Wednesday, 30 September 2020 18:36

# Base Quantities and Derived Quantities of Physics Sciences

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The measurement of base quantities can include various quantities such as length, time, temperature, electric current, velocity, acceleration, force, and many other base quantities. For example, if we want to measure the width of a table we use a ruler or ruler that has a certain scale. The result of measuring the width of the table that we measure is a number read on the ruler. In this case, the base quantity being measured is the length quantity. In general, a base quantity is something that can be expressed by a number or value. Measurement is the process of measuring a quantity, which is comparing the value of the quantity we are measuring with other similar quantities used as a reference. In terms of measuring the width of the table, we are comparing the width of the table with the length (similar quantity) of a ruler as a reference.

Another example is that we all know that Formula 1 cars move much faster than horses. But how many times faster? We cannot answer until we have information on the speed of a Formula 1 car and horse running speed. If you are saying that the running of an F1 car is 250 km/h and the horse's running speed is 50 km/h, we can immediately answer that a Formula 1 car is moving five times faster than a horse. The question now is there something that is not a magnitude? Something that can be represented by numbers is something that can be measured with a measuring instrument. Beauty, pleasure, for example, can they be measured with tools? It seems that beauty to one person is not necessarily as beautiful to another. So, beauty itself is very relative and cannot be measured exactly. So, beauty when viewed from the definition is not a base quantity. Likewise, when we measure the size reference used can also be different. For example, measuring the length of a table with a ruler is 140 cm. Conversely, if our reference is a span, we say the length of the table is, for example, 8 inches. Of course, the meaning of an inch here is not the same for everyone. So, we need to define what is called the units as the smallest measure of what the value of the base quantity is expressed in. So, if we express the length of the table in cm, for example, it is mentioned as 140 cm. Therefore, we need to standardize the units used so that they can be accepted by everyone wherever they are. That is, if we state the length of the table is 140 cm, the other person we tell will understand the meaning of the 140 cm.

From the explanation above, we know that base quantities are very important. base quantities are measurable properties of objects or natural phenomena. Length, mass, length of ball match time, air temperature, the hardness of objects, car speed, light brightness, energy stored in gasoline, electric current flowing in cables, electricity voltage, room light electric power, and water density are examples of the properties objects that can be measured. Then everything is a base quantity.

## BASE QUANTITIES

We already know that in physics we need standards to express the value of magnitude in order to be understood by all circles. So, we have to use an international unit whose definition is approved by an international scientific committee.

To explain standard units in physics, it can be determined by two means of the unit system, namely as follows:

• The units of mks (meters, kilograms and seconds) otherwise known as the metric system .
• The units of cgs (centimeters, grams and seconds) otherwise known as gaussian .

The mks unit is often used in physics, while the cgs unit is used more frequently in chemistry although it is not absolute. However, these two unit systems are widely used internationally.

Another unit system is the British unit system which is popularly used in several countries such as the United States, United Kingdom, Myanmar, and Liberia. In British units, the length is expressed in feet (ft), force in pounds, mass in slugs, and time in seconds (s).

The mks system uses meters for length, kilograms for mass, and seconds for time, the cgs system uses centimeters for measurement length, grams for measurement mass, and seconds for time. It is not necessary to choose which system to use in this case, but the mks system is a widely used unit system.

Note that although the systems mks and cgs are very similar, in the study of electric-magnetism in electrodynamics, the equations used in the two systems are quite different. Of course, between the three-unit systems, there is a conversion to one another. You can see an example below:

• 1 kg ( mks ) = 1000 gr ( cgs ) = 1 / 14.59 slug (British).
• 1 m ( mks ) = 100 cm ( cgs ) = 3,281 ft (British).

For the mks system, since 1960 through the international conference for weight and measurement, the ampere unit (A) has been included as the base unit (principal) so that it has become the mks system (meter-kilogram-second-ampere). The international system of units, SI ( sisteme international according to French) is a modern version of the metric system by international convention. With this SI system, there are seven principal quantities and quite a number of other quantities that can be derived from the principal quantity called derived quantities. The names of quantities, quantity symbols, units, unit symbols, and dimensions of the seven principal quantities can be stated as in the following table.

Table 1
Principal Quantities in Physics

 Principal Quantities Magnitude symbol Units Units symbol Dimensions Length l meter m [L] Mass m kilogram kg [M] Time t sekon s [T] Temperature T kelvin K [Q] Electric current i ampere A [I] Luminous Intensity I candela cd [J] Amount of substance n mole mol [N]

The giving of the symbol of quantity and unit above is an agreed international convention. At each Basic Amount, there are respective uses, among others, are:

1. Length is used to measure the length of the object.
2. Mass is used to measure the mass or material content of an object.
3. Time is used to measure the time interval of two events or events.
4. Electric Current is used to measure the electric current or the flow of electric charge from one place to another.
5. Temperature is used to measure how hot an object is.
6. Light intensity is used to measure how bright light falls on an object.
7. Amount of Substance is used to measure the number of particles contained in an object.

