CONCEPTUAL MAP
INTRODUCTION
Physical
quantities
Base
quantities
Prefixes
Derived
quantities
Scientific
notation
(standard form
Scalar
quantities
Vector
quantities
Dimensional
Analysis
*
PHYSICAL QUANTITIES
•A
quantity that can be measured.
•A physical quantities have numerical value
and unit of measurement.
•For example temperature 30 degrees
celcius, 30 is numerical value & ‘degree
celcius’ is the unit. Written as 30o C.
Temperature
Physical quantity
= 30 degree Celcius = 30o c
= numerical value x unit measurement
*
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
metre, kilogram and second respectively.
5. Prefixes are used to denote very big or very
small numbers.
BASE QUANTITIES
•Base
Quantities are physical quantities that cannot be derived from
other physical quantities.
•Scientific measurement using SI units (International System Units).
Table 1.1 Shows five base quantities and their respective SI units
Base
Quantities
Symbol
SI Unit
Symbol of
SI unit
Length
L
meter
m
Mass
m
kilogram
kg
Time
t
second
s
Temperature
T
Kelvin
K
Electric current
I
ampere
A
Chapter
1
Physical Quantities, Units and Measurement
Scalars and Vectors
• Vector quantities are quantities that have both
magnitude and direction
A Force
Magnitude = 100 N
Direction = Left
THEME ONE:
MEASUREMENT
Chapter
1
Physical Quantities, Units and Measurement
• Scalar quantities are quantities that have
magnitude only. Two examples are shown below:
Measuring Mass
THEME ONE:
MEASUREMENT
Measuring Temperature
Mass: The amount of matter in a body.
• SI Units: kilogram (kg)
• Common Units:
pounds (lbs) and ounces (oz)
1 kg is approx. 2.2 lbs
1 kg = 1000 g
1 oz = 28.35 g
This Platinum Iridium
cylinder is the
standard kilogram.
7
Length: A measure of distance.
• SI Unit: meter (m)
• Common Units: inches (in); miles (mi)
1 in = 2.54 cm = 0.0254 m
1 mi = 1.609 km = 1609 m
8
Volume: Amount of space occupied by a body.
• SI Unit: cubic meter (m3)
• Common Units: Liter (L) or milliliter (mL) or cubic centimeter (cm3)
9
Density: Amount of mass per unit volume of a substance.
• SI Units: kg/m3
• Common Units: g/cm3 or g/mL
10
Measuring Systems
International system
SI Unit (m K s)
International system
(c g s) Unit
International system
(f b s) Unit
1.2 SI Units
•
Example of derived quantity: area
Defining equation:
area = length × width
L
In terms of units: Units of area = m × m = m2
Defining equation:
W
volume = length × width × height
In terms of units: Units of volume = m × m × m = m3
Defining equation:
H
density = mass ÷ volume
In terms of units: Units of density = kg / m3 = kg m−3
L
W
1.2 SI Units
•
Work out the derived quantities for:
Defining equation:
velocity =
displaceme nt
time
In terms of units: Units of speed = m/s
Defining equation:
acceleration =
velocity
time
In terms of units: Units of acceleration = m/s2
Defining equation:
force = mass × acceleration
In terms of units: Units of force = Kg m/s2
1.2 SI Units
Defining equation:
Work = Force x Displacement
In terms of units: Units of Work = J = Kg m2/s2
Defining equation:
Energy = Mass x gravity x high
In terms of units: Units of Energy = J = Kg m2/s2
Defining equation:
Power = Force x displacement / time
In terms of units: Units of Power = W = Kg m2/s3
Defining equation:
Pressure = Force / area
In terms of units: Units of Pressure = Kg m /m2 s2 = Kg m-1/s2 = N/m2
DERIVED QUANTITIIES
•
Derived Quantities are physical quantities derived from combination
of base quantities through multiplication or division or both
Table 1.2 shows some of the derived quantities and their respective derived units
Derived Quantities
Symbol
Relationship with base quantities
Derived units
Area
A
Length x Length
m2
Volume
V
Length x Length x Length
m3
Density
ρ
Mass
Length x Length x Length
kg/m3
Velocity
v
Displacement
Time
m/s
Acceleration
a
Velocity
Time
m/s2
Force
F
Mass x Acceleration
N
Work
W
Force x Displacement
J
Energy
Ep
Ek
Mass x gravity x high =
½ x mass x velocity x velocity
J
Power
P
Force x Displacement
Time
W
Pressure
p
Force
Area
N/m 2
Temperature: is the measure of how hot or
cold an object is.
