Physical Quantity
- value of a physical property expressed in a numerical value and a unit of measurement
Base Quantities and Units
- Simplest units that cannot be expressed in terms of other SI base units
Base Quantity
Base Unit
Name
Symbol
Name
Symbol
Mass
m
Kilogram
kg
Length
l
Meter
m
Time
t
Second
s
Electric Current
I
Ampere
A
Thermodynamic Temperature
T
Kelvin
K
Amount of Substance
n
Mole
mol
Luminous Intensity
Candela
cd
Homogeneous Equation
- Units of each term on LHS = Units of each term on RHS
Prefixes
Order of Magnitude
Prefix
Symbol
Name
-12
Pico
p
Trillionth
-9
Nano
n
Billionth
-6
Micro
μ
Millionth
-3
Milli
m
Thousandth
-2
Centi
c
Hundredth
-1
Deci
d
Tenth
0
-
-
One
3
Kilo
k
Thousand
6
Mega
M
Million
9
Giga
G
Billion
12
Tera
T
Trillion
Errors and Uncertainties
- experimental error = measured value - true value
- Fractional error is the ratio of actual uncertainty to measured value
- Percentage error is the product of fractional error and 100%
- Note: Express uncertainties to 1 s.f
Combining Uncertainties a) Addition / Subtraction
- For c = a +/- b, Δc = Δa + Δb b) Multiplication / Division
- For p = ab or p= a / b, (Δp / p) = (Δa / a) + (Δb / b)
c) Scaling
- For r = ka, where k is a constant Δr = k (Δa)
d) Powers
- For s = a^n (Δs / s) = |n| (Δa / a)
e) Special Functions or complicated functions, Z
- ΔZ = (0.5) ( Zmax - Zmin)
Precision and Accuracy
- Precision refers to the closeness of a set of measurement
- Accuracy refers to agreement between the measured value and the true value of a quantity
Systematic and Random Error a) Random Error
- Deviations of the measured values from true value, with varying magnitude and sign
- Caused by environmental conditions, irregularity of quantity being measured and limitations of the measurement equipment or observer
- Reduced by either repeating or combining measurements
b) Systematic Error
- Deviations of the measured values from true value, with same magnitude and sign
- Examples: (i) Zero Errors
(ii) Parallex Errors
(iii) Background Radiation
Scalars and Vectors
- Scalar quantities are physical quantities without direction
- Vector quantities are physical quantities with direction
Addition and Subtraction of Coplanar Vectors a) 1D - Vresultant = Vboat + Valong / Vagainst b) 2D
- Parallelogram Method
- Triangle Method
- Component Method
- value of a physical property expressed in a numerical value and a unit of measurement
Base Quantities and Units
- Simplest units that cannot be expressed in terms of other SI base units
Homogeneous Equation
- Units of each term on LHS = Units of each term on RHS
Prefixes
Errors and Uncertainties
- experimental error = measured value - true value
- Fractional error is the ratio of actual uncertainty to measured value
- Percentage error is the product of fractional error and 100%
- Note: Express uncertainties to 1 s.f
Combining Uncertainties
a) Addition / Subtraction
- For c = a +/- b, Δc = Δa + Δb
b) Multiplication / Division
- For p = ab or p= a / b, (Δp / p) = (Δa / a) + (Δb / b)
c) Scaling
- For r = ka, where k is a constant
Δr = k (Δa)
d) Powers
- For s = a^n
(Δs / s) = |n| (Δa / a)
e) Special Functions or complicated functions, Z
- ΔZ = (0.5) ( Zmax - Zmin)
Precision and Accuracy
- Precision refers to the closeness of a set of measurement
- Accuracy refers to agreement between the measured value and the true value of a quantity
Systematic and Random Error
a) Random Error
- Deviations of the measured values from true value, with varying magnitude and sign
- Caused by environmental conditions, irregularity of quantity being measured and limitations of the measurement equipment or observer
- Reduced by either repeating or combining measurements
b) Systematic Error
- Deviations of the measured values from true value, with same magnitude and sign
- Examples: (i) Zero Errors
(ii) Parallex Errors
(iii) Background Radiation
Scalars and Vectors
- Scalar quantities are physical quantities without direction
- Vector quantities are physical quantities with direction
Addition and Subtraction of Coplanar Vectors
a) 1D
- Vresultant = Vboat + Valong / Vagainst
b) 2D
- Parallelogram Method
- Triangle Method
- Component Method