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CHAPTER 1

PHYSICAL QUANTITIES AND UNITS

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Physical Quantities & SI Units

Physics is the study of how the universe/world behaves and how the laws of nature operate.

Physics is a mathematical science. The underlying concepts and principles have a mathematical basis.

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Physical Quantities Physics involves the study of physical

quantities and its measurement. Accurate measurement is very important in

science particularly physics, known as the ‘scientific method’.

Scientific method: observe, measure, collect data & analyse to discover a pattern to make it a theory, and then law otherwise repeat or reject.

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A physical quantity is a quantity that can be measured e.g. length, mass or time of fall.

Physical quantities have a numerical value and unit but not always.

Some quantities have no units e.g. pi, ratios, radian, strain.

A physical quantity can be divided into base quantities and derived quantities.

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Base Quantities

Base quantities are the quantities that are conventionally accepted as functionally independent of one another.

It is a quantity that cannot be defined in terms of other physical quantities nor is it derived from other units, i.e. it is independent of other units.

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Common language of measurement units• Same as spoken languages, different systems of

measurement evolved throughout the world.• Examples: foot, furlongs, cubit, gantang, pounds,

carats, grains, kati etc.• Foot is the length of King Henry VII’s foot• Although units of measurement can be converted

between systems it is cumbersome and far better to have just one system

• Hence the System International (SI) system was born in 1960.

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7 base quantities

The Systême International (SI) is based on 7 fundamental or base quantities and its units are given below: Quantity Name of unit Unit symbol

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

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Beware !

• A distance of thirty metres should be written as 30 m and not 30 ms or 30 m s

• The letter ‘s’ is never included in a unit for the plural.

• If a space is left between 2 letters, the letters denote different units.

• So, 30 m s would mean thirty metre seconds and 30 ms would mean 30 milliseconds.

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Derived quantities and derived units

A derived quantity is a physics quantity that consists of some combination of base units.

It is a quantity which is derived from the base quantities and is a combination of base units through multiplying and/or dividing them, but never added or subtracted.

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All derived units are expressible as products or quotients of the base units

e.g N kg m s-2 and J kg m2 s-2. SI derived units are units of

measurement defined in the International System of Units (SI).

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Derived quantity & equations

• A derived quantity has a defining equation which defines the quantity in terms of other quantities.

• It enables us to express a derived unit in terms of base-unit equivalent. Example: F = ma ; Newton = kg m s-2

P = F/A ; Pascal = kg m s-2/m2 = kg m-1 s-2

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Some derived unitsDerived quantity Base equivalent units_____Symbol area square meter m² volume cubic meter m³ speed, velocity meter per second m/s or m s-1

acceleration meter per second squared m/s/s or m s-2

density kilogram per cubic meter kg m-3

amount concentration mole per cubic meter mol m-3

force kg m s-2 Newton work/energy kg m2 s-2 Joule power kg m2 s-3 Watt pressure kg m-1 s-2 Pascal frequency s-1 Hertz

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Magnitude/size• Magnitudes of physical quantities range from very

very large to very very small. • E.g. mass of sun is 1030 kg and mass of electron is

10-31 kg.• Hence, prefixes are used to describe these

magnitudes.

Common prefixes

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Order of magnitude in metres

• Earth to universe 1.4 x 1026

• Earth to Sun 1.5 x 1011

• Length of car 4• Diameter of hair 5 x 10-4

• Diameter of an atom 3 x 10-10

• Diameter of a nucleus 6 x 10-15

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Scientific notation

• Large and small values are usually expressed in scientific notation i.e. as a simple number multiplied by a power of ten.

• A value expressed in the A x 10n form where 1 A 10 is called the standard form scientific notation.

• There is far less chance of making a mistake with the number of zeroes

• E.g 154 000 000 would be written as 1.54 x 108

0.00034 would be written as 3.4 x 10-4

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Conversions

• Since there are so many base units and derived units, and orders of magnitudes, conversions from one unit to another is inevitable

• Let us try some conversions;

a) 30 mm2 = ? m2

b) 865 km h-1 = ? m s-1

c) 300 g cm-3 = ? kg m-3

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• a) 30 mm2 = ? m2

232 m10mm 1 262 m 10mm 1

25262 m 103.0or m 1030mm 30

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• b) 865 km h-1 = ? m s-1

11 s m 240h km 865

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• c) 300 g cm-3 = ? kg m-3

-353 m kg 103.0cm g 300