• SI Unit: Kelvin (K)
• Common Units: Celsius (ºC) or Fahrenheit (ºF)
Converting between K , ºC and ºF:
TK= TC+273.15
TC= TK – 273.15
TF= 9/5 TC + 32
TC= 5/9 (TF – 32)
16
Black board example
19.1
“When the thermometer is held in the mouth or under the
armpit of a living man in good health” it indicates 98 F
a) What is the temperature in Celsius
(centigrade)?
b) What is the temperature in Kelvin?
PREFIXES
Prefix
•
•
Prefixes :
are used to simplify the
description of physical
quantities that are either very
big or very small.
Table 1.4 Lists some commonly
used SI prefixes
Peta
tera
giga
mega
kilo
hekto
deka
deci
centi
milli
micro
nano
pico
Femto
Symbo
l
P
T
G
M
k
h
da
d
c
m
m
n
P
F
Value
1015
1012
109
106
103
102
10
10-1
10-2
10-3
10-6
10-9
10-12
10-15
STANDARD FORM
Standard form or scientific notation is used to express magnitude in
a simpler way. In scientific notation, a numerical magnitude can be
written as :
A x 10n,
where 1 ≤ A < 10 and n is an integer
Example 1.1 :
I.
II.
For each of the following, express the magnitude using a scientific notation.
The mean radius of the balloon = 100 mm
The mass of a butterfly = 0.0004 kg
Solution:
The mean radius of the balloon
= 100 mm
=100 x 10-3 m = 0.1 m
The mass of a butterfly
= 0.0004 kg
=0. 0004 x 103 g = 0.4 g
*
Dimensional Analysis
The word dimension in physics indicates the
physical nature of the quantity. For example
the distance has a dimension of length, and
the speed has a dimension of length/time.
The dimensional analysis is used to
check the formula, since the dimension
of the left hand side and the right hand
side of the formula must be the same.
Example
Using the dimensional analysis check that this equation x =
½ at2 is correct, where x is the distance, a is the acceleration
and t is the time.
Solution
x = ½ at2
This equation is correct because the dimension of the left and right side of the
equation have the same dimensions.
Example
Show that the expression v = vo + at is dimensionally
correct, where v and vo are the velocities and a is the
acceleration, and t is the time
Solution
The right hand side
[v] = L/T
The left hand side
L/T + L/T
Therefore, the expression is dimensionally correct.
Example
Suppose that the acceleration of a particle moving in circle of radius r with uniform
velocity v is proportional to the rn and vm. Use the dimensional analysis to
determine
the power n and m.
Solution
Let us assume a is represented in this expression
a = k rn vm
Where k is the proportionality constant of dimensionless unit.
The right hand side
n+m=1
and
m=2
Therefore. n =-1 and the acceleration a is
a = k r-1 v2
k=1
a= v2/r
Exercise
Part A:
See if you can determine the dimensions of the following quantities:
volume
acceleration (velocity/time)
density (mass/volume)
force (mass × acceleration)
charge (current × time)
Check your answers
You are correct if you wrote down:
1.Volume
L3
2.acceleration (velocity/time) L/T2
3.density (mass/volume)
M/L3
4.force (mass × acceleration) M·L/T2
5.charge (current × time)
I·T
Part B:
Now find the dimensions of these:
1.pressure (force/area)
2.(volume)2
3.electric field (force/charge)
4.work (in 1-D, force × distance)
5.energy (e.g., gravitational potential energy = mgh
6.square root of area
Check your
answers pressure (force/area)
1.
M·L-1·T-2
2.
(volume)2
L6
3.
electric field (force/charge)
M·L·I-1·T-3
4.
work (in 1-D, force × distance)
M·L2/T2
5.
energy (e.g., gravitational potential energy
= mgh = mass × gravitational acceleration M·L2/T2
× height)
6.
square root of area
L
Which one of the following quantities are dimensionless?
1-68
2-sin (68 )
3-e
4-force
5-6
6-frequency
7-log (0.0034)
What are the dimensions of the following?
1.[sin (wt)]
2.[3]
3.[force]
4.[height]
5.[frequency]
6.[displacement]
7.[area × volume]
8.[0.5 × volume]