GCE O-Level Physics Notes

Chapter 1: Measurements

Content:

  • Physical Quantities

  • SI Units

  • Prefixes

  • Scalars and Vectors

  • Measurement of Length and Time

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Learning Outcomes:

​Students should be able to

  • Show understanding that all physical quantities consist of a numerical magnitude and a unit.

  • Recall the following base quantities and their units:

    • mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)

  • Use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of the SI units:

    • nano (n), micro (µ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G)

  • Show an understanding of the orders of magnitude of the sizes of common objects ranging from a typical atom to the Earth.

  • State what is meant by scalar and vector quantities and give common examples of each.

  • Add two vectors to determine a resultant by a graphical method.

  • Describe how to measure a variety of lengths with appropriate accuracy by means of tapes, rules, micrometers and calipers, using a vernier scale as necessary.

  • Describe how to measure a short interval of time including the period of a simple pendulum with appropriate accuracy using stopwatches or appropriate instruments.

SI Units:

There are 7 base units:

Meters (m), Kilogram (kg), Second (s), Ampere (A), Kelvin (K), Mole (Mol), and Candela (cd)

Each unit corresponds with one of the 7 physical quantities:

Length, Mass, Time, Current, Temperature, Amount of Substance, and Light Intensity.

Base Quantity
Symbol
SI Units
Base Unit / Symbol for Units
Length
𝓛
metre
m
Mass
m
kilogram
kg
Time
t
second
s
Current
I
ampere
A
Temperature
T
Kelvin
K
Luminous Intensity
L
candela
cd
Amount of Substance
n
mole
mol

Derived Units:

Any unit that is defined in terms of the base units. They are expressed as products or quotients of base units.

Derived Quantities
Equation
Derived Units
Volume (V)
V=L^3
m^3
Area (A)
A=L^2,L ∶ Length
m^2
Acceleration (a)
a=Δv/Δt, Δ : "change in"
m s^-2
Velocity (v)
v=L/t, t : time
m s^-1
Density (ρ)
ρ=m/V, m : mass
kg m^-3
Force (N)
F=ma, m : mass, a : acceleration
kg m/s^2
Momentum (p)
p=mv
kg m s^-1
Work Done
W=fd, f : force, d : distance
(kg m^2)/s^2
Voltage
V=w/q, w : work done, c : charge, c=It, I : current; V=w/(It)
(kg m s^-2)/(s^3 *A)

Homogenous Equations:

An equation is said to be homogenous or dimensionally consistent if every term on both sides of the equation has the same base units.

A homogenous equation may not be true or correct.

Systematic Errors:

When all the readings of an experiment are consistently larger or smaller than the true value by a fixed amount.

Random Errors:

When the readings of an experiment are randomly scattered about a mean value.

Accuracy:

The degree of closeness of the experimental values to the true value.

Measured by comparing the average of multiple experimental readings to the true value.

Precision:

The degree of agreement between repeated measurements of the same quantity.

Scalar Quantity:

Physical quantities with magnitude only.

Vector Quantity:

Physical quantities with both magnitude and direction.

Prefix:

Signifies powers of 10, written before numbers to make them easier to read and understand.

Power
Prefix
Symbol
10^12
Tera
T
10^9
Giga
G
10^6
Mega
M
10^3
Kilo
k
10^-1
Deci
d
10^-2
Centi
c
10^-3
Milli
m
10^-6
Micro
µ
10^-9
Nano
n
10^-12
Pico
p

Uncertainty:

Uncertainty is the range of possible values within which the true value of the measurement lies.

1.
Addition
R=aX + bY
Absolute Uncertainty is ΔR=|a|ΔX+|b|ΔY
2.
Subtraction
R = aX - bY
Absolute Uncertainty is ΔR=|a|ΔX+|b|ΔY
3.
Product
R = aX * bY
Fractional Uncertainty is ΔR/R = ΔX/X + ΔY/Y
4.
Division
R = aX/Y
Fractional Uncertainty is ΔR/R = ΔX/X + ΔY/Y
5.
Product with Powers
R = (aX^m) * (Y^n)
Fractional Uncertainty is ΔR/R = |m|(ΔX/X) + |n|(ΔY/Y)
6.
Quotient with Powers
R = (aX^m)/(Y^n)
Fractional Uncertainty is ΔR/R = |m|(ΔX/X) + |n|(ΔY/Y)
7.
Special Functions
Any functions such as sine, cosine, etc.
Uncertainty of R is (Rmax + Rmin)/2, R = (Rmax + Rmin)/2 ± (Rmax - Rmin)/2