## Tuesday, 27 March 2012

### Base Quantity and Derived Quantity

(Reviewed and updated on 30/05/2016)

Quality and Quantity

1.      Quality refers to a non-quantitative characteristic of a matter or phenomenon that can be described. For examples: inverted or upright; virtual or real; red, green, blue, etc.; opaque or transparent; sweet, salty, sour or bitter; etc.

2.      Quantity:

·        Quantity refers to a characteristic of a matter or phenomenon that can be quantified. To quantify means to measure and give it a numerical value and a unit of measurement.

·        A unit of measurement indicates the size of that unit based on a measurement standard and together with the numerical value, they express the size of the physical quantity.

·        Examples of physical quantities:
o       Mass, weight
o       Length, area, volume
o       Time
o       Temperature
o       Electric current, voltage, resistance, charge
o       Number of particles in a matter
o       Brightness of light
o       Angle (of reflection, refraction…), etc.

·        In the past, for the same physical quantity, different units of measurement were used depending on the cultural backgrounds of the users. For examples:
o       For mass: kilograms, tonnes, pounds, ounces, grams…
o       For length: inches, feet, millimeters, centimeter, metres, etc.
o       For time: seconds, minutes, hours, days, etc.
o       For temperature: Celsius (or Centigrades), Fahrenheits, kelvins
This has caused difficulty in comparison and communication.

·        To overcome the difficulty, the SI (International System of Units) has chosen and standardized the units of measurement for all physical quantities – and, these chosen units of measurement are known as the SI units.

·        SI has recognized some physical quantities as base quantities and others as derived quantities. What are their differences?

Base Quantities & Base Units

1.      Base quantities are fundamental physical quantities that are not defined in terms of other physical quantities and upon which other physical quantities - known as derived quantities - are derived. The following physical quantities, units and symbols are chosen by the SI (International System of Units) as base quantities, base units and unit symbols:

Base Quantity (Symbol)                  Base Unit (Symbol)
Length (l)                                        metre (m)
Mass (m)                                        kilogram (kg)
Time (t)                                          second (s)
Electric current (I)                       ampere (A)  (2013 P1 Q1)
Temperature (T)                             kelvin (K)
(2006 P1 Q1 Pg. 48)

2.      The SI has recognised 7 quantities as base quantities and defined their base units as: metre, kilogram, second, ampere, Kelvin, mole and candela.

[Students' Common Misunderstanding / Error on "Electric Current":

1) Students - because they can easily remember electric current as I = V/R (Ohm's Law) or I = Q/t (rate of flow of electric charges) - tend to think that "electric current", I is a derived quantity: This is wrong!  Electric current (I) was chosen by SI to be a base quantity - a fundamental physical quantity. base quantity - though is not defined in terms of other quantities - can however be expressed in terms of other quantities. For example: the base quantity length (l) can be expressed in terms of "square  root of the area A of a square" and, that does not make length a derived quantity! Similarly, electric current (I) - though can be expressed in terms of I = V/R or, I = Q/t - is a base quantity as chosen by SI!

2) SI defines electric current of one ampere as the current that flows through 2 straight conductors of infinite length of negligible cross-sectional area placed 1 metre apart in vacuum that produces between the conductors a force of 2 x 10-7 newton per metre length of the conductors]

Derived Quantities & Derived Units

1.      Derived quantities are physical quantities which are derived from the base quantities by multiplication or division or both. For example, speed is a derived quantity of length (distance travelled) over time.

2.      Derived units are units of measurements (for derived quantities) which are derived from base units of the component base quantities by multiplication or division or both. In the case of the derived quantity, speed, its derived unit is metre/time (with unit symbol, m/s or ms-1).

3.      Some derived units have been given special names by SI. For examples:

Derived Quantity (Symbol) Formula            Derived Unit (Special Name)
·        Force (F)                     Mass x Acceleration     kg ms-2 (newton, N)
·        Pressure (P)                 Force/Area                   kg ms-2/m2 (pascal, Pa)
·        Frequency (f)                1/Period                       1/s = s-1 (hertz, Hz)
·        Work (W)                    Force x Displacemt       N x m (joule, J)
·        Power (P)                    Work/Time                   J/s (watt, W)
Electric charge (Q)        Current x Time                A s (coulomb, C)

(2011 P1 Q3 at pg. 280 - Weight being a measure of gravitational force is a derived quantity
2012 P1 at pg. 332 - What is the S.I. unit for density? Answer: D kg m-3 - avoid C)

------------------------------------------------------------------------------------------------

Segment Review Questions:

A)  Base Quantity and Derived Quantity

1.    What is a base quantity? Name 5 base quantities.

2.    Define derived quantity. And, state 5 derived quantities.

3.    State two main advantages of standardization of all units of measurement for physical quantities.

4.    Give the name and symbol of the SI unit of measurement for each of the following physical quantities:
a.       Length
b.      Mass
c.       Time
d.      Temperature
e.       Current
f.        Force
g.       Energy
h.       Power

5.    Some derived quantities have been given special names by SI (International System of Units). State these derived quantities (that you know of) and their special names.

----------------------------------------------
Reviewed and updated on 30/05/2016 by tutortan1@gmail.com
----------------------------------------------

Need Help In Physics, Chemistry and Maths in or around Petaling Jaya?

Good News: Vacant tuition slots are now up for grab!

(May 30th, 2016): Summer May/June 2016 IGCSE O-level and CIE AS/A2 exams are ending. As such, some tuition slots are available for grabs on '1st-come-1st-serve". The tuition slots are for:

* IGCSE: Math 0580
Math 0606
Physics 0625
Chemistry 0620

(Edexcel Maths and Physics; SPM Maths, Physics and Chemistry - hourly rates: min. RM80/hr 1-to-1 or RM50/hr/student for group of 2 to 4)

* CIE AS/A2: Chemistry 9701 (min RM110/hr 1-to-1)

WhatsApp me Douglas at: 011-2120 1608 or,
email: tutortan1@gmail.com

Thank you.

-----------------------------------------------------------