1. A physical quantity is a quantity that can be measured and consists of a numerical magnitude and a unit. There are two types of physical quantities: base quantities and derived quantities. 2. The seven base quantities in the International System of Units (SI) are length, mass, time, current, temperature, amount of substance and luminous intensity. Common base units include the meter, kilogram and second. 3. Measurements have uncertainty due to random and systematic errors. Random errors cause unpredictable fluctuations while systematic errors arise from faulty instruments or flawed methods. Precision refers to the closeness of repeated measurements while accuracy refers to how close measurements are to the true value.

1. PHYSICAL QUANTITIES
AND UNITS
Chapter 1

2. 1.1 Physical Quantities
Quantitative versus qualitative
• Most observation in physics are quantitative
• Descriptive observations (or qualitative) are usually imprecise
Qualitative Observations
How do you measure
artistic beauty?
Quantitative Observations
What can be measured with the
instruments on an aero-plane?

3. 1.1 Physical Quantities
• A physical quantity is one that can be measured and consists of
a magnitude and unit.
70
km/h

4.5 m

SI units
are
common
today
Vehicles
Not
Exceeding
1500 kg In
Unladen
Weight
Measuring length

4. 1.1 Physical Quantities
Are classified into two types:
• Base quantities
• Derived quantities
Base quantity
is like the brick – the
basic building block of
a house
Derived quantity is like
the house that was
build up from a collection
of bricks (basic quantity)

5. 1.2 SI Quantities and Base Units
SI Units – International System of Units
Base Quantities Name of Unit Symbol of Unit
length metre m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
amount of substance mole mol
luminous intensity candela cd

6. 1.2 SI Quantities and Base Units
• All units (not above) can be broken down to base units
• Homogeneity can be used to prove equations.
• An equation is homogenous if base units on left hand side
are the same as base units on right hand side.
For example, in the equation: v = u + at
the terms are v, u and at.
each term has the base units ms−1

7. 1.2 SI Units
This Platinum
Iridium cylinder
is the standard
kilogram.

8. 1.2 SI Units

9. 1.2 SI Units
•Example of derived quantity: area
Defining equation: area = length × width
In terms of units: Units of area = m × m = m2
Defining equation: volume = length × width × height
In terms of units: Units of volume = m × m × m = m3
Defining equation: density = mass ÷ volume
In terms of units: Units of density = kg / m3 = kg m−3

10. Home Work
• Work out the derived quantities for:
Defining equation: speed =
time
distance
In terms of units: Units of speed =
tim
e
velocity
In terms of units: Units of acceleration =
Defining equation: force = mass × acceleration
In terms of units: Units of force =
Defining equation: acceleration =
1.2 SI Units

11. 1.2 SI Units
• Work out the derived quantities for:
Defining equation: Pressure =
Area
Force
In terms of units: Units of pressure =
Defining equation: Work = Force × Displacement
In terms of units: Units of work =
Defining equation: Power =
Time
done
Work
In terms of units: Units of power =
Home Work

12. 1.2 SI Units
Derived Quantity
Relation with Base and Derived
Quantities
Unit Special Name
area length × width
volume length × width × height
density mass  volume
speed distance  time
acceleration change in velocity  time
force mass × acceleration newton (N)
pressure force  area pascal (Pa)
work force × distance joule (J)
power work  time watt (W)
Home work
Complete the table by writing the base units of each
Derived quantities

13. Work Example

14. 1.3 Prefixes
• Alternative writing method
• Using standard form
• N × 10n where 1  N < 10 and n is an integer
This galaxy is about 2.5 × 106
light years from the Earth.
The diameter of this
atom is about 1 ×
10−10 m.

15. Prefixes for SI Units
• The use of prefixes will make it more convenient to express physical
quantities that are either very big or very small.

16. Estimations
Estimations
Mass of a person 70 kg
Height of a person 1.5 m
Walking speed 1 ms-1
Speed of a car on the motorway 30 ms-1
Volume of a can of a drink 300 cm3
Density of water 1000 kgm-3
Density of air 1 kgm-3
Weight of an apple 1 N
Current in a domestic appliance 13 A
e.m.f of a car battery 12V
Hearing range 20 Hz to 20,000 Hz
Young’s Modulus of a material Something times× 1011

17. Work Example

18. Home Work
1. Calculate the area, in cm2, of the
top of a table with sides of 1.2m and
0.9m.

19. Home Work
2. Determine the number of cubic
meters in one cubic kilometer.

20. Home Work
3. Calculate the volume in m3 of a
wire of length 75cm and diameter
0.38mm.

21. Home Work
4 . Write down, using scientific notation,
the values of the following quantities:
a 6.8pF b 32μC c 60GW

22. Home Work
5. How many electric fires, each
rated at 2.5kW, can be powered
from a generator providing 2.0MW
of electric power?

23. 6. An atom of gold, Figure 1.5,
has a diameter of 0.26nm and
the diameter of its nucleus is
5.6 × 10−3pm. Calculate the
ratio of the diameter of the
atom to that of the nucleus.
Home Work
Figure 1.5 Atom of gold

24. 1. A physical quantity is a quantity that can be measured and
consists of a numerical magnitude and a unit.
2.The physical quantities can be classified into base quantities and
derived quantities.
3.There are seven base quantities: length, mass, time, current,
temperature, amount of substance and luminous intensity.
4.The SI units for length, mass and time are meter, kilogram and
second respectively.
5.Prefixes are used to denote very big or very small numbers.

25. Random & Systematic Errors
• Random and systematic errors are two types of
measurement errors that lead to uncertainty
• Measurements of quantities are made with the aim
of finding the true value of that quantity
• In reality, it is impossible to obtain the true value of any
quantity as there will always be a degree of uncertainty
• In reality, it is impossible to obtain the true value of any
quantity as there will always be a degree of uncertainty
• The uncertainty is an estimate of the difference between a
measurement reading and the true value

26. Random
error
• Random errors cause unpredictable fluctuations in an
instrument’s readings as a result of uncontrollable
factors, such as environmental conditions
• This affects the precision of the measurements
taken, causing a wider spread of results about the mean
value
To reduce random error:
• Repeat measurements several times and calculate an
average from them

28. Systematic
error
• Systematic errors arise from the use of faulty instruments
used or from flaws in the experimental method
• This type of error is repeated consistently every time
the instrument is used or the method is followed, which
affects the accuracy of all readings obtained
• Corrections or adjustments should be made to the technique
To reduce systematic errors:
• Instruments should be recalibrated, or different instruments
should be used

30. Precision & Accuracy
Precisi
on
• Precise measurements are ones in which there is very little
spread about the mean value, in other words, how close
the measured values are to each other
• If a measurement is repeated several times, it can be
described as precise when the values are very similar to,
or the same as, each other

31. Accura
cy
• A measurement is considered accurate if it is close
to the true value
• The accuracy can be increased by repeating
measurements and finding a mean of the results

33. Absolute and percentage
uncertainty
micrometer screw gauge:
12.34±0.01mm
meter rule: 12±1mm
vernier caliper:
12.3±0.1mm
A measurement of 46.0±0.5cm implies that the most likely value
is 46.0cm, but it could be as low as 45.5cm or as high as 46.5cm.
The absolute
uncertainty in the measurement is ±0.5cm. The percentage
uncertainty in the
measurement is ±(0.5/46) × 100% = ±1%.
For
example