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INTRODUCTION

Physical quantities

Base quantities

Derived quantities

PrefixesScientific notation

(standard form

Scalar quantities

Vector quantities

Dimensional Analysis

CONCEPTUAL MAP

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.

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Temperature = 30 degree Celcius = 30o cPhysical quantity = 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).

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

Table 1.1 Shows five base quantities and their respective SI units

Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement

T H E M E O N E : M E A S U R E M E N T

C h a p t e r 1

• Vector quantities are quantities that have both magnitude and direction

Magnitude = 100 N

Direction = Left

A Force

Scalars and Vectors

Physical Quantities, Units and MeasurementPhysical Quantities, Units and Measurement

T H E M E O N E : M E A S U R E M E N T

C h a p t e r 1

• Scalar quantities are quantities that have magnitude only. Two examples are shown below:

Measuring Mass Measuring Temperature

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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.

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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

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Volume: Amount of space occupied by a body.

• SI Unit: cubic meter (m3)

• Common Units: Liter (L) or milliliter (mL) or cubic centimeter (cm3)

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Density: Amount of mass per unit volume of a substance.

• SI Units: kg/m3

• Common Units: g/cm3 or g/mL

International systemSI Unit (m K s)

International system(c g s) Unit

International system(f b s) Unit

Measuring Systems

Length

Mass

time

Meter m

Kilogram Kg

Second S

centimeter cm

Gram g

Second S

Foot ft

Bound b

Second S

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

L

W

H

LW

1.2 SI Units

• Work out the derived quantities for:

Defining equation: velocity =

In terms of units: Units of speed = m/s

Defining equation: acceleration =

In terms of units: Units of acceleration = m/s2

Defining equation: force = mass × acceleration

In terms of units: Units of force = Kg m/s2

time

ntdisplaceme

timevelocity

Defining equation: Work = Force x Displacement

In terms of units: Units of Work = J = Kg m2/s2

1.2 SI Units

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

Defining equation: Pressure = Force / area

In terms of units: Units of Power = W = Kg m2/s3

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

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 MassLength x Length x Length

kg/m3

Velocity v DisplacementTime

m/s

Acceleration a VelocityTime

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 DisplacementTime

W

Pressure p ForceArea

N/m 2

Table 1.2 shows some of the derived quantities and their respective derived units

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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)

“When the thermometer is held in the mouth or under the armpit of a living man in good health” it indicates 98 F

Black board example 19.1

a) What is the temperature in Celsius (centigrade)?

b) What is the temperature in Kelvin?

PREFIXES

• Prefixes :• are used to simplify the

description of physical quantities that are either very big or very small.

Prefix Symbol

Value

Peta P 1015

tera T 1012

giga G 109

mega M 106

kilo k 103

hekto h 102

deka da 10

deci d 10-1

centi c 10-2

milli m 10-3

micro m 10-6

nano n 10-9

pico P 10-12

Femto F 10-15

Table 1.4 Lists some commonly used SI prefixes

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STANDARD FORMStandard 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 :

For each of the following, express the magnitude using a scientific notation.I.The mean radius of the balloon = 100 mmII.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.

Solutionx = ½ at2

This equation is correct because the dimension of the left and right side of the equation have the same dimensions.

ExampleShow 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/TThe left hand side L/T + L/T Therefore, the expression is dimensionally correct.

ExampleSuppose 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.

SolutionLet 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 answersYou 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

Check youranswers

1.pressure (force/area) 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 × height)

M·L2/T2

6. square root of area L

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 = mgh6.square root of area

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]