The document discusses measurement in physics. It covers: 1. The SI system of fundamental and derived units, including defining the 7 base units and giving examples of derived units. 2. Measurement uncertainties and errors, distinguishing between random and systematic errors and explaining how to reduce random errors. Precision is defined as having small random error, accuracy as having small systematic error. 3. Converting between different units, stating units in proper SI format, and expressing values using scientific notation and prefixes.

1. Topic 1
Physics and Physical
Measurement

2. Part I
SI system of fundamental and
derived units

3. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units

4. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system

5. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units

6. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities

7. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities
• State units in the accepted SI format

8. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities
• State units in the accepted SI format
• State values in scientific notation and in multiples
of units with appropriate prefixes

9. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities
• State units in the accepted SI format
• State values in scientific notation and in multiples
of units with appropriate prefixes

10. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system

11. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

12. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

13. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

14. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

15. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

16. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

17. 1.2 Measurement and Uncertainties
• State the fundamental units in the SI system
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of substance mole mol
Temperature kelvin K

18. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities
• State units in the accepted SI format
• State values in scientific notation and in multiples
of units with appropriate prefixes

19. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units

20. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units

21. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units
All other SI units used in this course are derived units. They
are based on fundamental units.

22. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units

23. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units
Quantity Symbol Base units
Volume m3 mxmxm
Speed ms−1 m/s
Force N kg x m/s2

24. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units
Quantity Symbol Base units
Volume m3 mxmxm
Speed ms−1 m/s
Force N kg x m/s2

25. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units
Quantity Symbol Base units
Volume m3 mxmxm
Speed ms−1 m/s
Force N kg x m/s2

26. 1.2 Measurement and Uncertainties
• Distinguish between fundamental and derived units
and give examples of derived units
Quantity Symbol Base units
Volume m3 mxmxm
Speed ms−1 m/s
Force N kg x m/s2

27. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities
• State units in the accepted SI format
• State values in scientific notation and in multiples
of units with appropriate prefixes

28. 1.2 Measurement and Uncertainties
• Convert between different units of quantities

29. 1.2 Measurement and Uncertainties
• Convert between different units of quantities

30. 1.2 Measurement and Uncertainties
• Convert between different units of quantities
1 kWh = 103 Wh = 103 Js−1 x 3600s = 3.6 x 106 J

31. 1.2 Measurement and Uncertainties
• Convert between different units of quantities
1 kWh = 103 Wh = 103 Js−1 x 3600s = 3.6 x 106 J
1 kWh = 3.6 x 106 J

32. 1.2 Measurement and Uncertainties
• Convert between different units of quantities
1 kWh = 103 Wh = 103 Js−1 x 3600s = 3.6 x 106 J
1 kWh = 3.6 x 106 J
1eV = 1.6 x 10−19 C x JC−1 = 1.6 x 10−19 J

33. 1.2 Measurement and Uncertainties
• Convert between different units of quantities
1 kWh = 103 Wh = 103 Js−1 x 3600s = 3.6 x 106 J
1 kWh = 3.6 x 106 J
1eV = 1.6 x 10−19 C x JC−1 = 1.6 x 10−19 J
1 eV = 1.6 x 10−19 J

34. 1.2 Measurement and Uncertainties
• Convert between different units of quantities
1 kWh = 103 Wh = 103 Js−1 x 3600s = 3.6 x 106 J
1 kWh = 3.6 x 106 J
1eV = 1.6 x 10−19 C x JC−1 = 1.6 x 10−19 J
1 eV = 1.6 x 10−19 J

35. 1.2 Measurement and Uncertainties
• Convert between different units of quantities
1 kWh = 103 Wh = 103 Js−1 x 3600s = 3.6 x 106 J
1 kWh = 3.6 x 106 J
1eV = 1.6 x 10−19 C x JC−1 = 1.6 x 10−19 J
1 eV = 1.6 x 10−19 J

36. 1.2 Measurement and Uncertainties
The SI system of fundamental and derived units
• State the fundamental units in the SI system
• Distinguish between fundamental and derived units
and give examples of derived units
• Convert between different units of quantities
• State units in the accepted SI format
• State values in scientific notation and in multiples
of units with appropriate prefixes

