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.
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
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
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
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.
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.
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
