did Grandma travel?
44𝑚 𝑠 = 44𝑚 1609𝑚 𝑚𝑖𝑙𝑒 1𝑠 60𝑠 𝑚𝑖𝑛 =44× mile/min=1.64mile/min
27𝑚𝑖𝑛× 1.64𝑚𝑖𝑙 𝑚𝑖𝑛 =44.3𝑚𝑖𝑙𝑒𝑠
44.3 miles

12. (3.281 feet)/(1 meter) = 1 and (1 meter) / (3.281 feet)=1
B) How to convert
Example 1 The World’s Highest Waterfall
The highest waterfall in the world is Angel Falls in Venezuela,
with a total drop of m. Express this drop in feet.
Since feet = 1 meter, it follows that
(3.281 feet)/(1 meter) = 1 and (1 meter) / (3.281 feet)=1
For meter  feet:

13. A football field is 100 yards long.
Convert 100km to miles
A football field is 100 yards long.
What is this distance expressed in meters?

14. C) unit convert chart

16. Reasoning Strategy: Converting Between Units
D) Summary
Reasoning Strategy: Converting Between Units
1. In all calculations, write down the units explicitly.
2. Treat all units as algebraic quantities. When
identical units are divided, they are eliminated
algebraically.
3. Use the conversion factors in reference tables. Be guided by the fact that multiplying or dividing an equation by a factor of 1 does not alter the equation.

17. time Two ways to think about time: What time is it?
3 P.M. Eastern Time on April 21, 2004,
How much time has passed?
3 hr: 44 min: 25 sec.
A quantity of time is often called a time interval.

18. Converting Mixed Units
You are asked for time in seconds.
You are given a time interval in mixed units.
1 hour = 3,600 sec minute = 60 sec
Do the conversion:
1 hour = 3,600 sec
26 minutes = 26 × 60 = 1,560 sec
Add all the seconds:
t = 3, , = 5, sec

19. Time Units

20. E) Practice
Example 2 Interstate Speed Limit
Express the speed limit of 65 miles/hour in terms of meters/second.
Use 5280 feet = 1 mile and 3600 seconds = 1 hour and
3.281 feet = 1 meter.

21. More practice 1. Convert 789 cm2 to m2 2. Convert 75.00 km/h to m/s
1m=100cm, 1m2=100cm *100cm=10000cm2
789 𝑐𝑚 2 =789 𝑐𝑚 2 × 1 𝑚 𝑐𝑚 2 = 𝑚 2
2. Convert km/h to m/s
km x 1000 m x 1 h___ = 20.83m/s
h km s

22. III Limits of Measurement
A). Accuracy and Precision

23. Accuracy - a measure of how close a measurement is to the true value of the quantity being measured.

24. Example: Accuracy
Who is more accurate when measuring a book that has a true length of 17.0cm?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

25. Precision – a measure of how close a series of measurements are to one another. A measure of how exact a measurement is.

26. Example: Precision
Who is more precise when measuring the same 17.0cm book?
Susan:
17.0cm, 16.0cm, 18.0cm, 15.0cm
Amy:
15.5cm, 15.0cm, 15.2cm, 15.3cm

27. Example: Evaluate whether the following are precise, accurate or both.
Not Precise
Not Accurate
Precise
Accurate
Precise

28. --Why significant figures is important
--Why significant figures is important? --What does significant figures in a number consist of? --How to record measurement with proper significant figures? (digram) --List the rules in counting significant figures (zero rules) --Rules in calculation: Multiplication rule Division rule Addition & subtraction rule Rule in calculate average

29. B) Significant Figures
The significant figures in a measurement include all of the digits that are known, plus one last digit that is estimated.

30. Centimeters and Millimeters
40.16 cm

31. The length of this miniature piezo electric motor is:
8.0 mm

32. B.1) Finding the Number of Sig Figs:
All non-zero digits are significant.
Zeros between two non-zero digits are significant.
Leading zeros are not significant.
Trailing zeros in a number containing a decimal point are significant.
trailing zeros in a number not containing a decimal point can be ambiguous. (scientific notation is the solution)

33. One convention about trailing zero
A bar placed over ( or under) the last significant figure; any trailing zeros following this are insignificant
Example:
500 has 1 s.f has 2 s.f.
500 has 2 s.f has 3 s.f.

