1.2 base and derived quantities

7/28/2019 1.2 Base and Derived Quantities

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1.2 Understanding

Base Quantities andDerived Quantities


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By the end of this lesson, students will be able to

explain what base quantities and derived

quantities are.

list base quantities and their units.

list some derived quantities and their units.

express quantities using prefixes.

express quantities using scientific notation.

express derived quantities as well as their unitsin terms of base quantities and base units.

solve problems involving conversion of units.


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Physical Quantities

A physical quantity is a quantity that can

be measured.

A physical quantity can be divided into

base quantity and derived quantity.


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

It is a quantity that cannot be defined in term of other

physical quantity.

The base quantities and its units are as in the table below.

Base Quantities


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Derived Quantities

A derived quantity is a Physics quantity

that is not a base quantity.

It is the quantities which derived from the

base quantities through multiplying and/or

dividing them


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Derived Unit

The derived unit is a combination of base unitsthrough multiplying and/or dividing them.

Can you think of any other derived quantities?


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Example

Find the derived unit of density.

Answer:


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Unit Conversion

Area and Volume


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Answer

a) 7.2 m = 7.2 x 102 cm

b) 0.32 m2 = 0.32 x 104 cm2 = 3.2 x 103 cm2

c) 0.0012 m3 = 0.0012 x 106 cm3 = 1.2 x 103 cm3

d) 5.6 cm = 5.6 x 10-2 m

e) 350 cm2 = 350 x 10-4 m2 = 3.5 x 10-2 m2

f) 45000 cm3 = 45000 x 10-6 m3 = 4.5 x 10-2 m3


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Example

Complete the following unit conversiona) 12 kmh-1 = __________ ms-1

b) 12 ms-1 = __________ kmh-1

Answer:

a) 112000 3.3360 60

mms

s

b) -1

12

12 1000 (1 )43.2

11

60 60 (1 h)

m

m kmkmh

ss


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Prefixes

Prefixes are the preceding factor used torepresent very small and very large

physical quantities in SI units.


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Conversion of Prefixes

1) Prefixes to normal number

Example 1

The frequency of the radio wave is 350MHz. What is the frequency of the radio

wave in Hz?

Answer

Mega (M) = 1,000,000 or 106

Therefore,

350MHz = 350 x 106Hz


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Example 2

The thickness of a film is 25nm. What is

the thickness in unit meter?

Answer

nano (n) = 0.000000001 or 10-9

Therefore

25nm = 25 x 10-9m


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2) Normal number to prefixes

Example 3

0.255 s is equal to how many ms.

Answer

mili (m) = 0.001 or 10-3

To write a normal number with prefixes,

we divide the number with the value of

the prefixes

0.0255 s = 0.0255 10-3 = 25.5 ms


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Example 4

Convert 265,500,000 W into GW.

Answer

Giga (G) = 1,000,000,000 or 109

Therefore

265,500,000 W = 265,500,000 109 =

0.2655GW


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Scientific Notation (Standard Form)

Scientific notation (also known as Standard

index notation) is a convenient way to write

very small or large numbers.

In this notation, numbers are separated into twoparts, a real numberwith an absolute value

between 1 and 10 and an order of magnitude

value written as a power of 10.

Physical quantities that are very big or very

small need to be written in the standard form so

that it is neat, simple and easy to read.


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Example

1. 2,600 = 2.6 x 103

2. 75,300,000 = 7.53 x 107

3. 0.00023 = 2.3 x 10-44. 0.00000004121 = 4.121 x 10-8


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Exercise

1.Convert the followingquantities into its SI units.

a) 5.7 cm = _______ m

b) 0.034 km = _______ m

c) 250 mm =_______ md) 550 =_______ s

e) 5670 nm =_______ m

f) 2.35 mJ =_______ J

g) 0.12 MW =_______ W

h) 37.2 mg =_______ g

i) 0.054 GV =_______ V

j) 93.5 MHz =_______ Hz

k) 28 mA =________ A

l) 150 =________ A

m) 200 pF =________ F

n) 0.075 Tm =_________ m


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2. Convert the following derived quantities in terms of base

units.

a) Acceleration (change in velocity / time)

b) Momentum (Mass X velocity)c) Density (Mass / volume)

d) Force (Mass X acceleration)

e) Impulse (Change in momentum)

f) Pressure (Force / Area)g) Work done (Force X displacement)

h) Electric charge (Current X time)


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3. Convert the following quantities to

the given units.

a) 0.25 mm2 = ______ m2

b) 150 mm3 = ______ m3

c) 0.062 cm2 =_______ m2

d) 1500 cm3 =_______ m3

e) 0.009 km2 =______ cm2

f) 0.25 g cm-3 =______ kg m-3

g) 180 kg m-3 =______ g cm-3

h) 300 cm s-1 =______ m s-1i) 72 km h-1 =______ m s-1

j) 18 m s-1 =_______ km h-1

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1.2 base and derived quantities

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