37. 1.2 Measurement and Uncertainties
• State units in the accepted SI format

38. 1.2 Measurement and Uncertainties
• State units in the accepted SI format

39. 1.2 Measurement and Uncertainties
• State units in the accepted SI format
m/s ms−1
m/s2 ms−2

40. 1.2 Measurement and Uncertainties
• State units in the accepted SI format
m/s ms−1
m/s2 ms−2

41. 1.2 Measurement and Uncertainties
• State units in the accepted SI format
m/s ms−1
m/s2 ms−2
• State values in scientific notation and in multiples of
units with appropriate prefixes

42. 1.2 Measurement and Uncertainties
• State units in the accepted SI format
m/s ms−1
m/s2 ms−2
• State values in scientific notation and in multiples of
units with appropriate prefixes

43. 1.2 Measurement and Uncertainties
• State units in the accepted SI format
m/s ms−1
m/s2 ms−2
• State values in scientific notation and in multiples of
units with appropriate prefixes
Speed of Light = 300000000 ms−1 = 3.0 x 108 ms−1

44. 1.2 Measurement and Uncertainties
• State units in the accepted SI format
m/s ms−1
m/s2 ms−2
• State values in scientific notation and in multiples of
units with appropriate prefixes
Speed of Light = 300000000 ms−1 = 3.0 x 108 ms−1
Wavelegth of blue light = 4.5 x 10−7 m = 450 nm

45. Part II
Uncertainty and error in
measurement

46. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement

47. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors

48. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy

49. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy
• Explain how the effects of random errors may be
reduced

50. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy
• Explain how the effects of random errors may be
reduced
• Calculate quantities and results of calculations to
the appropriate number of significant figures

51. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy
• Explain how the effects of random errors may be
reduced
• Calculate quantities and results of calculations to
the appropriate number of significant figures

52. 1.2 Measurement and Uncertainties
• Describe and give examples of random and
systematic errors

53. 1.2 Measurement and Uncertainties
• Describe and give examples of random and
systematic errors

54. 1.2 Measurement and Uncertainties
• Describe and give examples of random and
systematic errors
Random Error Systematic Error
It is a random error if you get lots of It is a systematic error if there is
slightly different readings when making a something wrong with equipment of
measurement method when taking a measurement
You can reduce the error by repeating the Error can not be reduced by repeating
measurement the measurement
Not easy to spot right away but it may
It is easy to spot random error when
become evident when a linear graph that
collecting data by the variance of the
should cross the origin has a relevant
readings
y-intercept

55. 1.2 Measurement and Uncertainties
• Describe and give examples of random and
systematic errors
Random Error Systematic Error
It is a random error if you get lots of It is a systematic error if there is
slightly different readings when making a something wrong with equipment of
measurement method when taking a measurement
You can reduce the error by repeating the Error can not be reduced by repeating
measurement the measurement
Not easy to spot right away but it may
It is easy to spot random error when
become evident when a linear graph that
collecting data by the variance of the
should cross the origin has a relevant
readings
y-intercept

56. 1.2 Measurement and Uncertainties
• Describe and give examples of random and
systematic errors
Random Error Systematic Error
It is a random error if you get lots of It is a systematic error if there is
slightly different readings when making a something wrong with equipment of
measurement method when taking a measurement
You can reduce the error by repeating the Error can not be reduced by repeating
measurement the measurement
Not easy to spot right away but it may
It is easy to spot random error when
become evident when a linear graph that
collecting data by the variance of the
should cross the origin has a relevant
readings
y-intercept

57. 1.2 Measurement and Uncertainties
• Describe and give examples of random and
systematic errors
Random Error Systematic Error
It is a random error if you get lots of It is a systematic error if there is
slightly different readings when making a something wrong with equipment of
measurement method when taking a measurement
You can reduce the error by repeating the Error can not be reduced by repeating
measurement the measurement
Not easy to spot right away but it may
It is easy to spot random error when
become evident when a linear graph that
collecting data by the variance of the
should cross the origin has a relevant
readings
y-intercept

58. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy
• Explain how the effects of random errors may be
reduced
• Calculate quantities and results of calculations to
the appropriate number of significant figures

59. 1.2 Measurement and Uncertainties
• Distinguish between precision and accuracy

60. 1.2 Measurement and Uncertainties
• Distinguish between precision and accuracy

61. 1.2 Measurement and Uncertainties
• Distinguish between precision and accuracy
An accurate experiment is one that has small systematic
error, whereas a precise experiment is one that has a small
random error

62. 1.2 Measurement and Uncertainties
• Distinguish between precision and accuracy
An accurate experiment is one that has small systematic
error, whereas a precise experiment is one that has a small
random error
An experiment may have great precision but be inaccurate

63. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy
• Explain how the effects of random errors may be
reduced
• Calculate quantities and results of calculations to
the appropriate number of significant figures

64. 1.2 Measurement and Uncertainties
• Explain how the effects of random errors may be
reduced

65. 1.2 Measurement and Uncertainties
• Explain how the effects of random errors may be
reduced

66. 1.2 Measurement and Uncertainties
• Explain how the effects of random errors may be
reduced
Random error can be reduced by taking repeated reading of a
measurement. Systematic error can not be reduced this way

67. 1.2 Measurement and Uncertainties
Uncertainty and error in measurement
• Describe and give examples of random and
systematic errors
• Distinguish between precision and accuracy
• Explain how the effects of random errors may be
reduced
• Calculate quantities and results of calculations to
the appropriate number of significant figures

68. 1.2 Measurement and Uncertainties
• Calculate quantities and results of calculations to
the appropriate number of significant figures

69. 1.2 Measurement and Uncertainties
• Calculate quantities and results of calculations to
the appropriate number of significant figures

70. 1.2 Measurement and Uncertainties
• Calculate quantities and results of calculations to
the appropriate number of significant figures
The number of significant figures should reflect the precision
of the value of the input data. The number of significant digits
in a result should not exceed that of the least precise value
upon which it depends.

71. 1.2 Measurement and Uncertainties
• Calculate quantities and results of calculations to
the appropriate number of significant figures
The number of significant figures should reflect the precision
of the value of the input data. The number of significant digits
in a result should not exceed that of the least precise value
upon which it depends.
e.g. 9.8 x 13.45 = 131.81
but the answer should be expressed in 2 significant figures:
1.3 x 102

72. Part III
Uncertainty in calculated
results

73. 1.2 Measurement and Uncertainties
Uncertainty in calculated results

74. 1.2 Measurement and Uncertainties
Uncertainty in calculated results
• State uncertainties as absolute, fractional and
percentage uncertainties.

75. 1.2 Measurement and Uncertainties
Uncertainty in calculated results
• State uncertainties as absolute, fractional and
percentage uncertainties.
• Determine the uncertainties in results.

76. 1.2 Measurement and Uncertainties
Uncertainty in calculated results
• State uncertainties as absolute, fractional and
percentage uncertainties.
• Determine the uncertainties in results.

77. 1.2 Measurement and Uncertainties
• State uncertainties as absolute, fractional and
percentage uncertainties.

78. 1.2 Measurement and Uncertainties
• State uncertainties as absolute, fractional and
percentage uncertainties.

79. 1.2 Measurement and Uncertainties
• State uncertainties as absolute, fractional and
percentage uncertainties.
Absolute Uncertainty
Room temperature = 22.5ºC ± 0.5

80. 1.2 Measurement and Uncertainties
• State uncertainties as absolute, fractional and
percentage uncertainties.
Absolute Uncertainty
Room temperature = 22.5ºC ± 0.5
Percent Uncertainty
Room temperature = 22.5ºC ± 2.2%

81. 1.2 Measurement and Uncertainties
Uncertainty in calculated results
• State uncertainties as absolute, fractional and
percentage uncertainties.
• Determine the uncertainties in results.

82. 1.2 Measurement and Uncertainties
• Determine the uncertainties in results.

83. 1.2 Measurement and Uncertainties
• Determine the uncertainties in results.

84. 1.2 Measurement and Uncertainties
• Determine the uncertainties in results.
For addition and subtraction, absolute uncertainties may
be added.