34. Standard decimal notation
Scientific notation
Write number in form: 𝑎× 10 𝑏
1≤𝑎<10, b is proper exponent
Standard decimal notation
Scientific notation 2
2×100
300
3×102 4,
×103
−53,000
−5.300×104
6,720,0 0 0,000
×109
0.2
2×10−1
0.000 000 007 51
7.51×10−9

35. How many sig figs? 7 2 3 5
x104 2 5 1

36. B.2)Sig Figs in Addition/Subtraction
Express the result with the same number of decimal places as the number in the operation with the least decimal places.
Ex: cm cm
5.3 cm
(Result is rounded to one decimal place)

37. B.3) Sig Figs in Multiplication/Division
Express the answer with the same sig figs as the factor with the least sig figs.
Ex: cm
x cm
6.4 cm2 (Result is rounded to two sig figs)

38. More example
2330 cm cm cm
2330𝑚 3.0𝑠 =780𝑚/𝑠

39. B.4) Constant and Counting Numbers
Constant number have infinite sig. figs.
Counting numbers have infinite sig figs.
Ex: 3 apples
Eg. π= ……

40. C) practice 2. Perimeter of the big circle
1.Calculate Volume of sphere with
2. Perimeter of the big circle

41. 𝐷=2.015𝑚+4.5 𝑚/𝑠×2.35𝑠 = A=𝜋 𝑟 2 = 𝜋 (1.25𝑚) 2 = Try the following=
(8.71 x )/0.056 =
𝐷=2.015𝑚+4.5 𝑚/𝑠×2.35𝑠 =
13m
A=𝜋 𝑟 2 = 𝜋 (1.25𝑚) 2 =
4.91m2

42. IV Dimension Analysis – some simple rules
1.In 𝒎𝒖𝒍𝒕𝒊𝒑𝒍𝒊𝒄𝒂𝒕𝒊𝒐𝒏 𝒐𝒓 𝒅𝒊𝒗𝒊𝒔𝒊𝒐𝒏: The product unit is the product of the individual unit of each of those variables. (Ditto for ratios.)
2. 𝐈𝐧 𝒂𝒅𝒅𝒊𝒕𝒊𝒐𝒏 𝒐𝒓 𝒔𝒖𝒃𝒕𝒓𝒂𝒄𝒕𝒊𝒐𝒏: Different terms can only added together in a sum if each term in the sum has the same unit type. (Ditto for subtraction.)

43. - Can Do: 50.0m + 20.55m=70.6m and 40m/s +11m/s =51m/s Example 1
- impossible: 40m + 20m/s
or 12.5 s - 20m2
- Can Do: 50.0m m=70.6m
and 40m/s +11m/s =51m/s
- Can Do, but need to convert into same unit:
40m + 11cm = 40m + 11cm × 1𝑚 100𝑐𝑚
= 40.11m

44. Example 2 The above expression yields: 4.5 m kg 4.5 g km A or B
Impossible to evaluate (dimensionally invalid)

45. IV Scalars and Vectors Definition
A scalar quantity is one that can be described
by a single number:
temperature, speed, mass
A vector quantity deals inherently with both
magnitude and direction:
velocity, force, displacement

46. By convention, the length of a vector
2. Graph a Vector
Arrows are used to represent vectors. The
direction of the arrow gives the direction of
the vector.
By convention, the length of a vector
arrow is proportional to the magnitude
of the vector.
8 lb
4 lb

48. 3. Vector Addition and Subtraction
Often it is necessary to add one vector to another. A)

49. example 1
3 m
5 m
8 m

50. B) Example 2

51. Example 2 continue
2.00 m
6.00 m

52. Example 2 continue R
2.00 m
6.00 m

53. 1.6 Vector Addition and Subtraction
6.32 m
2.00 m
6.00 m

54. C) When a vector is multiplied by -1, the magnitude of the
vector remains the same, but
the direction of the vector is
reversed.

55. Example 3
Given

56. 1.7 The Components of a Vector

57. 1.7 The Components of a Vector

58. 1.7 The Components of a Vector
It is often easier to work with the scalar components
rather than the vector components.

59. 1.7 The Components of a Vector
Example
A displacement vector has a magnitude of 175 m and points at
an angle of 50.0 degrees relative to the x axis. Find the x and y
components of this vector.

60. 1.8 Addition of Vectors by Means of Components

61. 1.8 Addition of Vectors by Means of Components

62. IV The Role of Units in Problem Solving (not included)
DIMENSIONAL ANALYSIS
[L] = length [M] = mass [T] = time
Is the following equation dimensionally correct?

63. 1.3 The Role of Units in Problem Solving
Is the following equation dimensionally correct?

64. 1.4 Trigonometry

65. 1.4 Trigonometry

66. 1.4 Trigonometry

67. 1.4 Trigonometry

68. 1.4 Trigonometry

69. 1.4 Trigonometry
Pythagorean theorem: