OBJECTIVES

1. Ability to define and understand base and derived quantities, distinguish standard units and system of unit, and fundamental quantities.

2. Ability to understand and apply converting units within a system or from one system of unit to another

3. Ability to understand and apply Dimensional Analysis.

DEFINITION

a physical quantity that can be counted or measured using standard size defined by custom or law.

Every measurement or quantitative statement requires a unit.

Example: If you say you’re driving a car 30 that doesn't mean anything. Are you driving it 30 miles/hour, 30 km/hour, or 30 ft/sec? 30 only means something when unit is attached to it.

• If a unit becomes officially accepted, it’s called Standard Unit.

• Group of Unit and Combination is called SYSTEM OF UNITS.Example: SI Units, British UnitsSI = International Systems of Units

STANDARD UNITS

• SI (Système International) Units also called Metric System

• All things in classical mechanics can be expressed in terms of base quantities:– Length (L) , MASS (M), TIME (T)

British Units:

L = inches, feet, miles,

M = slugs (pounds), T = seconds

MKS system CGS System

L = meters (m) centimeter (cm)

M = kilograms (kg) gram (g)

T = seconds (s) seconds (s)

PHYSICAL QUANTITIES- Physics is based on physical quantities. Eg: length,

mass, time, force and pressure.- Generally, physical quantity is a quantity that can be

measured.

Physical quantities Definition

Base quantities Fundamental quantities having their own dimensions. Eg: length, mass, time, electrical current, etc.

Derived quantities The quantity which derived from base quantity. Eg: force, energy, pressure, etc

BASE QUANTITIES IN SI SYSTEM

Name Symbol of quantity

Symbol of dimension

SI base unit

Length l L meter (m)

Time t T second (s)

Mass m M kilogram (kg)

Electrical current

I I Ampere (A)

Thermodynamic temperature

T Kelvin (K)

Amount of substance

n N mole

Luminous intensity

Iv J Candela (c)

DERIVED QUANTITIES FROM BASE QUANTITIES

Quantity Name Symbol of

quantity

SI unit Symbol of dimension

Force, Weight Newton N mkg/s2 LMT-2

Energy, Work, Heat

Joule J m2kg/s2 L2MT-2

Power, radian flux Watt W m2kg/s3 L2MT-3

Frequency Hertz Hz s-1 T-1

Pressure, Stress Pascal Pa m-1kg/s2 L-1MT-2

Electric charge or flux

Coulomb C As AT

Electrical potential difference

Volt V m2 kg s∙ ∙ −3∙A−1

L2MT-3A-1

Quantity Name Symbol of quantity

SI unit Symbol of dimension

Electric resistance, Impedance, Reactance

Ohm Ω m2kgs−3A−2 L2MT-3A-2

Electric capacitance

Farad F m−2kg−1s4A2 L-2M-1T4A2

Magnetic flux density,

magnetic induction

Tesla T kgs−2A−1 MT-2A-1

Magnetic flux Weber W m2kgs−2A−1 L2MT-2A-1

Inductance Henry H m2kgs−2A−2 L2MT-2A-2

DIMENSION

• From Latin word = "measured out"

a parameter or measurement required to define the characteristics of an object - i.e. length, width, and height or size and shape.

What are their units, dimensions and values?- 110 mg of sodium- 24 hands high- 5 gal of gasoline

DIMENSIONAL ANALYSIS

• PURPOSES:1) TO CHECK THE EQUATION2) ANALYSIS DIMENSION TO BUILD FORMULA

• Example (to check equation):Distance, d=vt2 ( velocity x time2 )

– Dimension on left side [d] = L– Dimension on right side [vt2] = L / T x T2 = L x T– L=LT? Left units and right units don’t match, the

equation must be wrong !!

Example 1

Remember: Force has dimensions of ML/T2

The force (F) to keep an object moving in a circle can be described in terms of the velocity, v, (dimension L/T) of the object, its mass, m, (dimension M), and the radius of the circle, R, (dimension L).– Which of the following formulas for F could be correct ?

R

mvF

2

2

R

vmF(a) (b) (c)F = mvR

Consider for RHS, since [F] = MLT-2

For (a);[mvR] = MLT-1L=ML2T-1 (incorrect)

For (b);[mv2R-2] = ML2T-2L-2 = MT-2 (incorrect)

For (c);[mv2R-1] = ML2T-2L-1 = MLT-2 (correct)

Answer is (c)

R

mvF

2

2

R

vmF(a) (b) (c)F = mvR

Solution

UNIT CONVERSIONS• To change units in different systems, or different units

in the same system.• Example:

Units in Different System Units in the Same System

1 inch = 2.54 cm(British SI)

1 yard = 1ft (British)

1 mile = 1.61 km(British SI)

1kg= 1000g(M.K.S to C.G.S in SI)

Example 2

• A hall bulletin board has an area of 2.5 m2. What is area in cm2?

Solution:conversion of area units (in the same SI unit: mks cgs). 1m = 100cm.So,

2

2422

1

10

1

10

m

cm

m

cm

242

242 105.2

1

105.2 cm

m

cmm

Convert miles per hour to meters per second.Given:– 1 inch = 2.54 cm– 1 m = 3.28 ft– 1 mile = 5280 ft – 1 mile = 1.61 km

s

m

s

m

s

hr

ft

m

mi

ft

hr

mi

hr

mi

2

1447.0

3600

1

28.3

1528011

Example 3

Solution:

QUIZ 1

When on travel in Kedah you rent a small car which consumes 6 liters of gasoline per 100 km. What is the MPG (mile per gallons) of the car ?

1L=1000cm3=0.3531ft3,1ft3=0.02832m3=7.481 gal

SIGNIFICANT FIGURES• The number of digits that matter in a measurement or calculation.

1. all non-zero digits are significant.2. in scientific notation all digits are significant3. Zeros may or may not be significant.

• those used to position the decimal point are not significant.• those used to position powers of ten ordinals may or may not

be significant.

• Examples:– 2 1 sig fig– 40 ambiguous, could be 1 or 2 sig figs– 4.0 x 101 2 sig figs (scientific notation)– 0.0031 2 sig figs– 3.03 3 sig figs

• When multiplying or dividing, the answer should have the same number of significant figures as the least accurate of the quantities in the calculation.

• When adding or subtracting, the number of digits to the right of the decimal point should equal that of the term in the sum or difference that has the smallest number of digits to the right of the decimal point.

• Examples:– 2 x 3.1 = 6– 3.1 + 0.004 = 3.1– 4.0 x 101 2.04 x 102 = 1.6 X 10-1