85. 1.2 Measurement and Uncertainties
• Determine the uncertainties in results.
For addition and subtraction, absolute uncertainties may
be added.
For multiplication, division and powers, percentage
uncertainties may be added.

86. 1.2 Measurement and Uncertainties
• Determine the uncertainties in results.
For addition and subtraction, absolute uncertainties may
be added.
For multiplication, division and powers, percentage
uncertainties may be added.
For other functions (trigonometric, logarithmic), the
mean highest and lowest possible answers may be
calculated to obtain the uncertainty range.

87. Part IV
Uncertainty in graphs

88. 1.2 Measurement and Uncertainties
Uncertainty in graphs

89. 1.2 Measurement and Uncertainties
Uncertainty in graphs
• Identify uncertainties as error bars in graphs.

90. 1.2 Measurement and Uncertainties
Uncertainty in graphs
• Identify uncertainties as error bars in graphs.
• State random uncertainty as an uncertainty range
(±) and represent it graphically as an “error bar”

91. 1.2 Measurement and Uncertainties
Uncertainty in graphs
• Identify uncertainties as error bars in graphs.
• State random uncertainty as an uncertainty range
(±) and represent it graphically as an “error bar”
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.

92. 1.2 Measurement and Uncertainties
Uncertainty in graphs
• Identify uncertainties as error bars in graphs.
• State random uncertainty as an uncertainty range
(±) and represent it graphically as an “error bar”
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.

93. 1.2 Measurement and Uncertainties
• Identify uncertainties as error bars in graphs.

94. 1.2 Measurement and Uncertainties
• Identify uncertainties as error bars in graphs.

95. 1.2 Measurement and Uncertainties
• Identify uncertainties as error bars in graphs.
Where relevant, uncertainties should be identified as error
bars in plotted quantities. No error bars are expected for
trigonometric or logarithmic functions.

96. 1.2 Measurement and Uncertainties
• Identify uncertainties as error bars in graphs.
Where relevant, uncertainties should be identified as error
bars in plotted quantities. No error bars are expected for
trigonometric or logarithmic functions.

97. 1.2 Measurement and Uncertainties
Uncertainty in graphs
• Identify uncertainties as error bars in graphs.
• State random uncertainty as an uncertainty range
(±) and represent it graphically as an “error bar”
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.

98. 1.2 Measurement and Uncertainties
Uncertainty in graphs
• Identify uncertainties as error bars in graphs.
• State random uncertainty as an uncertainty range
(±) and represent it graphically as an “error bar”
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.

99. 1.2 Measurement and Uncertainties
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.

100. 1.2 Measurement and Uncertainties
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.

101. 1.2 Measurement and Uncertainties
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.
y
x

102. 1.2 Measurement and Uncertainties
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.
y
Best Fit
x

103. 1.2 Measurement and Uncertainties
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.
y
Best Fit
Max Gradient
x

104. 1.2 Measurement and Uncertainties
• Determine the uncertainties in the gradient and
intercepts of a straight line graph.
y
Best Fit
Max Gradient
Min Gradient
x

105. 1.2 Measurement and Uncertainties
Example 1

106. 1.2 Measurement and Uncertainties
Example 1

107. 1.2 Measurement and Uncertainties
Example 1

108. 1.2 Measurement and Uncertainties
Example 1

109. 1.2 Measurement and Uncertainties
Example 1

110. 1.2 Measurement and Uncertainties
Example 1

111. 1.2 Measurement and Uncertainties
Example 1I

112. 1.2 Measurement and Uncertainties
Example 1I

113. 1.2 Measurement and Uncertainties
Example 1I

114. 1.2 Measurement and Uncertainties
Example 1I

115. 1.2 Measurement and Uncertainties
Example 1I

116. 1.2 Measurement and Uncertainties
Example 1I

117. 1.2 Measurement and Uncertainties
Example III

118. 1.2 Measurement and Uncertainties
Example III

119. 1.2 Measurement and Uncertainties
Example III

120. 1.2 Measurement and Uncertainties
Example III

121. 1.2 Measurement and Uncertainties
Example III

122. 1.2 Measurement and Uncertainties
Example III