Actually, we can choose another symbol as long as the definition is consistent with a symbol and the units used. The symbol for base quantities that is often used is based on Greek letters as in the following table.

Table 2
Greek Letters and Base Quantities Symbols

 Greek Letters Symbol (Lowercase) Symbol (Uppercase) alpha α Α beta β Β chi χ Χ delta δ Δ epsilon ε Ε eta η Η gamma γ Γ iota ι Ι kappa κ Κ lambda λ Λ mu μ Μ nu ν Ν omega ω Ω omicron ο Ο phi φ Φ pi π Π psi ψ Ψ rho ρ Ρ sigma σ Σ tao τ Τ theta θ Θ upsilon υ Υ xi ξ Ξ zeta ζ Ζ

## DERIVED QUANTITIES

Derived quantities are base quantities consisting of two or more quantities which can be derived from several principal quantities. For example, the derived of velocity is the quotient between distance and time. Other Derived quantities that are often used in everyday life, including acceleration, force, work, force, momentum. The following table is a quantity derived from several main quantities.

Table 3
Some Derived Quantities Obtained from Principal Quantities

 Derived Quantities Derived Units Name Symbol Name Symbol wide A meter squared m2 volume V cubic meter m3 speed v meters per second m/s acceleration a meters per second squared m/s2 momentum p kilogram meter per second kg m/s force F kilogram meter per second squared kg m/s2 energy W/E kilogram meter squared per second squared kg m2/s2 wave number k per meter m-1 frequency f hertz Hz specific gravity ρ kilograms per cubic meter kg/m3 electric current density J amperes per meter squared A/m2 magnetic field strength H amperes per meter A/m power P kilogram meter squared per second cubed kg m2/s3

Example:

Find the units of the following derived quantities.

• Force
• Potential energy
• Density of the liquid
• Pressure
• Momentum
• Speed

Problem Solving:

1. The unit of force is:
 F = m . a= kg m/s2

1. The unit of potential energy is:

Ep = m.g.h = kg. m/s2 . m = kg m2/s2.

1. The unit of density of a liquid is:

r = m/V = kg/m3.

1. The unit of pressure is:

P = F/A = (kg m/s2)/m2 = kg m3/s2.

1. The unit of momentum is: P = m.v = kg m/s.
2. The unit of speed is: v = s/t = m/s

Apart from the quantities above, there are also derived quantities that are given special names, as in the following table.

Table 4
Derived Quantities and Units with Special Names

 Derived Quantities Symbol Derived Units Name Symbol Units (SI) Units in Base Quantities Electric potential difference V volt V W/A kg·m2· s-3·A-1 Energy, effort E , W joule J N·m kg·m2· s-2 Magnetic flux F weber Wb V·s kg·m2· s-2·A-1 Frequency f hertz Hz - s-1 Force F newton N - kg·m· s-2 Electrical resistance R ohm W V/A kg·m2· s-3·A-2 Self inductance L henry H Wb/A kg·m2· s-2·A-2 Capacitance C farad F C/V kg-1·m-2· s4·A2 Electrical charge Q coulomb C - s·A Magnetic flux density B tesla T Wb/m2 kg·s-2·A-1 Field angle q radian rad - m·m-1 Space W steradian sr - m2·m-2 Pressure P pascal Pa N/m2 kg·m-1· s-2

It has also been explained that there are several unit systems, namely mks, cgs, and British. The table below shows the base quantities and their units in different unit systems.

Table 5
Differences in Derived Units in CGS and SI

 Quantities CGS Units Symbol SI Units Symbol Electric current biot Bi 10 amperes A Wave number kayser k 100 per meter m-1 Heat Energy calorie cal 4,1868 joule J Magnetic flux line li 10-8 weber Wb Force dyne dyn 10-5 newton N Illumination phot ph 104 lux lx Intensity lambert Lb 3183,099 candelas per meter squared cd·m-2 Magnetic field strength oersted Oe 79,577 472 amperes per meter A·m-1 Electric dipole moment debye D 3,33564 x 10-30 coulomb meter C·m Magnetic dipole moment emu emu 0,001 amperes meter squared A·m2 Electrical charge franklin Fr 3,3356 x 10-10 coulomb C Acceleration galileo Gal 0,01 meters per second squared m·s-2 Permeability darcy darcy 0,98692 x 10-12 meter squared m2 Magnetic flux density gauss G 10-4 tesla T Pressure barye ba 0,1 pascal Pa Energy erg erg 10-7 joule J Dynamic viscosity poise P 0,1 pascal second Pa·s

That is the lesson for Base Quantities and Derived Quantities and Unit. Hopefully, it can help those of you who are studying the quantities of physics. Thank you